Mathematicians from the United States

"Irrationality is the square root of all evil."

"Which statement seems more true: (1) I have a brain. (2) I am a brain."

"In fact, a sense of essence is, in essence, the essence of sense, in effect."

"The nice thing about having a brain is that one can learn, that ignorance can be supplanted by knowledge, and that small bits of knowledge can gradually pile up into substantial heaps."

"Solomon: Your entry in Wikipedia says that your work has inspired many students to begin careers in computing and artificial intelligence. Hofstadter: I have no interest in computers. The entry is filled with inaccuracies, and it kind of depresses me. Solomon: So fix it. Hofstadter: The next day someone will fix it back."

"If the meanings of true and false were switched, this sentence wouldn't be false."

"I am not shooting at immortality through my books, no. Nor do I think Chopin was shooting at immortality through his music. That strikes me as a very selfish goal, and I don't think Chopin was particularly selfish. I would also say that I think that music comes much closer to capturing the essence of a composer's soul than do a writer's ideas capture the writer's soul. Perhaps some very emotional ideas that I express in my books can get across a bit of the essence of my soul to some readers, but I think that Chopin's music probably does a lot better job (and the same holds, of course, for many composers). I personally don't have any thoughts about "shooting for immortality" when I write. I try to write simply in order to get ideas out there that I believe in and find fascinating, because I'd like to let other people be able share those ideas. But intellectual ideas alone, no matter how fascinating they are, are not enough to transmit a soul across brains. Perhaps, as I say, my autobiographical passages — at least some of them — get tiny shards of my soul across to some people. But such autobiographical story-telling is not nearly as effective a means of soul-transmission as is living with someone you love for many years of your lives, and sharing profound life goals with them — that's for sure!"

"The "Strange Loop" phenomenon occurs whenever, by moving upwards (or downwards) through levels of some hierarchial system, we unexpectedly find ourselves right back where we started."

"The proverbial German phenomenon of the verb-at-the-end about which droll tales of absentminded professors who would begin a sentence, ramble on for an entire lecture, and then finish up by rattling off a string of verbs by which their audience, for whom the stack had long since lost its coherence, would be totally nonplussed, are told, is an excellent example of linguistic recursion."

"Perhaps the most concise summary of enlightenment would be: transcending dualism. … Dualism is the conceptual division of the world into categories … human perception is by nature a dualistic phenomenon—which makes the quest for enlightenment an uphill struggle, to say the least."

"Relying on words to lead you to the truth is like relying on an incomplete formal system to lead you to the truth. A formal system will give you some truths, but as we shall soon see, a formal system, no matter how powerful—cannot lead to all truths."

"Below Every Tangled Hierarchy Lies An Inviolate Level"

"No reference is truly direct—every reference depends on some kind of coding scheme. It's just a question of how implicit it is."

"One of the basic tenets of Zen Buddhism is that there is no way to characterize what Zen is. No matter what verbal space you try to enclose Zen in, it resists, and spills over. It might seem, then, that all efforts to explain Zen are complete wastes of time. But that is not the attitude of Zen masters and students. For instance, Zen koans are a central part of Zen study, verbal though they are. Koans are supposed to be "triggers" which, though they do not contain enough information in themselves to impart enlightenment, may possibly be sufficient to unlock the mechanisms inside one's mind that lead to enlightenment. But in general, the Zen attitude is that words and truth are incompatible, or at least that no words can capture truth."

"This type of paradox is quite characteristic of Zen. It is an attempt to "break the mind of logic"."

"Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law."

"Reality includes creating every real connection and reference."

"The behavior of two individuals, consisting of effort which results in output, is considered to be determined by a satisfaction function which depends on remuneration (receiving part of the output) and on the effort expended. The total output of the two individuals is not additive, that is, together they produce in general more than separately. Each individual behaves in a way which he considers will maximize his satisfaction function. Conditions are deduced for a certain relative equilibrium and for the stability of this equilibrium, i.e., conditions under which it will not “pay” the individual to decrease his efforts. In the absence of such conditions "exploitation" occurs which may or may not lead to total parasitism."

"The first attempts to consider the behavior of so-called "random neural nets" in a systematic way have led to a series of problems concerned with relations between the "structure" and the "function" of such nets. The "structure" of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of "this" neuron synapsing on "that" one, but rather in terms of tendencies and probabilities associated with points or regions in the net."

"Whether sociology can ever become a full-fledged "science" (a description of a class of events predictable on the basis of deductions from a constant rationale) depends on whether the terms which sociologists employ to describe events can be analyzed into quantifiable observables."

"No map contains all the information about the territory it represents. The road map we get at the gasoline station may show all the roads in the state, but it will not as a rule show latitude and longitude. A physical map goes into details about the topography of a country but is indifferent to political boundaries. Furthermore, the scale of the map makes a big difference. The smaller the scale the less features will be shown."

"A fundamental value in the scientific outlook is concern with the best available map of reality. The scientist will always seek a description of events which enables him to predict most by assuming least. He thus already prefers a particular form of behavior. If moralities are systems of preferences, here is at least one point at which science cannot be said to be completely without preferences. Science prefers good maps."

"[It is a] well-known fact that the likely contacts of two individuals who are closely acquainted tend to be more overlapping than those of two arbitrarily selected individuals"

"It is misleading in a crucial way to view information as something that can be poured into an empty vessel, like a fluid or even energy."

"The transition from the concept of information in the technical (communication engineering) sense to the semantic (theory of meaning) sense was indeed difficult, if not impossible."

"The predictions of physical theories for the most part concern situations where initial conditions can be precisely specified. If such initial conditions are not found in nature, they can be arranged. Such arrangements are considerably easier to realize with inanimate than with animate matter, because the properties of animate matter are much more sensitive to being tampered with than inanimate matter. In particular, living tissue in vitro may behave quite differently than in situ. Controlled biological experiments are, of course, possible, but they are more difficult and their scope is more limited than that of physical experiments. For this reason, biology has had to depend to a greater extent than physics on theories of larger speculative scope, in which reasoning by imaginative analogy plays a more important role."

"A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions"

"There are two suffixes in our language (and similar ones in other European languages) which suggest organized knowledge. One is the venerable, academic "ology," that reminds one of university curricula and scholarship. The other is the energetic and somewhat mysterious "ics," which has a connotative flavor of magic. Where "ology" suggests academic isolation (ichthyology, philology) "ics" suggests a method of attack on life's problems. It contains a faint throwback to the ancient dreams of the philosopher's stone and of "keys" to the riddles of the universe. Ancient words ending in "ics" are mathematics and metaphysics. Of more recent origin are economics, statistics, semantics, and cybernetics."

"Who Are the Semanticists? To answer this question, let us go to the writings of those who make frequent references to semantics or to equivalent terms which have to do with the study of meaning. We find that a number of prominent thinkers have occupied themselves with this study. In England these include Whitehead, Russell, Ogden, Richards, Ayer, and others; in Austria (later scattered, fleeing from fascism), a group of writers who called themselves the Vienna Circle, which included Carnap and Frank (now in in the United States), Wittgenstein (now in England), and Neurath (deceased); the United States is represented by Charles Morris, and Poland by Tarski and Korzybski (deceased), both of whom emigrated to the United States."

"For a general semanticist, communication is not merely words in proper order properly inflected (as for the grammarian) or assertions in proper relation to each other (as for the logician) or assertions in proper relation to referents (as for the semanticist), but all these together, with the chain of 'fact to nervous system to language to nervous system to action."

""What is good in Korzybski's work," they say, "is not new, and what is new is not good." On the other hand, many "Korzybski-ites" proclaim that Korzybski's work has "nothing to do" with semantics. They go so far as to say that the very term "general semantics" was an unfortunate choice; that had Korzybski known what confusion would arise between semantics and general semantics he would not have used it at all. Korzybski himself has maintained that while semantics belongs to the philosophy of language and perhaps to the theory of knowledge, general semantics belongs to empirical science: that it is the foundation of a science of man, the basis of the first "non-aristotelian system," which has had no predecessor and which no academic semanticist has ever achieved."

"The accusations of cultism leveled against Korzybski's followers are not altogether unfounded. In the United States there is a large floating population of 'truthseekers'. Many of them lack the capacity of strenuous intellectual effort required in a fruitful pursuit of knowledge and wisdom; others lack the power of critical evaluation, which would enable them to tell the genuine from the false. Still others cannot be comfortable until they find a panacea to believe in. These people support 'movements' and cults. They are as likely to 'go for' Christian Science as for technocracy, for psychoanalysis as for theosophy, for the Great Books programme as for dianetics. And so inevitably one finds some of them among the adherents of general semantics ... Whether they were actually helped by general semantics or by other factors cannot be determined without sufficient controls. But they went about spreading the faith, thus giving a cultist flavour to the 'movement'."

"If Korzybski cannot be said to have established an empirical science, what then has he done? He has pointed a way toward the establishment of such a science. He was a precursor of an intellectual revolution which is just now beginning and which promises to match that of the Renaissance. If Korzybski is seen in this role, then the question of his originality or erudition is not important. He might have something of a dilettante in him. He might have pretended to have more specialized knowledge than he actually had. Great portions of his outlook might be found in the works of more modest and more meticulous workers, That is not important. He was a man of vision and an apostle. Such men are all too rare in our age of specialization."

"The outstanding feature of behavior is that it is often quite easy to recognize but extremely difficult or impossible to describe with precision."

"In the case of strategy and conscience, I am not sure. Here I believe, is essential incompatibility, not merely a result of misunderstanding. I do not believe one can bring both into focus. One cannot play chess if one becomes aware of the pieces as living souls and of the fact that the Whites and the Blacks have more in common with each other than with the players. Suddenly one loses all interest in who will be champion."

"The military forces of the revolutionary adversary are diffuse. One is never sure whether one has destroyed them unless one is ready to destroy a large portion of the population, and this usually conflicts with the political aim of the war and hence also violates a fundamental Clausewitzian principle"

"There are different levels of organization in the occurrence of events. You cannot explain the events of one level in terms of the events of another. For example, you cannot explain life in terms of mechanical concepts, nor society in terms of individual psychology. Analysis can only take you down the scale of organization. It cannot reveal the workings of things on a higher level. To some extent the holistic philosophers are right."

"It is one thing to say that the dwelling has symbolic and cosmological aspects... and another to say that it has been erected for ritual purposes and is neither shelter nor dwelling but a temple."

"The "flow of information" through human communication channels is enormous. So far no theory exists, to our knowledge, which attributes any sort of unambiguous measure to this "flow"."

"It is the shortcomings of game theory (as originally formulated) which force the consideration of the role of ethics, of the dynamics of social structure, and of social structure and of individual psychology in situations of conflict."

"In a game, the potentialities and evaluations of alternative outcomes must be taken into account, if the reactions of the opponents to each other's moves are to moves are to be understood or described systematically."

"Conflict... is a theme that has occupied the thinking of man more than any other, save only God and love. In the vast output of discourse on the subject, conflict has been treated in every conceivable way. It has been treated descriptively, as in history and fiction; it has been treated in an aura of moral approval, as in epos; with implicit resignation, as in tragedy; with moral disapproval, as in pacifistic religions. There is a body of knowledge called military science, presumably concerned with strategies of armed conflict. There are innumerable handbooks, which teach how to play specific games of strategy. Psychoanalysts are investigating the genesis of "fight-like" situations within the individual, and social psychologists are doing the same on the level of groups and social classes."

"At present game theory has, in my opinion, two important uses, neither of them related to games nor to conflict directly. First, game theory stimulates us to think about conflict in a novel way. Second, game theory leads to some genuine impasses, that is, to situations where its axiomatic base is shown to be insufficient for dealing even theoretically with certain types of conflict situations... Thus, the impact is made on our thinking process themselves, rather than on the actual content of our knowledge."

"We live in an age of belief-belief in the omnipotence of science. This belief is bolstered by the fact that the problems scientists are called on to solve are for the most part selected by the scientists themselves."

"A thorough understanding of game theory, should dim these greedy hopes. Knowledge of game theory does not make one a better card player, businessman or military strategist."

"Game theory applies to a very different type of conflict, now technically called a game. The well-known games such as poker, chess, ticktacktoe and so forth are games in the strict technical Bark and counterbark sense. But what makes parlor games games is not their entertainment value or detachment from real life."

"Although the drama of games of strategy is strongly linked with the psychological aspects of the conflict, game theory is not concerned with these aspects. Game theory, so to speak, plays the board. It is concerned only with the logical aspects of strategy."

"Whether game theory leads to clear-cut solutions, to vague solutions, or to impasses, it does achieve one thing. In bringing techniques of logical and mathematical analysis gives men an opportunity to bring conflicts up from the level of fights, where the intellect is beclouded by passions, to the level of games, where the intellect has a chance to operate."

"Many psychologists, sociologists and especially anthropologists and psychiatrists raise serious objections against routine attempts to "extend the methods of the physical sciences" to the study of man. These objections cannot be dismissed simply on the grounds that they are not constructive; for inherent in the objections may well be a conviction that there can never be a "behavioral science" as scientists understand science. Whether there can be such a science or not will be decided neither by citing successful applications of "scientific method" to carefully circumscribed sectors of human behavior nor by pointing out what has not yet been done. Therefore on the question of whether a can in principle be constructed, we shall take no sides. That some kinds of human behavior can be described and even predicted in terms of objectively verifiable and quantifiable data seems to us to have been established."

"Crisis in its simplest terms is defined as an upset in a steady state... the habitual problem-solving activities are not adequate and do not rapidly lead to the previously achieved balance state."

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results."

"Our first objective in undertaking the experimental program described here has been to gain some understanding of what goes on in long sequences of plays of Prisoner's Dilemma. We have attempted to gain this understanding by postulating a system going through a sequence of states and by attempting to formulate some mathematical models from which the dynamics of the system could be deduced. Once such a model is found, its parameters, properly interpreted, become the key terms in the emerging psychological theory. This strategy can be deemed successful, if the parameters so discovered are independent of the process itself, if they suggest further investigation, and if the further investigations, in turn, lead to a more inclusive theory."

"(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not."

"We must admit that it is extremely difficult to formulate a theory sufficiently general to encompass all possible sufficient causes of wars. With regard to necessary causes, however,... it is weapons. Without weapons wars could not be fought. We are told that, deprived of weapons, people would still fight with sticks and stones. This, however, need not concern us. We are concerned not just with fighting but with the sort of mass insanity that can destroy the entire civilization, the product of millenia of accumulated effort, in a matter of hours. And this can be done only with real, up-to-date weapons, not sticks and stones."

"[Education] seems to be the only hope: to spread enlightenment sufficiently wide so that people can no longer be manipulated to give consent to policies that will surely eventually lead to their own destruction."

"The American Revolution was ignited by the slogan ‘no taxation without representation’, a slogan suggested by democratic ideals... Ought not the present day version of the old slogan be ‘No annihilation without representation?"

"To gain knowledge, we must learn to ask the right questions; and to get answers, we must act, not wait for answers to occur to us."

"Centralization of society's vital services in giant computer centers, reservoirs, nuclear power plants, air- traffic control centers, 100-story skyscrapers, and government compounds increases its vulnerability. ... choosing his targets, today's saboteur could pollute a city's water supply, dynamite power transmission towers, cripple an airport control center, destroy a corporate or government computer center."

"The outcome of a non-constant-sum game may be dictated by the individual rationality of the respective players without satisfying a criterion of collective rationality."

"The purpose of formulating [a] conflict as a game is not that of resolving the conflict by 'solving the game.' It is that of displaying the structure of the conflict and thereby exposing features of it that may be concealed by rhetoric. In particular, appreciation of the peculiar structure of some of the so-called mixed—motive conflicts represented nonzero-sum games may change the conflicting parties' perception of their situation."

"In the US. Infantry Manual published during World War II, the soldier was told what to do if a live grenade fell into the trench where he and others were sitting: to wrap himself around the grenade so as to at least save the others. (If no one "volunteered," all would be killed, and there were only a few seconds to decide who would be the hero.)"

"Anatol Rapoport is a pioneer and lead-figure of the systems sciences, studies in conflict & cooperation, and peace research. He is professor emeritus of Psychology and Mathematics at the University of Toronto, Canada... Rapoport has spearheaded many scientific innovations, including the application of mathematical methods, first to Biology and later to the Social Sciences. Moreover, he is one of the rare thinkers who have contributed significantly to "marrying" philosophy and science. The originality and rigor of his thinking make his theoretical oeuvre extraordinarily resourceful, as well as unique in its ethical substance and esthetical appeal. Rapoport operates from a multidimensional background of experience and studies (see the following C.V.), embodying a deep humanistic commitment (cf. Rapoport 1994), and a profoundly systemic thinking."

"The social psychologist and game theorist Anatol Rapoport (creator of the winning Tit-for-Tat strategy in Robert Axelrod's legendary prisoner’s dilemma tournament) once promulgated a list of rules for how to write a successful critical commentary on an opponent's work. First, he said, you must attempt to re-express your opponent's position so clearly, vividly and fairly that your opponent says “Thanks, I wish I’d thought of putting it that way.” Then, you should list any points of agreement (especially if they are not matters of general or widespread agreement), and third, you should mention anything you have learned from your opponent. Only then are you permitted to say so much as a word of rebuttal or criticism."

"Why should I worry about dying? It's not going to happen in my lifetime!"

"I have free will, but not of my own choice. I have never freely chosen to have free will. I have to have free will, whether I like it or not!"

"If it is really true that you cannot resist them, then you are not sinning of your own free will and hence (at least according to me) not sinning at all."

"There is nothing like a naturalistic orientation to dispel all these morbid thoughts of "sin" and "free will" and "moral responsibility.""

"Medical opinions differed as to the cause of this "humor" disease."

"From what little was known about the subject, insincerity itself was regarded as another form of psychosis but one which was exceedingly rare."

"Humor could not flourish in a wholly serious and rational atmosphere."

"Metaphysical problems about "mind" versus "matter" arise only from epistemological confusions."

"Of course the falsity of the fact that you believe it is red implies that you don't believe it is red. But this does not mean that you believe it is not red!"

"I believe that either Jupiter has life or it doesn't. But I neither believe that it does, nor do I believe that it doesn't."

"A less obvious type of application (of non-cooperative games) is to the study of . By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration."

"The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation. The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games."

"We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other."

"I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia."

"By the time I was a student in high school I was reading the classic Men of Mathematics by E. T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime."

"As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results."

"Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort."

"At the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos."

"Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future."

"Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person."

"People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world."

"You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers."

"This man is a genius."

"... he gave his name to the Nash equilibrium – a position in a situation of competition or conflict in which both sides have selected a strategy, but where neither side can then independently change their strategy without ending up in a less desirable position. Such positions are common in everyday life, and in the interactions of business people, politicians and nations. He earned his early reputation, and his 1994 Nobel prize in economics, by proving mathematically that there is at least one Nash equilibrium lying in wait to trap us in every situation of competition or conflict where the parties are unwilling or unable to communicate."

"He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. However, my most vivid memory of this time is of the many games which were played in the common room. I was introduced to Go and Kriegspiel, and also to an ingenious topological game which we called Nash in honor of the inventor."

"As I said, I spent a great deal of time in the common room, and so did Nash. He was a very interesting character and full of ideas. He also used to wander in the corridors whistling things like Bach, which I had never really heard before — a strange way to be introduced to classical music! I saw quite a bit of him over those years and I also became interested in game theory, in which he was an important contributor. He was a very interesting person."

"When Freeman Dyson, the physicist, greeted John Forbes Nash, Jr. at the Institute for Advanced Study one day in the early 1990s, he hardly expected a response. A mathematics legend in his twenties, Nash had suffered for decades from a devastating mental illness. A mute, ghost-like figure who scrawled mysterious messages on blackboards and occupied himself with numerological calculations, he was known around Princeton only as “the Phantom.” To Dyson’s astonishment, Nash replied. He’d seen Dyson’s daughter, an authority on computers, on the news, he said. “It was beautiful,” recalled Dyson. “Slowly, he just somehow woke up.” Nash’s miraculous emergence from an illness long considered a life sentence was neither the first, nor last, surprise twist in an extraordinary life."

"[W]hile the book and the movie probed the conflicting complexities in Nash the man, neither delved deeply into Nash's math. So for most people today, his accomplishments remain obscure. Within the world of science, though, Nash's math now touches more disciplines than Newton's or Einstein's. What Newton's or Einstein's math did for the physical universe, Nash's math may now be accomplishing for the biological and social universe."

"The tools introduced by Nash gave rise to new powerful theories (convex integration, Nash-Moser scheme) which later would allow to attack many mathematical problems."

"I could prove God statistically. Take the human body alone — the chances that all the functions of an individual would just happen is a statistical monstrosity."

"Alas, irreverence has been subsumed by mere grossness, at least in the so-called mass media. What we have now — to quote myself at my most pretentious — is a nimiety of scurrility with a concomitant exiguity of taste. For example, the freedom (hooray!) to say almost anything you want on television about society's problems has been co-opted (alas!) by the freedom to talk instead about flatulence, orgasms, genitalia, masturbation, etc., etc., and to replace real comment with pop-culture references and so-called "adult" language. Irreverence is easy — what's hard is wit."

"Political satire became obsolete when Henry Kissinger was awarded the Nobel Peace Prize."

"Andrew Wiles gently smiles, Does his thing, and voila! Q.E.D., we agree, And we all shout hurrah! As he confirms what Fermat Jotted down in that margin, Which could've used some enlargin'."

"No one is more dangerous than someone who thinks he has "The Truth". To be an atheist is almost as arrogant as to be a fundamentalist. But then again, I can get pretty arrogant."

"I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!) without having to worry about God. Or if pi isn't enough, how about fractals? or quantum mechanics?"

"I would like to state at this time that I am not now and have never been... a member of the Boy Scouts of America. Their motto is, as you know, "Be Prepared!" and that is the name of this song."

"Don't solicit for your sister, that's not nice, Unless you get a good percentage of her price."

"If you're looking for adventure of a new and different kind, And you come across a Girl Scout who is similarly inclined, Don't be nervous, don't be flustered, don't be scared. Be prepared!"

"I always like to make explicit the fact that before I went off not too long ago to fight in the trenches, I was a mathematician by profession. I don't like people to get the idea that I have to do this for a living. I mean, it isn't as though I had to do this, you know, I could be making, oh, $3,000 a year just teaching."

"I am never forget the day I first meet the great Lobachevsky. In one word he told me secret of success in mathematics: Plagiarize! Plagiarize, Let no one else's work evade your eyes, Remember why the good Lord made your eyes, So don't shade your eyes, But plagiarize, plagiarize, plagiarize... Only be sure always to call it please "research"."

"In all probability I'll lose my virility And you your fertility And desirability, And this liability Of total sterility Will lead to hostility And a sense of futility, So let's act with agility While we still have facility, For we'll soon reach senility And lose the ability."

"I hold your hand in mine, dear, I press it to my lips. I take a healthy bite From your dainty fingertips. My joy would be complete, dear, If you were only here, But still I keep your hand As a precious souvenir."

"You know, of all the songs I have ever sung, that is the one I've had the most requests not to."

"I'd like to take you now, on wings of song as it were, and try and help you forget for a while your drab, wretched lives."

"All the world seems in tune On a spring afternoon, When we're poisoning pigeons in the park. Every Sunday you'll see My sweetheart and me, As we poison the pigeons in the park."

"When they see us coming, the birdies all try an' hide, But they still go for peanuts when coated with cyanide. My pulse will be quickenin', With each drop of strych-a-nine, We feed to a pigeon it just takes a smidgen To poison a pigeon in the park."

"Oh, soon we'll be out amid the cold world's strife. Soon we'll be sliding down the razor blade of life. Oooh."

"A few years ago, a motion picture version appeared of Sophocles' immortal tragedy "Oedipus Rex". This picture played only in the so-called art theaters, and it was not a financial success. And I maintain that the reason it was not a financial success... you're way ahead of me... was that it did not have a title tune which the people could hum, and which would make them actually eager to attend this particular...flick. So, I've attempted to supply this, and here then is the prospective title song from "Oedipus Rex"."

"There once lived a man named Oedipus Rex, You may have heard about his odd complex. His name appears in Freud's index 'Cause he loved his mother."

"His rivals used to say quite a bit That as a monarch he was most unfit. But still in all they had to admit That he loved his mother."

"Yes, he loved his mother like no other, His daughter was his sister and his son was his brother. One thing on which you can depend is, He sure knew who a boy's best friend is."

"So be sweet and kind to mother Now and then, have a chat! Buy her candy or some flowers or a brand-new hat But maybe you best let it go at that! Or you may find yourself with a quite complex ...Com-plex! ...and... You may end up like Oedipus I'd rather marry a duck-billed platypus! Than end up like poor Oedipus Rex!"

"The usual jokes about the Army aside, one of the many fine things one has to admit is the way that the Army has carried the American democratic ideal to its logical conclusion, in the sense that not only do they prohibit discrimination on the grounds of race, creed and color, but also on the grounds of ability."

"I recall this sergeant's informing me and my "room-mates" of this rather deplorable fact the army didn't have any official, excuse me, didn't have no official song and suggested that we work on this in our copious free time."

"I ache for the touch of your lips, dear, But much more for the touch of your whips, dear. You can raise welts Like nobody else, As we dance to the Masochism Tango."

"Take your cigarette from its holder, And burn your initials in my shoulder. Fracture my spine, And swear that you're mine, As we dance to the Masochism Tango."

""Life is like a sewer — what you get out of it depends on what you put into it." It's always seemed to me that this is precisely the sort of dynamic, positive thinking that we so desperately need today in these trying times of crisis and universal brouhaha."

"We will all go together when we go Every Hottentot and every Eskimo When We will all go simultaneous Oh, we all will go together when we go."

"I'm sure we all agree that we ought to love one another and I know there are people in the world that do not love their fellow human beings and I hate people like that"

"Any ideas expressed on this record should not be taken as representing Mr. Lehrer's true convictions, for indeed he has none. "If anyone objects to any statement I make," he has said, "I am quite prepared not only to retract it, but also to deny under oath that I ever made it.""

"I do have a cause, though. It is obscenity. I'm for it."

"But don't panic. Base eight is just like base ten really — if you're missing two fingers."

"Last December 13th, there appeared in the newspapers the juiciest, spiciest, raciest obituary it has ever been my pleasure to read. It was that of a lady named Alma Mahler Gropius Werfel, who had, in her lifetime, managed to acquire as lovers practically all of the top creative men in central Europe. And, among these lovers, who were listed in the obituary, by the way, which is what made it so interesting, there were three whom she went so far as to marry: One of the leading composers of the day, Gustav Mahler, composer of "Das Lied von der Erde" and other light classics, one of the leading architects, Walter Gropius, of the "Bauhaus" school of design, and one of the leading writers, Franz Werfel, author of the "Song of Bernadette" and other masterpieces. It's people like that who make you realize how little you've accomplished. It is a sobering thought, for example, that when Mozart was my age, he had been dead for two years."

"The loveliest girl in Vienna Was Alma, the smartest as well. Once you picked her up on your antenna, You'd never be free of her spell."

"And that is the story of Alma, Who knew how to receive and to give. The body that reached her embalma' Was one that had known how to live."

"Speaking of love, one problem that recurs more and more frequently these days, in books and plays and movies, is the inability of people to communicate with the people they love: husbands and wives who can't communicate, children who can't communicate with their parents, and so on. And the characters in these books and plays and so on, and in real life, I might add, spend hours bemoaning the fact that they can't communicate. I feel that if a person can't communicate, the very least he can do is to shut up."

"I feel that if any songs are gonna come out of World War III, we'd better start writing them now."

"Get in line in that processional, Step into that small confessional. There the guy who's got religion'll Tell you if your sin's original. If it is, try playin' it safer, Drink the wine and chew the wafer, Two, four, six, eight, Time to transubstantiate!"

"So get down upon your knees, Fiddle with your rosaries, Bow your head with great respect, And genuflect, genuflect, genuflect!"

"During National Brotherhood Week various special events are arranged to drive home the message of brotherhood — this year, for example, on the first day of the week, Malcolm X was killed, which gives you an idea of how effective the whole thing is. I'm sure we all agree that we ought to love one another, and I know there are people in the world who do not love their fellow human beings — and I hate people like that!"

"Oh, the white folks hate the black folks, And the black folks hate the white folks; To hate all but the right folks Is an old established rule."

"Oh, the poor folks hate the rich folks, And the rich folks hate the poor folks. All of my folks hate all of your folks, It's American as apple pie."

"Step up and shake the hand Of someone you can't stand, You can tolerate him if you try!"

"Oh, the Protestants hate the Catholics And the Catholics hate the Protestants, And the Hindus hate the Moslems, And everybody hates the Jews."

"It's only for a week so have no fear! Be grateful that it doesn't last all year!"

"What is it that put America in the forefront of the nuclear nations? And what is it that will make it possible to spend twenty billion dollars of your money to put some clown on the moon? Well, it was good old American know how, that's what, as provided by good old Americans like Dr. Wernher von Braun!"

"Don't say that he's hypocritical, Say rather that he's apolitical. "Once the rockets are up, who cares where they come down? That's not my department," says Wernher von Braun."

"But things I once thought were funny are scary now. I often feel like a resident of Pompeii who has been asked for some humorous comments on lava."

"People do their best satirical work when they’re young. I’m not interested in saying only the nasty. My mind doesn’t run that way anymore. I don’t know if the times are changing or I am."

"I really don't consider myself a performer by temperament."

"I don't appreciate poetry--I don't mind admitting that now, I don't understand poetry. We studied it in high school and college, but they never told us why it was good. I got A's on all the exams--"Hail to thee blithe spirit, bird thou never wert"-- what the hell does that mean? I have no idea."

"I remember when Richard Pryor said something about how in South Africa, all the black people should pick up guns and kill all the white people, and they went right on with the interview, and nobody stopped him on that. "Oh good old Richard, what a card." As long as you're billed as a comedian, I guess you can say anything."

"I think the people who say we need satire often mean, "We need satire of them, not of us.""

"People are stupider than anybody."

"I'm not tempted to write a song about George W. Bush. I couldn't figure out what sort of song I would write. That's the problem: I don't want to satirise George Bush and his puppeteers, I want to vaporise them. … And that's not funny. … OK, well, if I say that, I might get a shock laugh, but it's not really satire."

"Things are much more complicated. Feminism versus pornography, for example. There are a lot of feminists who think it is bad, but others think it's good. I have become, you might call it mature — I would call it senile — and I can see both sides. But you can't write a satirical song with 'but on the other hand' in it, or 'however'. It's got to be one-sided."

"The real issues I don't think most people touch. The Clinton jokes are all about Monica Lewinsky and all that stuff and not about the important things, like the fact that he wouldn't ban landmines."

"One of the problems I see with these comics on television, particularly cable television, is, since you can say anything in terms of sex and scatological references and so on, therefore, you should do it. So they all limit themselves to these subjects and this vocabulary. My objection is that it is a lack of articulateness … Irreverence is easy, but what is hard is wit. Wit is what these comedians lack."

"The audience usually has to be with you, I'm afraid. I always regarded myself as not even preaching to the converted, I was titillating the converted. The audiences like to think that satire is doing something. But, in fact, it is mostly to leave themselves satisfied. Satisfied rather than angry, which is what they should be."

"You can make fun with Saddam Hussein jokes … but you can't make fun of, say, the concentration camps. I think my target was not so much evil, but benign stupidity people doing stupid things without realising or, instead, thinking they were doing good."

"Dear Mr. Lehrer:"

"The best musical satirist of the 20th Century."

"Lehrer was able to express and to expose, in humorous verse and lilting music, some of the most powerful dangers of the second half of the century … Many of the causes of which Lehrer sang became, three decades later, part of the main creative impulse of mankind."

"Mr. Lehrer's muse is not fettered by such inhibiting factors as taste."

"Lehrer is that rarest of beasts a performer who was never seduced by the roar of the crowd and who rejected show business well before it had a chance to do the same to him. His concert tours were brief and motivated either by a desire to visit a new place (such as Australia, in 1960) or to test and polish material for a recording."

"I’ve always kind of considered him the J. D. Salinger of demented music."

"One naturally wonders if the problem of translation could conceivably be treated as a problem in cryptography. When I look at an article in Russian, I say: 'This is really written in English, but it has been coded in some strange symbols. I will now proceed to decode.'"

"Is science really gaining in its assault on the totality of the unsolved? As science learns one answer, it is characteristically true that it also learns several new questions. It is as though science were working in a great forest of ignorance, making an ever larger circular clearing within which, not to insist on the pun, things are clear... But as that circle becomes larger and larger, the circumference of contact with ignorance also gets longer and longer. Science learns more and more. But there is an ultimate sense in which it does not gain; for the volume of the appreciated but not understood keeps getting larger. We keep, in science, getting a more and more sophisticated view of our essential ignorance."

"Science has led to a multitude of results that affect men's lives. Some of these results are embodied in mere conveniences of a relatively trivial sort. Many of them, based on science and developed through technology, are essential to the machinery of modern life. Many other results, especially those associated with the biological and medical sciences, are of unquestioned benefit and comfort. Certain aspects of science have profoundly influenced men's ideas and even their ideals. Still other aspects of science are thoroughly awesome."

"The significant problems of living organisms are seldom those in which one can rigidly maintain constant all but two variables. Living things are more likely to present situations in which a half-dozen, or even several dozen quantities are all varying simultaneously, and in subtly interconnected ways. Often they present situations in which the essentially important quantities are either non-quantitative, or have at any rate eluded identification or measurement up to the moment. Thus biological and medical problems often involve the consideration of a most complexly organized whole."

"Is a virus a living organism? What is a gene, and how does the original genetic constitution of a living organism express itself in the developed characteristics of the adult? Do complex protein molecules "know how" to reduplicate their pattern, and is this an essential clue to the problem of reproduction of living creatures? All these are certainly complex problems, but they are not problems of disorganized complexity, to which statistical methods hold the key. They are all problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole. They are all, in the language here proposed, problems of organized complexity."

"Science is not gadgetry."

"In a perfect world an idea could be born, nourished, developed and made known to everyone, criticized and perfected, and put to good use without the crude fact of financial support ever entering in to the process. Seldom, if ever, in the practical world in which we live does this occur."

"Science attempts to analyze how things and people and animals behave; it has no concern whether this behavior is good or bad, is purposeful or not. But religion is precisely the quest for such answers: whether an act is right or wrong, good or bad, and why."

"I think that God has revealed Himself to many at many times and in many places. Indeed, He continuously reveals Himself to man today : every new discovery of science is a further "revelation" of the order which God has built into His universe."

"True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men."

"The Scientific Attitude and Fallibilism in Philosophical Writings of Peirce, selected and edited with an introducton by Justus Buchler. p. 49"

"Few persons care to study logic, because everybody conceives himself to be proficient enough in the art of reasoning already. But I observe that this satisfaction is limited to one's own ratiocination and does not extend to that of other men. We come to the full possession of our power of drawing inferences the last of all our faculties, for it is not so much a natural gift as a long and difficult art."

"The Protestant churches generally hold that the elements of the sacrament are flesh and blood only in a tropical sense; they nourish our souls as meat and the juice of it would our bodies. But the Catholics maintain that they are literally just that; although they possess all the sensible qualities of wafer-cakes and diluted wine. But we can have no conception of wine except what may enter into a belief, either —"

"It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man’s head, will sometimes act like an obstruction … in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty."

"The consciousness of a general idea has a certain "unity of the ego" in it, which is identical when it passes from one mind to another. It is, therefore, quite analogous to a person, and indeed, a person is only a particular kind of general idea."

"It is the man of science, eager to have his every opinion regenerated, his every idea rationalized, by drinking at the fountain of fact, and devoting all the energies of his life to the cult of truth, not as he understands it, but as he does not yet understand it, that ought properly to be called a philosopher. To an earlier age knowledge was power — merely that and nothing more; to us it is life and the summum bonum. Emancipation from the bonds of self, of one's own prepossessions, importunately sought at the hands of that rational power before which all must ultimately bow, — this is the characteristic that distinguishes all the great figures of nineteenth-century science from those of former periods."

"You are of all my friends the one who illustrates pragmatism in its most needful forms. You are a jewel of pragmatism."

"It is important to understand what I mean by semiosis. All dynamic action, or action of brute force, physical or psychical, either takes place between two subjects, — whether they react equally upon each other, or one is agent and the other patient, entirely or partially, — or at any rate is a resultant of such actions between pairs. But by "semiosis" I mean, on the contrary, an action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs."

"I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former."

"It has never been in my power to study anything, — mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semeiotic."

"The definition of definition is at bottom just what the maxim of pragmatism expresses."

"By an object, I mean anything that we can think, i.e. anything we can talk about."

"The entire universe is perfused with signs, if it is not composed exclusively of signs."

"Any character or proposition either concerns one subject, two subjects, or a plurality of subjects. For example, one particle has mass, two particles attract one another, a particle revolves about the line joining two others. A fact concerning two subjects is a dual character or relation; but a relation which is a mere combination of two independent facts concerning the two subjects may be called degenerate, just as two lines are called a degenerate conic. In like manner a plural character or conjoint relation is to be called degenerate if it is a mere compound of dual characters. A sign is in a conjoint relation to the thing denoted and to the mind. If this triple relation is not of a degenerate species, the sign is related to its object only in consequence of a mental association, and depends upon a habit. Such signs are always abstract and general, because habits are general rules to which the organism has become subjected. They are, for the most part, conventional or arbitrary. They include all general words, the main body of speech, and any mode of conveying a judgment. For the sake of brevity I will call them tokens."

"If the sign were not related to its object except by the mind thinking of them separately, it would not fulfil the function of a sign at all. Supposing, then, the relation of the sign to its object does not lie in a mental association, there must be a direct dual relation of the sign to its object independent of the mind using the sign. In the second of the three cases just spoken of, this dual relation is not degenerate, and the sign signifies its object solely by virtue of being really connected with it. Of this nature are all natural signs and physical symptoms. I call such a sign an index, a pointing finger being the type of the class. The index asserts nothing; it only says "There!" It takes hold of our eyes, as it were, and forcibly directs them to a particular object, and there it stops. Demonstrative and relative pronouns are nearly pure indices, because they denote things without describing them; so are the letters on a geometrical diagram, and the subscript numbers which in algebra distinguish one value from another without saying what those values are."

"I call a sign which stands for something merely because it resembles it, an icon. Icons are so completely substituted for their objects as hardly to be distinguished from them. Such are the diagrams of geometry. A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing. So in contemplating a painting, there is a moment when we lose the consciousness that it is not the thing, the distinction of the real and the copy disappears, and it is for the moment a pure dream, — not any particular existence, and yet not general. At that moment we are contemplating an icon."

"I have taken pains to make my distinction of icons, indices, and tokens clear, in order to enunciate this proposition: in a perfect system of logical notation signs of these several kinds must all be employed. Without tokens there would be no generality in the statements, for they are the only general signs; and generality is essential to reasoning. … But tokens alone do not state what is the subject of discourse ; and this can, in fact, not be described in general terms ; it can only be indicated. The actual world cannot be distinguished from a world of imagination by any description. Hence the need of pronoun and indices, and the more complicated the subject the greater the need of them."

"Now, to say that a lot of objects is finite, is the same as to say that if we pass through the class from one to another we shall necessarily come round to one of those individuals already passed; that is, if every one of the lot is in any one-to-one relation to one of the lot, then to every one of the lot some one is in this same relation."

"As the mathematics are now understood, each branch — or, if you please, each problem, — is but the study of the relations of a collection of connected objects, without parts, without any distinctive characters, except their names or designating letters. These objects are commonly called points; but to remove all notion of space relations, it may be better to name them monads. The relations between these points are mere complications of two different kinds of elementary relations, which may be termed immediate connection and immediate non-connection. All the monads except as serve as intermediaries for the connections have distinctive designations."

"A pair of statements may be taken conjunctively or disjunctively; for example, "It lightens and it thunders," is conjunctive, "It lightens or it thunders" is disjunctive. Each such individual act of connecting a pair of statements is a new monad for the mathematician."

"Of the fifty or hundred systems of philosophy that have been advanced at different times of the world's history, perhaps the larger number have been, not so much results of historical evolution, as happy thoughts which have accidently occurred to their authors. An idea which has been found interesting and fruitful has been adopted, developed, and forced to yield explanations of all sorts of phenomena. … The remaining systems of philosophy have been of the nature of reforms, sometimes amounting to radical revolutions, suggested by certain difficulties which have been found to beset systems previouslv in vogue; and such ought certainly to be in large part the motive of any new theory. … When a man is about to build a house, what a power of thinking he has to do, before he can safely break ground! With what pains he has to excogitate the precise wants that are to be supplied. What a study to ascertain the most available and suitable materials, to determine the mode of construction to which those materials are best adapted, and to answer a hundred such questions! Now without riding the metaphor too far, I think we may safely say that the studies preliminary to the construction of a great theory should be at least as deliberate and thorough as those that are preliminary to the building of a dwelling-house."

"To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. That a pitched coin should sometimes turn up heads and sometimes tails calls for no particular explanation; but if it shows heads every time, we wish to know how this result has been brought about. Law is par excellence the thing that wants a reason."

"The only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution. This supposes them not to be absolute, not to be obeyed precisely. It makes an element of indeterminacy, spontaneity, or absolute chance in nature. Just as, when we attempt to verify any physical law, we find our observations cannot be precisely satisfied by it, and rightly attribute the discrepancy to errors of observation, so we must suppose far more minute discrepancies to exist owing to the imperfect cogency of the law itself, to a certain swerving of the facts from any definite formula."

"The one primary and fundamental law of mental action consists in a tendency to generalisation. Feeling tends to spread ; connections between feelings awaken feelings; neighboring feelings become assimilated; ideas are apt to reproduce themselves. These are so many formulations of the one law of the growth of mind. When a disturbance of feeling takes place, we have a consciousness of gain, the gain of experience; and a new disturbance will be apt to assimilate itself to the one that preceded it. Feelings, by being excited, become more easily excited, especially in the ways in which they have previously been excited. The consciousness of such a habit constitutes a general conception. The cloudiness of psychological notions may be corrected by connecting them with physiological conceptions. Feeling may be supposed to exist, wherever a nerve-cell is in an excited condition. The disturbance of feeling, or sense of reaction, accompanies the transmission of disturbance between nerve-cells or from a nerve-cell to a muscle-cell or the external stimulation of a nerve-cell. General conceptions arise upon the formation of habits in the nerve-matter, which are molecular changes consequent upon its activity and probably connected with its nutrition."

"The law of habit exhibits a striking contrast to all physical laws in the character of its commands. A physical law is absolute. What it requires is an exact relation. Thus, a physical force introduces into a motion a component motion to be combined with the rest by the parallelogram of forces; but the component motion must actually take place exactly as required by the law of force. On the other hand, no exact conformity is required by the mental law. Nay, exact conformity would be in downright conflict with the law ; since it would instantly crystallise thought and prevent all further formation of habit. The law of mind only makes a given feeling more likely to arise. It thus resembles the "non-conservative" forces of physics, such as viscosity and the like, which are due to statistical uniformities in the chance encounters of trillions of molecules."

"The old dualistic notion of mind and matter, so prominent in Cartesianism, as two radically different kinds of substance, will hardly find defenders to-day. Rejecting this, we are driven to some form of hylopathy, otherwise called monism."

"The one intelligible theory of the universe is that of objective idealism, that matter is effete mind, inveterate habits becoming physical laws. But before this can be accepted it must show itself capable of explaining the tridimensionality of space, the laws of motion, and the general characteristics of the universe, with mathematical clearness and precision ; for no less should be demanded of every Philosophy."

"Three conceptions are perpetually turning up at every point in every theory of logic, and in the most rounded systems they occur in connection with one another. They are conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked. I call them the conceptions of First, Second, Third. First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation."

"The origin of things, considered not as leading to anything, but in itself, contains the idea of First, the end of things that of Second, the process mediating between them that of Third. A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one. The idea of the Many, because variety is arbitrariness and arbitrariness is repudiation of any Secondness, has for its principal component the conception of First. In psychology Feeling is First, Sense of reaction Second, General conception Third, or mediation. In biology, the idea of arbitrary sporting is First, heredity is Second, the process whereby the accidental characters become fixed is Third. Chance is First, Law is Second, the tendency to take habits is Third. Mind is First, Matter is Second, Evolution is Third."

"May some future student go over this ground again, and have the leisure to give his results to the world."

"When I have asked thinking men what reason they had to believe that every fact in the universe is precisely determined by law, the first answer has usually been that the proposition is a "presupposition " or postulate of scientific reasoning. Well, if that is the best that can be said for it, the belief is doomed. Suppose it be " postulated " : that does not make it true, nor so much as afford the slightest rational motive for yielding it any credence. It is as if a man should come to borrow money, and when asked for his security, should reply he "postulated " the loan. To "postulate" a proposition is no more than to hope it is true. There are, indeed, practical emergencies in which we act upon assumptions of certain propositions as true, because if they are not so, it can make no difference how we act. But all such propositions I take to be hypotheses of individual facts. For it is manifest that no universal principle can in its universality be compromised in a special case or can be requisite for the validity of any ordinary inference."

"In an article published in The Monist for January, 1891, I endeavored to show what ideas ought to form the warp of a system of philosophy, and particularly emphasized that of absolute chance. In the number of April, 1892, I argued further in favor of that way of thinking, which it will be convenient to christen tychism (from τύχη, chance). A serious student of philosophy will be in no haste to accept or reject this doctrine; but he will see in it one of the chief attitudes which speculative thought may take, feeling that it is not for an individual, nor for an age, to pronounce upon a fundamental question of philosophy. That is a task for a whole era to work out. I have begun by showing that tychism must give birth to an evolutionary cosmology, in which all the regularities of nature and of mind are regarded as products of growth, and to a Schelling-fashioned idealism which holds matter to be mere specialized and partially deadened mind."

"The tendency to regard continuity, in the sense in which I shall define it, as an idea of prime importance in philosophy conveniently may be be termed synechism. The present paper is intended chiefly to show what synechism is, and what it leads to."

"Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas."

"We are accustomed to speak of ideas as reproduced, as passed from mind to mind, as similar or dissimilar to one another, and, in short, as if they were substantial things; nor can any reasonable objection be raised to such expressions. But taking the word "idea" in the sense of an event in an individual consciousness, it is clear that an idea once past is gone forever, and any supposed recurrence of it is another idea. These two ideas are not present in the same state of consciousness, and therefore cannot possibly be compared."

"What distinct meaning can attach to saying that an idea in the past in any way affects an idea in the future, from which it is completely detached?"

"We have here a question of difficulty, analogous to the question of nominalism and realism."

"Some minds will jump here jump to the conclusion that a past idea cannot in any sense be present. But that is hasty and illogical. How extravagant too, to pronounce our whole knowledge of the past to be mere delusion! Yet it would seem that the past is completely beyond the bounds of possible experience as a Kantian thing-in-itself."

"How can a past idea be present?... it can only be going, infinitesimally past, less past than any assignable past date. We are thus brought to the conclusion that the present is connected to the past by a series of real infinitesimal steps."

"If the sensation that precedes the present by half a second were still immediately before me, then on the same principle, the sensation preceding that would be immediately present, and so on ad infinitum. Now, since there is a time [period], say a year, at the end of which an idea is no longer ipso facto present, it follows that this is true of any finite interval, however short."

"Consciousness must essentially cover an interval of time; for if it did not, we could gain no knowledge of time, and not merely no veracious cognition of it, but no conception whatever. We are therefore, forced to say that we are immediately conscious through an infinitesimal interval of time."

"In fact, this infinitesimally spread-out consciousness is a direct feeling of its contents as spread out. In an infinitesimal interval we directly perceive the temporal sequence of its beginning, middle, and end... Now upon this interval follows another, whose beginning is the middle of the former, and whose middle is the end of the former. Here we have an immediate perception of the temporal sequence of its beginning, middle and end, or say, of the second, third, and fourth instants."

"From these two immediate perceptions, we gain a mediate, or inferential perception of the relation of all four instants. This mediate perception is objectively, or as to the object being represented, spread over the four instants; but subjectively, or as itself the subject of duration, it is completely embraced in the second moment. (The reader will observe that I use the word instant to mean a point in time, and moment to mean an infinitesimal duration."

"Now, let there be an indefinite succession of these inferential acts of comparative perception; and it is plain that the last moment will contain objectively the whole series. Let there be, not merely an indefinite succession, but a continuous flow of inference through a finite time; and the result will be a mediate objective consciousness of the whole time in the last moment. In this last moment, the whole series will be recognized, or known as known before."

"Indeed, even this last moment will be recognized like the rest, at least, be just beginning to be so."

"Suppose a surface to be part red and part blue; so that every point on it is either red or blue, and of course, no part can be both red and blue. What then, is the color of the surface in the immediate neighborhood of the point. ...it follows that the boundary is half red and half blue. In like manner, we find it necessary to hold that consciousness essentially occupies time... Thus, the present is half past and half time to come. ...Take another case: the velocity of a particle at any instant of time is its mean velocity during an infinitesimal instant in which that time is consumed. Just so, my immediate feeling is my feeling through an infinitesimal duration containing the present instant."

"One of the most marked features about the law of mind is that it makes time to have a definite direction of flow from past to future. ...This makes one of the great contrasts between the law of mind and the law of physical force, where there is no more distinction between the two opposite directions in time than between moving northward and moving southward."

"Time with its continuity logically involves some other kind of continuity than its own. Time, as the universal form of change, cannot exist unless there is something to undergo change, and to undergo a change continuous in time, there must be a continuity of changeable qualities."

"The development of the human mind has practically extinguished all feelings, except a few sporadic kinds, [like] sound, colors, smells, warmth, etc., which now appear to be disconnected and separate."

"In the case of colors, there is a tridimensional spread of feelings. Originally all feelings may have been connected in the same way, and the presumption is that the number of dimensions was endless. For development essentially involves a limitation of possibilities. But given a number of dimensions of feeling, all possible varieties are obtainable by varying the intensities of the different elements."

"Accordingly, time logically supposes a continuous range of intensity of feeling. It follows then, from the definition of continuity, that when any particular kind of feeling is present, an infinitesimal continuum of all feelings differing infinitesimally from that, is present."

"Since space is continuous, it follows that there must be an immediate community of feeling between parts of mind infinitesimally close together. Without this, I believe it would have been impossible for any co-ordination to be established in the action of the nerve-matter of one brain."

"A finite interval of time generally contains an innumerable series of feelings; and when these become welded together in association the result is a general idea."

"The first character of a general idea so resulting is that it is living feeling. A continuum of this feeling, infinitesimal in duration, but still embracing innumerable parts, and also, though infinitesimal, entirely unlimited, is immediately present. And in its absence of boundedness a vague possibility of more than is present is directly felt."

"Second, in the presence of this continuity of feeling, nominalistic maxims appear futile. There is no doubt about one idea affecting another, when we can directly perceive the one generally modified and shaping itself into the other. Nor can there any longer be any difficulty about one idea resembling another, when we can pass along the continuous field of quality from one to the other and back again to the point which we had marked."

"Third, consider the insistency of an idea. The insistency of a past idea with reference to the present is a quantity which is less, the further back that past idea is, and rises to infinity as the past idea is brought up into coincidence with the present."

"Here we must make one of those inductive applications of the law of continuity which have produced such great results in all of the positive sciences. We must extend the law of insistency into the future. Plainly, the insistency of a future idea with reference to the present is a quantity affected by the minus sign; for it is the present that affects the future, if there be any effect, not the future that affects the present."

"Feeling which has not yet emerged into immediate consciousness is already affectible and already affected. In fact, this is habit, by virtue of which an idea is brought up into the present consciousness by a bond that has already been established between it and another idea while it was still in futuro."

"Wherever ideas come together they tend to weld into general ideas; and whenever they are generally connected, general ideas govern the connection; and these general ideas are living feelings spread out."

"In deduction the mind is under the dominion of a habit or association by virtue of which a general idea suggests in each case a corresponding reaction. This is the way the hind legs of a frog separated from the rest of the body, reason, when you pinch them. It is the lowest form of psychical manifestation."

"But no mental action seems necessary or invariable in its character. In whatever manner the mind has reacted under a given sensation, in that manner it is the more likely to react again; were this, however, an absolute necessity, habits would become wooden and ineradicable, and no room being left for the formulation of new habits, intellectual life would come to a speedy close. Thus, the uncertainty of the mental law is no mere defect of it, but is on the contrary of its essence. The truth is, the mind is not subject to "law," in the same rigid sense that matter is. It only experiences gentle forces which merely render it more likely to act a given way than it otherwise would be. There always remains a certain amount of arbitrary spontaneity in its action, without which it would be dead."

"Let me now try to gather up all these odds and ends of commentary and restate the law of mind, in a unitary way."

"First then, we find that when we regard ideas from a nominalistic, individualistic, sensualistic way, the simplest facts of mind become utterly meaningless. That one idea should resemble another or influence another, or that one state of mind should so much as be thought of in another is, from that standpoint, sheer nonsense."

"Second, by this and other means we are driven to perceive, what is quite evident in itself, that instantaneous feelings flow together in a continuum of feeling, which has in a modified degree the peculiar vivacity of feeling and has gained generality. And in reference to such general ideas, or continua of feeling, the difficulties about resemblance and suggestion and reference to the external, cease to have any force."

"Third, these general ideas are not mere words, nor do they consist in this, that certain concrete facts will every time happen under certain descriptions of conditions; but they are just as much, or rather far more, living realities than the feelings themselves out of which they are concreted. And to say that mental phenomenon are governed by law does not mean merely that they are describable by a general formula; but that there is a living idea, a conscious continuum of feeling which pervades them, and to which they are docile."

"Fourth, this supreme law, which is celestial and living harmony, does not so much as demand that the special ideas shall surrender their peculiar arbitrariness and caprice entirely; for that would be self-destructive. It only requires that they influence and be influenced by one another."

"Fifth, in what measure this unification acts, seems to be regulated only by special rules; or, at least, we cannot in our present knowledge say how far it goes. But it may be said that, judging by appearances, the amount of arbitrariness in the phenomenon of human minds is neither altogether trifling nor very prominent."

"Were the ends of a person already explicit, there would be no room for development, for growth, for life; and consequently there would be no personality. The mere carrying out of predetermined purposes is mechanical. This remark has an application to the philosophy of religion. It is that genuine evolutionary philosophy, that is, one that makes the principle of growth a primordial element of the universe, is so far from being antagonistic to the idea of a personal creator, that it is really inseparable from that idea; while a necessitarian religion is in an altogether false position and is destined to become disintegrated. But a pseudo-evolutionism which enthrones mechanical law above the principle of growth is at once scientifically unsatisfactory, as giving no possible hint of how the universe has come about, and hostile to all hopes of personal relations to God."

"The recognition by one person of another's personality takes place by means to some extent identical to the means by which he is conscious of his own personality. The idea of the second personality, which is as much as to say that second personality itself, enters within the direct consciousness of the first person, and is immediately perceived as his ego, though less strongly. At the same time, the opposition between the two persons is perceived, so that the externality of the second is perceived."

"But the extraordinary insight which some persons are able to gain of others from indications so slight that it is difficult to ascertain what they are, is certainly rendered more comprehensible by the view here taken."

"A difficulty which confronts the synechistic philosophy is this. In considering personality, that philosophy is forced to accept the doctrine of a personal God; but in considering communication, it cannot but admit that if there is a personal God, we must have a direct perception of that person and indeed be in personal communication with him. Now, if that be the case, the question arises how it is possible that the existence of this being should ever have been doubted by anybody. The only answer that I can at present make is that facts that stand before our face and eyes and stare us in the face are far from being, in all cases, the ones most easily discerned. That has been remarked since time immemorial."

"I think that I have succeeded in making it clear that this doctrine gives room for explanations of many facts which without it are absolutely and hopelessly inexplicable; and further that it carries along with it the following doctrines: first, a logical realism of the most pronounced type; second, objective idealism; third, tychism, with its consequent thoroughgoing evolutionism. We also notice that the doctrine presents no hindrences to spiritual influences, such as some philosophies are felt to do."

"A certain maxim of Logic which I have called Pragmatism has recommended itself to me for diverse reasons and on sundry considerations. Having taken it as my guide for most of my thought, I find that as the years of my knowledge of it lengthen, my sense of the importance of it presses upon me more and more. If it is only true, it is certainly a wonderfully efficient instrument. It is not to philosophy only that it is applicable. I have found it of signal service in every branch of science that I have studied. My want of skill in practical affairs does not prevent me from perceiving the advantage of being well imbued with pragmatism in the conduct of life."

"Be it understood, then, that what we have to do, as students of phenomenology, is simply to open our mental eyes and look well at the phenomenon and say what are the characteristics that are never wanting in it, whether that phenomenon be something that outward experience forces upon our attention, or whether it be the wildest of dreams, or whether it be the most abstract and general of the conclusions of science. The faculties which we must endeavor to gather for this work are three. The first and foremost is that rare faculty, the faculty of seeing what stares one in the face, just as it presents itself, unreplaced by any interpretation, unsophisticated by any allowance for this or for that supposed modifying circumstance. This is the faculty of the artist who sees for example the apparent colors of nature as they appear. When the ground is covered by snow on which the sun shines brightly except where shadows fall, if you ask any ordinary man what its color appears to be, he will tell you white, pure white, whiter in the sunlight, a little greyish in the shadow. But that is not what is before his eyes that he is describing; it is his theory of what ought to be seen. The artist will tell him that the shadows are not grey but a dull blue and that the snow in the sunshine is of a rich yellow. That artist's observational power is what is most wanted in the study of phenomenology. The second faculty we must strive to arm ourselves with is a resolute discrimination which fastens itself like a bulldog upon the particular feature that we are studying, follows it wherever it may lurk, and detects it beneath all its disguises. The third faculty we shall need is the generalizing power of the mathematician who produces the abstract formula that comprehends the very essence of the feature under examination purified from all admixture of extraneous and irrelevant accompaniments."

"When anything is present to the mind, what is the very first and simplest character to be noted in it, in every case, no matter how little elevated the object may be? Certainly, it is its presentness."

"The quality of feeling is the true psychical representative of the first category of the immediate as it is in its immediacy, of the present in its direct positive presentness. Qualities of feeling show myriad-fold variety, far beyond what the psychologists admit. This variety however is in them only insofar as they are compared and gathered into collections. But as they are in their presentness, each is sole and unique; and all the others are absolute nothingness to it — or rather much less than nothingness, for not even a recognition as absent things or as fictions is accorded to them. The first category, then, is Quality of Feeling, or whatever is such as it is positively and regardless of aught else."

"The next simplest feature that is common to all that comes before the mind, and consequently, the second category, is the element of Struggle."

"In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience. She says,"

"Understand me well. My appeal is to observation — observation that each of you must make for himself."

"Thus far, gentlemen, I have been insisting very strenuously upon what the most vulgar common sense has every disposition to assent to and only ingenious philosophers have been able to deceive themselves about. But now I come to a category which only a more refined form of common sense is prepared willingly to allow, the category which of the three is the chief burden of Hegel's song, a category toward which the studies of the new logico-mathematicians, Georg Cantor and the like, are steadily pointing, but to which no modern writer of any stripe, unless it be some obscure student like myself, has ever done anything approaching to justice."

"There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it; and in the long run, say in some thousands of generations, time will be economized by proceeding in an orderly manner, and by making it an invariable rule to try the simpler hypothesis first. Indeed, one can never be sure that the simpler hypothesis is not the true one, after all, until its cause has been fought out to the bitter end. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Speaking strictly, belief is out of place in pure theoretical science, which has nothing nearer to it than the establishment of doctrines, and only the provisional establishment of them, at that. Compared with living belief it is nothing but a ghost. If the captain of a vessel on a lee shore in a terrific storm finds himself in a critical position in which he must instantly either put his wheel to port acting on one hypothesis, or put his wheel to starboard acting on the contrary hypothesis, and his vessel will infallibly be dashed to pieces if he decides the question wrongly, Ockham's razor is not worth the stout belief of any common seaman. For stout belief may happen to save the ship, while Entia non sunt multiplicanda praeter necessitatem would be only a stupid way of spelling Shipwreck. Now in matters of real practical concern we are all in something like the situation of that sea-captain."

"Philosophy, as I understand the word, is a positive theoretical science, and a science in an early stage of development. As such it has no more to do with belief than any other science. Indeed, I am bound to confess that it is at present in so unsettled a condition, that if the ordinary theorems of molecular physics and of archaeology are but the ghosts of beliefs, then to my mind, the doctrines of the philosophers are little better than the ghosts of ghosts. I know this is an extremely heretical opinion."

"The third category of which I come now to speak is precisely that whose reality is denied by nominalism. For although nominalism is not credited with any extraordinarily lofty appreciation of the powers of the human soul, yet it attributes to it a power of originating a kind of ideas the like of which Omnipotence has failed to create as real objects, and those general conceptions which men will never cease to consider the glory of the human intellect must, according to any consistent nominalism, be entirely wanting in the mind of Deity."

"All nature abounds in proofs of other influences than merely mechanical action, even in the physical world. They crowd in upon us at the rate of several every minute. And my observation of men has led me to this little generalization. Speaking only of men who really think for themselves and not of mere reporters, I have not found that it is the men whose lives are mostly passed within the four walls of a physical laboratory who are most inclined to be satisfied with a purely mechanical metaphysics. On the contrary, the more clearly they understand how physical forces work the more incredible it seems to them that such action should explain what happens out of doors. A larger proportion of materialists and agnostics is to be found among the thinking physiologists and other naturalists, and the largest proportion of all among those who derive their ideas of physical science from reading popular books."

"The word "God," so "capitalised" (as we Americans say), is the definable proper name, signifying Ens necessarium; in my belief Really creator of all three Universes of Experience."

"Some words shall herein be capitalised when used, not as vernacular, but as terms defined. Thus an "idea" is the substance of an actual unitary thought or fancy; but "Idea," nearer Plato's idea of ἰδέα, denotes anything whose Being consists in its mere capacity for getting fully represented, regardless of any person's faculty or impotence to represent it."

"Of the three Universes of Experience familiar to us all, the first comprises all mere Ideas, those airy nothings to which the mind of poet, pure mathematician, or another might give local habitation and a name within that mind. Their very airy-nothingness, the fact that their Being consists in mere capability of getting thought, not in anybody's Actually thinking them, saves their Reality. The second Universe is that of the Brute Actuality of things and facts. I am confident that their Being consists in reactions against Brute forces, notwithstanding objections redoubtable until they are closely and fairly examined. The third Universe comprises everything whose being consists in active power to establish connections between different objects, especially between objects in different Universes. Such is everything which is essentially a Sign — not the mere body of the Sign, which is not essentially such, but, so to speak, the Sign's Soul, which has its Being in its power of serving as intermediary between its Object and a Mind."

"An "Argument" is any process of thought reasonably tending to produce a definite belief. An "Argumentation" is an Argument proceeding upon definitely formulated premisses. If God Really be, and be benign, then, in view of the generally conceded truth that religion, were it but proved, would be a good outweighing all others, we should naturally expect that there would be some Argument for His Reality that should be obvious to all minds, high and low alike, that should earnestly strive to find the truth of the matter; and further, that this Argument should present its conclusion, not as a proposition of metaphysical theology, but in a form directly applicable to the conduct of life, and full of nutrition for man's highest growth. What I shall refer to as the N.A. — the Neglected Argument — seems to me best to fulfil this condition, and I should not wonder if the majority of those whose own reflections have harvested belief in God must bless the radiance of the N.A. for that wealth. Its persuasiveness is no less than extraordinary; while it is not unknown to anybody. Nevertheless, of all those theologians (within my little range of reading) who, with commendable assiduity, scrape together all the sound reasons they can find or concoct to prove the first proposition of theology, few mention this one, and they most briefly. They probably share those current notions of logic which recognise no other Arguments than Argumentations."

"The hypothesis of God is a peculiar one, in that it supposes an infinitely incomprehensible object, although every hypothesis, as such, supposes its object to be truly conceived in the hypothesis. This leaves the hypothesis but one way of understanding itself; namely, as vague yet as true so far as it is definite, and as continually tending to define itself more and more, and without limit. The hypothesis, being thus itself inevitably subject to the law of growth, appears in its vagueness to represent God as so, albeit this is directly contradicted in the hypothesis from its very first phase. But this apparent attribution of growth to God, since it is ineradicable from the hypothesis, cannot, according to the hypothesis, be flatly false. Its implications concerning the Universes will be maintained in the hypothesis, while its implications concerning God will be partly disavowed, and yet held to be less false than their denial would be. Thus the hypothesis will lead to our thinking of features of each Universe as purposed; and this will stand or fall with the hypothesis. Yet a purpose essentially involves growth, and so cannot be attributed to God. Still it will, according to the hypothesis, be less false to speak so than to represent God as purposeless."

"Unless man have a natural bent in accordance with nature's, he has no chance of understanding nature at all."

"The difference between a pessimistic and an optimistic mind is of such controlling importance in regard to every intellectual function, and especially for the conduct of life, that it is out of the question to admit that both are normal, and the great majority of mankind are naturally optimistic."

"The third argument, enclosing and defending the other two, consists in the development of those principles of logic according to which the humble argument is the first stage of a scientific inquiry into the origin of the three Universes, but of an inquiry which produces, not merely scientific belief, which is always provisional, but also a living, practical belief, logically justified in crossing the Rubicon with all the freightage of eternity."

"My original essay, having been written for a popular monthly, assumes, for no better reason than that real inquiry cannot begin until a state of real doubt arises and ends as soon as Belief is attained, that "a settlement of Belief," or, in other words, a state of satisfaction, is all that Truth, or the aim of inquiry, consists in. The reason I gave for this was so flimsy, while the inference was so nearly the gist of Pragmaticism, that I must confess the argument of that essay might with some justice be said to beg the question. The first part of the essay, however, is occupied with showing that, if Truth consists in satisfaction, it cannot be any actual satisfaction, but must be the satisfaction which would ultimately be found if the inquiry were pushed to its ultimate and indefeasible issue. This, I beg to point out, is a very different position from that of Mr Schiller and the pragmatists of to-day. I trust I shall be believed when I say that it is only a desire to avoid being misunderstood in consequence of my relations with pragmatism, and by no means as arrogating any superior immunity from error which I have too good reason to know that I do not enjoy, that leads me to express my personal sentiments about their tenets. Their avowedly undefinable position, if it be not capable of logical characterisation, seems to me to be characterised by an angry hatred of strict logic, and even some disposition to rate any exact thought which interferes with their doctrines as all humbug. At the same time, it seems to me clear that their approximate acceptance of the Pragmaticist principle, and even that very casting aside of difficult distinctions (although I cannot approve of it), has helped them to a mightily clear discernment of some fundamental truths that other philosophers have seen but through a mist, and most of them not at all. Among such truths — all of them old, of course, yet acknowledged by few — I reckon their denial of necessitarianism; their rejection of any "consciousness" different from a visceral or other external sensation; their acknowledgment that there are, in a Pragmatistical sense, Real habits (which Really would produce effects, under circumstances that may not happen to get actualised, and are thus Real generals); and their insistence upon interpreting all hypostatic abstractions in terms of what they would or might (not actually will) come to in the concrete. It seems to me a pity they should allow a philosophy so instinct with life to become infected with seeds of death in such notions as that of the unreality of all ideas of infinity and that of the mutability of truth, and in such confusions of thought as that of active willing (willing to control thought, to doubt, and to weigh reasons) with willing not to exert the will (willing to believe)."

"If we endeavor to form our conceptions upon history and life, we remark three classes of men. The first consists of those for whom the chief thing is the qualities of feelings. These men create art. The second consists of the practical men, who carry on the business of the world. They respect nothing but power, and respect power only so far as it [is] exercized. The third class consists of men to whom nothing seems great but reason. If force interests them, it is not in its exertion, but in that it has a reason and a law. For men of the first class, nature is a picture; for men of the second class, it is an opportunity; for men of the third class, it is a cosmos, so admirable, that to penetrate to its ways seems to them the only thing that makes life worth living."

"Do not block the way of inquiry."

"The idea does not belong to the soul; it is the soul that belongs to the idea."

"Effort supposes resistance."

"The ordinary logic has a great deal to say about genera and species, or in our nineteeth century dialect, about classes. Now a class is a set of objects comprising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects comprising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the comtemplation of a fragment of a system to the envisagement of the complete system."

"It is ...easy to be certain. One has only to be sufficiently vague."

"Every man is fully satisfied that there is such a thing as truth, or he would not ask any question."

"To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs."

"Let us not pretend to doubt in philosophy what we do not doubt in our hearts."

"Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object."

"All the evolution we know of proceeds from the vague to the definite."

"Mere imagination would indeed be mere trifling; only no imagination is mere."

"Our whole past experience is continually in our consciousness, though most of it sunk to a great depth of dimness. I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way."

"Peirce, to my knowledge, is original and unique in stressing the problem of studying the rules that limit the class of possible theories. Of course, his concept of abduction, like Lorenz’s biological a priori, has a strongly Kantian flavor, and all derive from the rationalist psychology that concerned itself with the forms, the limits, and the principles that provide “the sinews and connections” for human thought, that underlie “that infinite amount of knowledge of which we are not always conscious,” of which Leibnitz spoke. It is therefore quite natural that we should link these developments to the revival of philosophical grammar, which grew from the same soil as an attempt, quite fruitful and legitimate, to explore one basic facet of human intelligence."

"Pierce wrote as a logician and James as a humanist."

"The principle of interpretation says that "a sign is something by knowing which we know something more" (Peirce). The Peircean idea of semiosis is the idea of an infinite process of interpretation."

"Peirce was concerned to explicate the idea of meaning whereas James was concerned to explicate the meaning of ideas."

"James called Peirce the most original thinker of their generation; Peirce placed himself somewhere near the rank of Leibniz. This much is now certain; he is the most original and versatile of America's philosophers and America's greatest logician."

"Peirce held that the continuity of space, time, ideation, feeling, and perception is an irreducible deliverance of science, and that an adequate conception of the continuous is an extremely important part of all the sciences. This doctrine he called “synechism,” a word deriving from the Greek preposition that means “(together) with.”"

"Peirce was a man of tremendous energy, producing a multitude of ideas, good, bad, and indifferent. He reminds on of a volcano spouting vast masses of rock, of which some, on examination, turn out to be nuggets of pure gold. He holds―and I confess that an examination of scientific inference has made me feel the force of this view―that man is adapted, by his congenital constitution, to the apprehension of natural laws which cannot be proved by experience, although experience is in conformity with them."

"Beyond doubt ... he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever."

"One of the greatest philosophers of all time."

"Ultimately, the last word is never ours. Peirce said: the meaning of my life is entrusted to others. [...] Which proves that truth is never something definitive; we are always mistaken. On a journey. It is no coincidence that I speak of the “transit of truth.”"

"Conceptual graphs are system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. The purpose of the system is to express meaning in a form that is logically precise, humanly readable, and computationally tractable."

"Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur."

"Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives."

"During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them."

"In retrospect... it is interesting to note that the original problem that started my research is still outstanding -- namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world."

"Industrial production, the flow of resources in the economy, the exertion of military effort in a war, the management of finances --all require the coordination of interrelated activities. What these complex undertakings share in common is the task of constructing a statement of actions to be performed, their timing and quantity (called a program or schedule), that, if implemented, would move the system from a given initial status as much as possible towards some defined goal"

"All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it."

"Industrial production, the flow of resources in the economy, the exertion of military effort in a war theater-all are complexes of numerous interrelated activities. Differences may exist in the goals to be achieved, the particular processes involved, and the magnitude of effort. Nevertheless, it is possible to abstract the underlying essential similarities in the management of these seemingly disparate systems."

"If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming."

"One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947, Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution. … The particular problem solved was one which had been studied earlier by George Stigler (who later became a Nobel Laureate) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution (expressed in 1945 dollars) was only 24 cents higher than the true minimum per year $39.69."

"The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight."

"Once stock prices reach the point at which it is hard to value them by logical methodology, stocks will be bought as they were in the late 1920s not for investment but to be unloaded at a still higher price. The ensuing break could be disastrous because panic psychology cannot be summarily altered or reversed by easing money policies."

"The world of antitrust is reminiscent of Alice’s Wonderland: everything seemingly is, yet apparently isn’t, simultaneously. It is a world in which competition is lauded as the basic axiom and guiding principle, yet "too much" competition is condemned as "cutthroat." It is a world in which actions designed to limit competition are branded as criminal when taken by businessmen, yet praised as "enlightened" when initiated by the government. It is a world in which the law is so vague that businessmen have no way of knowing whether specific actions will be declared illegal until they hear the judge’s verdict—after the fact."

"Capitalism is based on self-interest and self-esteem; it holds integrity and trustworthiness as cardinal virtues and makes them pay off in the marketplace, thus demanding that men survive by means of virtue, not vices. It is this superlatively moral system that the welfare statists propose to improve upon by means of preventative law, snooping bureaucrats, and the chronic goad of fear."

"An almost hysterical antagonism toward the gold standard is one issue which unites statists of all persuasions. They seem to sense—perhaps more clearly and subtly than many consistent defenders of laissez-faire—that gold and economic freedom are inseparable, that the gold standard is an instrument of laissez-faire and that each implies and requires the other."

"In the absence of the gold standard, there is no way to protect savings from confiscation through inflation. There is no safe store of value. If there were, the government would have to make its holding illegal, as was done in the case of gold. If everyone decided, for example, to convert all his bank deposits to silver or copper or any other good, and thereafter declined to accept checks as payment for goods, bank deposits would lose their purchasing power and government-created bank credit would be worthless as a claim on goods. The financial policy of the welfare state requires that there be no way for the owners of wealth to protect themselves."

"We are obviously all hurt by inflation. Everybody is hurt by inflation. If you really wanted to examine who percentage-wise is hurt the most in their incomes, it is the Wall Street brokers. I mean their incomes have gone down the most."

"Since becoming a central banker, I have learned to mumble with great incoherence. If I seem unduly clear to you, you must have misunderstood what I said."

"I guess I should warn you, if I turn out to be particularly clear, you've probably misunderstood what I said."

"Clearly, sustained low inflation implies less uncertainty about the future, and lower risk premiums imply higher prices of stocks and other earning assets.… But how do we know when irrational exuberance has unduly escalated asset values, which then become subject to unexpected and prolonged contractions as they have in Japan over the past decade?"

"For some, the benign inflation outcome of 1996 might be considered surprising, as resource utilization rates--particularly of labor--were in the neighborhood of those that historically have been associated with building inflation pressures. To be sure, an acceleration in nominal labor compensation, especially its wage component, became evident over the past year. But the rate of pay increase still was markedly less than historical relationships with labor market conditions would have predicted. Atypical restraint on compensation increases has been evident for a few years now and appears to be mainly the consequence of greater worker insecurity. In 1991, at the bottom of the recession, a survey of workers at large firms by International Survey Research Corporation indicated that 25 percent feared being laid off. In 1996, despite the sharply lower unemployment rate and the tighter labor market, the same survey organization found that 46 percent were fearful of a job layoff."

"Nor can private counterparties restrict supplies of gold, another commodity whose derivatives are often traded over-the-counter, where central banks stand ready to lease gold in increasing quantities should the price rise."

"The reason there is very little support for the gold standard is the consequences of those types of market adjustments are not considered to be appropriate in the 20th and 21st century. I am one of the rare people who have still some nostalgic view about the old gold standard, as you know, but I must tell you, I am in a very small minority among my colleagues on that issue."

"It hardly makes any difference who will be the next president. The world is governed by market forces."

"Intensive research in recent years into the sources of economic growth among both developing and developed nations generally point to a number of important factors: the state of knowledge and skill of a population; the degree of control over indigenous natural resources; the quality of a country's legal system, particularly a strong commitment to a rule of law and protection of property rights; and yes, the extent of a country's openness to trade with the rest of the world. For the United States, arguably the most important factor is the type of rule of law under which economic activity takes place. When asked abroad why the United States has become the most prosperous large economy in the world, I respond, with only mild exaggeration, that our forefathers wrote a constitution and set in motion a system of laws that protects individual rights, especially the right to own property. Nonetheless, the degree of state protection is sometimes in dispute. But by and large, secure property rights are almost universally accepted by Americans as a critical pillar of our economy. While the right of property in the abstract is generally uncontested in all societies embracing democratic market capitalism, different degrees of property protection do apparently foster different economic incentives and outcomes."

"American consumers might benefit if lenders provided greater mortgage product alternatives to the traditional fixed-rate mortgage."

"Rising interest rates have been advertised for so long and in so many places that anyone who has not appropriately hedged this position by now obviously is desirous of losing money."

"While local economies may experience significant price imbalances, a national severe price distortion seems most unlikely in the United States, given its size and diversity."

"Without calling the overall national issue a bubble, it's pretty clear that it's an unsustainable underlying pattern."

"A decline in the national housing price level would need to be substantial to trigger a significant rise in foreclosures, because the vast majority of homeowners have built up substantial equity in their homes despite large mortgage-market financed withdrawals of home equity in recent years."

"[There are] signs of froth in some local markets where home prices seem to have risen to unsustainable levels."

"That said, there can be little doubt that exceptionally low interest rates on ten-year Treasury notes, and hence on home mortgages, have been a major factor in the recent surge of homebuilding and home turnover, and especially in the steep climb in home prices. Although a 'bubble' in home prices for the nation as a whole does not appear likely, there do appear to be, at a minimum, signs of froth in some local markets where home prices seem to have risen to unsustainable levels."

"The resolution of our current account deficit and household debt burdens does not strike me as overly worrisome, but that is certainly not the case for our fiscal deficit, which, according to the Congressional Budget Office, will rise significantly as the baby boomers start to retire in 2008. Our fiscal prospects are, in my judgment, a significant obstacle to long-term stability because the budget deficit is not readily subject to correction by market forces that stabilize other imbalances."

"History has not dealt kindly with the aftermath of protracted periods of low risk premiums."

"If you get beyond the political rhetoric [and assembled a group to solve Social Security] it would take them 15 minutes. It would take them 15 minutes only because 10 minutes was used for pleasantries."

"I was aware that the loosening of mortgage credit terms for subprime borrowers increased financial risk. But I believed then, as now, that the benefits of broadened home ownership are worth the risk."

"I really didn't get it until very late in 2005 and 2006."

"We had a bubble in housing."

"Well, first of all, the Federal Reserve is an independent agency, and that means, basically, that there is no other agency of government which can overrule actions that we take. So long as that is in place and there is no evidence that the administration or the Congress or anybody else is requesting that we do things other than what we think is the appropriate thing, then what the relationships are don't, frankly, matter. And I've had very good relationships with presidents."

"I think Bill Clinton was the best Republican president we've had in a while."

"Cash is available and we should use that in larger amounts, as is necessary, to solve the problems of the stress of this."

"Those of us who have looked to the self-interest of lending institutions to protect shareholder's equity – myself especially – are in a state of shocked disbelief."

"Yes, I’ve found a flaw. I don’t know how significant or permanent it is. But I’ve been very distressed by that fact."

"The need for values is inbred. Their content is not."

"Modern dynamic economies do not stay still long enough to allow for an accurate reading of their underlying structures."

"It did not go without notice that Ayn Rand stood beside me as I took the oath of office in the presence of President Ford in the Oval Office. Ayn Rand and I remained close until she died in 1982, and I'm grateful for the influence she had on my life. I was intellectually limited until I met her."

"It's hard to overemphasize how important Ford's deregulation was. True, most of the benefits took years to unfold-rail freight rates, for example hardly budged at first. Yet deregulation set the stage for an enormous wave of creative destruction in the 1980s:..."

"Treasury Secretary Brady didn't like the Fed either. He and the president were friends and had a lot in common-both were wealthy, Yale educated patricians and members of Skull and Bones."

"We generally did not talk about the stock market very much at the Fed."

"Of course, shedding the debt burden would be a happy development for our country, but it would nevertheless pose a big dilemma for the Fed. Our primary lever of monetary policy was buying and selling treasury securities-Uncle Sam's IOU's. But as the debt was paid down, those securities would grow scarce, leaving the Fed in need of a new set of assets to effect monetary policy."

"I came to a stark realization: chronic surpluses could be almost as destabilizing as chronic deficits."

"Globalization was exerting a dis-inflationary impact."

"When trust is lost, a nation's ability to transact business is palpably undermined."

"The Fabians laid the groundwork for modern social democracy, and their influence on the world would end up being at least as powerful as that of Marx."

"In general, corruption tends to exist whenever governments have favors to extend, or something to sell."

"Over the years I have had the most contact with Lee Kuan Yew, most recently in 2006, and have always found him impressive, even though we do not always see eye to eye. I met him first when he was George Shultz's guest at the famous (or infamous, depending on your perspective) Bohemian Grove, a male only bonding retreat among the redwoods of California."

"An area in which more rather than less government involvement is needed, in my judgment, is the rooting out of fraud. It is the bane of any market system."

"The probability of ten consecutive heads is 0.1 percent; thus, when you have millions of coin tossers, or investors, in the end there will be thousands of very successful practitioners of coin tossing, or stock picking."

"From the development of the textile loom two centuries ago to today's Internet, output per hour has increased fifty fold."

"Much of the securitization took the form of collateralized debt obligations (CDOs) with senior credit tranches certified by rating agencies as AAA. It was the failure to properly price such risky assets that characterized the crisis."

"We are going through a period with no precedent in American history."

"I know you think you understand what you thought I said, but I'm not sure you realize that what you heard is not what I meant"

"I got to know a lot of people on Wall Street. I used to tell then that Alan Greenspan was a musician. He was at Juilliard when I was there, a clarinet major, and he played in the Henry Jerome Band at the . After he became chairman of the Fed, Time had his picture on the cover, and inside they had a picture of him with the Edison Hotel band. One of the guys said, "I don't understand something. Why did Greenspan give up the music business, to become an economist?" "Very simple," I told him, "you should have heard him play the clarinet.""

"If you look at the speeches he gave just before he left the Fed, it's pretty much “After me - the Deluge. I'm getting out while my reputation's intact”."

"If you want a simple model for predicting the unemployment rate in the United States over the next few years, here it is: It will be what Greenspan wants it to be, plus or minus a random error reflecting the fact that he is not quite God."

"Greenspan doesn't get out of bed before examining the political consequences."

"I would not only reappoint Mr. Greenspan -- if Mr. Greenspan should happen to die, God forbid -- I would do like was did in the movie, 'Weekend at Bernie's.' I'd prop him up and put a pair of dark glasses on him and keep him as long as we could."

"The most devoted member of (Ayn Rand's) inner circle was Alan Greenspan, former head of the US Federal Reserve. Among the essays he wrote for Rand were those published in a book he co-edited with her called Capitalism: The Unknown Ideal. Here, starkly explained, you'll find the philosophy he brought into government. There is no need for the regulation of business—even builders or Big Pharma—he argued, as 'the "greed" of the businessman or, more appropriately, his profit-seeking … is the unexcelled protector of the consumer.' As for bankers, their need to win the trust of their clients guarantees that they will act with honour and integrity. Unregulated capitalism, he maintains, is a 'superlatively moral system.'"

"I sometimes say that Alan Greenspan overdosed on Ayn Rand when he was young. He thought that if an axe murder happened in a free market it was probably all for the best."

"[He is] one of the biggest political hacks we have in Washington."

"Greenspan's reaction with regard to the stock-market bubble has caused two more bubbles to grow: a real-estate bubble and a consumer-debt bubble... History will judge him one of the worst Central Bankers ever."

"In my view, Alan Greenspan will go down in history as one of the worst chairmen of the Federal Reserve. Future textbooks will refer to Greenspan as an example of how not to run a central bank. In order to underline the bipartisan support that Wall Street has in Congress, during his time of leadership at the Fed he was hailed not only by Republicans but also by most Democrats as "the Maestro." This, despite his extremely conservative views, which called for, among other reactionary policies, the elimination of the minimum wage. In 2000, at a House Financial Services Committee hearing on bank mergers, I asked Greenspan, "Aren't you concerned that with such a growing concentration of wealth, if one of these huge institutions fails it will have a horrendous impact on the national and global economy?" Greenspan replied, "No, I'm not. I believe that the general growth in large institutions has occurred in the context of an underlying structure of markets in which many of the larger risks are dramatically-I should say, fully-hedged." Greenspan could not have been more wrong. Yet after leaving the Fed, he was hired to advise some of the biggest banks and wealthiest hedge fund managers in the world."

"Greenspan kept an eye on such fluctuations as the sale of vacuum cleaners in Cleveland to, as they say, " get a precise idea about where the economy is going," and of course he micromanaged us into chaos."

"When I was 15 years old, or 16, I carried around on the streets of Brooklyn a paperback copy of Plato's Republic, front cover facing outward. I had read only some of it and understood less, but I was excited by it and knew it was something wonderful."

"Whatever the practical origins of aesthetic discernment may have been, it has been used to create great works of art. When the very loftiest human creations are seen to derive from humble origins and functions, what needs revision is not our esteem for these creations but our notion of nobility."

"Our principles fix what our life stands for, our aims create the light our life is bathed in, and our rationality, both individual and coordinate, defines and symbolizes the distance we have come from mere animality. It is by these means that our lives come to more than what they instrumentally yield. And by meaning more, our lives yield more."

"Individuals have rights and there are things no person or group may do to them (without violating their rights). So strong and far-reaching are these rights that they raise the question of what, if anything, the state and its officials may do. How much room do individual rights leave for the state?"

"Our main conclusions about the state are that a minimal state, limited, to the narrow functions of protection against force, theft, fraud, enforcement of contracts, and so on, is justified, but any more extensive state will violate persons' rights not to be forced to do certain things, and is unjustified; and that the minimal state is inspiring as well as right."

"Some anarchists have claimed not merely that we would be better off without a state, but that any state necessarily violates people's moral rights and hence is intrinsically immoral. Our starting point then, though nonpolitical, is by intention far from nonmoral. Moral philosophy sets the background for, and boundaries of, political philosophy. What persons may and may not do to one another limits what they may do through the apparatus of a state, or do to establish such an apparatus."

"Is there really someone who, searching for a group of wise and sensitive persons to regulate him for his own good, would choose that group of people that constitute the membership of both houses of Congress?"

"There is no social entity with a good that undergoes some sacrifice for its own good. There are only individual people, different individual people, with their own individual lives. Using one of these people for the benefit of others, uses him and benefits the others. Nothing more."

"1. A person who acquires a holding in accordance with the principle of justice in acquisition is entitled to that holding. 2. A person who acquires a holding in accordance with the principle of justice in transfer, from someone else entitled to the holding, is entitled to the holding. 3. No one is entitled to a holding except by (repeated) applications of 1 and 2."

"A distribution is just if it arises from another just distribution by legitimate means."

"Whatever arises from a just situation by just steps is itself just."

"Justice in holdings is historical; it depends upon what actually has happened. We shall return to this point later."

"Some people steal from others, or defraud them, or enslave them, seizing their product and preventing them from living as they choose, or forcibly exclude others from competing in exchanges. None of these are permissible modes of transition from one situation to another."

"Whoever makes something having bought or contracted for all other held resources used in the process (transferring some of his holdings for these cooperating factors), is entitled to it. The situation is not one of something’s getting made, and there being an open question of who is to get it. Things come into the world already attached to people having entitlements over them."

"From each as they choose, to each as they are chosen."

"Taxation of earnings from labor is on a par with forced labor. Seizing the results of someone's labor is equivalent to seizing hours from him and directing him to carry on various activities."

"Lacking much historical information and assuming (1) that victims of injustice generally do worse than they otherwise would and (2) that those from the least well-off group in the society have the highest probabilities of being the (descendants of) victims of the most serious injustice who are owed compensation by those who benefited from the injustices, ... then a rough rule of thumb for rectifying injustices might seem to be the following: organize society so as to maximize the position of whatever group ends up least well-off in the society."

"These issues are very complex and are best left to a full treatment of the principle of rectification. In the absence of such a treatment applied to a particular society, one cannot use the analysis and theory presented here to condemn any particular scheme of transfer payments, unless it is clear that no considerations of rectification of injustice could apply to justify it. Although to introduce socialism as the punishment for our sins would be to go too far, past injustices might seem to be so great as to make necessary in the short run a more extensive state in order to rectify them."

"No state more extensive than the minimal state can be justified."

"Wittgenstein, Elizabeth Taylor, Bertrand Russell, Thomas Merton, Yogi Berra, Allen Ginsberg, Harry Wolfson, Thoreau, Casey Stengel, The Lubavitcher Rebbe, Picasso, Moses, Einstein, Hugh Hefner, Socrates, Henry Ford, Lenny Bruce, Baba Ram Dass, Gandhi, Sir Edmund Hillary, Raymond Lubitz, Buddha, Frank Sinatra, Columbus, Freud, Norman Mailer, Ayn Rand, Baron Rothschild, Ted Williams, Thomas Edison, H.L. Mencken, Thomas Jefferson, Ralph Ellison, Bobby Fischer, Emma Goldman, Peter Kropotkin, you, and your parents. Is there really one kind of life which is best for each of these people?"

"There will not be one kind of community existing and one kind of life led in utopia. Utopia will consist of utopias, of many different and divergent communities in which people lead different kinds of lives under different institutions. Some kinds of communities will be more attractive to most than others; communities will wax and wane. People will leave some for others or spend their whole lives in one. Utopia is a framework for utopias, a place where people are at liberty to join together voluntarily to pursue and attempt to realize their own vision of the good life in the ideal community but where no one can impose his own utopian vision upon others."

"Utopia is a meta-utopia: the environment in which Utopian experiments may be tried out; the environment in which people are free to do their own thing; the environment which must, to a great extent, be realized first if more particular Utopian visions are to be realized stably."

"Some communities will be abandoned, others will struggle along, others will split, others will flourish, gain members, and be duplicated elsewhere. Each community must win and hold the voluntary adherence of its members. No pattern is imposed on everyone, and the result will be one pattern if and only if everyone voluntarily chooses to live in accordance with that pattern of community."

"You can't satisfy everybody; especially if there are those who will be dissatisfied unless not everybody is satisfied."

"Though the framework is libertarian and laissez-faire, individual communities within it need not be, and perhaps no community within it will choose to be so. Thus, the characteristics of the framework need not pervade the individual communities. In this laissez-faire system it could turn out that though they are permitted, there are no actually functioning "capitalist" institutions; or that some communities have them and others don't or some communities have some of them, or what you will."

"It goes without saying that any persons may attempt to unite kindred spirits, but, whatever their hopes and longings, none have the right to impose their vision of unity upon the rest."

"In a free system any large, popular, revolutionary movement should be able to bring about its ends by such a voluntary process. As more and more people see how it works more and more will wish to participate in or support it. And so it will grow, without being necessary to force everyone or a majority or anyone into the pattern."

"One persistent strand in utopian thinking, as we have often mentioned, is the feeling that there is some set of principles obvious enough to be accepted by all men of good will, precise enough to give unambiguous guidance in particular situations, clear enough so that all will realize its dictates, and complete enough to cover all problems which actually arise. Since I do not assume that there are such principles, I do not presume that the political realm will whither away. The messiness of the details of a political apparatus and the details of how it is to be controlled and limited do not fit easily into one's hopes for a sleek, simple utopian scheme."

"Is not the minimal state, the framework for utopia, an inspiring vision? The minimal state treats us as inviolate individuals, who may not be used in certain ways by others as means or tools or instruments or resources; it treats us as persons having individual right with the dignity this constitutes. Treating us with respect by respecting our rights, it allows us, individually or with whom we please, to choose our life and to realize our ends and our conception of ourselves, insofar as we can, aided by the voluntary cooperation of other individuals possessing the same dignity. How dare any state or group of individuals do more. Or less."

"Robert Nozick, the Arthur Kingsley Porter Professor of Philosophy at Harvard University, always attacks his problems in a disconcertingly original way. … in The Examined Life, he took on nothing less than the meaning of life, a subject that academic philosophers tended to steer clear of — and still do, despite his best efforts. From Mr. Nozick you always expect fireworks, even if some of them go off in their box. His questions, hints, counterarguments and suggestions come so thick and fast that it is next to impossible to appreciate all of them. Start pondering a sentence and you will find yourself led away prematurely by a parenthetical question; think about the question and you will be dragged into a discursive footnote; from the bowels of the footnote, another parenthetical query will leap out at you. If you escape back to the main argument with your concentration intact (unlikely, after a while), the whole wearing business just starts over again. Yet it is worth the effort — certainly for regular readers of philosophy, and often for others."

"No contemporary philosopher possesses a more imaginative mind, broader interests, or greater dialectical abilities than Robert Nozick."

"His learning is enormous and interconnected … His ability to surround a subject, to anticipate objection, to see through weakness and pretense, to exact all the implications of a contention, to ask a huge number of relevant questions about a seemingly settled matter, to enlarge into full significance what has only been sketched by others, is amazing."

"Given the extensive involvement of state violence in the process by which the corporate elite not only achieved its wealth in the past but continues to maintain and augment it in the present, it is clear that the massive inequalities of wealth that characterise present-day ‘capitalist’ society are radically inconsistent with any approach to justice in holdings that is even remotely Nozickian."

"Nozick’s Theory, in spite of its apparent dedication to self-ownership, cannot escape the conclusion that women’s entitlement rights to those they produce must take priority of persons’ rights to themselves at birth. ... There is nothing about a woman’s production of an infant that does not easily fulfill the conditions of the principle of acquisition as Nozick specifies them."

"Hayek and Nozick both think that talk of distributive justice is misleading, because it suggests the presence of a distributing person or mechanism; in a developed economy there is no such thing, and in a free society, the attempt to institute such a thing would destroy all freedom. Hayek, however, supports this view with an account of the computational impossibility of deciding what to produce and distribute in order to achieve justice, while Nozick is more concerned to emphasize that the state has no right to seize the resources of individuals in order to distribute them according to any principle whatever."

"No one, not even a philosopher, is morally obligated to live as if the world were the way he wishes it were. Robert Nozick pays taxes and is entitled to enjoy the government benefits they finance --even benefits he thinks should not exist. Perhaps the libertarian philosopher should not be expected to opt out of rent control voluntarily. But should he be pursuing his landlord through the maze of rent control regulations like a man possessed? And should he be using his ability to make a nuisance of himself under these regulations for simple, if lawful, cash extortion? They say that policeman make the best burglars. After a few years on the job, they know all the tricks. The same thing seems to be true of philosophers. If you're looking for someone to manipulate a rent control ordinance, find an advocate of the free market."

"I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. It would be easy to give examples, to trace specific evolutions into the baroque and the very high baroque... Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas."

"For progress there is no cure.... The only safety possible is relative, and it lies in an intelligent exercise of day-to-day judgement."

"Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."

"The total subject of mathematics is clearly too broad for any one of us. I do not think that any mathematician since Gauss has covered it fully and uniformly, even Hilbert did not, and all of us are of considerably lesser width (quite apart from the question of depth) than Hilbert. It would therefore, be quite unrealistic not to admit, that any address I could possibly give would not be biased towards some areas in mathematics in which I have had some experience, to the detriment of others which may be equally or more important. To be specific, I could not avoid a bias towards those parts of analysis, logics, and certain border areas of the applications of mathematics to other sciences in which I have worked. If your Committee feels that an address which is affected by such imperfections still fits into the program of the Congress, and if the very generous confidence in my ability to deliver continues, I shall be glad to undertake it."

"A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful."

"The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work."

"It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe."

"When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system."

"It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature."

"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."

"Young man, in mathematics you don't understand things. You just get used to them."

"You don't have to be responsible for the world that you're in."

"The goys have proven the following theorem…"

"The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking."

"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

"You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong."

"If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other."

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

"There probably is a God. Many things are easier to explain if there is than if there isn't."

"If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?"

"Some people confess guilt to claim credit for the sin."

"It will not be sufficient to know that the enemy has only fifty possible tricks and that we can counter every one of them, but we must be able to counter them almost at the very instant they occur."

"One of the world's great mathematicians."

"John von Neumann was an enormous personality."

"Princeton was the place which had all these names—Einstein, Weyl, von Neumann—who were great figures at the time."

"I met him, but in a sense, he didn’t meet me. We were introduced at a game theory conference in 1955, two years before he died. I said, “Hello, Professor von Neumann,” and he was very cordial, but I don’t think he remembered me afterwards unless he was even more extraordinary than everybody says. I was a young person and he was a great star."

"I think I had some feeling that their minds [von Neumann and Weyl] were so far ahead of mine that it was difficult to follow their thoughts."

"If one applies an appropriately broad view of physics one must say that von Neumann had a quite outstanding insight into the problems of physics. Because he has done first-rate work, and he was the man who succeeded in giving a correct mathematical formulation of quantum mechanics, and this was the major theory in physics in the first half of the century."

"Nobody doubts that von Neumann was brilliant; everybody admits that."

"Nevertheless, it was generally agreed that von Neumann was the leading mathematical mind in the world at that time."

"By any standard, von Neumann, was one of the most creative and versatile scientists of the twentieth century."

"Von Neumann had a phenomenal capacity for doing mental computations of all kinds. His thought processes were extremely fast, and often he would see through to the end of someone’s argument almost before the speaker had got out the first few sentences. Recently, one of von Neumann’s colleagues said in affectionate explanation of von Neumann’s power, “You see, Johnny wasn’t human. But after living with humans for so long he learned how to do a remarkable imitation of one.”"

"One of the most brilliant mathematicians who ever lived."

"Von Neumann was considered to be the most brilliant of the young mathematicians."

"Von Neumann had an absolute paranoia about the Russians and favored a first nuclear strike. Einstein referred to him as a Denktier, a think animal."

"I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man."

"I always thought Johnny’s brain indicated that he belonged to a new species, an evolution beyond man."

"It’s impossible to truly understand the speed at which von Neumann’s brain worked and how he thought, even for the cleverest observers. I drop hints about how fast and clever he was, but I don’t pretend to fully understand or get to grips with his human side. I’m not sure if I can, as some of his friends even said that von Neumann was an alien, a superintelligent being that had studied humans and learned how to copy us perfectly."

"Probably the smartest man on Earth."

"He had the kind of mind that if you go in to see him with an idea, inside of five minutes he's five blocks ahead of you and sees exactly where it's going. His mind was just so fast and so accurate that there was no keeping up with him. There was nobody on earth, as far as I'm concerned, who was in his category."

"His mind was faster than anybody's."

"He stimulated people everywhere. Von Neumann was generous intellectually, because his resources were so enormous, that he never gave away anything that he couldn't do without. He was a fountainhead of information, and he didn't hold back because there was always much more in depth than he ever exposed at one time. I'm not exaggerating. This was indeed how he was. In the few decades that followed, I have had the experience of understanding what this was like, by working as a consultant for some groups who were at a technical level so far below what I knew myself, that what they felt was worth bickering about was in fact possible [?] that one could ignore it, because one knows one has much more in depth than that and that's not an important point. Let them bicker about it, or let them think that they did something great. He was precisely that way. He was in depth, more knowledgeable than any man, and I say this having worked with Wiener for four years, and Wiener was no slouch himself. Von Neumann was a giant. He was ahead of anybody."

"What Von Neumann contributed as far as the engineering was concerned, was simply the enormous confidence everybody had that a machine so simple, and with no more doodads on it could knock dead, so to speak, an enormous amount of the computation that needed to be done in this world for the next few decades. He never came over and said to make a circuit of this, but he did know so much more of the deeper aspects of mathematics and the practical aspects of computation than any of the rest of us. What he did essentially, was to serve as this unshakable confidence that said: "Go ahead, nothing else matters, get it running at this speed and this capability, and the rest of it is just a lot of nonsense.""

"John von Neumann's brilliant mind blazed over lattice theory like a meteor."

"I went in and started telling him about my thesis. He listened for about ten minutes and asked me a couple of questions, and then he started telling me about my thesis. What you have really done is this, and probably this is true, and you could have done it in a somewhat simpler way, and so on. He was a really remarkable man. He listened to me talk about this rather obscure subject and in ten minutes he knew more about it than I did. He was extremely quick. I think he may have wasted a certain amount of time, by the way, because he was so willing to listen to second- or third-rate people and think about their problems. I saw him do that on many occasions."

"At the age of 6 he was able to divide two eight-digit numbers in his head. By the age of 8 he had mastered college calculus and as a trick could memorize on sight a column in a telephone book and repeat back the names, addresses and numbers. History was only a “hobby,” but by the outbreak of World War I, when he was 10, his photographic mind had absorbed most of the contents of the 46-volume works edited by the German historian Oncken with a sophistication that startled his elders."

"Several years ago his wife gave him a 21-volume Cambridge History set, and she is sure he memorized every name and fact in the books. “He is a major expert on all the royal family trees in Europe,” a friend said once. “He can tell you who fell in love with whom, and why, what obscure cousin this or that czar married, how many illegitimate children he had and so on.” One night during the Princeton days a world-famous expert on Byzantine history came to the Von Neumann house for a party. “Johnny and the professor got into a corner and began discussing some obscure facet,” recalls a friend who was there. “Then an argument arose over a date. Johnny insisted it was this, the professor that. So Johnny said, ‘Let’s get the book.’ They looked it up and Johnny was right. A few weeks later the professor was invited to the Von Neumann house again. He called Mrs. von Neumann and said jokingly, ‘I’ll come if Johnny promises not to discuss Byzantine history. Everybody thinks I am the world’s greatest expert in it and I want them to keep on thinking that.'”"

"One day he was urgently summoned to the offices of the Rand Corporation, a government-sponsored scientific research organization in Santa Monica, Calif. Rand scientists had come up with a problem so complex that the electronic computers then in existence seemingly could not handle it. The scientists wanted Von Neumann to invent a new kind of computer. After listening to the scientists expound, Von Neumann broke in: “Well, gentlemen, suppose you tell me exactly what the problem is?” For the next two hours the men at Rand lectured, scribbled on blackboards, and brought charts and tables back and forth. Von Neumann sat with his head buried in his hands. When the presentation was completed, he scribbled on a pad, stared so blankly that a Rand scientist later said he looked as if “his mind had slipped his face out of gear,” then said, “Gentlemen, you do not need the computer. I have the answer.” While the scientists sat in stunned silence, Von Neumann reeled off the various steps which would provide the solution to the problem. Having risen to this routine challenge, Von Neumann followed up with a routine suggestion: “Let’s go to lunch.”"

"One day, during an ICBM meeting on the West Coast, a physicist employed by an aircraft company approached Von Neumann with a detailed plan for one phase of the project. It consisted of a tome several hundred pages long on which the physicist had worked for eight months. Von Neumann took the book and flipped through the first several pages. Then he turned it over and began reading from back to front. He jotted down a figure on a pad, then a second and a third. He looked out the window for several seconds, returned the book to the physicist and said, “It won’t work.” The physicist returned to his company. After two months of re-evaluation, he came to the same conclusion."

"After the last visitor had departed Von Neumann would retire to his second-floor study to work on the paper which he knew would be his last contribution to science. It was an attempt to formulate a concept shedding new light on the workings of the human brain. He believed that if such a concept could be stated with certainty, it would also be applicable to electronic computers and would permit man to make a major step forward in using these 'automata'. In principle, he reasoned, there was no reason why some day a machine might not be built which not only could perform most of the functions of the human brain but could actually reproduce itself, i.e., create more supermachines like it. He proposed to present this paper at Yale, where he had been invited to give the 1956 Silliman Lectures."

"Probably the greatest mathematician of the century."

""Johnny," as all his friends called him, was the only scientist of the era to whom the word "genius" was almost universally applied. He had an uncanny ability to handle complex mathematical calculations in seconds. When he was six years old he could divide one eight-digit number into another, entirely in his head."

"Then, of course, there was Neumann, who always knew everything anyhow."

"Weyl had a very tremendous respect for him, and I could see in this advanced, seminar when Weyl didn't know the answer he would say, "Neumann, how does that go?" We all realized this was a great mathematician."

"His effectiveness was largely due to his ever-present mental manipulatory quickness. He could literally "think on his feet," and much of his best work may have received its initial impulse in just this way. He had a prodigious memory, and legend has it that he knew all the facts and dates from many volumes of standard histories by heart."

"He was also a great reader of books on history throughout his life, and in both science and history his retentive memory was most remarkable."

"It was also well remembered about 25 years later by one of his colleagues here at the time, M. Plancherel, who mentioned it to me then as an example of the extraordinary ability H. Weyl had, shared only by J. von Neumann among the mathematicians he had known, to get into a new subject and bring an important contribution to it within a few months."

"Von Neumann was considered the leading mathematician in the United States."

"Great mathematician."

"He would seize on the fuzzy notions of others and, by dint of his prodigious mental powers, leap five blocks ahead of the pack. “You would tell him something garbled, and he’d say, ‘Oh, you mean the following,’ and it would come back beautifully stated,” said his onetime protégé, the Harvard mathematician Raoul Bott."

"Von Neumann is a great scientific hero to me because it seemed… he seemed to have something. And of course it may be envy rather than admiration, but it's good to envy someone like von Neumann."

"Mathematics is not a pompous activity, least of all in the hands of extraordinarily fast and penetrating minds like Johnny von Neumann."

"There was something endearing and personal about Johnny von Neumann. He was the cleverest man I ever knew, without exception. And he was a genius, in the sense that a genius is a man who has two great ideas. When he died in 1957 it was a great tragedy to us all."

"In a Silliman lecture ... John von Neumann, who was dying at the time, wrote some of the most splendid sentences he wrote in all his life ... He pointed out that there were good grounds merely in terms of electrical analysis to show that the mind, the brain itself, could not be working on a digital system. It did not have enough accuracy; or ... it did not have enough memory. ... And he wrote some classical sentences saying there is a statistical language in the brain ... different from any other statistical language that we use... this is what we have to discover. ...I think we shall make some progress along the lines of looking for what kind of statistical language would work."

"The greatest polymath of the 20th century."

"The crucial point: in Dr. von Neumann the Institute has perhaps the cleverest man in the world, and the really deciding factor in the end should, I am sure, be what he wants to do."

"Von Neumann was a very great mathematician. He made many important contributions in a wide range of fields."

"The manuscripts for both parts of the present volume were unfinished; indeed, they were both, in a sense, first drafts. There is one compensation in this: one can see von Neumann's powerful mind at work."

"He was about as likable a chap as you could imagine. There is just one short thing about him. I was riding in a Pullman one day in the lounge car after the war and I hadn't looked about me before I sat down; I was reading something and it had my full attention. From across came von Neumann. He sat down aside me and introduced himself. Well here was the man who, in my opinion, was the most able mathematician in the country in many ways and he felt that he needed to introduce himself to me. That's a type of modesty one can't help liking."

"He was a superb lecturer. Superb."

"He was incredible - the enormous perception that he had. For me, ever since, a standard of comparison has always been von Neumann. And if I say, "He reminds me of von Neumann," that's about the best compliment I can give anyone."

"He was incredibly perceptive."

"[He] thought so fast that he very often anticipated what one was going to say. . . . a pleasant agreeable person . . . the amazing logic of his thought processes."

"Von Neumann was capable of all sorts of remarkable things."

"The smartest man in the world."

"Genius of the highest order."

"Now the story doesn't end here. Before going on with it, however, I'd like to introduce you to Johnnie von Neumann, an incredible genius whose mind worked about as rapidly as the super high-speed computers he helped design."

"Bennie decided to approach Johnnie on the matter and arranged to travel to Princeton’s Institute for Advanced Study, headed up at the time by Oppenheimer, where Johnnie (and lesser geniuses such as Albert Einstein) was stationed."

"He did a tremendous amount of different things in mathematics, many of them revolutionary."

"Mr. von Neumann, in spite of his youth, is a completely exceptional personality ... who has already done very productive work ... and whose future development is being watched with great expectation in many places."

"Von Neumann I never could quite figure out. He was just too fast for me."

"Strange, contradictory, and controversial person; childish and good-humored, sophisticated and savage, brilliantly clever yet with very limited, almost primitive lack of ability to handle his emotions—an enigma of nature that will have to remain unsolved."

"[One early 1945 night,] he woke up and started talking at a speed which, even for him, was extraordinarily fast. “What we are creating now is a monster whose influence is going to change history, provided there is any history left, yet it would be impossible not to see it through, not only for the military reasons, but it would also be unethical from the point of view of the scientists not to do what they know is feasible, no matter what terrible consequences it may have. And this is only the beginning!” The concerns von Neumann voiced that night were less about nuclear weapons, and more about the growing powers of machines. “From here on, Johnny’s fascination and preoccupation with the shape of things to come never ceased,” concludes Klári’s account. For the next seven years he neglected mathematics and devoted himself to the advance of technology in all forms. “It was almost as if he knew that there was not very much time left.”"

"He had always done his writing at home during the night or at dawn. His capacity for work was practically unlimited."

"People would come to him because of his great insight."

"In von Neumann’s generation his ability to absorb and digest an enormous amount of extremely diverse material in a short time was exceptional; and in a profession where quick minds are somewhat commonplace, his amazing rapidity was proverbial."

"May have been the last representative of a once-flourishing and numerous group, the great mathematicians who were equally at home in pure and applied mathematics and who throughout their careers maintained a steady production in both directions."

"Perhaps an even greater genius than Einstein, of almost extraterrestrial brilliance."

"However, as noted earlier, one of his central objectives—as a mathematician—was to publish the generalized proof of the fixed point theorem. Was the economics merely a convenient vehicle for an essentially mathematical exercise for von Neumann? Genius that he was, perhaps that is all that he wanted to do at that time. Later, after meeting Oscar Morgenstern, he returns to economics, but only through their joint interest in the theory of games."

"Von Neumann was a great mathematician and had the reputation at that time of being the cleverest man in the world. He was supposed to be the intellectual force driving the whole development of computers. He was a great thinker and a great entrepreneur."

"I remember a talk that Von Neumann gave at Princeton around 1950, describing the glorious future which he then saw for his computers. Most of the people that he hired for his computer project in the early days were meteorologists. Meteorology was the big thing on his horizon. He said, as soon as we have good computers, we shall be able to divide the phenomena of meteorology cleanly into two categories, the stable and the unstable. The unstable phenomena are those which are upset by small disturbances, the stable phenomena are those which are resilient to small disturbances. He said, as soon as we have some large computers working, the problems of meteorology will be solved. All processes that are stable we shall predict. All processes that are unstable we shall control. He imagined that we needed only to identify the points in space and time at which unstable processes originated, and then a few airplanes carrying smoke generators could fly to those points and introduce the appropriate small disturbances to make the unstable processes flip into the desired directions. A central committee of computer experts and meteorologists would tell the airplanes where to go in order to make sure that no rain would fall on the Fourth of July picnic. This was John von Neumann's dream. This, and the hydrogen bomb, were the main practical benefits which he saw arising from the development of computers."

"Von Neumann compensated for these superhuman abilities with an earthy sense of humor and tireless social life, and tried, with mixed success, to blend in on a normal human scale."

"I got to know von Neumann and I thought he was very quick mentally in mathematics and things."

"I think he was a damn fast guy for figuring out what the other guy was doing and explaining it better."

"Johnny has a very good mind."

"The Alexanders gave humdinger, wonderful parties. I don't know whether they would be regarded as outlandish today, but they were certainly regarded as far out in those days. The phenomenal feature of von Neumann was that he could go to these parties and party and drink and whoop it up to the early hours of the morning, and then come in the next morning at 8:30, hold class, and give an absolutely lucid lecture. What happened is that some of the graduate students thought that the way to be like von Neumannn was to live like him, and they couldn't do it."

"Von Neumann was very impressive to talk with. He was very quick."

"In speed and understanding Von Neumann was certainly phenomenal. He could understand a proof even far from his own subject very fast. I remember once in Cambridge I told him a proof of interpolation that was not quite correct. By the time we met again I had a correct proof. Von Neumann told me, “Something seems to be wrong in that proof.” And it was really not his subject. He wasn’t that interested in it, but he was quite right."

"Our country’s greatest Jancsi."

"You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!"

"He is really a professional, isn’t he!"

"Dr. von Neumann is one of the very few men about whom I have not heard a single critical remark. It is astonishing that so much equanimity and so much intelligence could be concentrated in a man of not extraordinary appearance."

"Johnny von Neumann was the greatest mathematician around."

"Finally there came in the mail an invitation from the Institute for Advanced Study: Einstein. . . von Neumann. . .Weyl. . . all these great minds!"

"At about that time Einstein had agreed to serve as a consultant to our group but did not want to travel to Washington. So there had to be a liaison person and I was given that opportunity. Since Einstein did not know me, there had to be someone to introduce us. It then happened that I was introduced to Einstein by John von Neumann, one of the most important mathematicians of all time, and who had also become a consultant to our group. It was a very great experience for a new Ph.D. to be introduced to Einstein by Von Neumann!"

"Von Neumann was one of the greatest geniuses that ever lived."

"[Addressing Albert Tucker] The story goes that von Neumann's parents had all been lawyers and they sort of hoped that Johnny would be a good, lawyer. When he was sixteen or so they sort of tolerated his fiddling around with chemistry and mathematics. Finally they found out he wanted to be a mathematician, or chemist, or some mixture. They were very upset. Well, their attitude was that it wasn't too bad if he was going to pe a good one. So they inquired around who the best mathematician in his part of the world was, and it turned out to be Siegel. They had lots of money, and they arranged for Siegel to talk to Johnny. Afterwards they asked him, "Well, do you think he has any potential?" He said, "He knows more mathematics than I do now.""

"Von Neumann was also a delight to be with. His brainpower stuck out in every direction."

"Intellectual brilliance."

"Von Neumann would engage in any subject you wanted to discuss and within five minutes be right at the heart of the issue, even when he started off by saying, “I can discuss that not prejudiced by any facts.”"

"The most outstanding and at the same time versatile mathematician in the world in the second quarter of the 20th century."

"Around 1922–23, being then professor at Marburg University, I received from Professor Erhard Schmidt, Berlin (on behalf of the Redaktion of the Mathematische Zeitschrift) a long manuscript of an author unknown to me, Johann von Neumann, with the title Die Axiomatisierung der Mengenlehre, this being his eventual doctor dissertation which appeared in the Zeitschrift only in 1928, (Vol. 27). I was asked to express my view since it seemed incomprehensible. I don’t maintain that I understood everything, but enough to see that this was an outstanding work and to recognize ex ungue leonem. While answering in this sense, I invited the young scholar to visit me (in Marburg) and discussed things with him, strongly advising him to prepare the ground for the understanding of so technical an essay by a more informal essay which should stress the new access to the problem and its fundamental consequences. He wrote such an essay under the title, Eine Axiomatisierung der Mengenlehre, and I published it in 1925 in the Journal für Mathematik (vol. 154) of which I was then Associate Editor."

"I will not attempt to describe John von Neumann's unique abilities, but only say a little about the impression he made on us. The most striking was the enormous speed with which his brain worked. One could believe he already knew beforehand everything one asked him about. A little story illustrates this. Stefan Bergman […] went around and posed a problem to people. If one approached it directly, it required some calculation and the summation of a geometric series. But if one gave it a suitable twist, the solution became immediately apparent. When von Neumann promptly gave the correct answer, Bergman said: "You are the first of those I have asked who did not sum the geometric series." "No!" answered von Neumann, "I summed it.""

"John von Neumann is a kind of legendary mind ... Many people say he's like one of the smartest humans ever."

"I never ceased to be fascinated by electronic computers, and I feel that I have been privileged in having been initiated so marvellously by the Master himself. His mathematical achievements are far too subtle and technical for me to understand or to describe, but I can attest to the strength of his brain because I once saw him, for a bet, drink sixteen martinis in a row and then be still on his feet and quite lucid, though somewhat pessimistic in his utterances."

"IQ tests for geniuses have not yet been constructed, because one cannot expect the IQ-specialists to be geniuses, but one must suspect that the scale continues upwards to giddy heights of ability. Most of those who have known the mathematician John von Neumann have felt as slow and stupid in his presence as the dunce with the top of the form."

"A more interesting activity during that time was my periodic contact with Albert Einstein, who, along with other prominent experts such as John von Neumann, served as a consultant for the High Explosive Division."

"[On Rayleigh–Taylor instability] So, Fermi said, "Let me make a model; I'll have a broad tongue which moves into the dense material; I'll have a narrow tongue that moves away from it, and I'll just solve this numerically." So, he did some of that, but he wasn't quite satisfied with the solution. One afternoon around 4:50 p.m., John von Neumann came by and saw what Fermi had on the blackboard and asked what he was doing. So, [[Enrico Fermi|Enrico] told him, and John von Neumann said, "That's very interesting." He came back about 15 minutes later and gave him the answer. Fermi leaned against his doorpost and told me, "You know, that man makes me feel I know no mathematics at all.""

"Well, I was so flattered to be mentioned in a footnote by John von Neumann that it didn't occur to me that he hadn't actually credited us with what we were doing."

"The fact, however, remains that a lot of wonderful people never received the prize. Just take a few examples from among Hungarian physicists. Von Neumann never received the prize and neither did Szilard."

"That von Neumann was brilliant, perhaps a good deal more than brilliant, had been clear even in childhood."

"He is regarded as one of the giants of modern mathematics."

"One of the great mathematical universalists."

"While still very young, von Neumann showed tremendous intellectual and linguistic ability, and he once told the author that at six he and his father often joked with each other in classical Greek."

"One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes. Another time, I watched him lecture on some material written in German about twenty years earlier. In this performance von Neumann even used exactly the same letters and symbols he had in the original."

"Fantastic speed."

"I guess one of [Veblen's] greatest mathematical accomplishments was finding Johnny von Neumann and bringing him to Princeton University. At least I suppose that was his greatest achievement among many achievements."

"He [Veblen] delighted in Johnny von Neumann."

"Whenever you'd go into his office, having spent the last week working on something, and say, "Johnny, I've got an idea," and start to write, you'd get maybe the first half-a-line down before he'd say, "Yes, let me have the chalk." Then he'd get up there, and for the rest of the hour he would be putting it down in the way it ought to be done."

"He had another quality which I always thought was unbelievable. He and I worked at trying to prove something about bounds on eigen values one time without .any success. One day I saw in Math Reviews a statement that Kolmogorov or somebody had proved a theorem, and I said, "This is what so and so proved." He said, "Sure, this is how it goes." And he went to the blackboard and he proved it. Somehow, just knowing that it was true, and not just a conjecture of ours, made it possible for him to see the proof. I don't know how or why or what."

"At just about the time you could run your eye down the page, he would be turning it."

"I always remember one time, Bochner, von Neumann, and I were in a room, I guess Johnny's room in the Institute. Bochner was presenting material to us, and he got stuck. He hemmed and hawed for a while, and he said "If you'll wait a minute, I know where the book is that has the proof of this. I'll run upstairs and get it." Johnny said, "Don't do that, I don't know what book it's in, but I 'II prove it for you." And he did."

"So he had a remarkable mind, a really remarkable mind."

"It is the hallmark of a great mathematician that his output is prodigious and von Neumann was indeed a great mathematician."

"Of previous publications those of von Neumann have most strongly influenced the work presented here."

"In a 1948 Princeton talk, replying to a frequent affirmation that it's impossible to build a machine that can replace the human mind, von Neumann said: You insist that there is something that a machine can't do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that."

"The greatest polymath and fastest thinker of the 20th century."

"Now, just consider the smartest person who has ever lived. On almost everyone's shortlist here is John von Neumann... I mean, the impression that von Neumann made on the people around him, and this included the greatest mathematicians and physicists of his time, is fairly well-documented. If only half the stories about him are half true, there's no question he's one of the smartest people who has ever lived."

"Most of the legends, from childhood on, tell about his phenomenal speed in absorbing ideas and solving problems. At the age of 6 he could divide two eight-digit numbers in his head; by 8 he had mastered the calculus; by 12 he had read and understood Borel’s Théorie des Fonctions."

"The speed with which von Neumann could think was awe-inspiring."

"When his electronic computer was ready for its first preliminary test, someone suggested a relatively simple problem involving powers of 2. (It was something of this kind: what is the smallest power of 2 with the property that its decimal digit fourth from the right is 7? This is a completely trivial problem for a present-day computer: it takes only a fraction of a second of machine time.) The machine and Johnny started at the same time, and Johnny finished first."

"One famous story concerns a complicated expression that a young scientist at the Aberdeen Proving Ground needed to evaluate. He spent ten minutes on the first special case; the second computation took an hour of paper and pencil work; for the third he had to resort to a desk calculator, and even so took half a day. When Johnny came to town, the young man showed him the formula and asked him what to do. Johnny was glad to tackle it. "Let's see what happens for the first few cases. If we put n = 1, we get..." -- and he looked into space and mumbled for a minute. Knowing the answer, the young questioner put in "2.31?" Johnny gave him a funny look and said "Now if n = 2, ...", and once again voiced some of his thoughts as he worked. The young man, prepared, could of course follow what Johnny was doing, and, a few seconds before Johnny finished, he interrupted again, in a hesitant tone of voice: "7.49?" This time Johnny frowned, and hurried on: "If n = 3, then...". The same thing happened as before - Johnny muttered for several minutes, the young man eavesdropped, and, just before Johnny finished, the young man exclaimed: "11.06!" That was too much for Johnny. It couldn't be! No unknown beginner could outdo him! He was upset and he sulked till the practical joker confessed."

"As a writer of mathematics von Neumann was clear, but not clean; he was powerful but not elegant. He seemed to love fussy detail, needless repetition, and notation so explicit as to be confusing. To maintain a logically valid but perfectly transparent and unimportant distinction, in one paper he introduced an extension of the usual functional notation: along with the standard \phi(x) he dealt also with something denoted by \phi((x)). The hair that was split to get there had to be split again a little later, and there was \phi(((x))), and, ultimately, \phi((((x)))). Equations such as"

"I became Johnny’s assistant. How was it? Scary. The most spectacular thing about Johnny was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast."

"Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car."

"I was absolutely fascinated with von Neumann; I still am."

"I was fascinated by whatever von Neumann did."

"Throughout the world mathematicians and others had marvelled at the lightning speed with which von Neumann analyzed and solved complex problems."

"In this galaxy of stars von Neumann, a professor at the Institute, simply radiated excitement. His lectures on Hilbert Space, measure theory, rings of operators (called now von Neumann algebras), and continuous geometry, fascinated a large audience. At the daily afternoon tea he engaged some group in a most lively and stimulating discussion. With obvious delight he explained, clarified, and analyzed problems on the spot and gave help to one and all. But sometimes he would stand apart, deep in thought, his brown eyes staring into space, his lips moving silently and rapidly, and at such times no one ventured to disturb him."

"Professors at the university direct doctoral theses but those at the Institute do not. Unaware of this, in 1934 I asked von Neumann if he would direct my doctoral thesis. He replied Yes, and suggested the problem of identifying the Hilbert space closure and adjoint of nth-order linear differential operators. Marshall Stone, in his huge volume Linear transformations in Hilbert Space, had solved the case for first order and his methods generalized to higher orders. My not particularly outstanding thesis was accepted and I moved into an ardent study of continuous geometry. In 1936, as a postdoctoral Fellow at Yale, I found a partly new proof, with weaker axioms, for von Neumann's transitivity of perspectivity. Von Neumann invited me to visit Princeton and talk with him. He gave me most cordial encouragement, let me have his unpublished manuscripts to study, and later took the initiative to recommend me to Marshall Stone for a B. P. Instructorship at Harvard. This warm, generous concern made a deep impression on me."

"Von Neumann was a true genius, the only one I’ve ever known. I’ve met Einstein and Oppenheimer and Teller and—who’s the mad genius from MIT? I don’t mean McCulloch, but a mathematician. Any-way, a whole bunch of those other guys. Von Neumann was the only genius I ever met. The others were supersmart .... And great prima donnas. But von Neumann’s mind was all-encompassing. He could solve problems in any domain. . . . And his mind was always working, always restless. He walked into my living room one night and a half dozen people were already having cocktails, and he disappeared into a corner and stood with his back to us, hands behind him, and after about two minutes turned to me and said, “About two thirds of a liter a week, Leon.” And I had to think about it for three or four minutes, and finally I said, “Yeah, Johnny, that’s just about right.” He’d walked up to the nine-gallon tropical fish aquarium that stood on a table in the corner, had noted the temperature of the water, had made an estimate of the surface area, had seen the gap that existed between the overhead light and the glass to keep the fish from jumping out, made an estimate of the particular escape velocity of the water molecules, integrated and found out how much added water was needed each week for that aquarium. And he was right within a few percent. That’s the kind of thing he did all the time. Another thing that he isn’t known well for was his sense of humor. He really enjoyed dirty limericks. And though we never said anything to each other deliberately, it sort of evolved that whenever we came together, whether it was an hour or a month later, the name of the game was to see who could rush up the fastest and unload the largest number of new limericks. It turned out to be a delightful game. He had oodles of them; I was hard put to keep up with him. His memory was just beyond conception, a photograph for everything he ever learned or saw. Lightning calculator and head screwed on to boot—he put all of those together with a huge creative talent."

"Von Neumann did not seem particularly interested in studying chemistry. On the other hand, it is documented that he attended lectures by Haber, and the latter allegedly expressed to friends the wish that von Neumann should pursue an academic career in chemistry."

"Fraenkel later reported impressively that he only managed with great effort to work through von Neumann's work, which "differed from everything that had appeared up to then on the axiomatization of set theory" and introduced completely new concepts, and that he was immediately convinced of von Neumann's quite extraordinary talent."

"And about Johann von Neumann, the mathematics lecturers seem to have even told stories to their students during lectures, as Alexander Dinghas (1908–1974) vividly described in his memories: Thus, Issai Schur reported to students in a lecture that the student von Neumann, in a seminar where a proof of the "Minkowski theorem on the estimation of linear forms" was being treated, had stood up and "added great simplifications to the presented proof"."

"Fantastic mind."

"His extraordinariness lay in his mental abilities. These were so dazzling that some of his admiring colleagues were at a loss to describe them in ordinary human terms."

"Banesh Hoffmann: He thought very fast, yes, and he was extraordinarily subtle. He was most impressive. You've heard the story of Robertson driving van Neumann to somewhere. Von Neumann asked him what he was working on, and Robertson said such and such an equation. By the time they got to the end of the ride von Neumann had solved the equation in his head. Had you heard that?"

"Albert William Tucker: No, but it's typical."

"Banesh Hoffmann: Yes, he was incredible."

"As a mathematician, Steinhaus’s main strengths were his intelligence and an unerring instinct and taste in the choice of problems. In this respect he reminded me of John von Neumann, a mathematician whom he greatly liked and admired."

"Getting to know von Neumann better was one of the delights of my stay in Princeton. Apart from being one of the greatest mathematicians of our century, he was a wonderful companion."

"I was privileged to have known von Neumann personally and, like most mathematicians of my generation, I have been strongly influenced by his work and by his person."

"Unquestionably the nearest thing to a genius I have ever encountered."

"There were several times in my life that I’ve, one way or another, got that feeling, my gosh, here is a tremendous mathematician; for instance, Weil, von Neumann, Serre, Milnor, Atiyah. Well, those are obvious names."

"Certainly the greatest mathematician of that time."

"Richard Rhodes: Was he as extraordinary a mind as he has been described?"

"George Kistiakowsky: Yes, an extraordinary, fast mind. Extraordinarily fast mind."

"We were all drawn by von Neumann."

"It must have been a shattering experience to have grown up with von Neumann however bright one is."

"He was the quickest mathematician i have ever known."

"He was the most remarkable man. I’m always utterly surprised that his name is not common, household. It is a name that should be known to every American—in fact, every person in the world, just as the name of Einstein is. I am always utterly surprised how come he’s almost totally unknown. In fact, did you know – you did know, all right, you are an unusually well informed person. All people who had met him and interacted with him realized that his brain was more powerful than anyone’s they have ever encountered. I remember Hans Bethe even said, only half in jest, that von Neumann’s brain was a new development of the human brain. Only a slight exaggeration."

"People today have a hard time to imagine how brilliant von Neumann was. If you talked to him, after three words, he took over. He understood in an instant what the problem was and had ideas. Everybody wanted to talk to him."

"Mrs. Szegő often recalled that Szegő came home with tears in his eyes from his first encounter with the young prodigy."

"To gain a measure of von Neumann’s achievements, consider that had he lived a normal span of years, he would certainly have been a recipient of a Nobel Prize in economics. And if there were Nobel Prizes in computer science and mathematics, he would have been honored by these, too. So the writer of these letters should be thought of as a triple Nobel laureate or, possibly, a ​3 1⁄2-fold winner, for his work in physics, in particular, quantum mechanics."

"Von Neumann was addicted to thinking, and in particular to thinking about mathematics."

"Von Neumann combined, in a unique fashion, extreme quickness, very broad interests, and a fearsome technical prowess."

"Most mathematicians prove what they can, von Neumann proves what he wants." Once in a discussion about the rapid growth of mathematics in modern times, von Neumann was heard to remark that whereas thirty years ago a mathematician could grasp all of mathematics, that is impossible today. Someone asked him: "What percentage of all mathematics might a person aspire to understand today?" Von Neumann went into one of his five-second thinking trances, and said: "About 28 percent."

"He was admired by the brightest stars at Los Alamos: Oppenheimer, Bethe, Feynman, Peierls, Teller and many others; they acknowledged him as their superior for sheer brain power."

"Most scintillating intellect of this century."

"The most powerful brain."

"Historians have noted how Baron Eötvös’s educational efforts led to an explosion of genius — such luminaries as the physicists Edward Teller, Eugene Wigner, Leo Szilard, and the mathematician John von Neumann all came out of Budapest during the Eötvös era. The production of Hungarian scientists and mathematicians in the early twentieth century was so prolific that many otherwise calm observers believe Budapest was settled by Martians in a plan to infiltrate and take over the planet."

"As a matter of fact, he is very good."

"Stone told me that the two mathematicians in all the world who could be most helpful to my development were John von Neumann and Frederick Riesz. (His Hungarian name, Frigyes, became Frederick when anglicized). Von Neumann’s name was well known to me, of course."

"He was brilliant, spoke very fast, his English was quite fluent, he made remarkably few errors. A characteristic one was to talk about “infinite serious” for infinite series. No one ventured to correct his few lapses. I had met him recently at a party. The high point of the evening was a recitation race between him and Norbert Wiener. Somehow, someone recited a line from Lewis Carroll’s “The Hunting of the Snark.” Norbert, with his usual ebullience and sonorous voice, began reciting from line 1. Johnny started off in pursuit. Norbert accelerated, but Johnny came up even. We held our breaths as the lines poured out, on and on until they reached the end in a dead heat."

"The most brilliant mathematician of his generation."

"John von Neumann was the acknowledged genius of modern mathematics."

"The greeting, to a man or to a lady, was raising the hat completely off the head, simultaneously making a pronounced bow, all the while continuing to walk briskly forward. This courteous greeting was a Hungarian custom ingrained firmly in youth, and not easily forgotten in later years. I remember receiving such a greeting in 1950 in Cambridge, Massachusetts, across a 70 meter avenue, from that most courteous genius, John von Neumann."

"Von Neumann was certainly a true giant of the twentieth century, a figure more unique than rare in his astonishing capacity to join a theoretical intelligence of extraordinary depth to a very concrete view of science."

"In 1990 a thirty-five-year-old professor told me that “von Neumann took the fear out of learning math for all the professors who taught me.”"

"Eleven-year-old Johnny taught him [Wigner] set-theory math during Sunday afternoon walks."

"Wigner and others recall that Ratz’s recognition of Johnny’s mathematical talents was instant."

"Ratz turned his student over to the mathematicians at Budapest University, themselves men of no small renown. Professor Joseph Kurschak soon wrote to a university tutor, Gabriel Szego, saying that the Lutheran School had a young boy of quite extraordinary talent. Would Szego, as was the Hungarian tradition with infant prodigies, give some university teaching to the lad?"

"After Szego had done the initial coaching in 1915-16, tuition of schoolboy Johnny was taken over by other prominent mathematicians at Budapest University. He had contact with Kurschak, some with the brilliant Alfred Haar, and a little with the internationally known Frigyes Riesz. He was taught more directly by Michael Fekete (whose surname in Hungarian means “black”) and Leopold Fejer (feher is Hungarian for “white”)."

"There was allegedly an exception when one German professor praised the habit of asking Ph.D. students “unsolvable question” at their oral exams. If the student instantly said, “That's unsolvable”, he was deemed to have the right sharp set of mind. The professor put his favorite unsolvable equations on the blackboard as an illustration. Johnny muttered at the ceiling for a few minutes, and then solved some of them. A more typical occasion was when one professor propounded a new discovery that was actually quite wrong. This wrongdoer handled all the questions at the seminar devastatingly well, and there was discussion of his discovery at a private dinner that night. Johnny demolished the whole discovery by saying that he should have been asked a, b, and c . “Why didn't you ask that?” said the seminar organizer desperately. Johnny intimated that he did not like to be publicly rude."

"Von Neumann got very excited when J. M. put production functions on the board and jumped up, wagging his finger at the blackboard, saying (approx): “But surely you want inequalities, not equations there?” Jascha said that it became difficult to carry the seminar to conclusion because von Neumann was on his feet, wandering around the table, etc., while making rapid and audible progress on the linear programming theory of production. “The rapidity with which he made the connection and developed it,” said Arrow, “is in line with many anecdotes of von Neumann’s mental speed.”"

"On what was probably August 7, 1944, Goldstine took Johnny to see the ENIAC at Philadelphia. Before this visit Eckert told Goldstine he would be able to “tell whether von Neumann was really a genius by his first question. If this was about the logical structure of the machine, he would believe in von Neumann, otherwise not. Of course this was von Neumann’s first query.”"

"While all the other computer makers were generally heading in the same direction, von Neumann’s genius clarified and described the paths better than anyone else."

"All three of these men—Strauss, Quarles, and Gardner—thought that America’s technology for war could best be advanced by the man whom they regarded as America’s quickest-thinking scientific genius."

"He was building his computer. He was not just a person who told other guys to build a computer. He was always about details, "How are you going to do this? Which kind of gadget are you going to use for memory?" He was extraordinarily precise in these matters. At the same time he had written a book on the foundation of quantum mechanics, which I read with terror but great interest. He had written this book about games theory, which looked then extremely promising but of course was just the beginning. He had done this work about logic. I mean, in a way Von Neumann was the person who had performed the miracle. He was for me the model above all models."

"Much later, I was to find that my view of Von Neumann as a great man was completely confirmed."

"He was becoming more concerned with defense than with science. But it seemed that he was living proof that one could do science without really belonging to a “guild.” In fact, he was under extreme pressure at Princeton. From there, he left for Washington and was not planning to return. Luckily, von Neumann had realized that, by having failed to claim admission to any guild, I was leading a very dangerous life. A foundation executive told me much later that von Neumann had specifically asked him to watch after me, and to help in case of trouble."

"Phenomenon."

"Johnny von Neumann was the genius."

"I think we were right, though, in thinking he was several leaps ahead of the rest of us."

"Johnny von Neumann was very, very good and very quick and very sharp. He just was a universalist. He was not a mathematician."

"Johnny von Neumann who was very, very quick—I mean, you have no idea how quickly he would infer things and extrapolate them. Well, he was fantastic."

"He knew so much about physics and philosophy and even things like history. He was very, very sharp. He worked all the time."

"His talents were so obvious and his cooperative spirit so stimulating that he garnered the interest of many of us."

"Later, Tucker told me that he had gone to von Neumann and said, ‘This seems like very interesting work, but I can’t evaluate it. I don’t know whether it should really be called mathematics.’ Von Neumann replied, ‘Well, if it isn’t now, it will be someday—let’s encourage it.’ So I got my Ph.D.”"

"It is worth emphasizing that as great a mathematician as J. von Neumann never tired of repeating the fact that the errors of observation are what really matter. This is entirely in the spirit of Gauss. It is also noteworthy that von Neumann was firmly convinced that the intimate contact between mathematics and reality would produce, from time to time, decisive progress in mathematics."

"He worked with tremendous energy and fantastic speed."

"The fastest mind I ever met."

"I tried at that time to cast the unifying Dirac-Jordan transformation theory into a simpler and more easily understandable form and to convey its essence to Hilbert. When von Neumann saw this he cast it in a few days into an elegant axiomatic form much to the liking of Hilbert. (This is the origin of the paper “Ober die Grundlagen der Quantenmechanik” by Hilbert, von Neumann and myself . . .). The method used was that of integral operators. . . . This work set von Neumann on his way to his definite studies on the foundations of quantum mechanics."

"We are in what can only be described as a desperate need of your help. We have a good many theoretical people working here, but I think that if your usual shrewdness is a guide to you about the probable nature of our problems you will see why even this staff is in some respects critically inadequate...I would like you to come as a permanent, and let me assure you, honored member of our staff. A visit will give you a better idea of this somewhat Buck Rogers project than any amount of correspondence."

"I remember that there was a feeling of excitement and interest both in Hilbert’s lecture and in the lecture of von Neumann on the foundations of set theory — a feeling that one now finally was coming to grips with both the axiomatic foundation of mathematics and with the reasons for the applications of mathematics in the natural sciences."

"Morgenstern was once asked how a scholar outside the mainstream of economic thinking could make a contribution as original, innovative, and decisive as Johnny's. He replied that Johnny had an extraordinary capacity for picking the brains of a person whom he engaged in casual conversations. Once he saw from these that there was a problem of sufficient mathematical interest to warrant his spending time on it, he homed on to that subject like a guided missile."

"In my life I have met men even greater than Johnny, but none as brilliant. He shone not only in mathematics but was also fluently multilingual and particularly well-versed in history. One of his most remarkable abilities I soon came to note was his power of absolute recall."

"Von Neumann's reputation and fame have grown steadily since his death. His fantastic brain, and the breadth of his interests and undertakings, have become almost legendary."

"If doing physics meant proving theorems, you’d be a great physicist."

""Johnny" von Neumann, as he was always known among scientists, achieved fame first of all as a pure mathematician. I am not qualified to describe his contributions to pure mathematics, which usually related to the most recent, and most abstruse, branches of the subject at the time, but they certainly placed him among the leaders of modern mathematics. In the 1920s, he was interested in the development of quantum mechanics, then in rapid growth, which caused difficulty to many because of the bold use of new mathematical techniques. Von Neumann contributed greatly to making this new subject "respectable"; he pointed out the precise mathematical significance of the new developments and, at the same time, helped greatly to clarify the physical content of the new ideas. He was, in fact, quicker than many physicists in grasping the changes that were then taking place in physics Later he was a frequent visitor to the Atomic Weapons Project at Los Alamos. Here his particular quality of combining powerful mathematical insight with a very practical interest in the problems became familiar to all those associated with the project. He was never satisfied with showing that a problem could be solved on paper, but he took a personal interest in its quantitative application and in its practical realization. His many contributions, particularly to the hydrodynamics of shock waves and detonation waves, which are important both in the design of atomic weapons and in an understanding of their effects, were vital to the success of the project. For a man to whom complicated mathematics presented no difficulty, he could explain his conclusions to the uninitiated with amazing lucidity. After a talk with him one always came away with a feeling that the problem was really simple and transparent. About the same time, he became interested in the application of computing techniques to mathematical problems, and this led him to design the computer now in operation at Princeton and to planning out its applications both to practical problems and to abstract problems in nonlinear equations. He was the antithesis of the conventional image of the "long-haired" mathematics don. Always well-groomed, he had as lively views on international politics and practical affairs as on mathematical problems. His book on the Theory of Games, "including the theory of bluffing at poker," which has proved fruitful for many applications going beyond the field of games of chance and skill, is another example of the happy combination of his command of mathematics with an interest in practical matters. For the last few years, he was a member of the Atomic Energy Commission, and it is worth recording that in a field beset with much controversy, he retained the universal respect and confidence of those who did not agree with his views on policy as well as those who did."

"Another frequent visitor was John von Neumann, a brilliant mathematician, whom I knew from Germany. Although he was Hungarian, he did not have the extreme superficial politeness of many Hungarians. He liked good living and a good story. His mathematics was of the purest and most abstract kind, but he also understood physics and had written a book about quantum mechanics. He was extremely fast in solving practical problems, and contributed many useful ideas to the work of Los Alamos."

"Remarkable mathematician."

"The only student of mine I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann."

"Von Neumann was a calculating prodigy as well. He could divide two eight-digit numbers in his head with little effort. Cuthbert Hurd of IBM told me of von Neumann’s uncanny ability to create and revise computer programs (as long as fifty lines of assembly-language code!) in his head."

"In 1956 Good Housekeeping magazine ran an article on Klara von Neumann and her husband with the improbable title, “Married to a Man Who Believes the Mind Can Move the World.” One of the stranger examples of 1950s women’s magazine journalism, it is a dogged attempt to humanize a not entirely promising subject. “What’s it like to suspect your husband of being the smartest man on earth?” the article asks. “When Klara von Neumann, a slender brunette of Washington, D.C., glances at her husband, a plump, cheerful man who was born in Hungary fifty-two years ago, the thought sometimes occurs to her that she may be married to the best brain in the world.”"

"It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived."

"Under the force of Courant's plea, Trowbridge reconsidered Hilbert's request; and in the fall of 1926 von Neumann came to Göttingen as a Rockefeller Fellow. The young mathematicians there recognized that he was obviously a prodigy, but some were suspicious of what they saw as a certain “glibness” about him. They also found his mathematics “too abstract” for their taste. “We were wrong about that,” confessed Friedrichs, part of whose later work was to be strongly influenced by the work of von Neumann."

"All the mathematicians I have talked to have said that von Neumann had the quickest mind they ever knew."

"If someone gave a problem and von Neumann did not give an immediate solution, then it was an unsolvable problem."

"He was a multifaceted genius."

"There is also no objection to a mathematician’s doing physics, provided he is qualified. The prime example was von Neumann—when he did physics, he talked, thought, and calculated like a physicist (but faster). He understood all branches of physics (including elementary particles as they were known then), and chemistry and astronomy, and he had a talent for introducing those and only those mathematical ideas that were relevant to the physics at hand."

"Apart from my thesis, though, I cannot overlook the great influence on all of us of the sparkling lectures in real analysis given by Professor John von Neumann, a young man who had also come from Germany during this period. How well I remember his hurried arrivals in the classroom, a mere second late but wasting no time. With spectacular fluency he instantly made the hour come alive. No notes were ever needed, for his complete control and mastery of his subject and his lightning-fast blackboard-equations quickly reflected to us some of the greatness of his precocious mind. His audience will remember his beautifully complexioned cheeks that often radiated a cherubic smile, and his bright piercing brown eyes that seemed to glow with great vitality."

"No other mathematician in this century has had as deep and lasting an influence on the course of civilization."

"At this half-century birthday party I have two purposes. The first is to free the dynamic input/output paradigin from gratuitous misinterpretations. The second is to say something about the genius of John von Neumann, contrasting the fertility of his contributions to economics with that of past great mathematicians and non-economist celebrities. While memories are still green, we should preserve for the historical record some of the legends about this great genius."

"Evidence enough has been given for von Neumann’s genius and eminence in pure and applied mathematics."

"We economists are grateful for von Neumann’s genius. It is not for us to calculate whether he was a Gauss, or a Poincaré, or a Hilbert. He was the incomparable Johnny von Neumann. He darted briefly into our domain and it has never been the same since."

"A man so smart that he saw through himself."

"The author, who through his previous mathematical achievements has already placed himself in the forefront of German mathematicians, is only 23 years old and completed his studies in chemistry at the Eidgenössisches Polytechnikum in Zurich with the diploma examination. He combines penetrating abstract acumen with an astonishing speed in the productive assimilation of large bodies of scientific knowledge. This is undoubtedly an altogether extraordinary talent, which justifies unlimited hopes."

"Comparing this work with the habilitation thesis, one recognizes in how outstanding and promising a manner the highly gifted young researcher combines the ability for far-reaching abstraction with a powerful sense for constructive work and also for the advancement of concrete problems."

"Bethe, Fermi, and von Neumann could often be found sitting together in a quiet room inside the throbbing heart of the Theoretical Division, challenging each other to solve complex integral equations related to pressure waves. Sometimes Oppenheimer would join them. Von Neumann usually left these other three brilliant physicists in the dust."

"But when you were in real thinking trouble, you would go to von Neumann and nobody else."

"I remember having listened to Fermi’s discussions on hydrodynamics with von Neumann. (These took the strange form of competitions before Fermi’s office blackboard as each tried to solve the problem under study first; von Neumann, with his unmatched lightning-fast analytical skill, usually won)."

"The smartest person I've ever met."

"I was a graduate student—he was one of the great mathematicians of the world."

"Neumann was undoubtedly a genius. This meant among other things that be was able to learn a new subject in an incredibly short time. Before designing the computer, he took two weeks off to learn electronics, thus became able to supervise the construction of the hardware."

"One of the century’s most esteemed scientists."

"If any one person in the previous century personified the word polymath, it was von Neumann."

"His contributions to physics, mathematics, computer science, and economics rank him as one of the all-time intellectual giants of each field."

"A great mathematician in his or any era."

"A memory which seemed to operate with even more speed than his machines enabled him to bring up, from his vast and well-indexed mental filing system, stories appropriate to whatever occasion."

"John von Neumann was one of the greatest mathematicians of the 20th century."

"The first thing that people recall about John von Neumann is his phenomenal speed of thought. He didn’t have to remember things; he computed them. If he was asked a question and didn’t know the answer, he would think for three seconds and produce a response. Yet, fast thinking was not his most outstanding characteristic. He was also very deep. It is the breadth of his scientific heritage that amazes me the most."

"I think that in terms of mathematical intelligence, he was virtually unparalleled."

"Brilliant mathematician."

"Von Neumann was exceptionally widely known among mathematicians, and there are plenty of anecdotes related to him. I think that as a student, I heard from my professor A. Rényi the saying: ‘‘Other mathematicians prove what they can, Neumann what he wants.’’"

"He was one of the most attractive people I’ve ever known, attractive in the sense that he knew so much and could reason in front of people and show them what was going on so well, it was really quite wonderful. He also had a good sense of humor. ... He was wonderful, and I was really crushed when I found out that he had cancer."

"He had a real knack for calculatin."

"Two were in their early twenties: Eugene Wigner, who became a great theoretical physicist, and Johnny von Neumann, whose brilliance as a mathematician is internationally acknowledged."

"Johnny von Neumann was so valuable, not only as a mathematician but in virtually every field, that he was welcome to work with us even for very short periods. He was allowed to come and go freely."

"Johnny was the most versatile and brilliant scientist I have ever known. His mind operated at speeds that suggested neural superconductivity."

"I believe that if a mentally superhuman race ever develops, its members will resemble Johnny von Neumann."

"That deep, practically monomaniacal devotion to the thinking process is what set Johnny von Neumann apart from everyone else I have ever known."

"I have come to suspect that to most people thinking is painful. Some of us are addicted to thinking. Some of us find it a necessity. Johnny enjoyed it. I even have the suspicion that he enjoyed practically nothing else."

"Many people have wondered how Johnny von Neumann could think so fast and so effectively. How he could find so many original solutions, in areas where most people did not even notice the problems. I think I know a part of the answer, perhaps an important part, Johnny von Neumann enjoyed thinking. I have come to suspect that to most people, thinking is painful. Some of us are addicted to thinking. Some of us find it a necessity. Johnny enjoyed it. I even have a suspicion that he enjoyed practically nothing else. This explains a lot, because what you like, you do well. And he liked thinking, not just in mathematics. He liked thinking in the clear and complete manner of mathematicians, in every field; in mathematics, in physics, in the business world - his father was a banker - and in many other fields. He could and did talk to my 3-year-old son on his own terms, and I sometimes wondered whether his relation to the rest of us were a little bit similar. This also explains his effectiveness in connection with computing machines, because computing machines apply logical processes to fields: not only mathematics, but to others as yet untouched by the logical process. And it is very significant that this revolution, the revolution of the electronic brains, was practically initiated by Johnny von Neumann. I cannot think of Johnny now without remembering a very tragic circumstance when he was dying of cancer. His brain was affected. I visited him frequently and he was trying to do what he always tried to do. And he was trying to argue with me as he used to and it wasn't functioning anymore. And I think that he suffered from this loss more than I have seen any human to suffer in any other circumstance."

"I never could keep up with him."

"I'm sure that von Neumann threw off lots of ideas, as he went about, that led to Ph.D. theses."

"I feel that Weyl and von Neumann were the greatest mathematicians that I have known."

"Von Neumann was so terribly quick in lecturing that people had to slow him up by asking questions. It was understood in his classes. That people would ask questions to slow him up. I think he was quite aware of that and was grateful for this help from the audience. Von Neumann had a way of taking an idea that he had and explaining it very quickly and very clearly."

"I think the choice of von Neumann is clear by the criteria of getting the best mathematical talent in the world."

"No one that he had to compete with. But he nevertheless was a terrifically competitive person."

"[Addressing Banesh Hoffmann] He also thought very fast."

"Then in 1927, Zawirski told me a congress of mathematicians was to take place in Lwów and foreign scholars had been invited. He added that a youthful and extremely brilliant mathematician named John von Neumann was to give a lecture."

"Kuratowski also described von Neumann’s results and his personality. He told me how in a Berlin taxicab von Neumann had explained in a few sentences much more than he, Kuratowski, would have gotten by correspondence or conversation with other mathematicians about questions of set theory, measure theory, and real variables."

"He always demonstrated his fantastic and to some extent prophetic range of interests in mathematics and its applications and at the same time an objectivity which I admired enormously."

"As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self-confidence."

"For Wigner, von Neumann and thinking were synonymous."

"Quite aware that the criteria of value in mathematical work are, to some extent, purely aesthetic, he once expressed an apprehension that the values put on abstract scientific achievement in our present civilization might diminish: "The interests of humanity might change, the present curiosities in science may cease, and entirely different things may occupy the human mind in the future." One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue."

"Johnny was probably the most brilliant star in this constellation of scientists."

"I remember that in 1927, when he came to Lwów (in Poland) to attend a congress of mathematicians, his work in foundations of mathematics and set theory was already famous. This was already mentioned to us, a group of students, as an example of the work of a youthful genius."

"Von Neumann was a giant in the breadth of his knowledge."

"His quickness was quite remarkable."

"Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature."

"It is indeed supremely difficult to effectively refute the claim that John von Neumann is likely the most intelligent person who has ever lived."

"Universal mind."

"John von Neumann became one of the world’s greatest mathematicians and went on to father the digital computer, a device that is revolutionizing all walks of life."

"Especially as it brought me back in association with John von Neumann, whose great skill in mathematics I had first observed in Europe when he was a boy of seventeen."

"The extensive work Mathematische Begründung der Quantentheorie also testifies to the extraordinary talent of the author in the appropriation and assimilation of a large area of material."

"Incredible rapidity."

"His memory and unlimited scope of universal interests was amazing. At that time we probably did not attach any further significance to this, nor did we evaluate or even could have evaluated the incredible multiplicity and diversification of the innumerable subjects so discussed. But later, perhaps decades later, many of these subjects reappeared in his scientific work (directly, or in the background), and he had no difficulty in recovering these or related ideas from his memory as they became relevant in specific instances."

"Considered the smartest man alive."

"Throughout much of his career, he led a double life: as an intellectual leader in the ivory tower of pure mathematics and as a man of action, in constant demand as an advisor, consultant and decision-maker to what is sometimes called the military-industrial complex of the United States. My own belief is that these two aspects of his double life, his wide-ranging activities as well as his strictly intellectual pursuits, were motivated by two profound convictions. The first was the overriding responsibility that each of us has to make full use of whatever intellectual capabilities we were endowed with. He had the scientist's passion for learning and discovery for its own sake and the genius's ego-driven concern for the significance and durability of his own contributions. The second was the critical importance of an environment of political freedom for the pursuit of the first, and for the welfare of mankind in general. I'm convinced, in fact, that all his involvements with the halls of power were driven by his sense of the fragility of that freedom. By the beginning of the 1930s, if not even earlier, he became convinced that the lights of civilization would be snuffed out all over Europe by the spread of totalitarianism from the right: Nazism and Fascism. So he made an unequivocal commitment to his home in the new world and to fight to preserve and reestablish freedom from that new beachhead. In the 1940s and 1950s, he was equally convinced that the threat to civilization now came from totalitarianism on the left, that is, Soviet Communism, and his commitment was just as unequivocal to fighting it with whatever weapons lay at hand, scientific and economic as well as military. It was a matter of utter indifference to him, I believe, whether the threat came from the right or from the left. What motivated both his intense involvement in the issues of the day and his uncompromisingly hardline attitude was his belief in the overriding importance of political freedom, his strong sense of its continuing fragility, and his conviction that it was in the United States, and the passionate defense of the United States, that its best hope lay."

"Many mathematicians have suffered in fact by comparing themselves with von Neumann."

"I spent the rest of 1936 preparing for my trip to the United States, where von Neumann, with whom I had enjoyed friendly relations at least since 1930, had arranged for me to spend the second semester (from January through May, 1937) at the Institute for Advanced Study in Princeton."

"The relationship with Weyl was so close that the 22-year-old student von Neumann finished his lecture on axiomatics in February 1925 when Weyl had to take a health-related leave. In doing so, Weyl reported to the Swiss School Council that von Neumann, alongside Hilbert, was "the most expert among present mathematicians" in this field and that he himself in his lecture had "presented the subject in that form which had emerged from the unpublished investigations of Mr. Neumann.""

"John von Neumann was one whose talents reached so widely, I could talk to him about the puzzles of the geometry around what we today call a black hole."

"But John von Neumann had a marvelous interest in history. He had read the Cambridge Medieval History, [the] Cambridge Ancient History, and he had a phenomenal memory, so he could recite whole paragraphs from the Cambridge Ancient History and tell me about the Council of Nicea, for instance. But to become a member of the Atomic Energy Commission, I'm sure he was very useful, but it was so far removed from making use of this marvelous scientific imagination of his that I keep wondering if we made the best use of him."

"Von Neumann and Fermi, in particular, were enormously helpful. Both had the most stunning ability to listen to a recital of current problems for only an hour or two and then provide comments or calculations that would show the way to overcoming the problems. They also enriched the life of the lab by giving colloquium talks on almost every visit."

"The two mathematicians now or recently active in America who have adopted a similar point of view are—and I believe not by coincidence—two of the greatest forces in modern mathematics, namely, Hermann Weyl and John von Neumann."

"Neumann is one of the two or three top mathematicians in the world, is totally without national or race prejudice, and has an enormously great gift for inspiring younger men and getting them to do research."

"Young men like Heisenberg himself, Dirac, Wolfgang Paul and John von Neumann were making new discoveries almost every day. This feverish atmosphere is not one in which I function well."

"I have known a great many intelligent people in my life. I knew Max Planck, Max von Laue, and Werner Heisenberg. Paul Dirac was my brother-in-law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. And I have known many of the brightest younger scientists. But none of them had a mind as quick and acute as Jancsi von Neumann. I have often remarked this in the presence of those men, and no one ever disputed me."

"He understood mathematical problems not only in their initial aspect, but in their full complexity."

"Johnny was a most unusual person, a marvellously quick thinker, and was recognized as such in high school."

"Nobody knows all science, not even von Neumann did. But as for mathematics, he contributed to every part of it except number theory and topology. That is, I think, something unique."

"A deep sense of humor and an unusual ability for telling stories and jokes endeared Johnny even to casual acquaintances. He could be blunt when necessary, but was never pompous. A mind of von Neumann's inexorable logic had to understand and accept much that most of us do not want to accept and do not even wish to understand. This fact colored many of von Neumann's moral judgments. … Only scientific intellectual dishonesty and misappropriation of scientific results could rouse his indignation and ire — but these did — and did almost equally whether he himself, or someone else, was wronged."

"The accuracy of his logic was, perhaps, the most decisive character of his mind. One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch. "If one listens to von Neumann, one understands how the human mind should work," was the verdict of one of our perceptive colleagues... "If he analyzed a problem, it was not necessary to discuss it any further. It was clear what had to be done," said the present chairman of the U. S. Atomic Energy Commission."

"Perhaps one could find a body of phenomena which would make our concept-building ability less of a single stark fact by studying the concept-forming ability of animals. Perhaps the consciousness of animals is more shadowy than ours and perhaps their perceptions are always dreamlike. On the opposite side, whenever I talked with the sharpest intellect whom I have known -- with von Neumann -- I always had the impression that only he was fully awake, that I was halfway in a dream."

"“You have a good memory?” asked Kuhn. “Not like von Neumann’s,” replied Wigner."

"When Ratz saw how intelligent Jancsi was, he began giving him private lessons. . . . [Ratz] felt so privileged to tutor a phenomenon like Jancsi that he refused any money for it. His compensation was more subtle: the brush with a special kind of mind; the privilege of training that mind in a discipline that both of them loved."

"Our teachers were just enormously good, but the mathematics teacher was fantastic. He gave private classes to Johnny von Neumann. He gave him private classes because he realized that this would be a great mathematician."

"From talking to many people who knew him, I think I’ve gradually built up a decent picture of John von Neumann as a man. He would have been fun to meet. He knew a lot, was very quick, always impressed people, and was lively, social and funny."

"Von Neumann was extremely intelligent, and curious about everything. He looked like a cherub and sometimes acted like one; my three and five-year-old daughters delighted in climbing on him when he came to call at the house. He was very powerful and productive in pure science and mathematics and at the same time had a remarkably strong streak of practicality. He was one of the earliest pioneers in the design and construction of large electronic computers, he developed a strong interest in the technology of nuclear and other weapons, and he made a number of elegant inventions in each of these fields. This combination of scientific ability and practicality gave him a credibility with military officers, engineers, industrialists, and scientists that no one else could match. He was the clearly dominant advisory figure in nuclear missilery at the time, and everyone took his statements about what could and should be done very seriously."

"Other smart people commonly said that John von Neumann was the smartest person they had ever known. Although I worked with him for only five years—1952-57, and even then on just an occasional basis—I came to know him well enough to feel the same way. His accomplishments generally confirmed this view."

"As far as design theorists are concerned, theistic evolution is American evangelicalism's ill-conceived accommodation to Darwinism."

"Design theorists are no friends of theistic evolution."

"The fine-tuning of the universe, about which cosmologists make such a to-do, is both complex and specified and readily yields design. So too, Michael Behe's irreducibly complex biochemical systems readily yield design. The complexity-specification criterion demonstrates that design pervades cosmology and biology. Moreover, it is a transcendent design, not reducible to the physical world. Indeed, no intelligent agent who is strictly physical could have presided over the origin of the universe or the origin of life."

"The question rather is how we should do science and theology in light of the impending collapse of Enlightenment rationalism and scientific naturalism. These ideologies are on the way out. They are on the way out."

"My thesis is that all disciplines find their completion in Christ and cannot be properly understood apart from Christ."

"If we take seriously the word-flesh Christology of Chalcedon (i.e., the doctrine that Christ is fully human and fully divine) and view Christ as the telos toward which God is drawing the whole of creation, then any view of the sciences that leaves Christ out of the picture must be seen as fundamentally deficient."

"Christ is indispensable to any scientific theory, even if its practitioners do not have a clue about him."

"The scientific picture of the world championed since the Enlightenment is not just wrong but massively wrong. Indeed entire fields of inquiry, especially in the human sciences, will need to be rethought from the ground up in terms of intelligent design."

"How a designer gets from thought to thing is, at least in broad strokes, straightforward: (1) A designer conceives a purpose. (2) To accomplish that purpose, the designer forms a plan. (3) To execute the plan, the designer specifies building materials and assembly instructions. (4) Finally, the designer or some surrogate applies the assembly instructions to the building materials. What emerges is a designed object, and the designer is successful to the degree that the object fulfills the designer's purpose"

"Intelligent Design opens the whole possibility of us being created in the image of a benevolent God."

"The job of apologetics is to clear the ground, to clear obstacles that prevent people from coming to the knowledge of Christ.... And if there's anything that I think has blocked the growth of Christ as the free reign of the Spirit and people accepting the Scripture and Jesus Christ, it is the Darwinian naturalistic view.... It's important that we understand the world. God has created it; Jesus is incarnate in the world."

"The world is a mirror representing the divine life..."

"The mechanical philosophy was ever blind to this fact. Intelligent design, on the other hand, readily embraces the sacramental nature of physical reality. Indeed, intelligent design is just the Logos theology of John's Gospel restated in the idiom of information theory."

"Intelligent design is eminently falsifiable. Specified complexity in general and irreducible complexity in biology are within the theory of intelligent design the key markers of intelligent agency. If it could be shown that biological systems like the bacterial flagellum that are wonderfully complex, elegant, and integrated could have been formed by a gradual Darwinian process (which by definition is non-telic), then intelligent design would be falsified on the general grounds that one doesn't invoke intelligent causes when purely natural causes will do. In that case Occam's razor finishes off intelligent design quite nicely."

"The fact is that for complex systems like the bacterial flagellum no biologist has or is anywhere close to reconstructing its history in Darwinian terms. Is Darwinian theory therefore falsified? Hardly. I have yet to witness one committed Darwinist concede that any feature of nature might even in principle provide countervailing evidence to Darwinism. In place of such a concession one is instead always treated to an admission of ignorance. Thus it's not that Darwinism has been falsified or disconfirmed, but that we simply don't know enough about the biological system in question and its historical context to determine how the Darwinian mechanism might have produced it."

"From our vantage, materialism is not a neutral, value-free, minimalist position from which to pursue inquiry. Rather, it is itself an ideology with an agenda. What’s more, it requires an evolutionary creation story to keep it afloat. On scientific grounds, we regard that creation story to be false. What’s more, we regard the ideological agenda that has flowed from it to be destructive to rational discourse. Our concerns are therefore entirely parallel to the evolutionists’. Indeed, all the evolutionists’ worst fears about what the world would be like if we succeed have, in our view, already been realized through the success of materialism and evolution. Hence, as a strategy for unseating materialism and evolution, the term "Wedge" has come to denote an intellectual and cultural movement that many find congenial."

"I think the opportunity to deal with students and getting them properly oriented on science and theology and the relation between those is going to be important because science has been such an instrument used by the materialists to undermine the Christian faith and religious belief generally."

"This is really an opportunity to mobilize a new generation of scholars and pastors not just to equip the saints but also to engage the culture and reclaim it for Christ. That's really what is driving me."

"But there are deeper motivations. I think at a fundamental level, in terms of what drives me in this is that I think God's glory is being robbed by these naturalistic approaches to biological evolution, creation, the origin of the world, the origin of biological complexity and diversity. When you are attributing the wonders of nature to these mindless material mechanisms, God's glory is getting robbed...And so there is a cultural war here. Ultimately I want to see God get the credit for what he's done - and he's not getting it."

"And another thing I think we need to be aware of is that not every instance of design we see in nature needs to be directly attributed to God. Certainly as Christians we believe there is an angelic hierarchy - it's not just that there's this physical material world and there's God. There can be various hierarchies of intelligent beings operating, God can work through what can be called derived intelligences - processes which carry out the Divine will, but maybe not perfectly because of the fall."

"In the next five years, molecular Darwinism—the idea that Darwinian processes can produce complex molecular structures at the subcellular level—will be dead. When that happens, evolutionary biology will experience a crisis of confidence because evolutionary biology hinges on the evolution of the right molecules. I therefore foresee a Taliban-style collapse of Darwinism in the next ten years. Intelligent design will of course profit greatly from this."

"Theism (whether Christian, Jewish, or Muslim) holds that God by wisdom created the world. The origin of the world and its subsequent ordering thus results from the designing activity of an intelligent agent—God. Naturalism, on the other hand, allows no place for intelligent agency except at the end of a blind, purposeless material process. Within naturalism, any intelligence is an evolved intelligence. Moreover, the evolutionary process by which any such intelligence developed is itself blind and purposeless. As a consequence, naturalism makes intelligence not a basic creative force within nature but an evolutionary byproduct. In particular, humans (the natural objects best known to exhibit intelligence) are not the crown of creation, not the carefully designed outcome of a purposeful creator, and certainly not creatures made in the image of a benevolent God. Rather, humans are an accident of natural history."

"Thus, in a crucial way, the Kansas hearings repeat the pattern set by the Scopes Trial, which has been repeated many times since, namely, evolutionists escaped critical scrutiny by not having to undergo cross-examination. In this case, they accomplished the feat by boycotting the hearings. I therefore await the day when the hearings are not voluntary but involve subpoenas that compel evolutionists to be deposed and interrogated at length on their views."

"What I propose, then, is a strategy for interrogating the Darwinists to, as it were, squeeze the truth out of them."

"Thus, in its relation to Christianity, intelligent design should be viewed as a ground-clearing operation that gets rid of the intellectual rubbish that for generations has kept Christianity from receiving serious consideration."

"Even many Christians who have been raised and indoctrinated in a secular mindset … will say, 'Look, we're just going to have to accept the science of the day and try to make our peace with it theologically.' … And there is no peace theologically … ultimately with this view [Darwinian evolution]. But they accept it. And so, this idea of intelligent design becomes very threatening."

"The mountains of evidence are already there. The problem is that evidence is itself inherently hermeneutical, influenced by cognitive predispositions to interpret certain types of data as supporting/confirming certain types of conclusions. If one wears materialistic blinders, there can be no evidence for ID hence the constant refrain by people like Barbara Forrest and Eugenie Scott that there is no evidence for ID. There is none for them because they have shut their eyes to it."

"Why leap so quickly to the supernatural conclusion? Answer: because that's the hypothesis Dembski favors before ever considering the evidence."

"Even if we accept everything Dembski and his coauthors are saying about these theorems, this whole line of attack simply amounts to nothing. Most of us did not need difficult mathematical theorems to understand that Darwinian evolution can work only if nature has certain properties. The search problem confronted by evolution arises ultimately from the laws of physics, but it is well outside biology’s domain to wonder why those laws are as they are. Dembski and his cohorts argue that the fundamental constants of the universe encode information of a sort that can arise only from an intelligent source, but they have no more basis for this claim than they did for the comparable claim about genetic sequences."

"I often wonder if ID’s proponents, like Wells, Behe, Dembski, and Meyer, who still act as if they triumphed, ever lie awake at night and think about how badly they failed. For this is science, and the truth will out. But they’re still at it, like a cow walking in circles forever even after it’s been disconnected from the water mill."

"A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?"

"I can say this. I believe that the human mind, or even the mind of a cat, is more interesting in its complexity than an entire galaxy if it is devoid of life."

"Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick."

"The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity."

"There are, and always have been, destructive pseudo-scientific notions linked to race and religion; these are the most widespread and damaging. Hopefully, educated people can succeed in shedding light into these areas of prejudice and ignorance, for as Voltaire once said: "Men will commit atrocities as long as they believe absurdities.""

"In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance."

"Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all."

"I've never made a discovery myself, unless by accident. If you write glibly, you fool people. When I first met Asimov, I asked him if he was a professor at Boston University. He said no and … asked me where I got my Ph.D. I said I didn't have one and he looked startled. "You mean you're in the same racket I am," he said, "you just read books by the professors and rewrite them?" That's really what I do."

"There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry."

"Ever since I was a boy, I've been fascinated by crazy science and such things as perpetual motion machines and logical paradoxes. I've always enjoyed keeping up with those ideas. I suppose I didn't get into it seriously until I wrote my first book, Fads and Fallacies in the Name of Science. I was influenced by the Dianetics movement, now called Scientology, which was then promoted by John Campbell in Astounding Science Fiction. I was astonished at how rapidly the thing had become a cult."

"As I have often said, electrons and gerbils don't cheat. People do."

"Ideologues of all persuasions think they know how the economy will respond to the Administration's strange mixture of Lafferism and monetarism. Indeed, their self-confidence is so vast, and their ability to rationalize so crafty, that one cannot imagine a scenario for the next few years, that they would regard as falsifying their dogma. The failure of any prediction can always be blamed on quirky political decisions or unforeseen historical events."

"The greatest scandal of the century in American psychiatry … is the growing mania among thousands of inept therapists, family counselors, and social workers for arousing false memories of childhoood sexual abuse."

"Although Lewis Carroll thought of The Hunting of the Snark as a nonsense ballad for children, it is hard to imagine—in fact one shudders to imagine—a child of today reading and enjoying it."

"Debunking bad science should be constant obligation of the science community, even if it takes time away from serious research or seems to be a losing battle. One takes comfort from the fact there is no Gresham's laws in science. In the long run, good science drives out bad."

"Bad science contributes to the steady dumbing down of our nation. Crude beliefs get transmitted to political leaders and the result is considerable damage to society. We see this happening now in the rapid rise of the religious right and how it has taken over large segments of the Republican Party."

"We know from polls how ignorant the general public is about science. Almost half of all adults in the United States now believe in astrology and in angels and demons, and that we are being observed by aliens and UFOs who frequently abduct humans. More than half believe that evolution is an unverified a theory. Science education in our nation, especially in lower grades, is getting worse, not better. Several states are constantly doing their best to force public schools to teach creationism. Greedy publishers, interested only in profit, turn out book after book on astrology, ufology, the occult, dangerous programs to lose weight without exercising or cutting calories, and every known variety of dubious medicine. The electronic media are equal offenders. Every year I hope the tide is about to turn, and that contributors to television, radio, and the Internet will become so appalled by the flood of fake science they keep flinging at the public that they will at least try to tone it down. Alas, every year the flood gets worse."

"Suppose, however, there is not enough time for measures to be taken to prevent a collision, and earth is shattered by a giant NEO that will hurt us all into oblivion. What are the philosophical implications of such an event? This obviously is not a problem for atheists, agnostics, or pantheists because they are resigned to the fact that nature does not care a rap about preserving a species. What about theists? I’m inclined to think that even to them a certain extinction of humanity would be acceptable. The Biblical Jehovah, remember, is said to have drowned every man, woman, baby, and their pets, except for Noah and his family. If God can allow an earthquake to kill thousands, or the Black Death to wipe out half of Europe, surely she would have no scruples about allowing an asteroid to bring human history to a flaming end."

"Let the Bible be the Bible! It’s not about science. It’s not accurate history. It is a grab bag of religious fantasies written by many authors. Some of its myths, like the Star of Bethlehem, are very beautiful. Others are dull and ugly. Some express lofty ideals, such as the parables of Jesus. Others are morally disgusting."

"The King James Bible is a literary masterpiece best left unaltered. It is a classic to put on a shelf alongside the great fantasies of Homer, Virgil, Dante, Milton, and yes, even the Koran."

"For reasons that reflect popular ignorance of science, combined with a love of miracles, the notion that fresh eggs balance more easily on the first day of spring caught fire in the United States."

"Public infatuation with alternative medicines of all varieties shows no sign of abating. Acupuncture, homeopathy, aromatherapy, herbal remedies, chelation, iridology, therapeutic touch, magnet therapy, psychic healing, and so on are gaining new converts every day. The tragedies occur, of course, when gullible sufferers rely solely on such remedies and avoid seeking mainstream help. It would be good if we had some statistical evidence about the frequency of deaths following reliance on pseudomedicines."

"My attack on Freud brought a raft of angry letters from dedicated Freudians. One reader assured me that Freudianism is “alive and well.” True, but alive and well only among a dwindling remnant of Freud acolytes, not among the majority of today’s psychiatrists or intellectuals."

"This confusion of the certainty of mathematics within a formal system and the uncertainty of its applications to the world is a common mistake often made by ignorant sociologists."

"The deeper question that lies behind the above banalities is whether the rules of baseball are similar to or radically different from the rules of science. Clearly they are radically different. Like the rules of chess and bridge, the rules of baseball are made by humans. But the rules of science are not. They are discovered by observation, reasoning, and experiment. Newton didn’t invent his laws of gravity except in the obvious sense that he thought of them and wrote them down. Biologists didn’t “construct” the DNA helix; they observed it. The orbit of Mars is not a social construction. Einstein did not make up E=mc2 the way game rules are made up. To see rules of science as similar to baseball rules, traffic rules, or fashions in dress is to make a false analogy that leads nowhere."

"But that science moves inexorably closer to finding objective truth can only be denied by peculiar philosophers, naive literary critics, and misguided social scientists. The fantastic success of science in explaining and predicting, above all in making incredible advances in technology, is proof that scientists are steadily learning more and more about how the universe behaves."

"The curious notion that “truth” does not mean “correspondence with reality,” but nothing more than the successful passing of tests for truth, was dealt a death blow by Alfred Tarski’s famous semantic definition of truth: “snow is white” is true if and only if snow is white. The definition goes back to Aristotle. Most philosophers of the past, all scientists, and all ordinary people accept this definition of what they mean when they say some thing is true. It is denied only by a small minority of pragmatists who still buy John Dewey’s obsolete epistemology."

"Carlos Castaneda died in Westwood, California, in 1998. “His only real sorcery,” writes Kathryn Lindskoog in her entertaining book Fakes, Frauds, and Other Malarkey (1993), “was turning the University of California into an ass.” The next time you come close to a crow, try calling out “Hello Carlos!” If you are high enough on peyote, you might hear the bird answer."

"Although Jacobs has had no training in psychology, psychiatry, or hypnotherapy, he uses hypnotism to induce his patients (now more than seven hundred) to develop strong memories of horrendous abductions even though many patients had no such memories until hypnotized. Jacobs is convinced that five million Americans have been kidnapped at least once by aliens. One female patient, who worked in retail sales, had, according to Jacobs, one hundred abductions in one year, an average of one every three days!"

"To support his conviction that the Old Testament is accurate history, Newton worked out an elaborate chronology of earth’s history, drawing on astronomical data such as eclipses and star motions and legends such as that of Jason and the Argonauts, which he took to be genuine events. With incredible ingenuity he tried to harmonize biblical history with secular histories of the ancient world. It is sad to envision the discoveries in mathematics and physics Newton might have made if his great intellect had not been diverted by such bizarre speculations."

"His "Mathematical Games" column in Scientific American is one of the few bridges over C. P. Snow's famous "gulf of mutual incomprehension" that lies between technical and literary cultures."

"He writes about various kinds of cranks with the conscious superiority of the scientist, and in most cases one can share his sense of the victory of reason. But after half a dozen chapters this non-stop superiority begins to irritate; you begin to wonder about the standards that make him so certain he is always right. He asserts that the scientist, unlike the crank, does his best to remain open-minded. So how can he be so sure that no sane person has ever seen a flying saucer, or used a dowsing rod to locate water? And that all the people he disagrees with are unbalanced fanatics? A colleague of the positivist philosopher A. J. Ayer once remarked wryly "I wish I was as certain of anything as he seems to be about everything". Martin Gardner produces the same feeling."

"Gardner is the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us."

"He was not a mathematician—he never even took a maths class after high school—yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century."

"Without data, you're just another person with an opinion."

"Uncontrolled variation is the enemy of quality."

"That's all window dressing. That's not fundamental. That's not getting at change and the transformation that must take place. Sure we have to solve problems. Certainly stamp out the fire. Stamp out the fire and get nowhere. Stamp out the fires puts us back to where we were in the first place. Taking action on the basis of results without theory of knowledge, without theory of variation, without knowledge about a system. Anything goes wrong, do something about it, overreacting; acting without knowledge, the effect is to make things worse. With the best of intentions and best efforts, managing by results is, in effect, exactly the same, as Dr. Myron Tribus put it, while driving your automobile, keeping your eye on the rear view mirror, what would happen? And that's what management by results is, keeping your eye on results."

"The worker is not the problem. The problem is at the top! Management!"

"Learning is not compulsory; it's voluntary. Improvement is not compulsory; it's voluntary. But to survive, we must learn."

"Blame the process, not the people."

"They realized that the gains that you get by statistical methods are gains that you get without new machinery, without new people. Anybody can produce quality if he lowers his production rate. That is not what I am talking about. Statistical thinking and statistical methods are to Japanese production workers, foremen, and all the way through the company, a second language. In statistical control you have a reproducible product hour after hour, day after day. And see how comforting that is to management, they now know what they can produce, they know what their costs are going to be."

"I think that people here expect miracles. American management thinks that they can just copy from Japan—but they don't know what to copy!"

"In Europe and in America, people are now more interested in the cost of quality and in systems of quality-audit. But in Japan, we are keeping very strong interest to improve quality by use of methods which you started....when we improve quality we also improve productivity, just as you told us in 1950 would happen."

"Defects are not free. Somebody makes them, and gets paid for making them."

"Improve constantly and forever the system of production and service, to improve quality and productivity, and thus constantly decrease costs."

"Quality comes not from inspection, but from improvement of the production process."

"Part of America's industrial problems is the aim of its corporate managers. Most American executives think they are in the business to make money, rather than products or service...The Japanese corporate credo, on the other hand, is that a company should become the world's most efficient provider of whatever product and service it offers. Once it becomes the world leader and continues to offer good products, profits follow."

"The supposition is prevalent the world over that there would be no problems in production or service if only our production workers would do their jobs in the way that they were taught. Pleasant dreams. The workers are handicapped by the system, and the system belongs to the management."

"We cannot rely on mass inspection to improve quality, though there are times when 100 percent inspection is necessary. As Harold S. Dodge said many years ago, 'You cannot inspect quality into a product.' The quality is there or it isn't by the time it's inspected."

"Foremost is the principle that the purpose of consumer research is to understand the customer's needs and wishes, and thus design product and service that will provide better living for him in the future. A second principle is that no one can guess the future loss of business from a dissatisfied customer..."

"The aim of this book is to try to explain to top management of America that their job is to improve competitive position. One need not be an economist to understand from the papers that many American products are not competitive at home or abroad, lost to foreign invasion, causing unemployment at home. Failure of management to plan for the future and to foresee problems has nurtured waste of manpower, of materials and of machine time, all of which raise the manufacturers costs and the price the purchaser must pay. The consumer is not always willing to subsidize this waste."

"Loss of market begets unemployment. Emphasis has been on short-term profit, to the undernourishment of plans that might generate new product and service that would keep the company alive and provide jobs and more jobs. It is no longer socially acceptable performance to lose market and to dump hourly workers on to the heap of unemployed."

"The 14 points [for quality control] apply anywhere, to small organizations as well as to large ones...:"

"Statistical methods had taken fire in America around 1942, following a series of ten-day intensive courses for engineers, initiated by Stanford University on a suggestion from this author. The war department also gave courses at factories of suppliers. Brilliant applications attracted much attention, but the flare of statistical methods by themselves, in an atmosphere in which management did not know their responsibilities, burned, sputtered, fizzled and died out."

"Why waste knowledge?... No company can afford to waste knowledge. Failure of management to breakdown barriers between activities... is one way to waste knowledge. People that are not working together are not contributing their best to the company. People as they work together, feeling secure in the job reinforce their knowledge and efforts. Their combined output, when they are working together, is more than the sum of their separate"

"The prevailing style of management must undergo transformation. A system cannot understand itself. The transformation requires a view from outside. The aim of this chapter is to provide an outside view—a lens—that I call a system of profound knowledge. It provides a map of theory by which to understand the organizations that we work in. The first step is transformation of the individual. This transformation is discontinuous. It comes from understanding of the system of profound knowledge. The individual, transformed, will perceive new meaning to his life, to events, to numbers, to interactions between people. Once the individual understands the system of profound knowledge, he will apply its principles in every kind of relationship with other people. He will have a basis for judgment of his own decisions and for transformation of the organizations that he belongs to."

"The various segments of the system of profound knowledge proposed here cannot be separated. They interact with each other. Thus, knowledge of psychology is incomplete without knowledge of variation."

"A manager of people needs to understand that all people are different. This is not ranking people. He needs to understand that the performance of anyone is governed largely by the system that he works in, the responsibility of management."

"What is a system? A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment. (We are of course talking here about a man-made system.)"

"It is important that an aim never be defined in terms of a specific activity or method. It must always relate to a better life for everyone."

"Choice of aim is clearly a matter of clarification of values, especially on the choice between possible options."

"A system must be managed. It will not manage itself. Left to themselves in the Western world, components become selfish, competitive, independent profit centres, and thus destroy the system. . . . The secret is cooperation between components toward the aim of the organization. We can not afford the destructive effect of competition."

"To successfully respond to the myriad of changes that shake the world, transformation into a new style of management is required. The route to take is what I call profound knowledge - knowledge for leadership of transformation."

"Management’s job. It is management’s job to direct the efforts of all components toward the aim of the system. The first step is clarification: everyone in the organization must understand the aim of the system, and how to direct his efforts toward it. Everyone must understand the damage and loss to the whole organization from a team that seeks to become a selfish, independent, profit centre."

". . .the principle that where there is fear, there will be wrong figures. . . ."

"What is the variation trying to tell us about a process, about the people in the process?"

"Knowledge is theory. We should be thankful if action of management is based on theory. Knowledge has temporal spread. Information is not knowledge. The world is drowning in information but is slow in acquisition of knowledge. There is no substitute for knowledge."

"Experience by itself teaches nothing...Without theory, experience has no meaning. Without theory, one has no questions to ask. Hence without theory there is no learning."

"In God we trust. All others must bring data."

"Total Quality Management (TQM) in the Department of Defense is a strategy for continuously improving performance at every level, and in all areas of responsibility. It combines fundamental management techniques, existing improvement efforts, and specialized technical tools under a disciplined structure focused on continuously improving all processes. Improved performance is directed at satisfying such broad goals as cost, quality, schedule, and mission need and suitability. Increasing user satisfaction is the overriding objective. The TQM effort builds on the pioneering work of Dr. W. E. Deming, Dr. J. M. Juran, and others, and benefits from both private and public sector experience with continuous process improvement."

"Two of my favourite current management writers are Americans – Clayton Christensen and Peter Senge. My all-time favourite gurus are Peter Drucker, who became a greatly admired friend, and W. Edwards Deming. The thing that set these people apart from many other business commentators is that they didn’t propose any all - encompassing theories, they simply told it like it is. The fact is that life cannot be summarised as a simple set of rules; it’s far too complicated for that and it’s always changing. Unfortunately, all-encompassing panaceas do seem to be popular and certainly sell books, which is why I so value the objectivity of thought that each of these people brought to the debate."

"Let us imagine that the aboriginal-original human specimen was one of two brother apes, A and B; they were alike in every respect; both were animal space-binders; but something strange happened to B; he became the first time-binder, a human. … He had thus a new faculty, he belonged to a new dimension; but, of course, he did not realize it; and because he had this new capacity he was able to analyze his brother "A"; he observed "A is my brother; he is an animal; but he is my brother; therefore, I AM AN ANIMAL." This fatal first conclusion, reached by false analogy, by neglecting a fact, has been the chief source of human woe for half a million years and it still survives. … He [then] said to himself, "If I am an animal there is also in me something higher, a spark of some thing supernatural.""

"Humans can be literally poisoned by false ideas and false teachings. Many people have a just horror at the thought of putting poison into tea or coffee, but seem unable to realize that, when they teach false ideas and false doctrines, they are poisoning the time-binding capacity of their fellow men and women. One has to stop and think! There is nothing mystical about the fact that ideas and words are energies which powerfully affect the physico-chemical base of our time-binding activities. Humans are thus made untrue to "human nature." … The conception of man as a mixture of animal and supernatural has for ages kept human beings under the deadly spell of the suggestion that, animal selfishness and animal greediness are their essential character, and the spell has operated to suppress their REAL HUMAN NATURE and to prevent it from expressing itself naturally and freely."

"To regard human beings as tools — as instruments — for the use of other human beings is not only unscientific but it is repugnant, stupid and short sighted. Tools are made by man but have not the autonomy of their maker — they have not man's time-binding capacity for initiation, for self-direction, and self-improvement."

"Such as contribute most to human progress and human enlightenment — men like Gutenberg, Copernicus, Newton, Leibnitz, Watts, Franklin, Mendeleieff, Pasteur, Sklodowska-Curie, Edison, Steinmetz, Loeb, Dewey, Keyser, Whitehead, Russell, Poincaré, William Benjamin Smith, Gibbs, Einstein, and many others — consume no more bread than the simplest of their fellow mortals. Indeed such men are often in want. How many a genius has perished inarticulate because unable to stand the strain of social conditions where animal standards prevail and "survival of the fittest" means, not survival of the "fittest in time-binding capacity," but survival of the strongest in ruthlessness and guile — in space-binding competition!"

"There is a fundamental confusion between the notion of the older 'semantics' as connected with a theory of verbal 'meaning' and words defined by words, and the present theory of 'general semantics' where we deal only with neuro-semantic and neuro-linguistic living reactions of Smith, Smith, etc., as their reactions to neuro-semantic and neuro-linguistic environments as environments."

"The only link between the verbal and objective world is exclusively structural, necessitating the conclusion that the only content of all "knowledge" is structural. Now structure can be considered as a complex of relations, and ultimately as multi-dimensional order. From this point of view, all language can be considered as names for unspeakable entities on the objective level, be it things or feelings, or as names of relations. In fact... we find that an object represents an abstraction of a low order produced by our nervous system as the result of a sub-microscopic events acting as stimuli upon the nervous system."

""Say whatever you choose about the object, and whatever you might say is not it." Or, in other wordsː "Whatever you might say the object "is", well it is not." This negative statement is final, because it is negative."

"The map is not the territory … The only usefulness of a map depends on similarity of structure between the empirical world and the map..."

"Any organism must be treated as-a-whole; in other words, that an organism is not an algebraic sum, a linear function of its elements, but always more than that. It is seemingly little realized, at present, that this simple and innocent-looking statement involves a full structural revision of our language..."

"The main thesis of this non-Aristotelian system is that as yet we all (with extremely few exceptions) copy animals in our nervous processes, and that practically all human difficulties, mental ills … have this … component."

"Man's achievements rest upon the use of symbols.... we must consider ourselves as a symbolic, semantic class of life, and those who rule the symbols, rule us."

"The word is not the thing."

""What is good in Korzybski's work," they say, "is not new, and what is new is not good." On the other hand, many "Korzybski-ites" proclaim that Korzybski's work has "nothing to do" with semantics. They go so far as to say that the very term "general semantics" was an unfortunate choice; that had Korzybski known what confusion would arise between semantics and general semantics he would not have used it at all. Korzybski himself has maintained that while semantics belongs to the philosophy of language and perhaps to the theory of knowledge, general semantics belongs to empirical science: that it is the foundation of a science of man, the basis of the first "non-aristotelian system," which has had no predecessor and which no academic semanticist has ever achieved."

"Korzybski's book Science and Sanity is quite useless as a source of information about general semantics. It is embarrassingly vague and dilettantish, and greatly oversized at that (nearly 800 pages). I can, however, recommend three excellent articles from the collection Language, Meaning and Maturity, New York 1954, which includes selected papers chosen first of all from the periodical ETC for the period 1943-53. I mean the above mentioned work by Anatol Rapoport, "What Is Semantics?" and two works by : "Semantics. General Semantics and Related Disciplines" and "What Is Meant by Aristotelian Structure of Language?""

"Scientific language, which Korzybski used as his model of sane language, is almost exclusively extensional and denotative, or at least tries to be. The language of the mentally ill, most obviously "un-sane," is almost totally intensional and connotative. This is the language that does not correspond to anything "out there," and this is, in fact, how and perhaps even why the user is mentally ill. Korzybski's concern with keeping the conscious "connection" or correspondence between language and verifiable referents is, for all practical purposes, paralleled by the process of psychotherapy. In this process, which is largely "just talk," the purpose is to foster closer and more accurate correspondence between the patient's language and externally verifiable meanings."

"Following Korzybski, I put things in probabilities, not absolutes... My only originality lies in applying this zetetic attitude outside the hardest of the hard sciences, physics, to softer sciences and then to non-sciences like politics, ideology, jury verdicts and, of course, conspiracy theory."

"Yes, but when I discovered it, it stayed discovered."

"A few first rate research papers are preferable to a large number that are poorly conceived or half-finished. The latter are no credit to their writers and a waste of time to their readers."

"This duality can be pursued further and is related to a duality between past and future and the notions of control and knowledge. Thus we may have knowledge of the past but cannot control it; we may control the future but have no knowledge of it."

"My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.' When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'"

"Omni: Do you find it depressing that chess computers are getting so strong? Shannon: I am not depressed by it. I am rooting for the machines! I have always been on the machines' side. Ha-ha! Betty Shannon: Some people get livid when he says that. Shannon: I am not depressed by machines getting better. Whether people will be replaced by machines that have gotten smarter in all things, I can't say. Within a century or so, machines will be doing almost everything better than we can. They already do factory work better than we can, but the highly intellectual stuff is going to come later. It gets harder and harder as you get higher and higher in this game. Omni: Do you agree with Norbert Wiener's denial of any basic distinction between life and nonlife, man and machine? Shannon: That's a heavily loaded question there! I'm an atheist to begin with. I believe in evolutionary theory and that we are basically machines but of a very complex type, far more so than any machine that man has made yet. So that's both a yes and a no. Mechanical doesn't just mean that metal and gears are involved, of course. We are the extreme case: a natural mechanical device. I see no God involved. Omni: Will robots be complex enough to be friends of people? Shannon: I think so. I myself could very easily imagine that happening. I see no limit to the capabilities of machines. As microchips get smaller and faster, I can see them getting better than we are. I can visualize a time in the future when we will be to robots as dogs are to humans. Omni: Can you imagine a robot president of the United States? Shannon: Could be, but I think by then you wouldn't speak of the United States anymore. The world will have a totally different organization. Omni: Is it a big leap from the pedestrian routines of today's chess computers to machines that could grapple, seemingly in a creative, intuitive fashion, with the problems of higher mathematics? Shannon: I see computers proving theorems that have been sitting around that nobody's proved. I don't yet see them creating theories, that is, discovering a new branch of mathematics, as many great mathematicians have in the past. That's a broader, wider thing—more like writing a play—and will be a lot longer in coming. Omni: Is your famous proof that a reliable circuit can be built from unreliable components relevant to the brain's operations? Shannon: The brain can suffer all kinds of damage and yet can still handle things pretty well. It must use some redundancy to take care of faulty operations, such as the death of certain neurons. The modern desk computer generally has no redundancy, so if one part gets into trouble, that will show up in later operations. That we manage to live in spite of all kinds of internal troubles suggests that the brain's design involves a great deal of redundancy or parallelism of multiple units. Omni: Your paper shows that if the relays closed only sixty percent of the time when triggered, you could have highly effective circuitry. Could the brain be using such an approach? Shannon: That the brain has ten billion neurons probably means it was cheaper for biology to make more components than to work out sophisticated circuits. Yet I am totally astounded at how clever and sophisticated some of the things we see in human or animal bodies are. Such long-term, sophisticated changes could be what happened in the brain, but an easier way would be to use paralleling and multiplication to reduce errors of individual neuron operation. And when it all gets going, we have these clever people like Einstein. ... Omni: Has your ambition waned at all? Shannon: I was never motivated by the notion of winning prizes or the desire for financial gain. My motivation in science has always been curiosity about something: How is it put together? What laws or rules govern this situation? Are there any theorems one can prove about what one can or can’t do? After I had found answers, it was always painful to publish, which is where you get the acclaim. Many things I have done and never written up at all. Too lazy, I guess. I have got a file upstairs of unfinished papers! Ha-ha-ha! But that’s true of most of the good scientists I know. Just knowing for ourselves is probably our main motivation."

"Although perhaps of no practical importance, the question is of theoretical interest, and it is hoped that a satisfactory solution of this problem will act as a wedge in attacking other problems of a similar nature and of greater significance."

"Well, I got interested in it when Shannon's and Wiener's work appeared. The curious thing is that, during several years, between '41 and '45, Claude Shannon and I lived in the same house at 51 West 11th Street. It was a small brownstone belonging to an old Italian who rented studios. Shannon was in one and I in another."

"In the past, the community of scholars has made it a custom to furnish scientific information to any person seriously seeking it. However, we must face these facts: The policy of the government itself during and after the war, say in the bombing of Hiroshima and Nagasaki, has made it clear that to provide scientific information is not a necessarily innocent act, and may entail the gravest consequences. One therefore cannot escape reconsidering the established custom of the scientist to give information to every person who may inquire of him."

"The experience of the scientists who have worked on the atomic bomb has indicated that in any investigation of this kind the scientist ends by putting unlimited powers in the hands of the people whom he is least inclined to trust with their use."

"[T]he best material model of a cat is another, or preferably the same cat."

"The measures taken during the war by our military agencies, in restricting the free intercourse among scientists on related projects or even on the same project have gone so far that it is clear that if continued in time of peace, this policy will lead to the total irresponsibility of the scientist, and, ultimately, to the death of science. ...The interchange of ideas, which is one of the greatest traditions of science, must of course receive certain limitations when the scientist becomes an arbiter of life and death. ..."

"I do not expect to publish any future work of mine which may do damage in the hands of irresponsible militarists..."

"There are no answers, only cross-references."

"Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all. One of the chief duties of a mathematician in acting as an advisor to scientists is to discourage them from expecting too much of mathematicians."

"What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead."

"It is my thesis that machines can and do transcend some of the limitations of their designers... although they are theoretically subject to human criticism, such criticism may be ineffective until a time long after it is relevant. By the very slowness of our human activities, our effective control of our machines may be nullified. If the rules for victory in a war game do not correspond to what we actually wish for our country, it is more likely that such a machine may produce a policy which will win a nominal victory on points, at the cost of every interest we have at heart, even that of national survival."

"The terms "black box" and "white box" are convenient and figurative expressions of not very well determined usage. I shall understand by a black box a piece of apparatus, such as four-terminal networks with two input and two output terminals, which performs a definite operation on the present and past of the input potential, but for which we do not necessarily have any information of the structure by which this operation is performed. On the other hand, a white box will be similar network in which we have built in the relation between input and output potentials in accordance with a definite structural plan for securing a previously determined input-output relation."

"The most fruitful areas for the growth of the sciences were those which had been neglected as a no-man's land between the various established fields."

"Since Leibniz there has perhaps been no man who has had a full command of all the intellectual activity of his day. Since that time, science has been increasingly the task of specialists, in fields which show a tendency to grow progressively narrower... Today there are few scholars who can call themselves mathematicians or physicists or biologists without restriction. A man may be a topologist or a coleopterist. He will be filled with the jargon of his field, and will know all its literature and all its ramifications, but, more frequently than not, he will regard the next subject as something belonging to his colleague three doors down the corridor, and will consider any interest in it on his own part as an unwarrantable breach of privacy... There are fields of scientific work, as we shall see in the body of this book, which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology; in which every single notion receives a separate name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field. It is these boundary regions which offer the richest opportunities to the qualified investigator. They are at the same time the most refractory to the accepted techniques of mass attack and the division of labor. If the difficulty of a physiological problem is mathematical in essence, then physiologists ignorant of mathematics will get precisely as far as one physiologists ignorant of mathematics, and no further. If a physiologist who knows no mathematics works together with a mathematician who knows no physiology, the one will be unable to state his problem in terms that the other can manipulate, and the second will be unable to put the answers in any form that the first can understand... A proper exploration of these blank spaces on the map of science could only be made by a team of scientists, each a specialist in his own field but each possessing a thoroughly sound and trained acquaintance with the fields of his neighbors; all in the habit of working together, of knowing one another's intellectual customs, and of recognizing the significance of a colleague's new suggestion before it has taken on a full formal expression. The mathematician need not have the skill to conduct a physiological experiment, but he must have the skill to understand one, to criticize one, and to suggest one. The physiologist need not be able to prove a certain mathematical theorem, but he must be able to grasp its physiological significance and to tell the mathematician for what he should look. We had dreamed for years of an institution of independent scientists, working together in one of these backwoods of science, not as subordinates of some great executive officer, but joined by the desire, indeed by the spiritual necessity, to understand the region as a whole, and to lend one another the strength of that understanding."

"As to sociology and anthropology, it is manifest that the importance of information and communication as mechanisms of organization proceeds beyond the individual into the community. On the other hand, it is completely impossible to understand social communities such as those of ants without a thorough investigation of their means of communication, and we were fortunate enough to have the aid of Dr. Schneirla in this matter. For the similar problems of human organization, we sought help from the anthropologists Drs. Bateson and Margaret Mead; while Dr. Morgenstern of the Institute for Advanced Study was our adviser in the significant field of social organization belong to economic theory. His very important joint book on games with Dr. von Neumann, by the way, represents a most interesting study of social organization from the point of view of methods closely related to, although distinct from, the subject matter of cybernetics. Dr. Lewin and others represented the newer work on the theory of opinion sampling and the practice of opinion making, and Dr. F. C. S. Northrup was interested in assaying the philosophical significance of our work."

"As I have already hinted, one of the directions of work which the realm of ideas of the Macy meetings has suggested concerns the importance of the notion and the technique of communication in the social system. It is certainly true that the social system is an organization like the individual, that it is bound together by a system of communication, and that it has a dynamics in which circular processes of a feedback nature play an important part. This is true, both in the general fields of anthropology and sociology and in the more specific field of economics; and the very important work, which we have already mentioned, of von Neumann and Morgenstern on the theory of games enters into this range of ideas. On this basis, Drs. Gregory Bateson and Margaret Mead have urged me, in view of the intensely pressing nature of the sociological and economic problems of the present age of confusion, to devote a large part of my energies to the discussion of this side of cybernetics."

"Let it be remarked ... that an important difference between the way in which we use the brain and the machine is that the machine is intended for many successive runs, either with no reference to each other, or with a minimal, limited reference, and that it can be cleared between such runs; while the brain, in the course of nature, never even approximately clears out its past records. Thus the brain, under normal circumstances, is not the complete analogue of the computing machine but rather the analogue of a single run on such a machine. We shall see later that this remark has a deep significance in psychopathology and in psychiatry."

"}|Information is information|"

"The odors perceived by the ant seem to lead to a highly standardized course of conduct; but the value of a simple stimulus, such as an odor, for conveying information depends not only on the information conveyed by the stimulus itself but on the whole nervous constitution of the sender and receiver of the stimulus as well. Suppose I find myself in the woods with an intelligent savage who cannot speak my language and whose language I cannot speak. Even without any code of sign language common to the two of us, I can learn a great deal from him. All I need to do is to be alert to those moments when he shows the signs of emotion or interest. I then cast my eyes around, perhaps paying special attention to the direction of his glance, and fix in my memory what I see or hear. It will not be long before I discover the things which seem important to him, not because he has communicated them to me by language, but because I myself have observed them. In other words, a signal without an intrinsic content may acquire meaning in his mind by what he observes at the time, and may acquire meaning in my mind by what I observed at the time. The ability that he has to pick out the moments of my special, active attention is in itself a language as varied in possibilities as the range of impressions that the two of us are able to encompass. Thus social animals may have an active, intelligent, flexible means of communication long before the development of language."

"A group may have more group information or less group information than its members. A group of non-social animals, temporarily assembled, contains very little group information, even though its members may possess much information as individuals. This is because very little that one member does is noticed by the others and is acted on by them in a way that goes further in the group. On the other hand, the human organism contains vastly more information, in all probability, than does any one of its cells. There is thus no necessary relation in either direction between the amount of racial or tribal or community information and the amount of information available to the individual."

"As in the case of the individual, not all the information which is available to the race at one time is accessible without special effort. There is a well-known tendency of libraries to become clogged by their own volume; of the sciences to develop such a degree of specialization that the expert is often illiterate outside his own minute specialty. Dr. Vannevar Bush has suggested the use of mechanical aids for the searching through vast bodies of material. These probably have their uses, but they are limited by the impossibility of classifying a book under an unfamiliar heading unless some particular person has already recognized the relevance of that heading for that particular book. In the case where two subjects have the same technique and intellectual content but belong to widely separated fields, this still requires some individual with an almost Leibnizian catholicity of interest."

"It is the thesis of this book that society can only be understood through a study of the messages and the communication facilities which belong to it; and that in the future development of these messages and communication facilities, messages between man and machines, between machines and man, and between machine and machine, are destined to play an ever-increasing part"

"To live effectively is to live with adequate information."

"It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus. This complex of behavior is ignored by the average man, and in particular does not play the role that it should in our habitual analysis of society; for just as individual physical responses may be seen from this point of view, so may the organic responses of society itself. I do not mean that the sociologist is unaware of the existence and complex nature of communications in society, but until recently he has tended to overlook the extent to which they are the cement which binds its fabric together."

"What many of us fail to realize is that the last four hundred years are a highly special period in the history of the world. The pace at which changes during these years have taken place is unexampled in earlier history, as is the very nature of these changes. This is partly the results of increased communication, but also of an increased mastery over nature, which on a limited planet like the earth, may prove in the long run to be an increased slavery to nature. For the more we get out of the world the less we leave, and in the long run we shall have to pay our debts at a time that may be very inconvenient for our own survival."

"Progress imposes not only new possibilities for the future but new restrictions. It seems almost as if progress itself and our fight against the increase of entropy intrinsically must end in the downhill path from which we are trying to escape."

"May we have the courage to face the eventual doom of our civilization as we have the courage to face the certainty of our personal doom. The simple faith in progress is not a conviction belonging to strength, but one belong to acquiescence and hence to weakness."

"We are but whirlpools in a river of ever-flowing water. We are not the stuff that abides, but patterns that perpetuate themselves."

"Until we in the community have made up our minds that what we really want is expiation, or removal, or reform, or or the discouragement of potential criminals, we shall get none of these, but only a confusion in which crime breeds more crime."

"That country will have the greatest security whose informational and scientific situation is adequate to meet the demands that may be put on it—the country in which it is fully realized that information is important as a stage in the continuous process by which we observe the outer world, and act effectively upon it. In other words, no amount of scientific research, carefully recorded in books and papers, and then put into our libraries with labels of secrecy, will be adequate to protect us for any length of time in a world where the effective level of information is perpetually advancing."

"We are in the position of the man who has only two ambitions in life. One is to invent the universal solvent which will dissolve any solid substance, and the second is to invent the universal container which will hold any liquid. Whatever this inventor does, he will be frustrated."

"What sometimes enrages me and always disappoints and grieves me is the preference of great schools of learning for the derivative as opposed to the original, for the conventional and thin which can be duplicated in many copies rather than the new and powerful, and for arid correctness and limitation of scope and method rather than for universal newness and beauty, wherever it may be seen."

"Any labor which competes with slave labor must accept the economic conditions of slave labor."

"The sense of tragedy is that the world is not a pleasant little nest made for our protection, but a vast and largely hostile environment, in which we can achieve great things only by defying the gods; and that this defiance inevitably brings its own punishment."

"A faith which we follow upon orders imposed from outside is no faith, and a community which puts its dependence upon such a pseudo-faith is ultimately bound to ruin itself because of the paralysis which the lack of a healthy growing science imposes upon it."

"Physics is at present a mass of partial theories which no man has yet been able to render truly and clearly consistent. It has been well said that the modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday he is praying. . . that someone will find the reconciliation between the two views."

"We mathematicians who operate with nothing more expensive than paper and possibly printers' ink are quite reconciled to the fact that, if we are working in an active field, our discoveries will commence to be obsolete at the moment that they are written down or even at the moment they are conceived. We know that for a long time everything we do will be nothing more than the jumping off point for those who have the advantage of already being aware of our ultimate results. This is the meaning of the famous apothegm of Newton, when he said, "If I have seen further than other men, it is because I have stood on the shoulders of giants"."

"A significant idea of organization cannot be obtained in a world in which everything is necessary and nothing is contingent'"

"The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation."

"Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stonelike logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgement of values, quite parallel to the judgement of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician."

"The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus."

"[T]he future offers very little hope for those who expect that our new mechanical slaves will offer us a world in which we may rest from thinking. Help us they may, but at the cost of supreme demands upon our honesty and our intelligence. The world of the future will be an ever more demanding struggle against the limitations of our intelligence, not a comfortable hammock in which we can lie down to be waited upon by our robot slaves."

"His office was a few doors down the hall from mine. He often visited my office to talk to me. When my office was moved after a few years, he came in to introduce himself. He didn't realize I was the same person he had frequently visited; I was in a new office so he thought I was someone else."

"He wrote a very complicated integral on the blackboard, and then wrote '=6' with no intermediate steps. An intrepid student challenged him: Can you do that another way? He left the room for about 20 minutes. He returned, erased the '=6' and wrote '=6' saying that yes indeed he could."

"He was short and rotund. Because he stood close to the blackboard, students sat in seats far to the sides to be able to get an angled look at what he was writing. Only the graduate teaching assistant sat in the middle. This was still a problem because Wiener sometimes erased with the left hand what he wrote with the right hand."

"He went to a conference and parked his car in the big lot. When the conference was over, he went to the lot but forgot where he parked his car. He even forgot what his car looked like. So he waited until all the other cars were driven away, then took the car that was left."

"When he and his family moved to a new house a few blocks away, his wife gave him written directions on how to reach it, since she knew he was absent-minded. But when he was leaving his office at the end of the day, he couldn't remember where he put her note, and he couldn't remember where the new house was. So he drove to his old neighborhood instead. He saw a young child and asked her, "Little girl, can you tell me where the Wieners moved?" "Yes, Daddy," came the reply, "Mommy said you'd probably be here, so she sent me to show you the way home"."

"One day he was sitting in the campus lounge, intensely studying a paper on the table. Several times he'd get up, pace a bit, then return to the paper. Everyone was impressed by the enormous mental effort reflected on his face. Once again he rose from his paper, took some rapid steps around the room, and collided with a student. The student said, "Good afternoon, Professor Wiener." Wiener stopped, stared, clapped a hand to his forehead, said "Wiener — that's the word," and ran back to the table to fill the word "wiener" in the crossword puzzle he was working on."

"He drove 150 miles to a math conference at Yale University. When the conference was over, he forgot he came by car, so he returned home by bus. The next morning, he went out to his garage to get his car, discovered it was missing, and complained to the police that while he was away, someone stole his car."

"In appearance and behaviour, Norbert Wiener was a baroque figure, short, rotund, and myopic, combining these and many qualities in extreme degree. His conversation was a curious mixture of pomposity and wantonness. He was a poor listener. His self-praise was playful, convincing and never offensive. He spoke many languages but was not easy to understand in any of them. He was a famously bad lecturer."

"As I near the end of my personal recollections of life at M.I.T., it is impossible to refrain from relating my eye-witness stories about a brilliant man, Norbert Wiener, and his lovable eccentricities. I took two semester courses under Professor Wiener: one was Fourier Series and Fourier Integrals, and the other was, I believe, Operational Calculus. It is vivid in my memory that Professor Wiener would always come to class without any lecture notes. He would first take out his big handkerchief and blow his nose very vigorously and noisily. He would pay very little attention to his class and would seldom announce the subject of his lecture. He would face the blackboard, standing very close to it because he was extremely near-sighted. Although I usually sat in the front row, I had difficulty seeing what he wrote. Most of the other students could not see anything at all. It was most amusing to the class to hear Professor Wiener saying to himself, "This was very wrong, definitely." He would quickly erase all he had written down. He would then start all over again, and sometimes murmur to himself, "This looks all right so far." Minutes later, "This cannot be right either," and he would rub it all out again. This on- again, off-again process continued until the bell signaled the end of the hour. Then Professor Wiener would leave the room without even looking at his audience."

"As a human being Wiener was above all stimulating. I have known some who found the stimulus unwelcome. He could offend publicly by snoring through a lecture and then asking an awkward question in the discussion, and also privately by proffering information and advice on some field remote from his own to an august dinner companion. I like to remember Wiener as I once saw him late at night in Magdalen College, Oxford, surrounded by a spellbound group of undergraduates, talking, endlessly talking. We are all the poorer that he now talks no more."

"He was horrified by Hiroshima and the prominent role of scientists in the development of atomic weapons. The tremendous expense of the Manhattan Project, he argued, necessitated the use of bombs to justify the investment. But that was not the only compulsion, nor was it patriotism. "The pressure to use the bomb, with its full killing power," he wrote later, "was not merely great from a patriotic point of view but was quite as great from the point of view of the personal fortunes of people involved in its development." Wiener did not think that the use of the bomb on Japan, on Orientals, was without significance. "I was acquainted with more than one of these popes and cardinals of applied science, and I knew very well how they underrated aliens of all sorts, particularly those not of the European race.""

"Are physical forces alone at work there, or has evolution begotten something more complex, something not unakin to what we know on Earth as life?"

"The whole object of science is to synthesize, and so simplify; and did we but know the uttermost of a subject we could make it singularly clear."

"Formulae are the anaesthetics of thought, not its stimulants and to make any one think is far better worth while than cramming him with ill-considered, and therefore indigestible, learning."

"That Mars is inhabited by beings of some sort or other we may consider as certain as it is uncertain what these beings may be."

"War is a survival among us from savage times and affects now chiefly the boyish and unthinking element of the nation. The wisest realize that there are better ways for practicing heroism and other and more certain ends of insuring the survival of the fittest. It is something a people outgrow. But whether they consciously practice peace or not, nature in its evolution eventually practices it for them, and after enough of the inhabitants of a globe have killed each other off, the remainder must find it more advantageous to work together for the common good."

"So far as thought may peer into the past, the epic of our solar system began with a great catastrophe. Two suns met. What had been, ceased; what was to be, arose. Fatal to both progenitors, the event dated a stupendous cosmic birth."

"In the great desert of northern Arizona the traveller, threading his way across a sage-brush and cacti plain shut in by abrupt-sided shelves of land rising here and there some hundreds of feet higher, suddenly comes upon a petrified forest."

"Quantum mechanics is reformulated, in a way which eliminates its present dependence on the special treatment of observation of a system by an external observer."

"As an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree."

"The physical "reality" is assumed to be the wave function of the whole universe itself."

"[The Many-worlds interpretation is the] only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world."

"Hugh Everett's work has been described by many people in terms of many worlds, the idea being that every one of the various alternative histories, branching histories, is assigned some sort of reality."

"If you want to get an interesting perspective do not think of Hugh as a traditional 20th century physicist but more of a Renaissance man with interests and skills in many different areas. He was smart and lots of things interested him and he brought the same general conceptual methodology to solve them. The subject matter was not so important as the solution ideas."

"Someone once noted that Hugh Everett should have been declared a "national resource," and given all the time and resources he needed to develop new theories."

"My father, Hugh Everett, III, author of the Many Worlds Theory, was a quiet man during the eighteen or so years I shared a house with him. Turns out he was depressed over a sad childhood and then being dismissed as a kook, only later - too late - to be recognized as a genius."

"I think about how angry I was that my dad didn't take better care of himself. How he never went to a doctor, let himself become grossly overweight, smoked three packs a day, drank like a fish and never exercised. But then I think about how his colleague mentioned that, days before dying, my dad had said he lived a good life and that he was satisfied. I realize that there is a certain value in my father's way of life. He ate, smoked and drank as he pleased, and one day he just suddenly and quickly died. Given some of the other choices I'd witnessed, it turns out that enjoying yourself and then dying quickly is not such a hard way to go."

"Lysenkoism is held up by bourgeois commentators as the supreme demonstration that conscious ideology cannot inform scientific practice and that "ideology has no place in science." On the other hand, some writers are even now maintaining a Lysenkoist position because they believe that the principles of dialectical materialism contradict the claims of genetics. Both of these claims stem from a vulgarisation of Marxist philosophy through deliberate hostility, in the first case, or ignorance, in the second. Nothing in Marx, Lenin or Mao contradicts the particular physical facts and processes of a particular set of natural phenomena in the objective world, because what they wrote about nature was at a high level of abstraction. The error of the Lysenkoist claim arises from attempting to apply a dialectical analysis of physical problems from the wrong end. Dialectical materialism is not, and has never been, a programmatic method for solving particular physical problems. Rather, dialectical analysis provides an overview and a set of warning signs against particular forms of dogmatism and narrowness of thought. It tells us, "Remember that history may leave an important trace. Remember that being and becoming are dual aspects of nature. Remember that conditions change and that the conditions necessary to the initiation of some process may be destroyed by the process itself. Remember to pay attention to real objects in space and time and not lose them utterly in idealized abstractions. Remember that qualitative effects of context and interaction may be lost when phenomena are isolated." And above all else, "Remember that all the other caveats are only reminders and warning signs whose application to different circumstances of the real world is contingent.""

"It is time for students of the evolutionary process, especially those who have been misquoted and used by the creationists, to state clearly that evolution is a fact, not theory, and that what is at issue within biology are questions of details of the process and the relative importance of different mechanisms of evolution. It is a fact that the earth, with liquid water, is more than 3.6 billion years old. It is a fact that cellular life has been around for at least half of that period and that organized multicellular life is at least 800 million years old. It is a fact that major life forms now on earth were not at all represented in the past. There were no birds or mammals 250 million years ago. It is a fact that major life forms of the past are no longer living. There used to be dinosaurs and Pithecanthropus, and there are none now. It is a fact that all living forms come from previous living forms. Therefore, all present forms of life arose from ancestral forms that were different. Birds arose from nonbirds and humans from nonhumans. No person who pretends to any understanding of the natural world can deny these facts any more than she or he can deny that the earth is round, rotates on its axis, and revolves around the sun. The controversies about evolution lie in the realm of the relative importance of various forces in molding evolution."

"Parts and wholes evolve in consequence of their relationship, and the relationship itself evolves. These are the properties of things that we call dialectical: that one thing cannot exist without the other, that one acquires its properties from its relation to the other, that the properties of both evolve as a consequence of their interpenetration."

"The great attraction of cultural anthropology in the past was precisely that it seemed to offer such a richness of independent natural experiments; but unfortunately it is now clear that there has been a great deal of historical continuity and exchange among those "independent" experiments, most of which have felt the strong effect of contact with societies organized as modern states. More important, there has never been a human society with unlimited resources, of three sexes, or the power to read other people's minds, or to be transported great distances at the speed of light. How then are we to know the effect on human social organization and history of the need to scrabble for a living, or of the existence of males and females, or of the power to make our tongues drop manna and so to make the worse appear the better reason? A solution to the epistemological impotence of social theory has been to create a literature of imagination and logic in which the consequences of radical alterations in the conditions of human existence are deduced. It is the literature of science fiction. … [S]cience fiction is the laboratory in which extraordinary social conditions, never possible in actuality, are used to illumine the social and historical norm. … Science fiction stories are the Gedanken experiments of social science."

"With great perception, Sagan sees that there is an impediment to the popular credibility of scientific claims about the world, an impediment that is almost invisible to most scientists. Many of the most fundamental claims of science are against common sense and seem absurd on their face. Do physicists really expect me to accept without serious qualms that the pungent cheese that I had for lunch is really made up of tiny, tasteless, odorless, colorless packets of energy with nothing but empty space between them? Astronomers tell us without apparent embarrassment that they can see stellar events that occurred millions of years ago, whereas we all know that we see things as they happen. (…) Our willingness to accept scientific claims that are against common sense is the key to an understanding of the real struggle between science and the supernatural. We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door. The eminent Kant scholar Lewis Beck used to say that anyone who could believe in God could believe in anything. To appeal to an omnipotent deity is to allow that at any moment the regularities of nature may be ruptured, that miracles may happen."

"The fallacy of genetic determinism is to suppose that the genes "make" the organism. It is a basic principle of developmental biology that organisms undergo a continuous development from conception to death, a development that is the unique consequence of the interaction of the genes in their cells, the temporal sequence of environments through which the organisms pass, and random cellular processes that determine the life, death, and transformation of cells. As a result, even the fingerprints of identical twins are not identical. Their temperaments, mental processes, abilities, life choices, disease histories, and death certainly differ despite the determined efforts of many parents to enforce as great a similarity as possible."

"The vulgarization of Darwinism that sees the "struggle for existence" as nothing but the competition for some environmental resource in short supply ignores the large body of evidence about the actual complexity of the relationship between organisms and their resources."

"The social scientist is in a difficult, if not impossible position. On the one hand there is the temptation to see all of society as one's autobiography writ large, surely not the path to general truth. On the other, there is the attempt to be general and objective by pretending that one knows nothing about the experience of being human, forcing the investigator to pretend that people usually know and tell the truth about important issues, when we all know from our lives how impossible that is. How, then, can there be a "social science"? The answer, surely, is to be less ambitious and stop trying to make sociology into a natural science although it is, indeed, the study of natural objects. There are some things in the world that we will never know and many that we will never know exactly. Each domain of phenomena has its characteristic grain of knowability. Biology is not physics, because organisms are such complex physical objects, and sociology is not biology because human societies are made by self-conscious organisms. By pretending to a kind of knowledge that it cannot achieve, social science can only engender the scorn of natural scientists and the cynicism of the humanists."

"It is characteristic of the design of scientific research that exquisite attention is devoted to methodological problems that can be solved, while the pretense is made that the ones that cannot be solved are really nothing to worry about. On the one hand, biologists will apply the most critical and demanding canons of evidence in the design of measuring instruments or in the procedure for taking an unbiased samples of organisms to be tested, but when asked whether the conditions in the laboratory are likely to be relevant to the situation in nature, they will provide a hand-waving intuitive argument filled with unsubstantiated guesses and prejudices because, in the end, that is all they can do."

"The division between those who try to learn about the world by manipulating it and those who can only observe it had led, in natural science, to a struggle for legitimacy. The experimentalists look down on the observers as merely telling uncheckable just-so stories, while the observers scorn the experimentalists for their cheap victories over excessively simple phenomena. In biology the two camps are now generally segregated in separate academic departments where they can go about their business unhassled by their unbelievers. But the battle is unequal because the observers' consciousness of what it is to do "real" science has been formed in a world dominated by the manipulators of nature. The observers then pretend to an exactness that they cannot achieve and they attempt to objectify a part of nature that is completely accessible only with the air of subjective tools."

"[T]he psychic and physical characteristics of human beings, and the differences between individuals, are the consequence of an interaction between the genes that are present in the fertilized egg and the sequence of environmental circumstances that the developing organism experiences during its entire life history. With a few exceptions, like cystic fibrosis where possession of the defective genotype leads ineluctably to the disease, or language acquisition where the language spoken depends only on experience and not at all on genotype, human characteristics are all subject to this interaction of forces. There are, moreover, random events in cell growth and differentiation that are neither genetic nor environmental in the usual sense, and which play an extremely important part in development, especially in behavioral traits."

"An important consequence of the unique interaction between internal and external forces … is that knowledge of genetic differences contains no information at all about whether a characteristic can be changed by environmental and social arrangements. The most elementary error about genetics and development is to suppose that “genetic” is the opposite of “changeable” and that an answer to the question “how much can a trait be changed by social, historical, and individual circumstances” is given by an answer to the question “how important are genes.”"

"Genetics is the study of similarity between relatives, and the problem of human genetics is that, in a species with a family and social structure and a taboo against manipulating individual life histories experimentally, there is a confounding between the similarity of relatives that arises from biological causes and the similarity that arise from social causes."

"To say that genetic differences are relevant to hetero- and homosexuality is not, however, to say that there are “genes for homosexuality” or even that there is a “genetic tendency to homosexuality.” This critical point can be illustrated by an example I owe to the philosopher of science, Elliott Sober. If we look at the chromosomes of people who knit and those who do not, we will find that with few exceptions, knitters have two X chromosomes, while people with one X and one Y chromosome almost never knit. Yet it would be absurd to say that we had discovered genes for knitting. The possession of two X chromosomes causes an embryo, with rare exceptions, to develop into an anatomical and physiological female, while the possession of a Y chromosome leads almost always to male development, and in our culture women are taught to knit while men are not. The beauty of this example is its historical (and geographical) contingency. Had we made the observations before the end of the eighteenth century (or even now in a few Irish, Scottish and Newfoundland communities), the result would have been reversed. Hand knitting was men’s work before the introduction of knitting machines around 1790, and was turned into a female domestic occupation only when mechanization made it economically marginal."

"Lewontin visited an economics class... a few years ago to talk to the students. In a kind of neo-Darwinian jockeying, he said that evolutionary changes are due to the Fisher-Haldane mechanisms: mutation, emigration, immigration, and the like. ...His elaborate cost-benefit mathematical treatment was devoid of chemistry and biology. I asked him why... when he himself was pointing to serious flaws related to the fundamental assumptions, did he teach such nonsense? ...His response was that there were two reasons: the first was "P.E." …I asked. What is "P.E." …he replied, "P.E. is 'physics envy,'"… His second reason was even more insidious: if he didn't couch his studies in neo-Darwinian style... he wouldn't be able to obtain grant money that was set up to support this kind of work."

"The primary challenge of this cosmological transformation of consciousness is the awareness that each being in the universe is an origin of the universe. "The center of the cosmos" refers to that place where the great birth of the universe happened at the beginning of time, but it also refers to the upwelling of the universe as river, as star, as raven, as you, the universe surging into existence anew. The consciousness that learns it is at the origin point of the universe is itself an origin of the universe. The awareness that bubbles up each moment that we identify as ourselves is rooted in the originating activity of the universe. We are all of us arising together at the center of the cosmos."

"Earth was once molten rock, and now it makes spaceships."

"This is the greatest discovery of the scientific enterprise: You take hydrogen gas, and you leave it alone, and it turns into rosebushes, giraffes, and humans."

"With the appearance of the human, the coding process of life burst beyond the DNA molecule and began carving its information in stone!"

"If you if you take Buddhism and Christianity and so forth there's a kind of battle — a subtle sort of struggle taking place because they're not standing in a common ground but … take the Earth or ecology then suddenly they can begin to explore what they have to offer. So I do think I do think absolutely that … there will be a flourishing of religions, not a withering away. And they will flourish to the degree that they will move into the context of planet and universe. I even think that as a matter of fact that … some of the central insights of the religions are more powerfully presented by what we know about the universe now then when they were first formulated."

"There's a great phrase from Eric Jantsch … and he says, "these self-organizing dynamics are in every place in the universe, waiting at their marks". I love that phrase because you get that … the power for making water exists everywhere in the universe but the conditions have to be right. But if the conditions are right, then these self-organizing dynamics leap to it. So I think it's something like that, that the possibility for sentience has always been there but has been waiting for a chance to really display."

"The more I learn about light the more I realize, man, we don't know anything about light... It's just bizarre... a particle has its own proper time which slows down as you speed up. But at the speed of light... there's no time. That's bizarre … that we can, right now, as you know, see — interact with the light that has come from the birth of the universe. So … from our point of view, that light traveled for 14 billion years but from the point of view of the light it's the moment of creation."

"I think the discovery of nonlocality is touching in on the whole. So that these these seemingly separate events are somehow connected through the whole. … you have this larger enveloping field and we're, you know, just beginning to understand something about that... so I love that discovery although I don't think we're anywhere near really knowing what we've come upon."

"The break-through moments are unimaginable until they happen."

"I have a sense that something amazing is at work … I think our planet is actually moving into a time of profound harmony and fecundity and peace but whether that's going to take 600 years or 6 days I don't know. I mean, I think that as humans begin to take seriously... the planetary dimension of conscious self-awareness, then we will become homonized versions of natural selection — so that we will begin to make decision with the large scale dynamic of the planet in mind. So I see that we're actually entering into a transformation of the human species out of the modern period into this new era... It may take centuries... but like the past and it's catastrophes I think that's... what's taking place in the midst of so many hardships."

"What's evil for the hawk is the mouse because, you know, the mouse is quick and gets away but I did this one realization every scientist goes through at one point... if you gave the hawk power, the power of God, the first thing the hawk might do is to slow down the mouse. But then the hawk would lose it's speed. And then if you slow the mouse all the way down, so it can just barely move, the hawk would lose its flight. So that in a weird way the tension between those two say natural enemies is what gives birth to their beauty. So I definitely feel that the tension we have right now within the human community in particular — that those are ultimately going to be resolved with a deeper harmony and a deeper appreciation for one another."

"Every moment we're making decisions. If you want to understand the universe as a whole you'd have to include all those decisions including our own lives so that even in the future our presence is going to be felt one way or the other — so I think … our death as being — it's a death to a micro-phase self or a small self … it's a death into our larger self in that … this whole vast adventure is our larger identity."

"When, where, and how were you, Joseph Smith, first called? How old were you? and what were you qualifications? I was between fourteen and fifteen years of age. Had you been to college? No. Had you studied in any seminary of learning? No. Did you know how to read? Yes. How to write? Yes. Did you understand much about arithmetic? No. About grammar? No. Did you understand all the branches of education which are generally taught in our common schools? No. But yet you say the Lord called you when you were but fourteen or fifteen years of age? How did he call you? I will give you a brief history as it came from his own mouth. I have often heard him relate it. He was wrought upon by the Spirit of God, and felt the necessity of repenting of his sins and serving God. He retired from his father's house a little way, and bowed himself down in the wilderness, and called upon the name of the Lord. He was inexperienced, and in great anxiety and trouble of mind in regard to what church he should join. He had been solicited by many churches to join with them, and he was in great anxiety to know which was right. He pleaded with the Lord to give him wisdom on the subject; and while he was thus praying, he beheld a vision, and saw a light approaching him from the heavens; and as it came down and rested on the tops of the trees, it became more glorious; and as it surrounded him, his mind was immediately caught away from beholding surrounding objects. In this cloud of light he saw two glorious personages; and one, pointing to the other, said, "Behold my beloved son! hear ye him.""

"He saw the light gradually approaching him until it rested upon the tops of the trees. He beheld that the leaves of the trees were not consumed by it, although its brightness, apparently, was sufficient, as he at first thought, to consume everything before it. But the trees were not consumed by it, and it continued to descend until it rested upon him and enveloped him in its glorious rays. When he was thus encircled about with this pillar of fire his mind was caught away from every object that surrounded him, and he was filled with the visions of the Almighty, and he saw, in the midst of this glorious pillar of fire, two glorious personages, whose countenances shone with an exceeding great lustre. One of them spoke to him, saying, while pointing in the other, "This is my beloved Son in whom I am well pleased, hear ye him.""

"By and by an obscure individual, a young man, rose up, and, in the midst of all Christendom, proclaimed the startling news that God had sent an angel to him; that through his faith, prayers, and sincere repentance he had beheld a supernatural vision, that he had seen a pillar of fire descend from Heaven, and saw two glorious personages clothed upon with this pillar of fire, whose countenance shone like the sun at noonday; that he heard one of these personages say, pointing to the other, 'This is my beloved Son, hear ye him.' This occurred before this young man was fifteen years of age; and it was a startling announcement to make in the midst of a generation so completely given up to the traditions of their fathers; and when this was proclaimed by this young, unlettered boy to the priests and the religious societies in the State of New York, they laughed him to scorn. 'What!' said they, "visions and revelations in our day! God speaking to men in our day!" They looked upon him as deluded; they pointed the finger of scorn at him and warned their congregations against him. 'The canon of Scripture is closed up; no more communications are to be expected from Heaven. The ancients saw heavenly visions and personages; they heard the voice of the Lord; they were inspired by the Holy Ghost to receive revelations, but behold no such thing is to be given to man in our day, neither has there been for many generations past.' This was the style of the remarks made by religionists forty years ago. This young man, some four years afterwards, was visited again by a holy angel."

"By and by an obscure individual, a young man, rose up, and, in the midst of all Christendom, proclaimed the startling news that God had sent an angel to him;... This young man, some four years afterwards, was visited again by a holy angel."

"He saw in this light two glorious personages, one of whom spoke to him, pointing to the other, saying, "This is my beloved Son, hear ye him." This was a glorious vision given to this boy."

"[T]he heavens were opened, and two personages clothed in light or fire descended and stood before him. As soon as this light surrounded him, and he was enclosed or enveloped in it, his mind was caught away from earthly objects and things, and he saw these two glorious personages, their countenances shining with exceeding great brilliancy. One of them, while pointing to the other, addressed him in this language, "Behold my beloved son, hear ye him.""

"Finally the light rested down upon and overwhelmed him in the midst of it, and his mind at the same time seemed to be caught away from surrounding objects, and he saw nothing excepting the light and two glorious personages standing before him in the midst of this light. One of these personages, pointing to the other, said-"Behold my beloved Son, hear ye him.""

"In the year 1823 the angel first came to him, telling him about the plates, also telling him that he would return one year afterwards, when he would give him further instruction. Why this delay? why not commit to his charge the plates at once? It was because of his want of experience. It is true, he had previously received a heavenly vision some four years before, in which he had seen the face of God, the Father."

"God prior to this time, had given revelation to this youth, on many occasions. The first one that he gave to him was in the spring of 1820, before Joseph Smith was of the age of fifteen. Then a wonderful revelation was given to him, the first one he ever received. In a great and glorious open vision, in answer to his prayers, there was the manifestation of two of the great personages in the heavens-not angels, not messengers, but two persons that hold the keys of authority over all the creations of the universe. Who were they? God the Eternal Father and his Son Jesus Christ, through whom God the Father made the worlds!"

"Jesus appeared unto the ancient Nephites, in the northern part of what we call South America…"

"The Apostles were put to death; they were hunted from nation to nation; they wandered about in sheep skins and goat skins in the dens and caves of the earth, of whom the world was unworthy. Their followers were put to death by hundreds, by thousands, by tens of thousands; and after a while there sprang up a people that pretended to be Christians--followers of the meek and lowly Jesus, having no apostles, no inspired men, no revelation, no ministration of angels, none of the characteristics, except a few forms, of the Christian Church as it existed in the first century of the Christian era. This class of men, calling themselves Christian, uniting with the various forms of the pagan religion, adopting many of their ceremonies and institutions, became very popular, and finally some of the pagans embraced Christianity and were placed, as it were, upon the throne, and what they termed Christianity became very popular indeed."

"But by and by the time came when the Christian Church apostatized and turned away, and began to follow after their own wisdom, and the Prophets and Apostles ceased, so far as the affairs of the Christian Church on the earth were concerned. Revelations, and visions, and the various gifts of the spirit were also taken away, according to their unbelief and apostacy; but in the latter days God intends to again raise up a Christian Church upon the earth. Do not be startled, you who think that God will no more have a Church on the earth, for he has promised that he would again have one, and that he would set up his kingdom, and when he does you may look out for a great many Prophets and inspired men; and if you ever see a Church arise, calling itself a Christian Church, and it has not inspired Apostles like those in ancient times, you may know that it is a spurious church, and that it makes pretensions to something that it does not enjoy. If you ever find a church called a Christian Church that has no men to foretell future events, you may know, at once, that it is not a Christian Church. If you find a Christian Church that has not the ancient gifts, for instance the gift of healing, opening the eyes of the blind, unstopping the ears of the deaf, causing the tongue of the dumb to speak and the lame to walk; if you ever find a people calling themselves a Christian Church and they have not these gifts among them, you may know with a perfect knowledge that they do not agree with the pattern given in the New Testament. The Christian Church is always characterized with inspired men, whose revelations are just as sacred as any contained in the Bible; and, if written and published, just as binding upon the human family. The Christian Church will always lay hands upon the sick in the name of Jesus, in order that the sick may be healed. The Christian Church will always have those among its members who have heavenly visions, the ministration of angels, and the various gifts that are promised according to the Gospel."

"We planted our crops in the spring, and they came up, and were looking nicely, and we were cheered with the hopes of having a very abundant harvest. But alas! it very soon appeared as if our crops were going to be swallowed up by a vast horde of crickets, that came down from these mountains-crickets very different to what I used to be acquainted with in the State of New York. They were crickets nearly as large as a man's thumb. They came in immense droves, so that men and women with brush could make no headway against them; but we cried unto the Lord in our afflictions, and the Lord heard us, and sent thousands and tens of thousands of a small white bird. I have not seen any of them lately. Many called them gulls, although they were different from the seagulls that live on the Atlantic coast. And what did they do for us? They went to work, and by thousands and tens of thousands, began to devour them up, and still we thought that even they could not prevail against so large and mighty an army. But we noticed, that when they had apparently filled themselves with these crickets, they would go and vomit them up, and again go to work and fill themselves, and so they continued to do, until the land was cleared of crickets, and our crops were saved. There are those who will say that this was one of the natural courses of events, that there was no miracle in it. Let that be as it may, we esteemed it as a blessing from the hand of God; miracle or no miracle, we believe that God had a hand in it, and it does not matter particularly whether strangers believe or not."

"Another great change happened nearly two thousand years after the earth was made. It was baptized by water. A great flow of water come, the great deep was broken up, the windows of heaven were opened from on high, and the waters prevailed upon the face of the earth, sweeping away all wickedness and transgression-a similitude of baptism for the remission of sins. God requires the children of men to be baptized. What for? For the remission of sins. So he required our globe to be baptized by a flow of waters, and all of its sins were washed away, not one sin remaining."

"The Universalists think they are very charitable. Why? Because they send all to heaven, whether they are good or evil, saints or sinners. Murderers, drunkards, and all classes of society are to dwell together in heaven. And what a heaven it would be!—Methodists contending against Baptists, and Baptists against Methodists, Presbyterians against Quakers, Roman Catholics against Protestants, and Nothingarians against Sectarians, and Sectarians against Nothingarians; and then add to the whole catalogue of contending sects drunkards, blasphemers, whoremongers, murderers, and every species of wicked beings, all jumbled up together. Oh, what a happy place! Brother Kimball says—"And all of them with a revolver and bowie knife at their sides.""

"Sir, I am fully sensible of the greatness of that freedom, which I take with you on the present occasion; a liberty which seemed to me scarcely allowable, when I reflected on that distinguished and dignified station in which you stand, and the almost general prejudice and prepossession, which is so prevalent in the world against those of my complexion. I suppose it is a truth too well attested to you, to need a proof here, that we are a race of beings, who have long labored under the abuse and censure of the world; that we have long been looked upon with an eye of contempt; and that we have long been considered rather as brutish than human, and scarcely capable of mental endowments. Sir, I hope I may safely admit, in consequence of that report which hath reached me, that you are a man far less inflexible in sentiments of this nature, than many others; that you are measurably friendly, and well disposed towards us; and that you are willing and ready to lend your aid and assistance to our relief, from those many distresses, and numerous calamities, to which we are reduced. Now Sir, if this is founded in truth, I apprehend you will embrace every opportunity, to eradicate that train of absurd and false ideas and opinions, which so generally prevails with respect to us ; and that your sentiments are concurrent with mine, which are, that one universal Father hath given being to us all ; and that he hath not only made us all of one flesh, but that he hath also, without partiality, afforded us all the same sensations and endowed us all with the same faculties ; and that however variable we may be in society or religion, however diversified in situation or color, we are all of the same family, and stand in the same relation to him. Sir, if these are sentiments of which you are fully persuaded, I hope you cannot but acknowledge, that it is the indispensible duty of those, who maintain for themselves the rights of human nature, and who possess the obligations of Christianity, to extend their power and influence to the relief of every part of the human race, from whatever burden or oppression they may unjustly labor under ; and this, I apprehend, a full conviction of the truth and obligation of these principles should lead all to."

"How pitiable is it to reflect, that although you were so fully convinced of the benevolence of the Father of Mankind, and of his equal and impartial distribution of these rights and privileges, which he hath conferred upon them, that you should at the same time counteract his mercies, in detaining by fraud and violence so numerous a part of my brethren, under groaning captivity and cruel oppression, that you should at the same time be found guilty of that most criminal act, which you professedly detested in others, with respect to yourselves"

"Evil communication corrupts good manners. I hope to live to hear that good communication corrects bad manners."

"Presumption should never make us neglect that which appears easy to us, nor despair make us lose courage at the sight of difficulties."

"Now let us look too at Benjamin Banneker. Look at his correspondence with Thomas Jefferson. Here's a man, some end part in the absolute center of slavery who laid out the plans for Washington, D.C. Here was a man who had been a slave, and his parents were slaves. One must perceive this and see that he was not caught up by that same system which will smother in an attempt to protect. And one walks down the same century and sees the list of thousands of Black people who said "I've got to break away. Thank you for your caring but I must break away." You cannot blame the family for its attempts to say, "Stay, I can hold you. As long as I can touch you I feel more secure." No matter how it says it. The family may say "You'll never make it." Whatever it says it means stay with me so I can keep my eyes on you. The family is not to be blamed for that."

"I thank you, sincerely, for your letter of the 19th instant, and for the Almanac it contained. No body wishes more than I do, to see such proofs as you exhibit, that nature has given to our black brethren talents equal to those of the other colors of men ; and that the appearance of the want of them, is owing merely to the degraded condition of their existence, both in Africa and America. I can add with truth, that no body wishes more ardently to see a good system commenced, for raising the condition, both of their body and mind, to what it ought to be, as far as the imbecility of their present existence, and other circumstances, which cannot be neglected, will admit. I have taken the liberty of sending your Almanac to Monsieur de Condozett, Secretary of the Academy of Sciences at Paris, and Member of the Philanthropic Society, because I considered it as a document, to which your whole color had a right for their justification, against the doubts which have been entertained of them. I am with great esteem, Sir, Your most obedient Humble Servant…"

"The golden age of mathematics - that was not the age of Euclid, it is ours. (p. 268)"

"For twenty years programming languages have been steadily progressing toward their present condition of obesity; as a result, the study and invention of programming languages has lost much of its excitement. Instead, it is now the province of those who prefer to work with thick compendia of details rather than wrestle with new ideas. Discussions about programming languages often resemble medieval debates about the number of angels that can dance on the head of a pin instead of exciting contests between fundamentally differing concepts. Many creative computer scientists have retreated from inventing languages to inventing tools for describing them. Unfortunately, they have been largely content to apply their elegant new tools to studying the warts and moles of existing languages."

"Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language.""

"Much of my work has come from being lazy. I didn't like writing programs, and so, when I was working on the IBM 701 (an early computer), writing programs for computing missile trajectories, I started work on a programming system to make it easier to write programs."

"Well, that's a subject interested me a lot because I've seen so many young people in our culture today, that emphasizes the success all the time and is always pointing to this success of researchers and developing some wonderful new thing. This pressure to succeed I found has caused many young students who I thought would make a very good researcher start doing research and then finding it they failed again and again and again and became discouraged very rapidly because the media makes it, creates the impression they should succeed right away. So they leave research and I think it's a great shame that young people have to understand research is 90% failure. It's very painful to the ego to fail again and again and again. I know I've done an awful a lot of failing in my career and I think that young students should recognize that what's research is about and if they can't stand failing then don't try to do the research. But it can be borne."

"You need the willingness to fail all the time. You have to generate many ideas and then you have to work very hard only to discover that they don’t work. And you keep doing that over and over until you find one that does work ."

"One of the principal objects of theoretical research is to find the point of view from which the subject appears in the greatest simplicity."

"His true monument lies not on the shelves of libraries, but in the thoughts of men, and in the history of more than one science."

"In all these papers we see a love of honest work, an aversion to shams, a caution in the enunciation of conclusions, a distrust of rash generalizations and speculations based on uncertain premises. He was never anxious to add one more guess on doubtful matters in the hope of hitting the truth, or what might pass as such for a time, but was always ready to take infinite pains in the most careful testing of every theory. With these qualities was united a modesty which forbade the pushing of his own claims and desired no reputation except the unsought tribute of competent judges."

"The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results."

"We avoid the gravest difficulties when, giving up the attempt to frame hypotheses concerning the constitution of matter, we pursue statistical inquiries as a branch of rational mechanics."

"Mathematics is a language."

"The whole is simpler than its parts."

"Anyone having these desires will make these researches."

"I wish to know systems."

"A mathematician may say anything he pleases, but a physicist must be at least partially sane."

"If I have had any success in mathematical physics, it is, I think, because I have been able to dodge mathematical difficulties."

"Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realizing the ideal of the unselfish, Christian gentleman. In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life."

"In the last generation, this country produced one of the most eminent men of science in the whole world. His name was quite unknown among us while he lived, and it is still unknown. Yet I may say without too great exaggeration that when I heard it mentioned in a professional assembly in the Netherlands two years ago, everybody got down under the table and touched their foreheads to the floor. His name was Josiah Willard Gibbs."

"On the one hand, the student has been informed by some writers that the only certain way lies in the use of the entropy-function and the thermodynamic potentials; on the other hand, he is told with equal authority that the method used by the original investigators has been the consideration of cyclic processes, and that the former method is nothing but a mathematical (perhaps unnecessary) refinement of the results obtained by the latter. These extreme attitudes appear to me to be unfortunate, and more especially when one observes the physical clearness introduced by the use of cyclic processes, but at the same time remembers that most of the results obtained by separate investigators using cyclic processes had, with a great many more, previously been found by J. Willard Gibbs by means of a purely analytical method."

"Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from that moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics."

"Willard Gibbs is the type of the imagination at work in the world. His story is that of an opening up which has had its effect on our lives and our thinking; and, it seems to me, it is the emblem of the naked imagination —which is called abstract and impractical, but whose discoveries can be used by anyone who is interested, in whatever "field"— an imagination which for me, more than that of any other figure in American thought, any poet, or political, or religious figure, stands for imagination at its essential points."

"...only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead."

"Maxwell, and then Boltzmann, and then... J. Willard Gibbs... expended enormous intellectual effort in devising... , or... . The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy. The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ..."

"Many men have had intuitions well ahead of their time; and this is not least true in mathematical physics. Gibbs' introduction of probability into physics occurred well before there was an adequate theory of the sort of probability he needed. But for all these gaps it is, I am convinced, Gibbs rather than Einstein or Heisenberg or Planck to whom we must attribute the first great revolution of twentieth century physics."

"[Gibbs' 1878] paper stands today as one of the most profound contributions to the world of human thought and […] places him with the greatest of the world's geniuses."

"... a comparison of the American regard for inventive skill as opposed to skill in pure science. Our greatest inventive genius, Thomas A. Edison, was all but canonized by the American public, and a legend has been built around him. One cannot, I suppose, expect that achievements in pure science would receive the same public applause that came to inventions as spectacular and as directly influential on ordinary life as Edison’s. But one might have expected that our greatest genius in pure science, Josiah Willard Gibbs, who laid the theoretical foundations for modern physical chemistry, would have been a figure of some comparable acclaim among the educated public. Yet Gibbs, whose work was celebrated in Europe, lived out his life in public and even professional obscurity at Yale, where he taught for thirty-two years. Yale, which led American universities in its scientific achievements during the nineteenth century, was unable in those thirty-two years to provide him with more than a half dozen or so graduate students who could understand his work, and never took the trouble to award him an honorary degree."

"... the magnificent structure of Gibbsian statistical mechanics [cannot] be viewed as founded upon ideal classical gases, Boltzmannian kinetic theory, and the virial and cluster expansions for dilute fluids! True, this last route was still frequently retravelled in textbooks more than 50 years after Gibbs’ major works were published; but it deeply misrepresents the power and range of statistical mechanics... asking ‘‘What does statistical mechanics convey to a physicist?’’ and replying: ‘‘It means that one can compute the second-virial coefficient to correct the ideal gas laws!’’ Of course, historically, that is not a totally irrelevant remark; but it is extremely misleading and, in effect, insults one of America’s greatest theoretical physicists, Josiah Willard Gibbs."

"The possibility and significance of fractional angular momentum is discussed, and some simple physical realizations of it are mentioned. This leads naturally to consideration of the possibility of fractional quantum statistics, which is seen to be a possibility inherent in the kinematics of 2+1 dimensional quantum mechanics. Both sorts of fractionalization are intimately related to theories, and the classic considerations of Aharonov and Bohm on the significance of the vector potential in quantum mechanics. The meaning and importance of discrete gauge invariance in continuum theories is pointed out. Fractional statistics is shown to have a simple dynamical realization in the dynamics of charge-flux tube composites. Fractional statistics is shown to occur very naturally in the most geometrical quantum field theories in 2+1 dimensions, that is in the nonlinear sigma model and in quantum electrodynamics."

"Quite undeservedly, the ether has acquired a bad name."

"The answer to the ancient question "Why is there something rather than nothing?" would then be that ‘nothing’ is unstable."

"Exoplanet astronomy will systematically survey our galaxy, gathering information on the masses, orbits, geology, and atmospheres of millions of planets. As a byproduct, we will learn how rare life is and what conditions it requires. What we discover might support tests and refinements of anthropic reasoning."

"How do we get from symmetric laws to asymmetric appearances? (arrow of time problem) ... Why are the fundamental laws symmetric? ("naturality" problem) ..."

"To me, dark matter is matter. It looks like matter, it quacks like matter, it waddles like matter. It has many, many properties that indicate it's matter. And I think I know what matter it is!"

"17:48 of 40:44"

"[S]ome scientists focus on ideal beauty, others on empirical truth. My own approach, following a great tradition going back to Copernicus, Galileo and Kepler, has been to use beauty as a guide to truth."

"Physics is my religious belief. In the sense that in physics we discover a fantastically wonderful world out there that’s rich in potential, rich in realization, and that has ample scope for fantasy, because the laws are so strange and there’s so much stuff out there to understand. And when you understand it, you understand how that could be. I learn that I myself am very small. But I am also very large because I contain multitudes, as Walt Whitman said. I can process information. I can understand things. I can imagine. I can have fun. That’s the essence of my religion. I learn my religion from the study of what the world is and how it works."

"Does Michael Jackson or Archie Bunker or the president of General Motors need to know about quantum mechanics? Of course not. You can live a full life without that. But if you don’t believe that the universe is understandable, then it leads to the notion that one idea is just as good as another. And that’s horrible."

"Science teaches us to be very suspicious of grand generalizations...Aristotle had a set theory of the universe, and he didn’t get too far. Galileo started with simple things like pendulums and balls sliding down inclined planes, and he got much further. You never find surprises when you think in terms of broad generalities. Both quantum mechanics and relativity grew out of trying to really understand essentially simple things."

"If you don’t have all the clues, you can still do parts of the puzzle. There may be huge parts of the puzzle that we don’t even know about...It means that future generations can have the same kind of fun that we’re having."

"The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time... As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion. ...Harmony ...can be considered a special kind of rhythm. ...pure musical tones are produced when the vibrations are... periodic or... repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm—or, in mathematical language, if their periods are in proportion. Kepler... in the third book of Harmonice mundi... attempted to make other... related, connections between musical harmony and mathematical proportion."

"So let us listen to the light—what music do we hear? For one thing, we can elicit from each chemical element its own, unique chord. You may sometimes have noticed that a bright yellow flash is produced if ordinary table salt is sprinkled on a flame...a first bare hint of the subject of flame spectra... The fact that different elements emit light with different color characteristics is exploited by the makers of fireworks."

"If you pass the light from a sodium flash through a prism, you get a pattern very different from the familiar continuous rainbow that Newton elicited from natural sunlight. Instead of a continuous pattern, in which all gradations of pure color are apparently represented, the sodium flash generates a series of lines of light. ...in the musical analogy, sodium produces a chord where sunlight produced all possible tones—"white noise." Other elements produce other chords."

"To understand this radiation [ cosmic microwave background ], it is easier to begin thinking about the radiation from a very hot gas like that inside a neon light. The same neon... is, at room temperature, utterly transparent... The character of matter in general changes abruptly when it gets heated above 3,000 degrees or so. Below this temperature, matter is electrically neutral... At high temperatures in a neon light, the electrically charged pieces of atoms become unstuck. Frequent and violent collisions break down neutral atoms into electrons and unbalanced nuclei. Matter in this state is called plasma, and it radiates much of its collision energy in the form of light. ...a gas of neutral atoms (like air) is virtually transparent. The free [charged] nuclei and electrons of plasma, by contrast, couple to light's electromagnetic fields and absorb it very efficiently. ...You ...see light only from the borderline layer of neon between opaque plasma and transparent neutral atoms."

"Sam Treiman... has quoted something he called Treiman's theorem... Impossible things usually don't happen. ...With the discovery of radioactivity... it suddenly became apparent that the "impossible" was happening all the time. Uranium, thorium, radium... fit all the requirements of chemical elements. They could not be broken down by any of the standard methods... But occasionally... atoms of these elements spontaneously changed into other kinds of atoms. ...So what is left of the doctrine of the elements? Is alchemy reinstated? Not at all. The point is that the doctrine fails only under rare or special conditions. ...We can isolate the conditions in which they do, and retain a more restricted but still useful concept of the "impossible.""

"As the idea of permanence of objects has faded, the idea of permanence of physical laws has become better established and more powerful."

"What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation."

"What should be most significant to us are not physical artifacts, but the meaning they embody. ...whenever we create paintings, songs, poems, books, computer programs—or ideas in the minds of children—we do something of this sort."

"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures... In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all."

"Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable—and for humanity, remarkably fortunate—circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem."

"Once helium burning has occurred... the next possible reaction—carbon burning—is not necessarily slow... This reaction involves ...a strong as opposed to a weak interaction. ...Carbon burning results in magnesium. ...Taking a cross section of a highly evolved star would reveal a system of many layers. The inner layers have been subjected to the largest pressures, thereby forced to the highest temperatures, and burned the furthest; the outermost layers, by contrast, have not burned at all. Thus, as we proceed from outside in, there will be an outermost layer with the initial mix of hydrogen and helium, a layer of mostly helium, a layer of carbon, a layer of magnesium, and so on. ...So we arrive at the picture of a star, in the latest stages of its evolution... now composed of mostly carbon nuclei and other explosive material."

"It is delightful in itself when we are able to interpret features of the present as signs confirming our understanding of the past."

"In a sense, all of Earth glows in the dark. The energy release from natural radioactivity, the lingering fluorescence of stellar explosions, keeps Earth dynamic. It melts the core and keeps it flowing, and heats the crust and mantle, with consequences ranging from the generation of earth's magnetic field to earthquakes and the motion of continents. By contrast, Luna and Mars, because they are smaller, derive less energy from radioactive decays. Geologically, they are dead."

"The result will be points of quiescence—technically known as nodes—where the air's density varies not at all, and no sound is heard. Note the paradox here: either sphere alone creates a sound wave at this point; two spheres together add up to no sound there at all. Two sources can add up to give less than one. This is the essence of destructive interference. (When two sources are giving the same instruction, the resulting vibration bears not twice but four times the energy. This phenomenon, oxymoronically known as constructive interference, may seem puzzling.)"

"In science... the ultimate judges are not experts but experiments."

"Particles that, like 4He, show constructive interference are said to be bosons—a shorthand term for "particles obeying Bose–Einstein statistics." …One way to recognize bosons is their tendency to imitate one each other. ...the presence of one boson increases the chance that another of its identical siblings will also appear in the same spot. There's an attraction between them. We will speak ...of an attractive identity force drawing together identical bosons. Lasers are a spectacular example..."

"When two identical 3He atoms collide... the interference is destructive. Particles that behave like 3He atoms are called fermions, short for "particles obeying Fermi–Dirac statistics." ...while bosons imitate one another... the "identity force" between fermions acts like a repulsion, and the probability of finding a fermion at some point in space is reduced if some of its identical siblings are nearby. ...It is the repulsive identity forces between electrons that support white dwarf stars... against their own gravity."

"There is a simple rule for composite objects, such as nuclei or atoms. The rule is that if such an object contains an odd number of fermions, the composite object is a fermion. Otherwise, it is a boson. ...this simple rule doesn't care at all about the number of bosons in the composite object."

"If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. ...in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg ...The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies]—so they all tend to converge, as desired."

"In the table—and in nature—we find (leaving aside the antineutrino) fifteen fundamental fermions, with diverse strong, weak, and electromagnetic charges. ...They are so closely related by symmetry transformations that they are, so to speak, no more than different faces of the same cube."

"When we view nature stripped to essentials, so to speak, in this Unification Table, what we see is... a five bit register. ...It is in just this form that data is stored and manipulated within a digital computer. ...Every particle, then, can be specified by a five-bit word and stored in a five-bit register. It's eerie that even the odd restriction on how many minus signs are allowed is reminiscent of a trick used in computers, to detect errors in transmission. You see, if allowed words must have an odd number of minus signs, any single error in transmission of a word can be detected. ...our world might be an intricate program working itself out on a gigantic computing machine."

"Thinking along these lines will help prepare us for the day when we—or more likely, our distant descendents—will develop the machinery and cleverness to begin to program [create] worlds ourselves..."

"It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake."

"The main problem with many nonscientific world models is the vigor with which they insist upon their rightness. Once a world model claims to be completely right, it is no longer open to any changes. ...Closed systems can be comforting, but they are limited. ...It's not the best we can do. Neither is extreme "open-mindednesss" that slides into "empty headedness"—the ideal that we can never really know anything."

"The whole idea of science is really to listen to nature, in her own language, as part of a continuing dialogue."

"We have heard that nature can sing some strange and unfamiliar songs. In coming to appreciate these songs, we develop a heightened perception... leavened by an admixture of our own creation..."

"We evolved to be good at learning and using rules of thumb, not at searching for ultimate causes and making fine distinctions. Still less did we evolve to spin out long chains of calculation that connect fundamental laws to observable consequences. Computers are much better at it!"

"For many centuries before modern science, and for the first two and a half centuries of modern science, the division of reality into matter and light seemed self-evident. ...As long as the separation between the massive and the massless persisted, a unified description of the physical world could not be achieved."

"An ordinary mistake is one that leads to a dead end, while a profound mistake is one that leads to progress. Anyone can make an ordinary mistake, but it takes a genius to make a profound mistake."

"Different ways of writing the same equation can suggest very different things, even if they are logically equivalent. ...In Einstein's original 1905 paper, you do not find the equation E = mc2. What you find is m = E/c2. ...the title of the paper is a question: "Does the Inertia of a Body Depend on Its Energy Content?" …If we can explain mass in terms of energy, we'll be improving our description of the world. We'll need fewer ingrediants in our world-recipe."

"E = mc2 really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc2 simply doesn't apply. ...For moving bodies, the correct mass-energy equation is E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}} where v is the velocity. For a body at rest (v=0), this becomes E = mc2. ...we must consider the special case of particles with zero mass... examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and v = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. ...The energy E of a photon is proportional to the frequency f of the light it represents. ...they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant."

"Knowing how to calculate something is not the same as understanding it. Having a computer to calculate the origin of mass for us may be convincing, but is not satisfying. Fortunately we can understand it too."

"Intelligent creatures [that] evolved to live deep within the atmosphere of a gas giant planet could be deluded, for eons, into thinking that the Universe is an approximately homogeneous expanse of gas, filling a three-dimensional space, but featuring anisotropic laws of motion (which we would ascribe to the planet’s gravitational field). Are we human scientists comparably blinkered?"

"If the “universe” contains everything that exists, what can be outside it? If the answer is “Things that don’t exist”, then “multiverse” becomes an idea in the domain of psychology, not physics."

"The “Copernican Principle” or “Cosmic Mediocrity”... states, basically, that Earth does not occupy a privileged place in the universe. Universality asserts more, namely that there are no privileged places or times."

"In the past scientists have repeatedly reached “intellectual closure” on inadequate pictures of the universe, and underestimated its scale."

"A common habit of thought... is the idea that space is [a] simple receptacle in which bodies move around, with no two bodies present at the same point. ...In modern quantum physics generally, and in the standard model of fundamental physics in particular, physical space appears as a far more flexible framework. Many kinds of particles can be present at the same point in space at the same time. Indeed, the primary ingredients of the standard model are not particles at all, but an abundance of quantum fields, each a complex object in itself, and all omnipresent."

"The traditional “cosmological” Multiverse considers that there might be physical realms inaccessible to us due to their separation in space-time. The quantum Multiverse arises from entities that occupy the same space-time, but are distant in Hilbert space – or in the jargon, decoherent."

"The happy coincidences between life’s requirements and nature’s choices of parameter-values might be just a series of flukes, but one could be forgiven for beginning to suspect that something deeper is at work. That suspicion is the first deep root of anthropic reasoning."

"The phase transition paradigm: The standard model of fundamental physics incorporates, as one of its foundational principles, the idea that “empty space” or “vacuum” can exist in different phases, typically associated with different amounts of symmetry. Moreover, the laws of the standard model itself suggest that phase transitions will occur, as functions of temperature. Extensions of the standard model to build in higher symmetry (gauge unification or especially supersymmetry) can support effective vacua with radically different properties, separated by great distance or by domain walls. That would be a form of failure of universality, in our sense, whose existence is suggested by the standard model."

"In most theoretical embodiments of inflationary cosmology, the currently observed universe appears as a small part of a much larger multiverse. In this framework to hold throughout the universe need not hold through all space. They can be accidents of our local geography, so to speak. If that is so, then it is valid – indeed, necessary – to consider selection effects. It may be that some of the “fundamental constants”, in particular, cannot be determined by theoretical reasoning, even in principle, because they really are different elsewhere."

"To put it crudely, theorists can be tempted to think along the lines “If people as clever as us haven’t explained it, that’s because it can’t be explained – it’s just an accident.” I believe there are at least two important regularities among standard model parameters that do have deeper explanations, namely the unification of couplings and the smallness of the QCD θ parameter. There may well be others."

"Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may be enough to avoid Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. According to the Schrödinger equation, the wave function evolves in a completely predictable way. But in practice we never have access to the full wave function, either at present or in the future, so this “predictability” is unattainable. If the wave function provides the ultimate description of reality — a controversial issue! — we must conclude that “God plays a deep yet strictly rule-based game, which looks like dice to us.”"

"Einstein’s great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the opposite of a simple truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one we started with, gives a nice example: “Naïveté is doing the same thing over and over, and always expecting the same result.”"

"… one can still say that quantum mechanics is the key to understanding magnetism. When one enters the first room with this key there are unexpected rooms beyond, but it is always the master key that unlocks each door."

"To have a good memory the first thing you have to do is to trust your memory."

"Eppie's memory is like sticky flypaper."

"I have no health for a soldier, and as I have no expectation of serving my country in that way, I am spending my time in the old trifling manner, and am so taken with optics, that I do not know whether, if the enemy should invade this part of the country, as Archimedes was slain while making geometrical figures on the sand, so I should die making a telescope."

"I do not design a machine which will give the ignorant in astronomy a just view of the solar system, but would rather astonish the skilful and curious observer by a most accurate correspondence between the situations and motions of our little representatives of our heavenly bodies and the situations and motions of those bodies themselves. I would have my orrery really useful by making it capable of informing us truly of the astronomical phenomena for any particular point of time, which I do not find that any orrery yet made can do."

"The direct tendency of (Astronomy) is to dilate the heart with universal benevolence, and to enlarge its views."

"See the sage Rittenhonse, with ardent eye, Lift the long tube and pierce the starry sky; Clear in his view the circling systems roll, And broader splendours gild the central pole. He marks what laws th' eccentric wand'rers bind, Copies Creation in his forming mind, And bids, beneath his hand, in semblance rise, With mimic orbs, the labours of the skies. There wond'ring crowds with raptur'd eye behold The spangled heav'ns their mystic maze unfold; While each glad sage his splendid hall shall grace, With all the spheres that cleave th' ethereal space."

"'America had not yet produced one good poet.' When we shall have existed as a people as long as the Greeks did before they produced a Homer, the Romans a Virgil, the French a Racine and Voltaire, the English a Shakespeare and Milton, should this reproach be still true, we will inquire from what unfriendly causes it has proceeded, that the other countries of Europe and quarters of the earth shall not have inscribed any name in the roll of poets. But neither has America produced 'one able mathematician, one man of genius in a single art or a single science.' In war we have produced a Washington, whose memory will be adored while liberty shall have votaries, whose name shall triumph over time, and will in future ages assume its just station among the most celebrated worthies of the world, when that wretched philosophy shall be forgotten which would have arranged him among the degeneracies of nature. In physics we have produced a Franklin, than whom no one of the present age has made more important discoveries, nor has enriched philosophy with more, or more ingenious solutions of the phenomena of nature. We have supposed Mr. Rittenhouse second to no astronomer living: that in genius he must be the first, because he is self-taught. As an artist he has exhibited as great a proof of mechanical genius as the world has ever produced. He has not indeed made a world; but he has by imitation approached nearer its Maker than any man who has lived from the creation to this day."

"Before the nineteenth century, writers on education portayed the "improvement of mind" as an activity mainly suited to gentlemen. ...both Thomas Jefferson and Benjamin Rush had venerated David Rittenhouse as an example of how arduous philosophical investigation might elevate the child of humble parents. But Jefferson and Rush tagged Rittenhouse as a genius, and hence untypical, and each employed Rittenhouse as ammunition in a debate among educated gentlemen. Jefferson invoked Rittenhouse in his Notes on the State of Virginia, a book he wrote to disabuse French philosophes of the notion that all specied degenerated in the New World; Rush used his eulogy of Rittenhouse before the select audience of the American Philosophical Society to ridicule colleges for requiring students to learn the ancient languages."

"The year 1775 opened with a project intended to bring the abilities of Rittenhouse more effectually into the service of science. The Philosophical Society addressed the colonial legislature of Pennsylvania, praying it to establish a public observatory, and commit it to the care of Rittenhouse. Had the circumstances of the times permitted this project to be carried into effect, it would have enabled him to occupy a great space in the history of astronomy. He had already shown himself the equal, in point of learning and skill as an observer, to any practical astronomer then living; nothing was wanting to make him rank with the Flamsteads, the Halleys, and the Maskelynes, but that he should be permitted to devote his whole mind to this pursuit, and be furnished with those instruments and accommodations, for which no private fortune will suffice. Other men might have been found as well, nay, better qualified for the political pursuits and public offices in which it became his fate to spend the rest of his life; but America has never yet produced any individual who has manifested so great a capacity for extending the domain of practical astronomy. To arrange the details of a disorganized and depreciating currency, to collect and disburse a scanty and ill-paid revenue, were thereafter to be the pursuits of our philosopher; and he was to expend upon the estimates and returns of the tax-gatherer those powers of mind which were capable of grasping, and that mechanical skill which sufficed to imitate, the vast mechanism of the universe."

"It was during the residence of our ingenious philosopher with his father in the country that he made himself master of Sir Isaac Newton's Principia, which he read in the English translation of Mr. Motte. It was here, likewise, he became acquainted with the science of fluxions; of which sublime invention he believed himself, for a while, to be the author, nor did he know for some years afterwards that a contest had been carried on between Sir Isaac Newton and Leibnitz for the honor of the great and useful discovery. What a mind was here! Without literary friends or society, and with but two or three books, he became, before he had reached his four and twentieth year, the rival of two of the greatest mathematicians in Europe."

"Among the books he inherited from his uncle was an English translation of the "Principia" of Newton. Such was the progress which he made in mathematical knowledge, although now destitute of any aid, that he was enabled to accomplish the perusal of this work, for the proper understanding of which so much acquaintance with geometry and algebra is necessary, before he had attained his nineteenth year. Newton, as is well known, from deference to the practice of the ancient philosophers, adopts in this work the synthetic method of demonstration, and gives no clue to the analytic process by which the truth of his propositions was first discovered by him. Unlike the English followers of this distinguished philosopher, who contented themselves, for a time, with following implicitly in the path of geometric demonstration, which he had thus pointed out, Rittenhouse applied himself to search for an instrument, which might be applied to the purpose of similar discoveries, and in his researches attained the principles of the method of fluxions. So ignorant was he of the progress which this calculus had made, and of the discussions in relation to its invention and improvement, that he for a time considered it as a new discovery of his own. In this impression, however, he could not have long continued; as he made, in his nineteenth year, an acquaintance who was well qualified to set him right in this important point."

"The most noted mathematician and astronomer of early times [in the U.S.] was not a professor in a college, nor had he been trained within college walls. We have reference to David Rittonhouse."

"His invention, whatever it may have been, was not of sufficient importance to deserve the name of an "invention of fluxions." If Rittenhouse actually made an invention of such transcending magnitude before the age of twenty, and at a time when he had hardly begun his scientific studies, how is it that he made not the slightest approach to any similar discovery during the forty-four years of his maturer life? Though always a passionate lover of scientific pursuits, he made no original contributions whatever to the science of pure mathematics. Science is indebteded to him chiefly for his orreries and the observations of the transit of Venus. ...the alleged invention of fluxions was little more than a "rumor set afloat by idle gossip." It serves to show us, however, in what unbounded admiration he was held by his countrymen."

"As a mechanic, Rittenhouse became celebrated for the extreme exactness and finish of his workmanship. Especially celebrated were his chronometer clocks. It was while thus engaged in the manufacture of clocks that he planned and executed an instrument which brought into play both his mechanical and mathematical skill. ...the orrery. It was, indeed, intended to be a sort of a perpetual astronomical almanac, in which the results, instead of being exhibited in tables, were to be actually exhibited to the eye. His orrery greatly exceeded all others in precision. It attracted very general attention among well informed persons... There arose a lively competition between different colleges in this country for the possession of this orrery."

"Only two transits of Venus had been observed before his time, and of these, the first, in 1639, had been seen by only two persons. These transits happen so seldom that there cannot be more than two in one century, and in some centuries none at all. But the transits of Venus are the best means we have for determining the parallax of the sun. ...The observations were a success and established for Rittenhonse the reputation of an exact and careful astronomer. ...During the transit Rittenhouse saw one phenomenon which escaped the notice of all other astronomers. When the planet had advanced about half of its [Venus'] diameter upon the sun, that part of the edge of the planet which was off the sun's disc appeared illuminated, so that the outline of the entire planet could be seen. But a complete circle of light around Venus would indicate that more than half of Venus is illuminated. This can happen... only when the rays of light are refracted by an atmosphere. Hence... Venus is surrounded, like the earth, by an atmosphere. But this appearance of a ring of light was not confirmed by other astronomers, and the statement of Rittenhouse excited no attention for nearly a century, until his observation was at last confirmed by other astronomers."

"If our astronomer be judged by the original contributions which, under existing adverse circumstances, he actually did make to astronomy and mathematics, then it must be admitted that he can not be placed in the foremost rank of astronomers then living. Friends will judge him by what he might have done; the world at large will judge him by what he actually accomplished. Our greatest indebtedness to Rittenhouse lies not in the original contributions he made to science, but rather in the interest which he aroused in astronomical pursuits, and in the diffusion of scientific knowledge in the New World which resulted from his efforts."

"What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force."

"Ideality is preëminently the foundation of Mathematics."

"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."

"Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences; but it is the Key of an ever open door which refuses to be shut, and through which the whole world is crowding, to make free, in unrestrained license, with the precious treasures within, thoughtless both of lock and key, of the door itself, and even of Science, to which it owes such boundless possessions, the New World included. The door is wide open and all may enter, but all do not enter with equal thoughtlessness. There are a few who wonder, as they approach, at the exhaustless wealth, as the sacred shepherd wondered at the burning bush of Horeb, which was ever burning and never consumed. Casting their shoes from off their feet and the world's iron-shod doubts from their understanding, these children of the faithful take their first step upon the holy ground with reverential awe, and advance almost with timidity, fearful, as the signs of Deity break upon them, lest they be brought face to face with the Almighty."

"The Key! it is of wonderful construction, with its infinity of combination, and its unlimited capacity to fit every lock. … it is the great master-key which unlocks every door of knowledge and without which no discovery which deserves the name — which is law, and not isolated fact — has been or ever can be made. Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications; he may have exalted it into his idol and worshipped it; he may have degraded it into his toy . . . when he should have been hard at work with it, using it for the benefit of mankind and the glory of his Creator."

"Ascend with me above the dust, above the cloud, to the realms of the higher geometry, where the heavens are never clouded; where there is no impure vapour, and no delusive or imperfect observation, where the new truths are already arisen, while they are yet dimly dawning on the world below; where the earth is a little planet; where the sun has dwindled to a star; where all the stars are lost in the Milky Way to which they belong; where the Milky Way is seen floating through space like any other nebula; where the whole great girdle of nebulae has diminished to an atom and has become as readily and completely submissive to the pen of the geometer, and the slave of his formula, as the single drop, which falls from the clouds, instinct with all the forces of the material world."

"Descend from the infinite to the infinitesimal. Long before . . . observation had begun to penetrate the veil under which Nature has hidden her mysteries, the restless mind sought some principle of power strong enough and of sufficient variety to collect and bind together all parts of a world. This seemed to be found, where one might least expect it, in abstract numbers. Everywhere the exactest numerical proportion was seen to constitute the spiritual element of the highest beauty."

"Throughout nature the omnipresent beautiful revealed an all-pervading language spoken to the human mind, and to man's highest capacity of comprehension. By whom was it spoken? Whether by the gods of the ocean, or the land, by the ruling divinities of the sun, moon, and stars, or by the dryads of the forest and the nymphs of the fountain, it was one speech and its written cipher was cabalistic. The cabala were those of number, and even if they transcended the gemetricl skill of the Rabbi and the hieroglyphical learning of the priest of Osiris, they were, distinctly and unmistakably, expressions of thought uttered to mind by mind; they were the solutions of mathematical problems of extraordinary complexity."

"The very spirits of the winds, when they were sent to carry the grateful harvest to the thirsting fields of Calabria, did not forget the geometry which they had studied in the caverns of Æolus and of which the geologist is daily discovering the diagrams."

"There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress. There can be no reasonable doubt that it was part of the Creator's plan. How easily might the whole order have been transposed! How readily might we have been assigned to some complicated system which our feeble and finite powers could not have unravelled!"

"Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application. But on the contrary, it is a singular fact, and one quite consonant with the principles of sound logic, that its first and general use is mostly to be expected from its want of significance. The interpretation is a trammel to the use. Symbols are essential to comprehensive argument."

"The familiar proposition that all A is B, and all B is C, and therefore all A is C, is contracted in its domain by the substitution of significant words for the symbolic letters. The A, B, and C, are subject to no limitation for the purposes and validity of the proposition; they may represent not merely the actual, but also the ideal, the impossible as well as the possible. In Algebra, likewise, the letters are symbols which, passed through a machinery of argument in accordance with given laws, are developed into symbolic results under the name of formulas. When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought. But the most noted instance is the symbol called the impossible or imaginary, known also as the square root of minus one, and which, from a shadow of meaning attached to it, may be more definitely distinguished as the symbol of semi-inversion. This symbol is restricted to a precise signification as the representative of perpendicularity in quaternions, and this wonderful algebra of space is intimately dependent upon the special use of the symbol for its symmetry, elegance, and power."

"The strongest use of the symbol is to be found in its magical power of doubling the actual universe, and placing by its side an ideal universe, its exact counterpart, with which it can be compared and contrasted, and, by means of curiously connecting fibres, form with it an organic whole, from which modern analysis has developed her surpassing geometry."

"I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future."

"Mathematics is the science which draws necessary conclusions."

"The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims ; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law. Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation."

"The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks."

"All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole. Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra. In all other algebras both relations must be combined, and the algebra must conform to the character of the relations."

"There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches."

"I always had the feeling that his attitude toward his loved science was that of a devoted worshipper, rather than a clear expounder. Although we could rarely follow him, we certainly sat up and took notice. … To him mathematics was not a humanly devised instrument of investigation, it was Philosophy itself, the divine revealer of TRUTH."

"He was one of the most stimulating men I have ever known."

"Peirce stood alone — a mountain peak whose absolute height might be hard to measure, but which towered above the surrounding country."

"Benjamin Peirce's lectures dealt, to be sure, with the higher mathematics, but also with theories of the universe and the infinities of nature, and with man's power to deal with infinities and infinitesimals alike. His University Lectures were many a time way over the heads of his audience, but his aspect, his manner, and his whole personality held and delighted them."

"He was such a great, big ray of Light and Goodness, always so simple, cheerful and showing more than amiability, that his great power did not seem to assert itself."

"Of the great mathematician as an instructor several of his pupils who ventured on the higher planes of the science have written. These were youths who, though they could follow him but a few steps in that rarefied atmosphere, had the privilege of a glimpse now and then into shining infinities wherein this giant sped rejoicing on."

"Authority was nothing to Peirce. He took his own path up the mountain. … Like Pythagoras, Peirce taught that everything owes its existence and consistency to the harmony which he considered the basis of all beauty, and found music in the revolving spheres."

"His talk was informal, often far above their heads. "Do you follow me?" asked the Professor one day. No one could say Yes. "I'm not surprised," said he; "I know of only three persons who could." At Paris, the year after, at the great Exposition, Flagg stood before a mural tablet whereon were inscribed the names of the great mathematicians of the earth for more than two thousand years. Archimedes headed, Peirce closed the list; the only American."

"He gave us his "Curves and Functions", in the form of lectures; and sometimes, even while stating his propositions, he would be seized with some mathematical inspiration, would forget pupils, notes, everything, and would rapidly dash off equation after equation, following them out with smaller and smaller chalk-marks into the remote corners of the blackboard, forsaking his delightful task only when there was literally no more space to be covered, and coming back with a sigh to his actual students. There was a great fascination about these interruptions; we were present, as it seemed, at mathematics in the making; it was like peeping into a necromancer's cell, and seeing him at work; or as if our teacher were one of the old Arabian algebraists recalled to life."

"Looking back over the space of fifty years since I entered Harvard College, Benjamin Peirce still impresses me as having the most massive intellect with which I have ever come in contact, and as being the most profoundly inspiring teacher I ever had. … As soon as he had finished the problem or filled the blackboard he would rub everything out and begin again. He was impatient of detail, and sometimes the result would not come out right; but instead of going over his work to find the error, he would rub it out, saying that he had made a mistake in a sign somewhere, and that we should find it when we went over our notes. Described in this way it may seem strange that such a method of teaching should be inspiring; yet to us it was so to the highest degree. We were carried along by the rush of his thought, by the ease and grasp of his intellectual movement. The inspiration came, I think, partly from his treating us as highly competent pupils, capable of following his line of thought even through errors in transformations; partly from his rapid and graceful methods of proof, which reached a result with the least number of steps in the process, attaining thereby an artistic or literary character; and partly from the quality of his mind which tended to regard any mathematical theorem as a particular case of some more comprehensive one, so that we were led onward to constantly enlarging truths."

"Benjamin Peirce deserves recognition, not only as a founding father of American mathematics, but also as a founding father of modern abstract algebra."

"It is not given to us — it is given to but few men of any generation — to roam those Alpine solitudes of science to which his genius reached."

"When this wizard stepped down from his post, crossed his moat, and opened his garden gate, nothing could be more attractive than the vistas and plantations he opened to our view. … Few men could suggest more while saying so little, or stimulate so much while communicating next to nothing that was tangible and comprehensible. The young man that would learn the true meaning of apprehension as distinct from comprehension, should have heard the professor lecture..."

"Most of us have grown so blase about computer developments and capabilities — even some that are spectacular — that it is difficult to believe or imagine there was a time when we suffered the noisy, painstakingly slow, electromechanical devices that chomped away on punched cards."

"I read once that the true mark of a pro — at anything — is that he understands, loves, and is good at even the drudgery of his profession."

"The author discusses valueless measures in pointless spaces."

"'André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That's one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity."

"Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared."

"Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"

"What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up."

"I like words more than numbers, and I always did."

"It takes a long time to learn to live — by the time you learn your time is gone."

"I was too near it then to see how shallow it all was..."

"The purpose of computing is insight, not numbers."

"As a practicing computer veteran, this reviewer has the habit of looking at the hypothesis of a theorem and asking:"

"Typing is no substitute for thinking."

"The only generally agreed upon definition of mathematics is "Mathematics is what mathematicians do." [...] In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D.C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become."

"Without real experience in using the computer to get useful results the computer science major is apt to know all about the marvelous tool except how to use it. Such a person is a mere technician, skilled in manipulating the tool but with little sense of how and when to use it for its basic purposes."

"Indeed, one of my major complaints about the computer field is that whereas Newton could say, "If I have seen a little farther than others, it is because I have stood on the shoulders of giants," I am forced to say, "Today we stand on each other's feet." Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way. Science is supposed to be cumulative, not almost endless duplication of the same kind of things."

"The Postulates of Mathematics Were Not on the Stone Tablets that Moses Brought Down from Mt. Sinai."

"The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around."

"Just as there are odors that dogs can smell and we cannot, as well as sounds that dogs can hear and we cannot, so too there are wavelengths of light we cannot see and flavors we cannot taste. Why then, given our brains wired the way they are, does the remark, "Perhaps there are thoughts we cannot think," surprise you?"

"The calculus is probably the most useful single branch of mathematics. ...I have found the ability to do simple calculus, easily and reliably, was the most valuable part of mathematics I ever learned."

"Understanding the methods of calculus is vital to the creative use of mathematics... Without this mastery the average scientist or engineer, or any other user of mathematics, will be perpetually stunted in development, and will at best be able to follow only what the textbooks say; with mastery, new things can be done, even in old, well-established fields."

"Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty."

"Continuous distributions are basic to the theory of probability and statistics, and the calculus is necessary to handle them with any ease."

"Statistics should be taught early so that the concepts are absorbed by the student's flexible, adaptable mind before it is too late."

"Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. ...The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated."

"The methods of mathematics are the main topic of the course, not a long list of finished mathematical results with such highly polished proofs that the poor student can only marvel at the results, with no hope of understanding how mathematics is actually created by practicing mathematicians."

"You live in an age that is dominated by science and engineering. ...Thus if you wish to be effective in the world and to achieve the things that you want, it is necessary to understand both science and engineering (and those require mathematics)."

"Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow."

"Probability and statistics are now so obviously necessary tools for understanding many diverse things that we must not ignore them even for the average student."

"Calculus is the mathematics of change. ...Change is characteristic of the world."

"Probability is the mathematics of uncertainty. ...many modern theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential."

"Most mathematics books are filled with finished theorems and polished proofs, and to a surprising extent they ignore the methods used to create mathematics. It is as if you merely walked through a picture gallery and never told how to mix paints, how to compose pictures, or all the other "tricks of the trade.""

"In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval." ...most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics."

"The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity."

"If you expect to continue learning all your life, you will be teaching yourself much of the time. You must learn to learn, especially the difficult topic of mathematics."

"The beauty of mathematics often makes the subject matter much more attractive and easier to master."

"When a theory is sufficiently general to cover many fields of application, it acquires some "truth" from each of them. Thus... a positive value for generalization in mathematics."

"There is no agreed upon definition of mathematics, but there is widespread agreement that the essence of mathematics is extension, generalization, and abstraction... [which] often bring increased confidence in the results of a specific application, as well as new viewpoints."

"We are mainly interested in the processes... not... in presenting mathematics in its most abstract form. ...we will often begin with concrete forms and then exhibit the process of abstraction."

"Science and mathematics... have added little to our understanding of such things as Truth, Beauty, and Justice. There may be definite limits to the applicability of the scientific method."

"Mathematics, being very different from the natural languages, has its corresponding patterns of thought. Learning these patterns is much more important than any particular result... They are learned by the constant use of the language and cannot be taught in any other fashion."

"Theorems... record more complex patterns of thinking that once shown to be valid need not be repeated every time they are needed."

"Calculus systematically evades a great deal of numerical calculation."

"Faced with almost an infinity of details you cannot afford to deal constantly with the specific; you must learn to embrace more and more detail under the cover of generality."

"There is no unique, correct answer in most cases. It is a matter of taste, depending on the circumstances... and the particular age you live in. ...Gradually, you will develop your own taste, and along the way you may occasionally recognize that your taste may be the best one! It is the same as an art course."

"A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done."

"When you yourself are responsible for some new application in mathematics... then your reputation... and possibly even human lives, may depend on the results you predict. It is then the need for mathematical rigor will become painfully obvious to you. ...Mathematical rigor is the clarification of the reasoning used in mathematics. ...a closer examination of the numerous "hidden assumptions" is made. ...Over the years there has been a gradually rising standard of rigor; proofs that satisfied the best mathematicians of one generation have been found inadequate by the next generation. Rigor is not a yes-no property of a proof... it is a vague standard of careful treatment that is currently acceptable to a particular group."

"We do not always know what we are talking about. ...Troubles... can be made to arise whenever what is being said includes itself—a self-referral situation."

"We intend to teach the doing of mathematics. The applications of these methods produce the results of mathematics (which usually is only what is taught)... There is also a deliberate policy to force you to think abstractly...it is only through abstraction that any reasonable amount of useful mathematics can be covered. There is simply too much known to continue the older approach of giving detailed results."

"It is easy to measure your mastery of the results via a conventional examination; it is less easy to measure your mastery of doing mathematics, of creating new (to you) results, and of your ability to surmount the almost infinite details to see the general situation."

"In the long run, the methods are the important part of the course. It is not enough to know the theory; you should be able to apply it."

"The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish."

"This text is organized in the "spiral" for learning. A topic... is returned to again and again, each time higher up in the spiral. The first time around you may not be completely sure of what is going on, but on the repeated returns to the topic it should gradually become clear. This is necessary when the ideas are not simple but require a depth of understanding..."

"Besides the theory there are a lot of small technical details that must be learned so well that you can recall them almost instantaneously, such as the trigonometric identities... put one part of the identity on one side of a 3 x 5 card and the other part on the other side. Using these flash cards you can, in the odd moments of your daily life, learn the mechanical parts of the course. ...for this kind of low-level material many short learning sessions are much more efficient than a few long, intense ones; but this is not necessarily true for larger ideas. ...most students will not use such trivial devices as flash cards; it seems to be beneath their dignity. They suffer accordingly."

"There are so many ways of being wrong and so few ways of being right that it is much more economical to study successes."

"Although textbooks (and professors) like to make definite statements indicating that they know what they are talking about, there is in fact a great deal of uncertainty and ambiguity in the world. ...we will not evade this question but rather explore (overexplore?) it. ...great progress is often made when what was long believed to be true is now seen to be perhaps not the whole truth. Thus the text often uses words... to cause you to think about the uncertainess and even the arbitrariness of much of our current conventions and definitions, to ponder about your acceptance of them."

"It is not easy to become an educated person."

"When you are famous it is hard to work on small problems. [...] The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you. [...] The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after."

"Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance."

"I noticed the following facts about people who work with the door open or the door closed. I notice that if you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But 10 years later somehow you don't quite know what problems are worth working on; all the hard work you do is sort of tangential in importance. He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important."

"One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to. [...] The average scientist, so far as I can make out, spends almost all his time working on problems which he believes will not be important and he also doesn't believe that they will lead to important problems. [...] In summary, I claim that some of the reasons why so many people who have greatness within their grasp don't succeed are: they don't work on important problems, they don't become emotionally involved, they don't try and change what is difficult to some other situation which is easily done but is still important, and they keep giving themselves alibis why they don't."

"Probability is too important to be left to the experts. [...] The experts, by their very expert training and practice, often miss the obvious and distort reality seriously. [...] The desire of the experts to publish and gain credit in the eyes of their peers has distorted the development of probability theory from the needs of the average user. The comparatively late rise of the theory of probability shows how hard it is to grasp, and the many paradoxes show clearly that we, as humans, lack a well grounded intuition in the matter. Neither the intuition of the man in the street, nor the sophisticated results of the experts provides a safe basis for important actions in the world we live in."

"If the prior distribution, at which I am frankly guessing, has little or no effect on the result, then why bother; and if it has a large effect, then since I do not know what I am doing how would I dare act on the conclusions drawn?"

"Since I was trying to teach "style" of thinking in science and engineering, and "style" is an art, I should therefore copy the methods of teaching used for the other arts—once the fundamentals have been learned. How to become a great painter cannot be taught in words... Art teachers usually let the advanced student paint, and then make suggestions... more or less as the points arise in the student's head—which is where learning is supposed to occur!"

"Great results in science and engineering are "bunched" in the same person too often for success to be a matter of random luck."

"Teachers should prepare the student for the student's future, not for the teacher's past."

"Apparently an "art"—which almost by definition cannot be put into words—is probably best communicated by approaching it from many sides and doing so repeatedly, hoping thereby students will finally master enough of the art, or if you wish, style, to significantly increase their future contributions to society."

"The past is... much more uncertain—or even falsely reported—than is usually recognized."

"I am concerned with educating and not training you. ...Education is what, when, and why to do things. Training is how to do it. Either one without the other is not of much use. You might think education should precede training, but the kind of educating I am trying to do must be based on your past experiences and technical knowledge."

"Either you will be a leader, or a follower, and my goal is for you to be a leader."

"In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it. Of course, you seldom, if ever, see either pure state."

"All of engineering involves some creativity to cover the parts not known, and almost all of science includes some practical engineering to translate the abstractions into practice."

"Much of present science rests on engineering tools, and as time goes on, engineering seems to involve more and more of the science part. ...the two fields are growing together! ...and now there is not enough time to allow us the leisure which comes from separating the two fields."

"It is obvious: The past was once the future and the future will become the past."

"Often it is not physical limitations... but rather it is human made laws, habits, and organizational rules, regulations, personal egos, and inertia, which dominate the evolution of the future."

"It is probable that the future will be more limited by the slow evolution of the human animal and the corresponding human laws, social institutions, and organizations than it will be by the rapid evolution of technology."

"Unforeseen technological inventions can completely upset the most careful predictions."

"In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance √n. ...the accuracy of the vision matters less than you suppose, getting anywhere is better than drifting, there are potentially many paths to greatness for you... No vision, not much of a future."

"In forming your plan for your future you need to distinguish three different questions: What is possible? What is likely to happen? What is desirable to have happen? In a sense the first is Science... The second is Engineering.. The third is ethics, morals, or... value judgements. ...you will probably have an idea of how to alter things to make the more desirable future occur ...having a vision is what tends to separate the leaders from the followers."

"The standard process of organizing knowledge into departments, and subderpartments, and further breaking it up into separate courses, tends to conceal the homogeneity of knowledge, and at the same time to omit much which falls between the courses."

"You ought to try to make significant contributions to humanity rather than just get along through life comfortably... the life of trying to achieve excellence in some area is in itself a worthy goal... A life without a struggle on your part to make yourself excellent is hardly a life worth living. ...a life without such a goal... is merely existing..."

"Transmission through space (typically signaling) is the same as transmission through time (storage)."

"The more complex the designed system the more field maintenance must be central to the final design. Only when field maintenance is part of the original design can it be safely controlled... This applies to both mechanical things and to human organizations."

"Somewhere in the mid-to-late 1950s in an address to the President and V.Ps of Bell Laboratories I said, "At present we are doing 1 out of 10 experiments on the computers and 9 in the labs, but before I leave it will be 9 out of 10 on the machines". They did not believe me... by now we do somewhere between 90% to 99% on the machines... And this trend will go on!"

"We must not forget, in all the enthusiasm for computer simulations, occasionally we must look at Nature as She is."

"The people at the bottom do not have the larger, global view, but at the top they do not have the local view of all the details, many of which can often be very important, so either extreme gets poor results."

"An idea which arises in the field, based on the direct experience of the people doing the job, cannot get going in a centrally controlled system... The not invented here (NIH) syndrome is one of the major curses of our society..."

"The Buddha told his disciples, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense". I say the same to you—you must assume the responsibility for what you believe."

"Unfortunately... the ADA language was designed by experts, and it shows all the non-humane features you can expect from them. It is... a typical Computer Science hacking job—do not try and understand what you are doing, just get it running. As a result of this poor psychological design... although a government contract may specify the programming be in ADA, probably over 90% will be done in FORTRAN, debugged, tested, and then painfully, by hand, be converted to a poor ADA program, with a high probability of errors!"

"The fundamentals of language are not understood to this day. ...Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish."

"When you take a course in Euclidean geometry is not the teacher putting a... learning program into you? ...You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems. ...Are you sure you are not merely "programmed" in life by what by chance events happens to you?"

"We are beginning to find not only is intelligence not adequately defined so arguments can be settled scientifically, but a lot of other associated words like, computer, learning, information, ideas, decisions, expert behavior—all are a bit fuzzy..."

"This is the type of AI I am interested in—what can the human and machine do together, and not in the competition which can arise. ...There are doubts as to what fraction of the population can compete with computers, even with nice interactive prompting menus."

"The feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others!"

"We constantly use the word "simplify", but its meaning depends on what you are going to do next, and there is no uniform definition."

"Perhaps thinking should be measured not by what you do but by how you do it."

"I know that the great Hilbert said, "We will not be driven out of the paradise Cantor has created for us," and I reply, "I see no reason for walking in!" Indeed, in time, as more and more people get used to computers, I am inclined to believe that we here on this Earth will decide that the computable numbers are enough."

"Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results they themselves seem to deny any meaning. Is that to be the mathematics we are to use to understand the world we live in?"

"[Oddly enough, Putnam believes part of the attraction of some of these formalisms is their obscurity]. "I think part of the appeal of mathematical logic is that the formulas look mysterious - you write backward Es!""

"It was Rudolf Carnap’s dream for the last three decades of his life to show that science proceeds by a formal syntactic method; today no one to my knowledge holds out any hope for that project."

"These papers are all written from what is called a realist perspective. The statements of science are in my view either true or false (although it is often the case that we don't know which) and their truth or falsity does not consist in their being highly derived ways of describing regularities in human experience. Reality is not a part of the human mind; rather the human mind is a part - and a small part at that - of reality."

"If the importance of science does not lie in its constituting the whole of human knowledge, even less does it lie, in my view, in its technological applications. Science at the best is a way of coming to know, and hopefully a way of acquiring some reverence for, the wonders of nature. The philosophical study of science, at the best, has always been a way of coming to understand both some of the nature and some of the limitations of human reason. These seem to me to be sufficient grounds for taking science and philosophy of science seriously; they do not justify science worship."

"In closing, I can only apologize for not having given any positive account of either mathematical truth or mathematical necessity. I can only say that I have not given such an account because I think that the search for such an account is a fundamental mistake. It is not that there is nothing special about mathematics; it is that, in my opinion, the investigation of mathematics must presuppose and not seek to account for the truth of mathematics. But this is the beginning of another paper and not the end of this one."

"The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets'. (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory."

"The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction."

"The philosophy of physics is continuous with physics itself. Just as certain issues in the Foundations of Mathematics have been discussed by both mathematicians and by philosophers of mathematics, so certain issues in the philosophy of physics have been discussed by both physicists and by philosophers of physics. And just as there are issues of a more epistemological kind that tend to concern philosophers of mathematics more than they do working mathematicians, so there are issues that concern philosophers of physics more than they do working physicists."

"In conclusion, then, no satisfactory interpretation of quantum mechanics exists today. The questions posed by the confrontation between the Copenhagen interpretation and the hidden variable theorists go to the very foundations of microphysics, but the answers given by hidden variable theorists and Copenhagenists are alike unsatisfactory. Human curiosity will not rest until those questions are answered, but whether they will be answered by conceptual innovations within the framework of the present theory or only within the framework of an as yet unforeseen theory is unknown. The first step toward answering them has been attempted here. It is the modest but essential step of becoming clear on the nature and magnitude of the difficulties."

"Analytic philosophers - both in the 'constructivist' camp and in the camp that studies 'the ordinary use of words' - are disturbingly unanimous in regarding 2-valued logic as having a privileged position: privileged, not just in the sense of corresponding to the way we do speak, but in the sense of having no serious rival for logical reasons. If the foregoing analysis is correct, this is a prejudice of the same kind as the famous prejudice in favor of a privileged status for Euclidean geometry (a prejudice that survives in the tendency to cite 'space has three dimensions' as some kind of 'necessary' truth). One can go over from a 2-valued to a 3-valued logic without totally changing the meaning of 'true' and 'false'; and not just in silly ways, like the ones usually cited (e.g. equating truth with high probability, falsity with low probability, and middlehood with 'in between' probability)."

"I might try to save the view that 'future contingents' have no truth value by saying that even present-tense statements have no truth value if they refer to the outcome of events that are so far away that a causal signal informing me of the outcome could not have reached me-now without traveling faster than light. In other words, I might attempt saying that statements about events that are in neither the upper half nor the lower half of my light-cone have no truth value. In addition, statements about events in the upper half of my light-cone have no truth value, since they are in my future according to every coordinate system. So only statements about events in the lower half of my light-cone have a truth value; only events that are in 'my past* according to all observers are determined."

"To sum up: we have seen that of the three notions of 'partial interpretation' discussed, each is either unsuitable for Carnap's purposes (starting with observation terms), or incompatible with a rather minimal scientific realism; and, in addition, the second notion depends upon gross and misleading changes in our use of language. Thus in none of these senses is 'a partially interpreted calculus in which only the observation terms are directly interpreted' an acceptable model for a scientific theory."

"In sum, a theory is only accepted if the theory has substantial, non-ad hoc, explanatory successes. This is in accordance with Popper; unfortunately, it is in even better accordance with the 'inductivist' accounts that Popper rejects, since these stress support rather than falsification."

"Carnap was driven from Germany by Hitler, and his position has been condemned in the Soviet Union as 'subjective idealism*. Even in the United States, there have been a great many who could not understand this attempt to turn philosophy into a scientific discipline with substantive scientific results, and who have been led to extreme and absurd misinterpretations of the work I have been reporting to you here. Few, perhaps, would have expected traditional empiricism to lead to the development of a speculative theory of ' universal learning machines'; and yet, in retrospect, a concern with systematizing inductive logic has been the oldest concern of empiricist philosophers from Bacon on. No one can yet predict the outcome of this speculative scientific venture. But it is amply clear, whether this particular venture succeeds or fails, that the toleration of philosophical and scientific speculation brings rich rewards and that its suppression leads to sterility."

"In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets."

"Truth and falsity are the most fundamental terms of rational criticism, and any adequate philosophy must give some account of these, or failing that, show that they can be dispensed with."

"I have not attempted in these papers to put forward any grand view of the nature of philosophy; nor do I have any such grand view to put forward if I would. It will be obvious that I do not agree with those who see philosophy as the history of 'howlers', and progress in philosophy as the debunking of howlers. It will also be obvious that I do not agree with those who see philosophy as the enterprise of putting forward a priori truths about the real world (since, for one thing, there are no a priori truths, in my view). I see philosophy as a field which has certain central questions, for example, the relation between thought and reality, and, to mention some questions about which I have not written, the relation between freedom and responsibility, and the nature of the good life. It seems obvious that in dealing with these questions philosophers have formulated rival research programs, that they have put forward general hypotheses, and that philosophers within each major research program have modified their hypotheses by trial and error, even if they sometimes refuse to admit that that is what they are doing. To that extent philosophy is a 'science'. To argue about whether philosophy is a science in any more serious sense seems to me to be hardly a useful occupation. The important thing is that in spite of the stereotypes of science and philosophy that have become blinkers inhibiting the view of laymen, scientists, and philosophers, science and philosophy are interdependent activities; philosophers have always found it essential to draw upon the scientific knowledge of the time, and scientists have always found it essential to do a certain amount of philosophy in their very scientific work, even if they denied that that was what they were doing. It does not seem to me important to decide whether science is philosophy or philosophy is science as long as one has a conception of both that makes both essential to a responsible view of the real world and of man's place in it."

"The techniques employed by philosophers of physics are usually the very ones being employed by philosophers of a less specialized kind (especially empiricist philosophers) at the time. Thus Mill's philosophy of science largely reflects Hume's associationism; Reichenbach's philosophy of science reflects Viennese positivism with its conventionalism, its tendency to identify (or confuse) meaning and evidence, and its sharp dichotomy between 'the empirical facts' and 'the rules of the language'; and (coming up to the present time) Toulmin's philosophy of science is an attempt to give an account of what scientists do which is consonant with the linguistic philosophy of Wittgenstein. For this reason, errors in general philosophy can have a far-reaching effect on the philosophy of science. The confusion of meaning with evidence is one such error whose effects are well known: it is the contention of the present paper that overworking of the analytic-synthetic distinction is another root of what is most distorted in the writings of conventional philosophers of science."

"I do not agree with Quine, that there is no analytic-synthetic distinction to be drawn at all. But I do believe that his emphasis on the monolithic character of our conceptual system and his negative emphasis on the silliness of regarding mathematics as consisting in some sense of 'rules of language', represent exceedingly important theoretical insights in philosophy. I think that what we have to do now is to settle the relatively trivial question concerning analytic statements properly so called ('All bachelors are unmarried'). We have to take a fresh look at the framework principles so much discussed by philosophers, disabusing ourselves of the idea that they are 'rules of language' in any literal or lexicographic sense; and above all, we have to take a fresh look at the nature of logical and mathematical truths. With Quine's contribution, we have to face two choices: We can ignore it and go on talking about the 'logic' of individual words. In that direction lies sterility and more, much more, of what we have already read. The other alternative is to face and explore the insight achieved by Quine, trying to reconcile the fact that Quine is overwhelmingly right in his critique of what other philosophers have done with the analytic-synthetic distinction with the fact that Quine is wrong in his literal thesis, namely, that the distinction itself does not exist at all. In the latter direction lies philosophic progress. For philosophic progress is nothing if it is not the discovery of new areas for dialectical exploration."

"In short, analytic statements are statements which we all accept and for which we do not give reasons. This is what we mean when we say that they are true by 'implicit convention'. The problem is then to distinguish them from other statements that we accept, and do not give reasons for, in particular from the statements that we unreasonably accept. To resolve this difficulty, we have to point out some of the crucial distinguishing features of analytic statements (e.g. the fact that the subject concept is not a law-cluster concept), and we have to connect these features with what, in the preceding section, was called the 'rationale' of the analytic-synthetic distinction. Having done this, we can see that the acceptance of analytic statements is rational, even though there are no reasons (in the sense of' evidence') in connection with them."

"It is evident that Feyerabend is misusing the term 'meaning.' He is not alone in such misuse: in the last thirty years, misusing the term 'meaning' has been one of the most common, if least successful, ways of 'establishing' philosophical propositions. But how did this distressing state of affairs come to be? The blame must be placed squarely upon the Logical Positivists. The 'Verifiability Theory of Meaning' ('the meaning of a sentence is its method of verification') was, from the first, nothing but a persuasive redefinition. If to call metaphysical propositions 'meaningless' were only to assert that these propositions are empirically untestable, it would be harmless (the metaphysicians always said that their assertions were neither empirically testable nor tautologies); but, of course, it is not harmless, because the Positivist hopes that we will accept his redefinition of the term 'meaning,' while retaining the pejorative connotations of being 'meaningless' in the customary {linguistic) sense, i.e. being literally without sense."

"Why, then, is semantics so hard? In terms of the foregoing, I want to suggest that semantics is a typical social science. The sloppiness, the lack of precise theories and laws, the lack of mathematical rigor, are all characteristic of the social sciences today. A general and precise theory which answers the questions (i) why do words have the different sorts of functions they do? and (2) exactly how does conveying core facts enable one to learn the use of a word? is not to be expected until one has a general and precise model of a language-user; and that is still a long way off. But the fact that Utopia is a long way off does not mean that daily life should come to a screeching halt. There is plenty for us to investigate, in our sloppy and impressionistic fashion, and there are plenty of real results to be obtained. The first step is to free ourselves from the oversimplifications foisted upon us by the tradition, and to see where the real problems lie. I hope this paper has been a contribution to that first step."

"On another possible world or another planet a word might be associated with much the same stereotype and much the same criteria as our term 'water', but it might designate XYZ and not H₂O. At least this could happen in a prescientific era. And it would not follow that XYZ was water; it would only follow that XYZ could look like water, taste like water, etc. What 'water' refers to depends on the actual nature of the paradigms, not just on what is in our heads."

"Before I give the argument, let us consider why it seems so strange that such an argument can be given (at least to philosophers who subscribe to a 'copy' conception of truth). We conceded that it is compatible with physical law that there should be a world in which all sentient beings are brains in a vat. As philosophers say, there is a 'possible world' in which all sentient beings are brains in a vat. (This 'possible world' talk makes it sound as if there is a place where any absurd supposition is true, which is why it can be very misleading in philosophy.) The humans in that possible world have exactly the same experiences that we do. They think the same thoughts we do (at least, the same words, images, thought-forms, etc., go through their minds). Yet, I am claiming that there is an argument we can give that shows we are not brains in a vat. How can there be? And why couldn't the people in the possible world who really are brains in a vat give it too? The answer is going to be (basically) this: although the people in that possible world can think and 'say' any words we can think and say, they cannot (I claim) refer to what we can refer to. In particular, they cannot think or say that they are brains in a vat {even by thinking 'we are brains in a vat)."

"Even if we consider not words by themselves but rules deciding what words may appropriately be produced in certain contexts — even if we consider, in computer jargon, programs for using words — unless those programs themselves refer to something extra-linguistic there is still no determinate reference that those words possess. This will be a crucial step in the process of reaching the conclusion that the Brain-in-a-Vat Worlders cannot refer to anything external at all (and hence cannot say that they are Brain-in-a-Vat Worlders)."

"What we have is a device for producing sentences in response to sentences. But none of these sentences is at all connected to the real world. If one coupled two of these machines and let them play the Imitation Game with each other, then they would go on 'fooling' each other forever, even if the rest of the world disappeared! There is no more reason to regard the machine's talk of apples as referring to real world apples than there is to regard the ant's 'drawing' as referring to Winston Churchill."

"To me, believing that some correspondence intrinsically just is reference (not as a result of our operational and theoretical constraints, or our intentions, but as an ultimate metaphysical fact) amounts to a magical theory of reference. Reference itself becomes what Locke called a 'substantial form' (an entity which intrinsically belongs with a certain name) on such a view. Even if one is willing to contemplate such unexplainable metaphysical facts, the epistemological problems that accompany such a metaphysical view seem insuperable. For, assuming a world of mind- independent, discourse-independent entities (this is the presupposition of the view we are discussing), there are, as we have seen, many different 'correspondences' which represent possible or candidate reference relations (infinitely many, in fact, if there are infinitely many things in the universe)."

"Even though the model referred to satisfies the theory, etc., it is 'unintended'; and we recognize that it is unintended from the description through which it is given (as in the intuitionist case). Models are not lost noumenal waifs looking for someone to name them; they are constructions within our theory itself. and they have names from birth."

"Let me close with a picture. My picture of our situation is not the famous Neurath picture of science as the enterprise of reconstructing a boat while the boat floats on the open ocean, but it is a modification of it. I would change Neurath's picture in two ways. First, I would put ethics, philosophy, in fact the whole culture, in the boat, and not just 'science', for I believe all the parts of the culture are inter- dependent. And, second, my image is not of a single boat but of a fleet of boats. The people in each boat are trying to reconstruct their own boat without modifying it so much at anyone time that the boat sinks, as in the Neurath image. In addition, people are passing supplies and tools from one boat to another and shouting advice and encouragement (or discouragement) to each other. Finally, people sometimes decide they don't like the boat they're in and move to a different boat altogether. (And sometimes a boat sinks or is abandoned.) It's all a bit chaotic; but since it is a fleet, no one is ever totally out of signalling distance from all the other boats. There is, in short, both collectivity and individual responsibility. If we hanker for more, is that not our old and unsatisfiable yearning for Absolutes?"

"If reason is both transcendent and immanent, then philosophy, as culture-bound reflection and argument about eternal questions, is both in time and eternity. We don't have an Archimedean point; we always speak the language of a time and place; but the rightness and wrongness of what we say is not just for a time and a place."

"To require that all of these must be reducible to a single version is to make the mistake of supposing that 'Which are the real objects?' is a question that makes sense independently of our choice of concepts."

"The problem with all this--the problem I discussed in the first lecture--is that if the causes/background conditions distinction is fundamentally subjective, not descriptive of the world in itself, then current philosophical explanations of the metaphysical nature of reference are bankrupt."

"Now, moral philosophers generally prefer to talk about virtues, or about (specific) duties, rights, and so on, rather than about moral images of the world. There are obvious reasons for this; nevertheless, I think that it is a mistake, and that Kant is profoundly right. What we require in moral philosophy is, first and foremost, a moral image of the world, or rather--since, here again, I am more of a pluralist than Kant--a number of complementary moral images of the world."

"No sane person should believe that something is 'subjective' merely because it cannot be settled beyond controversy."

"What I am saying, then, is that elements of what we call "language" or "mind" penetrate so deeply into what we call "reality" that the very project of representing ourselves as being "mappers" of something "language-independent" is fatally compromised from the very start. Like Relativism, but in a different way, Realism is an impossible attempt to view the world from Nowhere. In this situation it is a temptation to say, "So we make the world," or "our language makes up the world," or "our culture makes up the world"; but this is just another form of the same mistake. If we succumb, once again we view the world-the only world we know-as a product. One kind of philosopher views it as a product from a raw material: Unconceptualized Reality. The other views it as a creation ex nihilo. But the world isn't a product. It's just the world."

"Philosophers today are as fond as ever of apriori arguments with ethical conclusions. One reason such arguments are always unsatisfying is that they always prove too much; when a philosopher 'solves' an ethical problem for one, one feels as if one had asked for a subway token and been given a passenger ticket valid for the first interplanetary passenger-carrying space ship instead."

"Part of what makes moral philosophy an anachronistic field is that its practitioners continue to argue in this very traditional and aprioristic way even though they themselves do not claim that one can provide a systematic and indubitable 'foundation' for the subject. Most of them rely on what are supposed to be 'intuitions' without claiming that those intuitions deliver uncontroversial ethical premises, on the one hand, or that they have an ontological or epistemological explanation of the reliability of those intuitions, on the other."

"To successfully adjudicate ethical problems, as opposed to 'solving' them, it is necessary that the members of the society have a sense of community. A compromise that cannot pretend to be the last word on an ethical question, that cannot pretend to derive from binding principles in an unmistakeably constraining way, can only derive its force from a shared sense of what is and is not reasonable, from loyalties to one another, and a commitment to 'muddling through' together."

"A few years ago I had occasion to visit Peru, and I got to know a fine philosopher and a truly wonderful human being-Francisco Miro Casada. Miro Casada has been an idealist all his life, while being, at the same time, a man of great experience (a former member of several governments and a former Ambassador to France). I found him a man who represents the social democratic vision in its purest form. Talking to him, and to my other friends in Peru (who represented quite a spectrum of political opinion), I heard something that was summed up in a remark he, Miro Casada, made to me, "Whenever you have a Republican president, we get a wave of military dictatorships in Latin America"."

"The similarity between Marxism and neoconservativism might be expressed in the following way: both perspectives say that certain injustices can't be cured under our present system of political democracy and mixed economy. The Marxist concludes that we have to overthrow the present system and the neoconservative concludes that we have to live with the injustices. But they are both wrong."

"My own view is that philosophy at its best has always, in every period, included some philosophers who brilliantly represent the moral face of the subject and some philosophers who brilliantly represent the theoretical face, as well as some geniuses whose insights span and unite both sides of the subject. To renounce either the moral ambitions of philosophy or its theoretical ambitions is not just to kill the subject of philosophy; it is to commit intellectual and spiritual suicide."

"To me it seems clear that the descriptions of human life we find in the novels of Tolstoy or George Eliot are not mere entertainment; they teach us to perceive what goes on in social and individual life. And such descriptions require the many subtle distinctions that ordinary language has made available to us. The question of the relevance or irrelevance of “how we speak” is not just a question for philosophers, although it is that too. It is a question for philosophers because once ordinary language is laughed out of the room, philosophical theories are no longer held responsible at all to the ways we actually speak and actually live; but it is a question for more than just philosophers because, at bottom, contempt for ordinary language is contempt for all the humanities."

"Philosophy was never just ontotheology, and even when philosophers were concerned with ontotheology, they were concerned with much more than that. That is the first reason that the idea of a fundamental “crisis” in philosophy and of the “end of philosophy” is deeply mistaken. And if the questions of philosophy are indeed “unsettleable,” in the sense that they will always be with us, that is a wonderful thing, not something to be regretted."

"What we are left with, if what I have said so far is right, is a conclusion that I initially found very distressing: either GRW or some successor, or else Bohm or some successor, is the correct interpretation—or, to include a third possibility to please Itamar Pitowski, we will just fail to find a scientific realist interpretation which is acceptable. (And the ghost of Bohr will laugh, and say, ‘I told you all along that the human mind cannot produce a realist interpretation of quantum mechanics’!)"

"He’s a quantum philosopher. I can’t understand him and his position at the same time."

"Every new discovery in science brings with it a host of new problems, just as the invention of the automobile brought with it gas stations, roads, garages, mechanics, and a thousand other subsidiary details."

"No longer was light analogous to the discharge of a blunderbuss, but rather to the pulsating flight of birds."

"Origami helps in the study of mathematics and science in many ways. … Using origami anyone can become a scientific experimenter with no fuss."

"Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise."

"The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data."

"The tool that is so dull that you cannot cut yourself on it is not likely to be sharp enough to be either useful or helpful."

"Last time, I asked: "What does mathematics mean to you?" And some people answered: "The manipulations of numbers, the manipulation of structures." And if I had asked what music means to you, would you have answered: "The manipulation of notes?""

"I am not here concerned with intent, but with scientific standards, especially the ability to tell the difference between a fact, an opinion, a hypothesis, and a hole in the ground."

"I don't like the nonsense that passes for rational discourse so often in our society. I am very much bothered by the inaccuracies, ambiguities, code words, slogans, catch phrases, public relation devices, sweeping generalizations, and stereotypes, which are used (consciously or otherwise) to influence people."

"Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended."

"The acceleration of technological progress has been the central feature of this century."

"We can solve many problems thousands of times faster than natural selection. Now, by creating the means to execute those simulations at much higher speeds, we are entering a regime as radically different from our human past as we humans are from the lower animals."

"I have argued above that we cannot prevent the Singularity, that its coming is an inevitable consequence of the humans' natural competitiveness and the possibilities inherent in technology. And yet … we are the initiators. Even the largest avalanche is triggered by small things. We have the freedom to establish initial conditions, make things happen in ways that are less inimical than others. Of course (as with starting avalanches), it may not be clear what the right guiding nudge really is..."

"The work that is truly productive is the domain of a steadily smaller and more elite fraction of humanity."

"Quit crossing your fingers, Wim; the only thing that’ll ever save you from is the respect of educated men."

"Wil wondered fleetingly if she might be psychopathic, and not merely young and naive."

"There may have been some time in the past when a group calling themselves astrologers could produce results. I don’t know, and the matter doesn’t interest me, for I live in the present. In our time the men working in the name of astrology are incapable of producing results, are conscious frauds."

"Even as my conscious mind concluded that we were under fire, I threw myself on the ground and flatten into the lowest profile possible. You’ve heard the bromide about combat making life more real. I don’t know about that, but it’s certainly true that when you are flat against the ground with your face in the dirt, the whole universe looks different."

"Our system is founded on the Concept of Chaos. The universe is basically a dark and Unhappy place—a place where evil and injustice and randomness rule. The ironic thing is that the very act of organization creates the potential for even greater ruin. Social organizations have a natural tendency to become monopolistic and inflexible. When they finally break down, it is a catastrophic debacle. So, we must except a great deal of disorder and violence in our lives if we are to avoid a complete blow up later."

"The closer a Citizen came to the centers of power, the more of a madhouse the universe became."

"She was obviously an idealist: that is, someone who can twist his every vice into self-righteous morality."

"Some dreams take a long time in dying. Some get a last minute reprieve…and that can be even worse."

"One of his many mottos was, “If you didn’t figure it out yourself, you don’t understand it.”"

"Every state religion he’d ever seen had a core of hypocrisy. That was why he’d been against bringing “Hrala” ashore—he knew the priests would never accept their theology suddenly incarnate."

"Principal Alcalde was into a long speech, about the fast-changing world and the need for Fairmont to revolutionize itself from semester to semester. At the same time they must never forget the central role of modern education, which was to teach the kids how to learn, how to pose questions, how to be adaptable—all without losing their moral compass."

"Over the last twenty years, the worldwide net had come to be a midden of bogus sites and recursive fraudulence…telling truth from fantasy was often the hardest thing about using the web."

"That was the old saying: Once your secret is outed anywhere, however briefly, it is outed forever. “Oh, I don’t know,” said Juan. “The way to cover a slip is to embellish it, hide it in all sorts of fake secrets.”"

"Did you ever think? Old-fashioned writing is the ultimate in context tagging. It’s passive, informative, and present exactly where you need it."

"How to explain? How to describe? Even the omniscient viewpoint quails."

"Poor humans; they will all die." "Poor us; we will not."

"The hours came to minutes, the minutes to seconds. And now each second was as long as all the time before."

"Peregrine Wickwrackrum was of two minds about evil: when enough rules get broken, sometimes there is good amid the carnage."

"The voice was gentle, like a scalpel petting the short hairs of your throat."

"Politics may come and go, but Greed goes on forever."

"He was guided by what he saw rather than by what he wanted to believe."

"Life is a green madness just now, trying to squeeze the last bit of warmth from the season."

"I say, let’s learn more and then speculate."

"Sometimes terror and pain are not the best levers; deception, when it works, is the most elegant and least expensive manipulation of all."

"If during the last thousand seconds you have received any High-Beyond-protocol packets from "Arbitration Arts," discard them at once. If they have been processed, then the processing site and all locally netted sites must be physically destroyed at once. We realize that this means the destruction of solar systems, but consider the alternative. You are under Transcendent attack."

"Hexapodia as the key insight... I haven’t had a chance to see the famous video from Straumli Realm, except as an evocation. (My only gateway onto the Net is very expensive.) Is it true that humans have six legs?"

"It was not called the Net of a Million Lies for nothing."

"We've watched the Homo Sapiens interest group since the first appearance of the Blight. Where is this "Earth" the humans claim to be from? "Half way around the galaxy," they say, and deep in the Slow Zone. Even their proximate origin, Nyjora, is conveniently in the Slowness. We see an alternative theory: Sometime, maybe further back than the last consistent archives, there was a battle between Powers. The blueprint for this "human race" was written, complete with communication interfaces. Long after the original contestants and their stories had vanished, this race happened to get in position where it could Transcend. And that Transcending was tailor-made, too, re-establishing the Power that had set the trap to begin with.We're not sure of the details, but a scenario such as this is inevitable. What we must do is also clear. Straumli Realm is at the heart of the Blight, obviously beyond all attack. But there are other human colonies. We ask the Net to help in identifying all of them. We ourselves are not a large civilization, but we would be happy to coordinate the information gathering, and the military action that is required to prevent the Blight's spread in the Middle Beyond. For nearly seventeen weeks, we've been calling for action. Had you listened in the beginning, a concerted strike might have been sufficient to destroy the Straumli Realm. Isn't the Fall of Relay enough to wake you up? Friends, if we act together we still have a chance.Death to vermin."

"Well, what do you know," Pham said. "Butterflies in jackboots."

"He claimed that nearby gun thunder cleared the mind—but most everybody else agreed it made you daft."

"Effective translation of natural languages comes awfully close to requiring a sentient translator program."

"All his life he had lived by the law. Often his job had been to stop acts of revenge....And now revenge was all that life had left for him."

"Sometimes the biggest disasters aren’t noticed at all—no one’s around to write horror stories."

"Over the last few weeks, some newsgroups have been full of tales of war and battle fleets, of billions dying in the clash of species. To all such—and those living more peaceably around them—we say look out on the universe. It does not care, and even with all our science there are some disasters that we can not avert. All evil and good is petty before Nature. Personally, we take comfort from this, that there is a universe to admire that cannot be twisted to villainy or good, but which simply is."

"The heart of manipulation is to empathize without being touched."

"“I have come to kill you.” The death’s heads shrugged. “You have come to try.”"

"If there be only hours, at least learn what there is time to learn."

"Peregrine Wickwrackscar was flying. A pilgrim with legends that went back almost a thousand years—and not one of them could come near to this!"

"They’re very good at reaching nonsense conclusions from insufficient information."

"Technical people don’t make good slaves. Without their wholehearted cooperation, things fall apart."

"So high, so low, so many things to know."

"Interesting problem, pain. So helpful, so obnoxious."

"The old truths still hold: without a sustaining civilization, no isolated collection of ships and humans can rebuild the core of technology."

"So even in hell, there are clowns."

"Politics may come and go, but trade goes on forever."

"Being alone was something he was very good at. There was so much to learn."

"The essence of real creativity is a certain playfulness, a flitting from idea to idea without getting bogged down by fixated demands. Of course, you don’t always get what you thought you were asking for. From this era on, I think invention will be the parent of necessity—and not the other way around."

"Didn’t Underhill understand? All decent societies agreed on basic issues, things that meant the healthy survival of their people. Things might be changing, but it was self-serving nonsense to throw the rules overboard."

"Funny how the least attempt at deception always seems to make life more complicated."

"Yet, even with the greatest care, a technological civilization carried the seeds of its own destruction. Sooner or later, it ossified and politics carried it into a fall."

"Civilizations rise and fall, but all technical civilizations know the greatest secrets now. They know which social mechanisms normally work, and which ones quickly fail. They know the means to postpone disaster and evade the most foolish catastrophes. They know that even so, each civilization must inevitably fall."

"Pham was overwhelmed by the other things that Gunnar Larson had to say, the advice that might be worthless but that had the stench of wisdom."

"There had been an era of ubiquitous law enforcement, and some kind of distributed terror."

"There was an old Qeng Ho saying, “You know you’ve stayed too long when you start using the locals’ calendar.”"

"“Do you think she really believes what she’s saying?” “Sure she believes it. That’s what makes her so funny.”"

"There is a deepness in the sky, and it extends forever."

"This was the sort of desperate hallucination he must guard against. If you raise your desires high enough, certainty can grow out of the background noise."

"Viki was awed by all the incredible quackery. Daddy thought such things were amusing—“like religion but not so deadly.”"

"“We think the governance has opted for ubiquitous law enforcement.” Pham whistled softly. Now every embedded computing system, down to a child’s rattle, was a governance utility. It was the most extreme form of social control ever invented. “So now they have to run everything.” The notion was terribly seductive to the authoritarian mind."

"What do you do when your dream dies?"

"What do you do when your dream dies? Dreams die in every life. Everyone gets old. There is promise in the beginning when life seems so bright. The promise fades when the years get short."

"So what do you do when your dream dies? When your dream dies, you give it up."

"The hard facts are extraordinary, without adding superstitious mumbo-jumbo."

"Yes, we did quite well. But then, telling people what they want to believe is an easy job."

"The more you realized what the stars really were, the more you realized what the universe must really be."

"“But see, your theory ‘explains’ all sorts of things without helping to do anything, much less providing tests for itself.”"

"So much technology, so little talent."

"In instituting the , the has recognized the dual character of mathematics. On the one hand, mathematics is one of the essential emanations of the human spirit,—a thing to be valued in and for itself, like art or poetry. made notable contributions to this side of mathematics in his work on and multiple algebras. On the other hand, mathematics is the handmaiden and the helper of the other sciences, both in their most abstract generalizations and in their most concrete applications in industry."

"The importance of the theory of s in physical problems is due to the fact that when coordinates are used to describe physical phenomena (e.g. those studied in geometry) it is usually the case that the coordinates are no part of the phenomena themselves. They are generally put into the description by the observer. Therefore it is desirable to have the description in such terms that when stated in terms of one coordinate system, it can be read off easily in terms of other systems. Such statements will employ invariants of one sort or another."

"In the late 1920s and early 1930s, Veblen carried out three extraordinary initiatives. He helped to create the original . He influenced ’s decision to locate the in Princeton rather than Newark. And he became a founding member of the , which brought hundreds of refugees to Princeton and other universities."

"Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth."

"The creative scientist lives in a 'wildness of logic,' where reason is the handmaiden and not the master."

"Historians often do not mention the truly important features of daily life, like games, concentrating instead on tedious political maneuvering."

"There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians.’ an ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians... Feynman is a magician of the highest caliber."

"Unrestricted abstraction tends to divert attention from whole areas of application whose very discovery depends of the features that the abstract point of view rules out as being accidental."

"Creative people live in two worlds. One is the ordinary world which they share with others and in which they are not in any special way set apart from their fellow men. The other is private and it is in this world that the creative acts take place."

"In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the “ordinary” and the “magicians.’’ An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works. Richard Feynman is a magician of the highest caliber. Hans Bethe, whom Dyson considers to be his teacher, is an “‘ordinary genius’’; so much so that one may gain the erroneous impression that he is not a genius at all. But it was Feynman, only slightly older than Dyson, who captured the young man’s imagination. To be a physicist must have meant to him to be like Feynman and this, alas, was impossible. And so Dyson fell back on the source of strength he always had in reserve: the mastery of mathematical technique."

"In the summer of 1930 my academic future, however, was not uppermost in my mind. I had been stricken by an acute attack of a disease which at regular intervals afflicts all mathematicians and, for that matter, all scientists: I became obsessed by a problem."

"I had a phenomenal memory and could recite long poems by Russian poets, mainly Pushkin. Except for an unusual memory, I was not precocious in any respect and somewhat later, to the chagrin of my father, I was inordinately slow learning the multiplication tables."

"When one is young, and seventeen is very young, one lives in the present. The future, even the near future, is cloaked in unreality."

"There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory."

"Independence is the central concept of probability theory and few would believe today that understanding what it meant was ever a problem."

"There was hardly a page in Markov's book which did not feature the normal law and it cast a spell over me from which I have never fully recovered. Adding to the fascination was the impression that somehow the normal law was the key to mysterious and elusive world of chance phenomena."

"As an introduction to America, my ten months in Baltimore were superb. I find it difficult to find words to convey the feeling of decompression, of freedom, of being caught in a sweep of unimagined and unimaginable grandeur. It was a life on a different scale with more of everything - more air to breathe, more things to see, more people to know."

"Where there is independence there must be the normal law."

"As a mathematician Erdös is what in other fields is called a "natural". If a problem can be stated in terms he can understand, though it may belong to a field with which he is not familiar, he is as likely as, or even more likely than, the experts to find a solution."

"I didn't even try to penetrate the comics, though many years later I came, somewhat grudgingly, to admire Pogo."

"I prefer concrete things and I don't like to learn more about abstract stuff than I absolutely have to."

"Actually, my solution generated considerable further work and the "dog-flea" model keeps cropping up from time to time in unexpected contexts."

"I then reached for a time honored tactic used by mathematicians: if you can't solve the real problem, change it into one you can solve."

"Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man's curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man's desire to probe the workings of his own mind."

"When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics."

"The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts."

"The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space."

"The manner in which mathematical theories are applied does not depend on preconceived ideas; it is a purposeful technique depending on, and changing with, experience."

"The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry."

"Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities."

"Only yesterday the practical things of today were decried as impractical, and the theories which will be practical tomorrow will always be branded as valueless games by the practical man of today."

"When a coin is tossed, it does not necessarily fall heads or tails; it can roll away or stand on its edge."

"This means that if in a city seven accidents occur each week, then (assuming that all possible distributions are equally likely) practically all weeks will contain days with two or more accidents, and on the average only one week out of 165 will show a uniform distribution of one accident per day."

"Simple methods will soon lead us to results of far reaching theoretical and practical importance. We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted notions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued."

"To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual."

"The notion of conditional probability is a basic tool of probability theory, and it is unfortunate that its great simplicity is somewhat obscured by a singularly clumsy terminology."

"Infinite product spaces are the natural habitat of probability theory."

"The theory of independent experiments is the analytically simplest and most advanced part of probability theory."

"It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption."

"The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has nothing to do with imperfections of physical coins; it endows nature with memory, or, in our terminology, it denies the stochastic independence of successive trials. Marbe's theory cannot be refuted by logic but is rejected because of empirical support."

"Warning. It is usual to read into the law of large numbers things which it definitely does not imply. If Peter and Paul toss a perfect coin 10,000 times, it is customary to expect that Peter will be in the lead roughly half the time. This is not true. In a large number of different coin-tossing games it is reasonable to expect that any fixed moment heads will be in the lead in roughly half of all cases. But it is quiet likely that the player who ends at the winning side has been in the lead for practically the whole duration of the game. Thus, contrary to widespread belief, the time average for any individual game has nothing to do with the ensemble average at any given moment."

"The painful experience of many gamblers has taught us the lesson that no system of betting is successful in improving the gambler's chances. If the theory of probability is true to life, this experience must correspond to a provable statement."

"Note the situation is different when the player is permitted to vary his stakes. In this case there exist advantageous strategies, and the game depends on the strategy."

"It has been suggested that an army of monkeys might be trained to pound typewriters at random in the hope that ultimately great works of literature would be produced. Using a coin for the same purpose may save feeding and training expenses and free the monkeys for other monkey business."

"The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game."

"Much harm was done by the misleading suggestive power of this name. It must be understood that a fair game may be distinctly unfavorable to the player."

"This faulty intuition as well as many modern applications of probability theory are under the strong influence of traditional misconceptions concerning the meaning of the law of large numbers and of a popular mystique concerning a so-called law of averages."

"It is not necessary to think of gambling places; the statistician who applies statistical tests is engaged in a dignified sort of gambling, and in his case the distribution of the random variables changes from occasion to occasion."

"The fact that the mean recurrence time is infinite implies that the chance fluctuations in an individual prolonged coin-tossing game are far removed from the familiar pattern governed by the normal distribution."

"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction."

"It is seen that continued shuffling may reasonably be expected to produce perfect "randomness" and to eliminate all traces of the original order. It should be noted, however, that the number of operations required for this purpose is extremely large."

"In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions."

"It should be noted that this duration is considerably longer than we naively expect. If two players with 500 dollars each toss a coin until one is ruined, the average duration of the game is 250,000 trials. If a gambler has only one dollar and his adversary has 1000, the average duration is 1000 trials."

"three repairman per twenty machines are much more economical than one repairman per six machines."

"Anyone writing a probability text today owes a great debt to William Feller, who taught us all how to make probability come alive as a subject matter. If you find an example, an application, or an exercise that you really like, it probably had its origin in Feller's classic text, An Introduction to Probability Theory And (Its) Applications."

"Ethical judgments can be [should be] included in the scope of science"

"The individuation process, as the way of development and maturation of the psyche, does not follow a straight line, nor does it always lead onwards and upwards. The course it follows is rather “stadial”, consisting of progress and regress, flux and stagnation in alternating sequence. Only when we glance back over a long stretch of the way can we notice the development. If we wish to mark out the way somehow or other, it can equally well be considered a “spiral”, the same problems and motifs occurring again and again on different levels."

"If the chance of error alone were the sole basis for evaluating methods of inference, we would never reach a decision, but would merely keep increasing the sample size indefinitely."

"There would be cases where we would not want to accept an hypothesis even though the evidence gives a high d.c. [degree of confirmation] score, because we are fearful of the consequences of a wrong decision."

"The complete analysis of the methods of scientific inference shows that the theory of inference in science demands the use of ethical judgments"

"[Scientists whose work has no clear, practical implications would want to make their decisions considering such things as:] the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment."

"[C. West Churchman exposed the indifferentist position of some researchers — planners belonging to this school in the following terms:] And if our clients blow up the world, land us in starvation or totalitarianism, that is too bad, but we remained pure in heart to the last, didn't we?"

"One cannot help but be struck by the diversity that characterizes efforts to study the management process. If it is true that psychologists like to study personality traits in terms of a person's reactions to objects and events, they could not choose a better stimulus than management science. Some feel it is a technique, some feel it is a branch of mathematics, or of mathematical economics, or of the "behavioral sciences," or of consultation services, or just so much nonsense. Some feel it is for management (vs. labor), some feel it ought to be for the good of mankind — or for the good of underpaid professors."

"Another way of emphasizing this diversity is to argue that if one cannot forecast (predict), one does not have a theory, and that forecasting is the weakest link in the chain of the management sciences at present. Indeed, if one cannot predict one cannot measure, and if one cannot measure, then there is no "theory.""

"This text grew from the lecture material for the "Short Course in Operations Research" which has been offered annually (since 1952) by Case Institute of Technology."

"No science has ever been born on a specific day. Each science emerges out of a convergence of an increased interest in some class of problems and the development of scientific methods, techniques, and tools which are adequate to solve these problems. Operations Research (O.R.) is no exception. Its roots are as old as science and the management function. Its name dates back only to 1940."

"O.R.'s initial development began in the United Kingdom during World War II and was quickly taken up in the United States. This start took place in a military context. After the war O.R. moved into business, industry and civil government. This movement was slower in the United States than in the United Kingdom but in 1951 industrial O.R. took hold in this country and has since developed very rapidly."

"An objective of O.R. as it emerged from this evolution of industrial organization, is to provide managers of the organizations with a scientific basis for solving problems involving the interaction of the components of the organization in the best interest of the organization as a whole. A decision which is best for the organization as a whole is called optimum decision."

"The comprehensiveness of OR’s aim is an example of a ‘systems’ approach, since ‘system’ implies an interconnected complex of functionally related components."

"This text is oriented toward human organizations since this has been the emphasis in the practice of O.R. in business and industry."

"The systems approach to problems does not mean that the most generally formulated problem must be solved in one research project. However desirable this may be, it is seldom possible to realize it in practice. In practice, parts of the total problem are usually solved in sequence. In many cases the total problem cannot be formulated in advance but the solution of one phase of it helps define the next phase. For example, a production control project may require determination of the most economic production quantities of different items. Once these are found it may turn out that these quantities cannot be produced on the available equipment in the available time. This, then, gives rise to a new problem whose solution will affect the solution obtained in the first phase."

"The concern of OR with finding an optimum decision, policy, or design is one of its essential characteristics. It does not seek merely to define a better solution to a problem than the one in use; it seeks the best solution... [It] can be characterized as the application of scientific methods, techniques, and tools to problems involving the operations of systems so as to provide those in control of the operations with optimum solutions to the problems."

"Analysis of the mathematical form and underlying principles of games was made by von Neumann " as early as 1928. In this early work von Neumann was not so much interested in executive-type problems as he was in the logical foundations of quantum mechanics. It was not until 1944, when von Neumann and Morgenstern published their now well known Theory of Games and Economic Behavior, that the mathematical treatment of games "took fire.""

"We have overwhelming evidence that available information plus analysis does not lead to knowledge. The management science team can properly analyse a situation and present recommendations to the manager, but no change occurs. The situation is so familiar to those of us who try to practice management science that I hardly need to describe the cases."

"How can we design improvement in large systems without understanding the whole system, and if the answer is that we cannot, how is it possible to understand the whole system?"

"[ Wicked problems are ] social problems which are ill formulated, where the information is confusing, where there are many clients and decision-makers with conflicting values, and where the ramifications in the whole system are thoroughly confusing."

"Deception, in turn , suggests morality: the morality of deceiving people into thinking something is so when it is not.[...] The moral principle is this: whoever attempts to tame a part of a wicked problem, but not the whole, is morally wrong."

"What seems to emerge is not a moral reprimand of the management scientist, but rather a moral problem of the profession, a wicked moral problem."

"Lindblom (1959) and Churchman (1967) make it clear that the assumption of synoptic or complete rationality in planning systems is not only inadequate in a methodological sense, but illegitimate in an ethical or professional sense."

"When one is considering systems it's always wise to raise questions about the most obvious and simple assumptions."

"It is sheer nonsense to expect that any human being has yet been able to attain such insight into the problems of society that he can really identify the central problems and determine how they should be solved. The systems in which we live are far too complicated as yet for our intellectual powers and technology to understand."

"It is only natural to expect that improvement can occur in certain sectors of the system without our having delved deeply into the characteristics of the whole system. Thus, for example, there is a tradition in Western thought that parts of the whole system can be studied and improved more or less in isolation from the rest of the system. So deeply ingrained is this concept of social improvement in Western thought that we naturally think it proper to subdivide our society into functional elements. We think it proper that each element develop its own criteria of improvement and that the elements be as free as possible from the interference of the other parts of the social structure... Men have neglected a very serious problem in defining improvement. The problem is very simple: How can we design improvement in large systems without understanding the whole system, and if we the answer is that we cannot, how is it possible to understand the whole system?"

"The problem of systems improvement is the problem of the 'ethics of the whole system'."

"The idea of a ‘system approach’ is both quite popular and quite unpopular. It’s popular because it sounds good to say that the whole system is being considered, but it’s quite unpopular because it sounds either like a lot of nonsense or else downright dangerous – so much evil can be created under the guise of serving the whole."

"We are always obliged to think about the larger system. If we fail to do this, then our thinking becomes fallacious."

"The ultimate meaning of the systems approach, therefore, lies in the creation of a theory of deception and in a fuller understanding of the ways in which the human being can be deceived about his world and in an interaction between these different viewpoints."

"The scientist has to have a way of thinking about the environment of a system that is richer and more subtle than a mere looking at for boundaries. He does this by noting that, when we say that something lies ‘outside’ the system, we mean that system can do relatively little about its characteristics or its behavior. Environment, in effect, makes up the things and people that are ‘fixed’ or ‘given’, from the system’s point of view."

"The management of a system has to deal with the generation of the plans for the system, i.e., consideration of all of the things we have discussed, the overall goals, the environment, the utilization of resources and the components. The management sets the component goals, allocates the resources, and controls the system performance."

"For the scientist a model is also a way in which the human though processes can be amplified. This method often takes the form of models that can be programmed into computers. At no point, however, the scientist intend to loose control of the situation because off the computer does some of his thinking for him. The scientist controls the basic assumptions and the computer only derives some of the more complicated implications."

"In general, we can say that the larger the system becomes, the more the parts interact, the more difficult it is to understand environmental constraints, the more obscure becomes the problem of what resources should be made available, and deepest of all, the more difficult becomes the problem of the legitimate values of the system."

"However a systems problem is solved—by a planner, scientist, politician, antiplanner, or whomever—the solution is wrong, even dangerously wrong. There is bound to be deception in any approach to the system."

"It's not as though we can expect that next year or a decade from now someone will find the correct systems approach and all deception will disappear. This, in my opinion, is not in the nature of systems. What is in the nature of systems is a continuing perception and deception, a continuing re-viewing of the world, of the whole system, and of its components. The essence of the systems approach, therefore, is confusion as well as enlightenment. The two are inseparable aspects of human living."

"A systems approach begins when first you see the world through the eyes of another."

"There are no experts in the systems approach"

"The systems approach is not a bad idea"

"Operations research '(OR) is the securing of improvement in social systems by means of scientific method"

"The systems approach goes on to discovering that every world-view is terribly restricted."

"To know that we are measuring real change we need to have a strong theoretical base."

"The theory of the nature of mathematics is extremely reactionary. We do not subscribe to the fairly recent notion that mathematics is an abstract language based, say, on set theory. In many ways, it is unfortunate that philosophers and mathematicians like Russell and Hilbert were able to tell such a convincing story about the meaning-free formalism of mathematics. In Greek, mathematics simply meant learning, and we have adapted this... to define the term as "learing to decide." Mathematics is a way of preparing for decisions through thinking. Sets and classes provide one way to subdivide a problem for decision preparation; a set derives its meaning from decision making, and not vice versa."

"A system may actually exist as a natural aggregation of component parts found in Nature, or it may be a man-contrived aggregation – a way of looking at a problem which results from a deliberate decision to assume that a set of elements are related and constitute such a thing called ‘a system."

"Knowledge can be considered as a collection of information, or as an activity, or as a potential. If we think of it as a collection of information, then the analogy of a computer's memory is helpful, for we can say that knowledge about something is like the storage of meaningful and true strings of symbols in a computer."

"To conceive of knowledge as a collection of information seems to rob the concept of all of its life. Knowledge resides in the user and not in the collection. It is how the user reacts to a collection of information that matters."

"Knowledge is a potential for a certain type of action, by which we mean that the action would occur if certain tests were run. For example, a library plus its user has knowledge if a certain type of response will be evoked under a given set of stipulations."

"Design, properly viewed, is an enormous liberation of the intellectual spirit, for it challenges this spirit to an unbounded speculation about possibilities."

"The religious Weltanschauung, … describes a certain kind of relationship – such as love, adoration and obedience – between men and other men, or between men and some superior being. or between men and "Nature"."

"Inquiry is the creation of knowledge or understanding; it is the reaching out of a human being beyond himself to a perception of what he may be or could be, or what the world could be or ought to be."

"Common to all these enemies is that none of them accepts the reality of the "whole system": we do not exist in such a system. Furthermore, in the case of morality, religion, and aesthetics, at least a part of our reality reality as human is not "in" any system, and yet it plays a central role in our lives. To me these enemies provide a powerful way of learning about the systems approach, precisely because they enable the rational mind to step outside itself and to observe itself (from the vantage point of the enemies)."

"We must face the reality that the enemies offer: what's really happening in the human world is politics, or morality, or religion, or aesthetics. This confrontation with reality is totally different from the rational approach, because the reality of the enemies cannot be conceptualized, approximated, or measured."

"Finally we should note the basic assumption of the classical laboratory-namely, that nature is neither capricious nor secretive. If nature were capricious, she would tell one observer one thing and another observer a quite different thing... Also nature is not secretive, in the sense that she will not forever hide certain aspects of her being..."

"The enemies will be asking reasonable questions, like Isn't politics the way matters are really decided, and isn't the rational systems approach simply one political device, to be used when politically expedient? Or isn't morality essentially inexpressible in terms of concepts and words, and doesn't this essentially ineffable quality of our lives lead us humans to decide the way we do? Or, isn't religious imagery really the basis of all our perspectives and concepts, including the perspective of the systems approach? And what is it that carries the values we humans cherish? It is not the ego or the mind, but, say our basic aesthetic feeling, which cannot be conceptualized. And finally, and most generally, why is a rational, holistic approach desirable for the human species, especially since it so often gets out of hand, missing the vital essence of the specific and individual, the here and now, encompassing "everything" to the exclusion of every thing?"

"For the goal planner, reality stops at the boundaries of the problem. For the objective- planner, it stops at the boundaries set by feasibility and to some extent by responsibility. For the ideal-planner, there are no "real" boundaries."

"The story begins with a somewhat disgruntled hero, who perceived of the world as populated with stupid people, everywhere committing the environmental fallacy. The fallacy was a case not merely of the “mind’s falling into error,” but rather of the mind leading all of us into incredible dangers as it first builds crisis and then attacks crisis. Like all heroes, this one looked about for resources, for aids that would help in a dangerous battle, and he found plenty of support – in both the past and the present. It won’t hurt to summarize the story thus far. If the intellect is to engage in the heroic adventure of securing improvement in the human condition, it cannot rely on “approaches,” like politics and morality, which attempt to tackle problems head-on, within the narrow scope. Attempts to address problems in such a manner simply lead to other problems, to an amplification of difficulty away from real improvement. Thus the key to success in the hero’s attempt seems to be comprehensiveness. Never allow the temptation to be clear, or to use reliable data, or to “come up to the standards of excellence,” divert you from the relevant, even though the relevant may be elusive, weakly supported by data, and requiring loose methods. Thus the academic world of Western twentieth century society is a fearsome enemy of the systems approach, using as it does a politics to concentrate the scholars’ attention on matters that are scholastically respectable but disreputable from a systems-planning point of view."

"Enemies are hostile, out to stop you, to eliminate you and your ideas; they are also to be loved, even as yourself."

"Suppose we consider, not the rationality of holism, but its spirituality. Holism traditionally says that a collection of beings may have a collective property that cannot be inferred from the properties of its members."

"I am often inclined to put the implementation questions first, ie, "Can anything be changed?" Should the implementation question not accompany the whole process from its very beginning to its very end?"

"It would be a good thing, if the systems planner's germination was moral outrage and not just a mild felt need. In other words, I do not think we should view the major problems of the world today with calm objectivity. We shouldn't first ask ourselves for a precise and operational definition of malnutrition. We should begin with 'kids are starving in great numbers, damn it all!"

"The design of my philosophical life is based on an examination of the following question: is it possible to secure improvement in the human condition by means of the human intellect? The verb 'to secure' is (for me) terribly important, because problem solving often appears to produce improvement, but the so-called 'solution' often makes matters worse in the larger system (e.g., the many food programs of the last quarter century may well have made world-wide starvation even worse than no food programs would have done.) The verb ‘to secure' means that in the larger system over time the improvement persists. I have to admit that the philosophical question is much more difficult than my very limited intellect can handle. I don't know what 'human condition' and 'human intellect' mean, though I've done my best to tap the wisdom of such diverse fields as depth psychology, economics, sociology, anthropology, public health, management science, education, literature, and history. But to me the essence of philosophy is to pose serious and meaningful questions that are too difficult for any of us to answer in our lifetimes. Wisdom, or the love of wisdom, is just that: thought likes solutions, wisdom abhors them."

"If the story of my early years with Russ sound like they were years of battle, then the sound is correct."

"Everybody's daily life consists of problems arising from what you decided yesterday. Managers understand that. Mathematicians want to solve a theorem, publish the results and walk away clean. Managers never walk away clean. The real world is a very dirty place. Clarity is supposed to be the objective of science. I disagree. I think the objective of science is confusion, because confusions carries you into problems."

"I was an Editor-in-Chief of Philosophy of Science during its early years. Now, over a half century later, I have to admit that I was not very clear what the journal was about, except that it tried to reflect on the meaning of science and its relation to other human activities. At this time I am even less sure of its purposes."

"Prediction of events is a central problem to which students of decision making have also addressed themselves. See, for example, Simon (1957), Churchman (1948), Bross (1953)."

"General systems theory is considered as a formal theory (Mesarovic, Wymore), a methodology (Ashby, Klir), a way of thinking (Bertalanffy, Churchman), a way of looking at the world (Weinberg), a search for an optimal simplification (Ashby, Weinberg), didactic method (Boulding, Klir, Weinberg), metalanguage (Logren), and profession (Klir)."

"Churchman recognized in his critical systemic thinking that the human mind is not able to know the whole. … Yet the human mind, for Churchman, may appreciate the essential quality of the whole. For Churchman, appreciation of this essential quality begins … when first you see the world through the eyes of another. The systems approach, he says, then goes on to discover that every worldview is terribly restricted. Consequently, with Churchman, a rather different kind of question about practice surfaces. … That is, who is to judge that any one bounded appreciation is most relevant or acceptable? Each judgment is based on a rationality of its own that chooses where a boundary is to be drawn, which issues and dilemmas thus get on the agenda, and who will benefit from this. For each choice it is necessary to ask, What are the consequences to be expected insofar as we can evaluate them and, on reflection, how do we feel about that? As Churchman points out, each judgment of this sort is of an ethical nature since it cannot escape the choice of who is to be the client—the beneficiary—and thus which issues and dilemmas will be central to debate and future action. In this way, the spirit of C. West Churchman becomes our moral conscience. A key principle of systemic thinking, according to Churchman, is to remain ethically alert. Boundary judgments facilitate a debate in which we are sensitized to ethical issues and dilemmas."

"Systems thinking, as written about and practiced by Russell Ackoff, C. West Churchman, Peter Checkland and others, contained within it many of the impulses that motivate the application of design ideas to strategy, organization, society, and management. Ideas such as engaging a broad set of stakeholders, moving beyond simple metrics and calculations, considering idealized options and using scenarios to explore them, shifting boundaries to reframe problems, iteration, the liberal use of diagrams and rich pictures, and tirelessly searching for a better set of alternatives were all there. If the business and management community had bought it, we would not be having the many discussions about design, design thinking, and expanding management education to engage the intuitive, to embrace values, to look beyond available choices."

"Managers within organizations sometimes confront a type of problem that is difficult to solve, in part, because the problems involve many stakeholders with diverse perspectives. The different assumptions from each perspective result in differing views of the problem and potential solutions. It is difficult to produce a satisfactory potential solution when the formulation of the problem definition is the major concern and when applying a potential solution risks unintended consequences. Churchman (1967, p. 141) writes that the solutions proposed to solve these problems "often turned out to be worse than the symptoms""

"We see that each surface is really a pair of surfaces, so that, where they appear to merge, there are really four surfaces. Continuing this process for another circuit, we see that there are really eight surfaces etc and we finally conclude that there is an infinite complex of surfaces, each extremely close to one or the other of two merging surfaces."

"Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood, and there will undoubtedly always be many challenging problems to solve. nevertheless, I believed that some of the unsolved meteorological problems were more fundamental, and I felt confident that I could contribute to some of their solutions."

"By showing that certain deterministic systems have formal predictability limits, Ed put the last nail in the coffin of the Cartesian universe and fomented what some have called the third scientific revolution of the 20th century, following on the heels of relativity and quantum physics... He was also a perfect gentleman, and through his intelligence, integrity and humility set a very high standard for his and succeeding generations."

"There is no need to enlarge upon the importance of a realistic theory explaining how individuals choose among alternate courses of action when the consequences of their actions are incompletely known to them. It is no exaggeration to say that every choice made by human beings would meet this description if attention were paid to the ultimate implications."

"Among economic phenomena which have in some way been tied up with the existence of uncertainty, three classes may be distinguished: (1) those which by their very definition are concerned with uncertainty; (2) those which are not related to uncertainty by definition but nevertheless have no other conceivable explanation; (3) those whose relation to uncertainty is more remote and disputable."

"The businessman may be compared with two other types of individuals who are essentially concerned with behavior under uncertainty ― the scientist and the statistician. The scientist must choose, on the basis of limited information, among the innumerable logically conceivable laws of nature, a limited number. He cannot know whether his decisions are right or wrong, and, indeed, it is none too clear what is meant by those terms. There is a long history of attempts to reduce scientific method to system, including many which introduce probability theory, but it cannot be said that any great formal success has attended these efforts. If we were to compare the businessman to the scientist, we would be forced to the melancholy conclusion that little of a systematic nature can be said about the former’s decision-making processes. The statistician typically finds himself in situations more similar to that of the businessman. The problem of statistics can be formulated roughly as follows. It is known that one out of a number of hypotheses about a given situation is true. The statistician has the choice of one of a number of different experiments (a series of experiments can be regarded as a single experiment, so that drawing a sample of any size can be included in this schema), the outcome of any one of which is a random variable with a probability distribution depending on which of the unknown hypotheses is correct. On the basis of that outcome, the statistician must take some action (accept or reject a hypothesis, estimate the mean of a distribution to be some particular value, accept or reject a lot of goods, recommend a change in production methods, and so on), the consequences of which depend on the action taken and on the hypothesis that is actually true."

"Traditional welfare economics shows that there are certain of these combinations that will be preferred by all the voters, which permits us to eliminate the others without too much discussion. However, there will always remain an irreducible kernel of possibilities among which the choice rests on a combination or aggregation of individual ethical attitudes about distribution."

"Ever since I encountered Hicks’s Value and Capital while I was still a graduate student, I had the aim of completing and extending his vision of the economic system in its purest form. This was not because I believed that the economic world was perfectly competitive or that it was clearly self-equilibrating; after all, Chamberlin, Robinson, and Keynes were dominant intellectual influences, and I had the even more powerful influence of the facts of massive unemployment and large corporations. But the idea that the economic world was a general system, with all parts interdependent, seemed (and seems) to me to be an essential of good analysis. I regret what appears to be a revival of single-market thinking both among monetarists and among some of the younger empirical analysts. Then as now, the only game in town that offered a general system of economic interdependence was general competitive equilibrium, an idea to which the name of Leon Walras is imperishably linked. At least, such a system would provide a starting point for analysis of the market’s imperfections."

"L. Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market."

"Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or ."

"The government may be regarded as a decision-making entity. Among the decisions it makes are the formation of economic policy and the collection of economic-statistical information. In all modern nations the economic policies of the government are significant activities, if for no other reason than the high proportion of national income which passes through the Treasury; but of course in many countries much more ambitious economic planning is aimed at, though not necessarily achieved. Economic statistics, on the other hand, if one is to judge by expenditures, form only an insignificant proportion of a government's activities and are the least developed precisely in those underdeveloped countries which have the greatest felt needs for economic plans."

"Government economic policy, like almost any realistic decision problem, has two fundamental characteristics: it is sequential and it is uncertain."

"In view of the magnitude of an economic system, it would take only a very small percentage of improvement in economic stability or growth to make almost any conceivable data collection worthwhile. The situation is analogous to reported results of the use of linear programming in industry; the gains are small in proportion to previous profit levels but still very much larger than the costs of the programming. No country is adequate in respect to its data. In particular the underdeveloped countries, with their ambitious programs, might well ponder whether or not the marginal productivity of investment in better economic statistics is perhaps not higher than almost any conceivable alternative; they have more need and fewer data."

"Decision theory, as it has grown up in recent years, is a formalization of the problems involved in making optimal choices. In a certain sense — a very abstract sense, to be sure — it incorporates among others operations research, theoretical economics, and wide areas of statistics, among others."

"The formal structure of a decision problem in any area can be put into four parts: (1) the choice of an objective function defining the relative desirability of different outcomes; (2) specification of the policy alternatives which are available to the agent, or decision-maker, (3) specification of the model, that is, empirical relations that link the objective function, or the variables that enter into it, with the policy alternatives and possibly other variables; and (4) computational methods for choosing among the policy alternatives that one which performs best as measured by the objective function."

"Strictly speaking, decision theory really is concerned only with the fourth part of the division given above, that is, the determination of the computational methods for optimization. Given the determination of the other three factors―the objective function, the range of policy alternatives, and the model―the ideal picture is that someone, presumable the firm that hires the operations researcher, hands him, on a silver platter, an objective function. By talking to the engineers, or by looking into a few scientific laws, he determines the policy alternatives available and also the model."

"Speaking very broadly, almost any human action involves choice; the external environment delimits a range of possible actions at any given moment but does not usually reduce that range to a single alternative. The formulation of a theory of human action in some sphere as a theory of choice means its presentation as a functional relation associating with each possible range of alternatives a chosen one among them."

"Learning, as studied by psychologists, closely resembles sequential analysis in some aspects. Learning experiments usually consist of a series of trials in which the subject’s choices are sometimes rewarded and sometimes not. The individual, after making many choices, eventually begins to discriminate between the proper response and the improper one. At some point, presumably, he could terminate the experiment, at least in the sense of disregarding the further observations and making the same choice each time."

"Index numbers are, of course, desired for purposes other than to measure the cost of living. One obvious possibility is to consider some subset of cost-of- living items, such as food. The logic of the preceding argument goes through precisely provided we assume that the distribution of food expenditures in any period among different foods depends only on the total volume of food expenditures and is independent of the prices of other goods, for any given total volume of food expenditures. This does not deny substitution between foods and other commodities, but we assume that the total effect of this substitution is already reflected in the choice of a volume of food expenditures. In a broad way, similar considerations apply to the pricing of producers’ goods, which should be interpreted as reflecting indirectly consumers’ preferences. However, there is undoubtedly a good deal more in the detailed working out of the theory that has never been developed."

"In a capitalist democracy there are essentially two methods by which social choices can be made: voting, typically used to make ‘political’ decisions, and the market mechanism, typically used to make ‘economic’ decisions. In the emerging democracies with mixed economic systems Great Britain, France, and Scandinavia, the same two modes of making social choices prevail, though more scope is given to the method of voting and to decisions based directly or indirectly on it and less to the rule of the price mechanism. Elsewhere in the world, and even in smaller social units within the democracies, the social decisions are sometimes made by single individuals or small groups and sometimes (more and more rarely in this modern world) by a widely encompassing set of traditional rules for making the social choice in any given situation, for example, a religious code."

"In addition to ignoring game aspects of the problem of social choice, we will also assume in the present study that individual values are taken as data and are not capable of being altered by the nature of the decision process itself. This, of course, is the standard view in economic theory (though the unreality of this assumption has been asserted by such writers as Veblen, Professor J. M. Clark, and Knight) and also in the classical liberal creed. If individual values can themselves be affected by the method of social choice, it becomes much more difficult to learn what is meant by one method’s being preferable to another."

"The problem of measuring utility has frequently been compared with the problem of measuring temperature. This comparison is very apt. Operationally, the temperature of a body is the volume of a unit mass of a perfect gas placed in contact with it (provided the mass of the gas is small compared with the mass of the body). Why, it might be asked, was not the logarithm of the volume or perhaps the cube root of the volume of the gas used instead? The reason is simply that the general gas equation assumes a particularly simple form when temperature is defined in the way indicated. But there is no deeper significance."

"The concept of rationality used throughout this study is at the heart of modern economic analysis, and it cannot be denied that it has great intuitive appeal; but closer analysis reveals difficulties."

"If the total number of alternatives is two, the method of majority decision is a social welfare function which satisfies Conditions 2–5 and yields a social ordering of the two alternatives for every set of individual orderings."

"If there are at least three alternatives which the members of the society are free to order in any way, then every social welfare function satisfying Conditions 2 and 8 and yielding a social ordering satisfying Axioms I and II must be either imposed or dictatorial."

"The idealist doctrine then may be summed up by saying that each individual has two orderings, one which governs him in his everyday actions, and one which would be relevant under some ideal conditions and which is in some sense truer than the first ordering. It is the latter which is considered relevant to social choice, and it is assumed that there is complete unanimity with regard to the truer individual ordering."

"From the point of view of seeking a consensus of the moral imperative of individuals, such consensus being assumed to exist, the problem of choosing an electoral or other choice mechanism, or, more broadly, of choosing a social structure, assumes an entirely different form from that discussed in the greater part of this study."

"In this aspect, the case for democracy rests on the argument that free discussion and expression of opinion are the most suitable techniques of arriving at the moral imperative implicitly common to all. Voting, from this point of view, is not a device whereby each individual expresses his personal interests, but rather where each individual gives his opinion of the general will."

"Invention is here interpreted broadly as the production of knowledge. From the viewpoint of welfare economics, the determination of optimal resource allocation for invention will depend on the technological characteristics of the invention process and the nature of the market for knowledge."

"In an ideal socialist economy, the reward for invention would be completely separated from any charge to the users of information. In a free enterprise economy, inventive activity is supported by using the invention to create property rights; precisely to the extent that it is successful, there is an underutilization of the information."

"To sum up, we expect a free enterprise economy to underinvest in invention and research (as compared with an ideal) because it is risky, because the product can be appropriated only to a limited extent, and because of increasing returns in use. This underinvestment will be greater for more basic research. Further, to the extent that a firm succeeds in engrossing the economic value of its inventive activity, there will be an underutilization of that information as compared with an ideal allocation."

"If the government and other nonprofit institutions are to compensate for the underallocation of resources to invention by private enterprise, two problems arise: how shall the amount of resources devoted to invention be determined, and how shall efficiency in their use be encouraged? These problems arise whenever the government finds it necessary to engage in economic activities because indivisibilities prevent the private economy from performing adequately (highways, bridges, reclamation projects, for example), but the determination of the relative magnitudes is even more difficult here."

"The choice among these alternatives in any given case depends on the degree of difficulty consumers have in making the choice unaided, and on the consequences of errors of judgment. It is the general social consensus, clearly, that the laissez-faire solution for medicine is intolerable. The certification proposal never seems to have been discussed seriously."

"According to this point of view, knowledge is, so to speak, a by-product of production or of investment. In research, on the contrary, it can be said that knowledge is the primary product. The distinction between products and by-products is not important for ordinary goods, because in a competitive regime the marginal costs of the two must be equal. But since knowledge does not have the normal properties of an economic good, it is necessary to study each mode of its production."

"To conclude, I argue that the government should not display risk aversion in its behavior. Hence, the proper procedure is to compute the expected values of benefits and costs, and discount them at a riskless rate, contrary to the view of Hirshleifer (1964, p. 85). Suppose the future to be unknown; it is known that one of a set of states will prevail, and their probabilities are known (or believed in). A given state means a complete description of all production possibilities, so that all uncertainties are resolved when the state is known. To summarize some earlier discussions (Arrow, 1964b; Deberu, 1959, chap 7; Hrishleifer, 1964, pp. 80-85), we can achieve an optimal allocation if we imagine markets in all possible commodity-options, a commodity-option being an obligation to deliver a fixed amount of a given commodity if, and only if, a given state prevails."

"The fundamental fact which causes the need for discussing public values at all is that all significant actions involve joint participation of many individuals. Even the apparently simplest act of individual decision involves the participation of a whole society. It is important to note that this observation tells us all non-trivial actions are essentially the property of society as a whole, not of individuals. It is quite customary to think of each individual as being able to undertake actions on his own (e.g., decisions of consumption, produc- tion, and exchange, moving from place to place, forming and dissolving families). Formally, a social action is then taken to be the resultant of all individual actions. In other words, any social action is thought of as being factored into a sequence of individual actions."

"To conclude, then, we must in a general theory take as our unit a social action, that is, an action involving a large proportion or the entire domain of society. At the most basic axiomatic level, individual actions play little role. The need for a system of public values then becomes evident; actions being collective or interpersonal in nature, so must the choice among them. A public or social value system is essentially a logical necessity."

"The only rational defense of what may be termed a liberal position, or perhaps more precisely a principle of limited social preference, is that it is itself a value judgment. In other words, an individual may have as part of his value structure precisely that he does not think it proper to influence consequences outside a limited realm. This is a perfectly coherent position, but I find it difficult to insist that this judgment is of such overriding importance that it outweighs all other considerations. Personally, my values are such that I am willing to go very far indeed in the direction of respect for the means by which others choose to derive their satisfactions."

"I interpret moral obligation as the carrying out of agreements which may, however, be implicit. Thus, a society in which everyone immediately executed his aggressive impulses would be untenable. Therefore, there is an agreement that I will refrain from aggressive actions, which in themselves give me satisfaction, in return for your not taking aggressive action against me. However, conscious agreements to achieve these ends are much too costly in terms of information and bargaining. Therefore, as societies have evolved they have found it economical to make these agreements at an unconscious, implicit level. Internalized feelings of guilt and right are essentially unconscious equivalents of agreements that represent social decisions."

"In this case of unrestricted income distribution, the dimensionality of the issue space is the same as the number of individuals. Thus, as Tullock argues, political resolution of distributional issues is apt to be possible only if only a few parameters of the income distribution are under consideration, not the whole distribution. Why this restriction of the scope of choice should occur is not easy to explain on simple economic grounds. On the other hand, the restriction does conform to the long-standing view of writers on ethics, of whom Kant is perhaps most conspicuous, that decisions on distribution ought to be made as if by an impartial observer, who considers then only the mean, a measure of inequality, and perhaps one or two further parameters characterizing the income distribution, but not specifically who gets what. If voters acted like Kantian judges, they might still differ, but the chances of coming to an agreement by majority decision would be much greater than if voters consulted egoistic values only. Does this suggest that ethics may have survival value for political systems and therefore descriptive as well as prescriptive significance?"

"There are two approaches to a theory of general equilibrium in an imperfectly competitive environment; most writers who touch on public policy questions implicitly accept one or the other of these prototheories without always recognizing that they have made such a choice. One assumes that all transactions are made according to the price system, that is, the same price is charged for all units of the same commodity; this is the monopolistic competition approach. The alternative approach assumes unrestricted bargaining; this is the game theory approach. The first might be deemed appropriate if the costs of bargaining were high relative to the costs of ordinary pricing, while the second assumes costless bargaining."

"Because the costs of transmission are nonnegligible, even situations which are basically certain become uncertain for the individual; the typical economic agent simply cannot acquire in a meaningful sense the knowledge of all possible prices, even where they are each somewhere available. Markets are thus costly to use, and therefore the multiplication of markets, as for contingent claims as suggested above, becomes inhibited."

"I want, however, to conclude by calling attention to a less visible form of social action: norms of social behavior, including ethical and moral codes. I suggest as one possible interpretation that they are reactions of society to compensate for market failures. It is useful for individuals to have some trust in each other's word. In the absence of trust it would become very costly to arrange for alternative sanctions and guarantees, and many opportunities for mutually beneficial cooperation would have to be, foregone."

"It is difficult to conceive of buying trust in any direct way (though it can happen indirectly, for example, a trusted employee will be paid more as being more valuable); indeed, there seems to be some inconsistency in the very concept. Nonmarket action might take the form of a mutual agreement. But the arrangement of these agreements and especially their continued extension to new individuals entering the social fabric can be costly. As an alternative, society may proceed by internalization of these norms to the achievement of the desired agreement on an unconscious level."

"Despite the favorable properties of the price system, I am no unrestrained admirer of it. Some of its limits in the urban context will be stressed below. It is not possible, however, to understand the city as an economic problem without first understanding the virtues of the free market system in performing its role of allocating resources."

"The case for equality may be made on other than utilitarian grounds; thus J. Rawls has, argued for maximizing the minimum utility, rather than the sum of utilities, as an ethical criterion, and this criterion would tend toward output equality and therefore strong input progressivity."

"Dynamic analysis may have deeper implications if we depart from the analysis of stationary states. The frim must now serve some additional roles. In the absence of futures markets, the firm must serve as a forecaster and as a bearer of uncertainty. Further, from a general equilibrium point of view, the forecasts of others become relevant to the evaluation of the firm's shares and therefore possibly of the firm's behavior."

"In any case the empirical evidence can only be made meaningful with at least a minimum of theoretical analysis."

"Property systems are in general not completely self-enforcing. They depend for their definition upon a constellation of legal procedures, both civil and criminal. The course of the law itself cannot be regarded as subject to the price system. The judges and the police may indeed be paid, but the system itself would disappear if on each occasion they were to sell their services and decisions. Thus the definition of property rights based on the price system depends precisely on the lack of universality of private property and of the price system. This ties in with the third hypothesis put forward in section I. The price system is not, and perhaps in some basic sense cannot be, universal. To the extent that it is incomplete, it must be supplemented by an implicit or explicit social contract. Thus one might loosely say that the categorical imperative and the price system are essential complements."

"While economic theory in general may be defined as the theory of how an economic condition or an economic development is determined within an institutional framework, the deals with how to judge whether one condition can be said to be better in some way than another and whether it is possible, by altering the institutional framework, to achieve a better condition than the present one."

"Nevertheless, when all due allowances are made, the coherence of individual economic decisions is remarkable. As incomes rise and demands shift, for example, from food to clothing and housing, the labor force and productive facilities follow suit. Similarly, and even more surprising to the layman, there is a mutual interaction between shifts in technology and the allocation of the labor force. As technology improves exogenously, through innovations, the labor made redundant does not become permanently unemployed but finds its place in the economy. It is truly amazing that the lessons of both theory and more than a century of history are still so misunderstood. On the other hand, a growing accumulation of instruments of production raises real wages and in turn induces a rise in the prices of labor-intensive commodities relative to those which use little labor. All these phenomena show that by and large and in the long view of history, the economic system adjusts with a considerable degree of smoothness and indeed of rationality to changes in the fundamental facts within which it operates."

"My own interest first centered on the relations between Pareto efficiency and competitive equilibrium. In particular, there was considerable discussion among economists in the late 1940’s about the inefficiencies resulting from rent control and different proposals for arriving at the efficiency benefits of a free market by one or another transition route. Part of the informal efficiency arguments hinged on the idea that under rent control people were buying the wrong kind of housing, say, excessively large apartments. It struck me that an individual bought only one kind of housing, not several. The individual optima were at corners, and therefore one could not equate marginal rates of substitution by going over to a free market. Yet diagrammatic analysis of simple cases suggested to me that the traditional identification of competitive equilibrium and Pareto efficiency was correct but could not be proved by the local techniques of the differential calculus."

"In fact, is is not a mere empirical accident that not all the contingent markets needed for efficiency exist but a necessary fact with deep implications for the workings and structure of economic institutions. Roughly speaking, information about particular events, even after they have occurred, is not spread evenly throughout the population. Two people cannot enter into a contract contingent on the occurrence of a certain event or state if only one of them in fact will know that the event has occurred. A particular example of this is sometimes known as “moral hazard” in the insurance and economic literature. The very existence of insurance will change individual behavior in the direction of less care in avoiding risks."

"General competitive equilibrium above all teaches the extent to which a social allocation of resources can be achieved by independent private decisions coordinated through the market. We are assured indeed that not only can an allocation be achieved, but the result will be Pareto efficient. But, as has been stressed, there is nothing in the process which guarantees that the distribution be just. Indeed, the theory teaches us that the final allocation will depend on the distribution of initial supplies and of ownership of firms. If we want to rely on the virtues of the market but also to achieve a more just distribution, the theory suggests the strategy of changing the initial distribution rather than interfering with the allocation process at some later stage."

"The forces of competition and the tendency to profit-maximization operate to mitigate these differences. However, the basic fact of a personnel investment prevents these counteracting tendencies from working with full force. In the end, we remain with wage differences coupled with tendencies to segregation."

"The conventional view among economists is that education adds to an individual's productivity and therefore increases the market value of his labor. From the viewpoint of formal theory, it does not matter how the student's productivity is increased, but implicitly it is assumed that the student receives cognitive skills through his education. Educators, on the other hand, have long felt that the activity of education is a process of socialization, with the latent content of the process—the acquisition of skills such as the carrying out of assigned tasks, getting along with others, regularity, punctuality, and the like—being at least as important as the manifest objectives of conveying information. This last doctrine has been revived by radical economists, though with a negative rather than a positive valuation. But from the viewpoint of economic theory, the socialization hypothesis is just as much a human capital theory as the cognitive skill acquisition hypothesis. Both hypotheses imply that education supplies skills that lead to higher productivity. I would like to present a very different view. Higher education, in this model, contributes in no way to superior economic performance; it increases neither cognition nor socialization. Instead, higher education serves as a screening device in that it sorts out individuals of differing abilities, thereby conveying information to the purchasers of labor."

"There is also one particularly needed elaboration of the model (which is not to say that it doesn't cry out for elaboration in many other directions). This is the relation between college filtering and on-the-job filtering. Once an employee has been hired, the employer can gradually draw on more directly obtained information to determine his productivity. However, this filtering may be costly. To the extent that the employer does filter and does so accurately, the Value of the college filter is reduced. The employer pays the average product of a group with given educational achievement only during the period before his own filter has become effective. Conversely, however, an increase in the college population will mean (and has meant) a depreciation in the quality of non-college students (this is not necessarily the same as a decrease in the quality of college students)."

"The problem of interpersonal comparison of utilities seems to bother economists more than philosophers. As already indicated, utility or satisfaction or any other similar concept appears in economic theory as an explanation of individual behavior, for example, as a consumer. Specifically, it is hypothesized that the individual chooses his consumption so as to maximize his utility, subject to the constraints imposed by his budget. But, for this purpose, a quantitatively measurable utility is a superfluous concept. All that is needed is an ordering, that is, a statement for each pair of consumption patterns as to which is preferred."

"Let us turn from the epistemological problems of the current decision-maker for society to those in the original position. Individuals are supposed to know the laws of the physical and the social worlds, but not to know who they are or will be. But empirical knowledge is after all uncertain, and even in the original position individuals may disagree about the facts and laws of the universe."

"To the extent that individuals are really individual, each an autonomous end in himself, to that extent they must be somewhat mysterious and inaccessible to each other. There cannot be any rule that is completely acceptable to all. There must, or so it now seems tome, be the possibility of unadjudicable conflict, which may show itself logically as paradoxes in the process of social decision-making."

"Once the capital goods prices are known, it is clear that the consumption goods prices are uniquely determined; for each consumption good, the activity chosen will be the one which is cheapest in its use of capital goods, valued at the known capital goods prices. Thus, all balanced growth prices in an indecomposable pure capital model with no joint production are determined by the technology."

"The members of an economy—the firms, the consumers, the investors, and the government—make choices. To give a common name to them all, I will refer to them as agents, for indeed their most salient characteristic is that they act. That they make choices implies that they have alternatives, that what was chosen was not inevitable but was in fact only one in a range of opportunities. The opportunities available to a consumer are determined by the income he has and the prices he has to pay for commodities of different use-values."

"The economic value of information offers no great mysteries in itself. It is easy to prove that one can always do better, whether as a producer or as a consumer, by basing decisions on a signal, provided the signal and the economic variables are not independently distributed. But this remark has an implication for economic decisions; the economic agent is willing to pay for information, for signals."

"I expect that ethical codes and informal nonprice organizations will continue to evolve where needed, for example in the control of product quality, to permit transactions which would be impossible because of differential information in markets where all individuals behaved in a purely selfish manner. The evolution of ethical codes is facilitated by the fact that productive units are organizations, not individuals, and individuals are mobile among these organizations."

"May I remark, especially for the benefit of economists, that consideration of the medical care market and of the insurance situation represents not only an application of economic principles but also a reconsideration of some of the principles that we take for granted."

"We have the possibility of diverting other resources to the medical field, but that means some subtraction somewhere else. We are sufficiently close to full employment that there is no great amount of unused resources to draw upon for this purpose. We do, of course, draw to some extent upon doctors trained in other countries, but quantitatively speaking, this is not very much of a help. The basic scarcity problem cannot be avoided."

"There is little warrant for the belief that we know the laws of history well enough to make projections of any great reliability. Most of the turning points of history, great and small, were surprises to both their participants and the analysts of the day, whatever their doctrine."

"We find that capitalism, like any very complex system, contains within itself contradictory tendencies, but there is no reason to suppose they are fatal, at least in the foreseeable future. We do find implied in these contradictions some social tasks: the completion of the tasks involved in the achievement of macroeconomic stability, the redistribution of income and power to improve the sense of justice in the arrangements of society, by which I mean the inseparable elements of the liberty and equality of individuals, and, perhaps hardest, the increase in the sense of individual and local control over one's destiny in the workplace and the small society. These aims are mutually reinforcing, not competitive."

"From a theoretical viewpoint, one might say that the market is in a strange sort of equilibrium; there is some shadowy sort of price at which supply and demand are equated at zero. But this price is not performing much of a signaling function."

"The terms of trade with the outside world should not be regarded as freely given to the firm. In a world with a large number of commodities, even knowing the prices of relevant commodities involves the costly acquisition of certain kinds of information."

"An organization is typically composed of changing individuals. Now any individual generally has access to many communication channels, of which this particular organization is only one. In particular, education is such a channel. Thus, the organization is getting the benefit of a considerable amount of information which is free to it."

"I think we may safely agree that the notion of democracy has two components, both indispensable: 1) the securing of the freedom of the individual so that he may develop his individual potential; 2) a symmetric mutual respect of the individuals in the society for each other. These aims are, as has been frequently remarked, partly competitive; but, it must also be stressed, they are to a very considerable extent complementary. A hierarchical society marked by great inequalities in power and esteem will surely not tolerate the liberties of those most disadvantaged. Conversely a world in which individuals have their liberties tightly confined must be one in which there are large inequalities of power."

"Let us start with elementals. Income and property are certainly the instruments of an individual’s freedom. Clearly the domain of choice is enhanced by increases in those dimensions. It is true not merely in the sense of expanded consumer choice but also in broader contexts of career and opportunity to pursue one’s own aims and to develop one’s own potential. Unequal distribution of property and of income is inherently an unequal distribution of freedom. Thus a redistribution of income, to the extent that it reduces the freedom of the rich, equally increases that of the poor. Their control of their lives is increased."

"The aim of achieving an equal distribution of political power requires a restriction on the inequalities of wealth and income."

"The domain of the theory of social choice is not in principle the same as that of a theory of justice. In some directions, it is clearly wider, since it is supposed to cover all decision that must be made collectively. On the other hand, it is possible to hold that propositions about distributive justice are not necessarily propositions about collective decisions."

"As indicated, I retain the view that the outcome should be an ordering. Presumably, the weakest possible outcome of a constitution would be a choice function, a mapping of each feasible set of alternatives into a chosen subset. Again, one cannot avoid some consistency relations among the choices from different feasible sets. Various conditions weaker than a full ordering have been proposed, but, in my judgement, they do not lead to interesting conclusions. Unless they are implausibly weak, these conditions do not lead to noticeably greater freedom in the selection of social choice procedures."

"This is by no means a "formal" matter. Clearly, the intuition behind the continuity requirement is a small step in the direction of utilitarian ethics; even the worst-off member of the society might be made to suffer if there is enough benefit to others. The assumption of diminishing marginal utility implies with regard to usual policy alternatives that there are better ways of improving the lot of better-off members than by hurting the worst-off. But there is one striking case, of great practical importance, where our intuition is in favor of utilitarianism is some form as against any minimax rule. I refer to allocation over time. Typically, we expect future generations to be better off than we are. Should we save for them either directly or in the form of public investments? A maximin rule would surely say no. But if investment is productive, so that, in terms of goods, the next generation gains more than we lose, we usually feel that some investment is worthwhile even though the recipients will be better off than we are."

"The incompleteness of property rights in general creates well-known problems in welfare economics, being in fact the basic component of externalities. In particular, markets for future commitments are relatively under-developed compared with those for the present or immediate future. Individuals have to supply for themselves expectations as to future developments in order to make decisions with consequences extending into the future, e.g., investments. These expectations, for example of prices or of supply availabilities, are not "property," but they influence the use of property and are taken into account in the present legal system. For example, an obligation to sell a product for the next few years at a given price is understood in the law to hold only if conditions do not change in a strongly unexpected way; this understanding does not require explicit statement."

"If markets were sufficiently complete, with all futures periods and all uncertain contingencies already provided for in the contracts, the concept of property would cease to be problematic. All decisions would have been made in advance, and there would be no further questions of transfers to treat as just or unjust. Because in fact many of these markets do not exist, there are direct non-market relations which affect individuals' levels of satisfaction. Voluntary transfers become possible, but not all conceivable transfers can be made. Hence, voluntary transfers become biassed in direction, and the possible injustice of the whole system of transfers must be recognized."

"Democracy is a form of government in which political decisions are ultimately governed by the bulk of the adult population, though, of course, usually indirectly through election of representatives. It is fair to say that political liberties, freedom of speech and of the press, are so closely inherent in meaningful democracy as to constitute part of the definition. But one can perfectly well imagine democracy without freedom of religion or in a society where every move is reported and internal passports are needed. Whether or not these restrictions are incompatible with the persistence of democracy is a contingent question, not a tautologous consequence of a definition."

"What can be concluded? We cannot be sure that the principles of democracy and socialism are compatible until we can observe a viable society following both principles. But there is no convincing evidence or reasoning which would argue that a democratic-socialist movement is inherently self-contradictory. Nor need we fear that gradual moves in the direction of increasing government intervention will lead to an irreversible move to “serfdom.”"

"Social theories are also social facts. Whatever explanatory value the “Marxist” or “conservative” models may have, they surely cannot be regarded as established with any degree of firmness. Yet excessive confidence in one or the other may have serious consequences. If “conservatives” believe too strongly that any move to socialism undermines democracy, then they may indeed act in accordance with the “Marxist” model, and vice versa. (Robert Merton long ago alerted us to “self-confirming” and “self-denying” social theories; here we have a pair of rival theories which are “other-confirming.”)"

"To sum up, the basic values that motivated my preference for socialism over capitalism were (1) efficiency in making sure that all resources were used, (2) the avoidance of war and other political corruptions of the pursuit of profits, (3) the achievement of freedom from control by a small elite, (4) equality of income and power, and (5) encouragement of cooperative as opposed to competitive motives in the operation of society."

"The comparative economic efficiency of capitalism and socialism remains one of the most controversial areas. The classical socialist argument is that the anarchy of production under capitalism leads to great wastage. An appeal to the virtues of the price system is, in fact, only a partial answer to this critique. The central argument, which implies the efficiency of a competitive economic system, presupposes that all relevant goods are available at prices that are the same for all participants and that supplies and demands of all goods balance. Now virtually all economic decisions have implications for supplies and demands on future markets. The concept of capital, the very root of the term “capitalism,” refers to the setting-aside of resources for use in future production and sale. Hence, goods to be produced in the future are effectively economic commodities today. For efficient resource allocation, the prices of future goods should be known today. But they are not. Markets for current goods exist and enable a certain coherence between supply and demand there. But very few such markets exist for delivery of goods in the future. Hence, plans made by different agents may be based on inconsistent assumptions about the future. Investment plans may be excessive or inadequate to meet future demands or to employ the future labor force."

"Ironically, the current conservative model explaining the supposed association of capitalism and democracy relates to the Marxist as a photographic negative to a positive. It too suggests that the political “superstructure” is determined by the “relations of production.” The conservative model contrasts the dispersion of power under capitalist democracy with its concentration under socialism. Political opposition requires resources. The multiplicity of capitalists implies that any dissenting voice can find some support. Under socialism, the argument goes, the controlling political faction can deny its opponents all resources and dismiss them from their employment. This theoretical argument presupposes a monolithic state. It is something of a chicken-and-egg proposition. If the democratic legal tradition is strong, there are many sources of power in a modern state. Adding economic control functions may only increase the diversity of interests within the state and therefore alternative sources of power. It is notoriously harder for the government to regulate its own agencies than private firms. Socialism may easily offer as much pluralism as capitalism. The overpowering force in all these arguments is the empirical evidence of the Soviet Union and the other Communist countries, and it is strong. But the contrary proposition, that capitalism is a positive safeguard for democracy, is hardly a reasonable inference from experience. The example of Nazi Germany shows that no amount of private enterprise prevents the rise of totalitarianism. Indeed, it is hard to see that capitalism formed a significant impediment. Nor is Nazi Germany unique; Fascist Italy, Franco’s Spain, and the recurrent Latin American dictatorships are illustrative counterexamples to the proposition that capitalism implies democracy."

"If the markets for durable goods are peculiarly sensitive to price anticipations, while those for perishable goods are more sensitive to current prices, then there is a little more scope for explaining economic fluctuations."

"I disagree with the widely accepted proposition that econometric models should have expectations consistent with them. To the extent, it is argued, that the economic theory underlying the model involves anticipations, the anticipations that appear in the model as determining individual behavior should be equal to the forecasts made from the model. More generally, in fact, I would disagree with the weaker proposition that anticipations made by individuals should be necessarily dependent on broadly available general data about the economy and in particular about government actions."

"I have argued that forecasts will be based on more information than is contained in econometric models and in general on information differing from agent to agent. I also want to argue that they will not necessarily use all the information contained in an econometric model. In fact, the two propositions are intimately linked though they seem to move in opposite directions. We have to assume that information-processing ability is scarce. As I have already said, this is one of the main justifications for and explanations of a decentralized economy. But then it follows that an individual concentrates on acquiring the information most useful to him and will have to crowd out the information which is less useful. In particular, information that is broadly pertinent to the economy as a whole may have very little predictive power for the future of an individual."

"The meaning of information is precisely a reduction in uncertainty. From the viewpoint of economics or decision theory, uncertainty is relevant because it concerns the consequences of decisions. An individual making a decision may be supposed to be choosing one among a set of feasible alternatives. In general, these alternatives are themselves plans extending in time, and he will want to choose the one that yields the most satisfying consequences. These may be profits in successive periods for a business firm, or they may be other satisfactions, such as consumption, power, bequests, or interesting challenges. It can be assumed that the individual compares the entire set of consequences deriving from each alternative in his decision set with those of the others and chooses the preferred one."

"If the state of information (the set of signals received) is given and constant, then optimal choice is a problem of decision making under a given uncertainty, a situation that has been the subject of considerable analysis in the last thirty years. The problems of the economics of information proper arise when the probability distribution of states of the world is a variable. In the language adopted here, the signals received can vary. The existence of signals creates two important possibilities for the improvement of decision making. The first is taking advantage of the existence of signals. If the individual knows that a signal will be received before the decision has to be made, his optimal choice should be a function of the signal. We can think, alternatively but equivalently, of making the decision after the receipt of the signal and basing it on the probability distributions of consequences conditional on the signal, or of making the decision in advance for all possible values of the signal."

"The need for coordination has two basic causes: the various members (e.g., production units) are competing for a common pool of resources, financial and material; and different decisions complement or substitute for each other. For both reasons, the effectiveness of decisions made by one participant is influenced by the decisions of another. With limitations on the flow of information, the decisions themselves cannot be coordinated. That would require transferring all the information available, precisely what is to be avoided. It has been emphasized earlier that when information will be available, the individual should choose a decision function, a policy or strategy that determines what his actual decision should be for each possible signal he receives. Hence, ideally, in an organization there should be prior agreement on decision functions or strategies for all participants."

"The competitive system can be viewed as an information and decision structure. Initially, each agent in the economy has a very limited perspective. The household knows only its initial holdings of goods (including labor power) and the satisfactions it could derive from different combinations of goods acquired and consumed. The firm knows only the technological alternatives for transforming inputs into outputs. The “communication” takes the form of prices. If the correct (equilibrium) prices are announced, then the individual agents can determine their purchases and sales so as to maximize profits or satisfactions. The prices are then, according to the pure theory, the only communication that needs to be made in addition to the information held initially by the agents. This makes the market system appear to be very efficient indeed; not only does it achieve as good an allocation as an omniscient planner could, but it clearly minimizes the amount of communication needed."

"Finding out the prices of a large range of commodities is itself a costly enterprise, and knowledge of this fact by price setters is itself enough to create incentives for inefficient market behavior. If one individual has more information about the quality of a good than the second, the first may exploit the situation, and the second, distrusting him, may not take advantage of what is in fact a desirable trade."

"Collective action is a means of power, a means by which individuals can more fully realize their individual values."

"Trust is an important lubricant of a social system. It is extremely efficient; it saves a lot of trouble to have a fair degree of reliance on other people's word. Unfortunately this is not a commodity which can be bought very easily. If you have to buy it, you already have some doubts about what you have bought."

"As is by now well known, attempts to form social judgments by aggregating individual expressed preferences always lead to the possibility of paradox."

"There are many other organizations beside the government and the firm. But all of them, whether political party or revolutionary movement, university or church, share the common characteristics of the need for collective action and the allocation of resources through nonmarket methods."

"It is this thinking which I think gives rise to the greatest tragedies of history, this sense of commitment to a past purpose which reinforces the original agreement precisely at a time when experience has shown that it must be reversed."

"The purpose of organizations is to exploit the fact that many (virtually all) decisions require the participation of many individuals for their effectiveness."

"Uncertainty means that we do not have a complete description of the world which we fully believe to be true."

"In eras when authority or at least specific authorities have been questioned, there is more tendency to examine the roots of and the need for authority. The owl of Minerva flies not in the dusk but in the storm."

"Any argument seeking to establish the presence of irrational economic behavior always meets a standard counterargument: if most agents are irrational, then a rational individual can make a lot of money; eventually, therefore, the rational individuals will take over all the wealth. Hence, rational behavior will be the effective norm. There are two rebuttals to the counterargument. (1) Not all arbitrage possibilities exist. For example, corporate profits, even though they may be down, are very distinctly positive in real terms after all necessary adjustments, including taxes. Yet there seems no way by which the average investor in corporate securities can get a positive real rate of return. (2) More important, if everyone else is “irrational,” it by no means follows that one can make money by being rational, at least in the short run. With discounting, even eventual success may not be worthwhile. Consider, for example, a firm that engages in research and development which depresses the current profit and loss statement. Irrational investors look only at this information, and therefore the price of the stock is below the expected value of future dividends based on the profitable outcomes of the research and development. In a perfectly working market with rational individuals, stock prices would gradually rise as the realization date approached, but prices in the actual market would be constant. A rational investor would understand the future value of the stocks, but he or she could not realize any part of this gain during the gestation period. Although the rational investor may get rewarded eventually if the stock is held long enough, he or she is losing liquidity during an intervening period which may be long. Hence, the demand for the stock even by the rational buyers will be depressed. As Keynes argued long ago, the value of a security depends in good measure on other people’s opinions."

"The Soviet Union and its satellite Socialist countries in Eastern Europe have typically avoided unemployment and business cycles, except as they are induced through their trade with the Western World. But on the other hand they are clearly inefficient and wasteful, at least relative to the West. As repeated statements by the socialist economists themselves make clear, the excessive concentration of economic decision-making is a prime cause of the inefficiency. There are recurring demands for "liberalization," even by the highest authorities (Yuri Andropov, the effective head of the Soviet Union, being the latest example), but they are responded to only mildly or not at all. Clearly, a really major step toward decentralization of economic power, to the plant managers or the workers themselves, is perceived as a threat to the system."

"I was early regarded as having unusual intellectual capacity. I was an omnivorous reader, and I added to that a desire to systematize my understanding. As a result, history, for example, was not merely a set of dates and colorful stories; I could understand it as a sequence in which one event flowed out of another. This sense of order crystallized during my high-school and college years into a predominant interest in mathematics and mathematical logic."

"Multiple discoveries are in fact very common in science and for much the same reason. Developments in related fields with different motivation help one to understand a difficult problem better. Since these developments are public knowledge, many scholars can take advantage of them. It is pleasant to the ego to be first or among the first with a new discovery. However, in this case at least, the evidence is clear that the development of general equilibrium theory would have gone on quite as it did without me."

"Studying oneself is not the most comfortable of enterprises. One is caught between the desire to show oneself in the best possible light and the fear of claiming more than one’s due."

"I want to stress that rationality is not a property of the individual alone, although it is usually presented that way. Rather, it gathers not only its force but also its very meaning from the social context in which it is embedded."

"Certainly, there is no general principle that prevents the creation of an economic theory based on other hypotheses than that of rationality."

"Not only is it possible to devise complete models of the economy on hypotheses other than rationality, but in fact virtually every practical theory of macroeconomics is partly so based. The price- and wage- rigidity elements of Keynesian theory are hard to fit into a rational framework, though some valiant efforts have been made. … But if the Keynesian model is a natural target of criticism by the upholders of universal rationality, it must be added that monetarism is no better. I know of no serious derivation of the demand for money from a rational optimization. … The use of rationality in these arguments is ritualistic, not essential."

"Gibbard's work was a bombshell. That was very exciting. I didn't know about Satterthwaite's work for a couple of years, but it was very much the same thing. I had taken the liberty of abstracting from manipulability in my thesis and I never went back to that issue. What's surprising is not really that there is an impossibility of non-manipulability, but that the issues should be essentially the same. That strikes one as a remarkable coincidence."

"The problem I have with utilitarianism is not that it is excessively rational, but that the epistemological foundations are weak. My problem is: What are those objects we are adding up? I have no objection to adding them up if there's something to add. But the one thing I retain from utilitarianism is that, basically, judgements are based on consequences. Certainly that's the sort of thing we do in the theory of the single individual under uncertainty; you make sure utility is defined only over the consequences. I view rights as arrangements which may help you in achieving a higher utility level."

"The tension between chaotic behavior and perfect foresight was observed. Start with an equilibrium dynamics of a standard type derived from the hypothesis that future prices are predicted perfectly. Suppose that the solution to the difference equations characterizing the solution exhibits chaotic behavior. Is it realistic to assume that the future, even though deterministic, is in fact predictable? Clearly, part of the lessons drawn by natural scientists, especially meteorologists, from nonlinear dynamics is precisely the opposite; chaotic behavior implies that small errors of observation in the starting position may lead to virtually total unpredictability after some period of time. This creates no difficulties of consistency when the predictor is not part of the system being predicted. But when the predictors are the economic agents being examined, there is a fundamental inconsistency. This epistemological antinomy is reinforced by the empirical observation that actual behavior of prices of assets such as securities could never reasonably have been predicted; if it had, there would have been much more buying or selling at earlier stages."

"The implications for planning are ambiguous. On the one hand, the optimal allocation under increasing returns will not be obtained under free markets. In fact, as I have already remarked, the competitive equilibrium is not even viable, and the outcome will be some kind of imperfect competition. But optimal allocation under increasing returns is difficult. For one thing, the optimisation requires the use of integer programming, a procedure intrinsically more complex than linear programming, and impossible to carry out for large systems even with the most powerful computers. Even more serious are the data demands. The information needed is widely dispersed among the industries and cannot be effectively communicated. It is for these reasons that decentralised decision-making with some element of monopoly is likely to be more efficient."

"Even Ricardo's most famous accomplishment, the law of comparative advantage in foreign trade, is incomplete, though not wrong."

"The uncertainty of the future is inescapable, one must think about it and arrive at plans for action. A statement attributed to a number of thinkers is, "Prediction is very difficult, especially of the future." Postdiction, knowing what went on in the past, is also difficult. The past, however, is our basis for understanding the future."

"As a general rule, the greater the uncertainty, the better to avoid large and irreversible commitments, to the extent that it is possible. When the famous 1930s gangster, Dutch Schultz, was dying, his incoherent last remarks were taken down by a stenographer. One of them was. "Don't make no bull moves." His words are a lesson for the kind of future that one might choose. Maintaining flexibility or keeping ones options open, is key in these matters."

"I am old-fashioned enough to retain David Hume’s view that one can never derive “ought” propositions from “is” propositions. The two issues, method and value, are distinct."

"Information, one of the fundamental determinants of production, laps over from one firm to another, yet the firm has so far seemed reasonably sharply defined in terms of legal ownership. It seems to me there must be increasing tensions between legal relations and fundamental economic determinants. Small symptoms are already appearing in the legal and economic spheres. There is continual difficulty in defining intellectual property. The United States courts, at least, have come up with some strange definitions of property."

"Unfortunately, the word 'learning' is a very general word. It isn't a very specific theory and we can have a lot of learning models, and it's unlikely that any one is going to track. When you talk about learning, you talk about the human mind adapting to conditions, and we haven't nailed that down very well. This is always an objection to the whole idea of bounded rationality. Not that it's wrong, but if it's right, it doesn't actually tell you what to do. Rationality is unique. That isn't really quite true, but at least under many circumstances it is. To say that we're not at the top of a hill gives you a lot of variety as to where you might be. So the problem with bounded rationality is not that it's wrong. On the contrary, I think it's very apt to be correct. It's just that its predictions are a lot more vague than those implied by rationality. At the moment, I don't know what to do about that."

"I think one of the things we learned from the physicists and also the theoretical biologists is the idea that when you're dealing with very complex systems you're going to get a large variety of behavior which can be interpreted as hill climbing, but hill climbing with a lot of modifications, hill climbing with big jumps occasionally. This is an elaboration of the idea of the learning model. The learning model story takes off from psychology, but the adaptive processes take off from biology and physics. They have the same story. One thing it does suggest in some sense is that we have to be more modest in what we claim."

"The slippery role of information as an economic good is of deep significance to economic behavior, especially in the relatively information-rich modern economy. It is an economic good in the traditional sense; it is valuable, and it is costly. But it has a peculiar algebra. Adding one ton of steel to another permits more to be done; repeating the same item of information does not add anything useful. On the other hand, supplying a ton of steel to another reduces the steel available to the supplier; supplying information to another does not reduce the information available to the supplier."

"The conflict of incentives and information is increasingly leading to a diffusion of responsibility for medical decisions. The simple picture of the physician making decisions for the patient has certainly become more complicated. Patients always had a role in choosing to seek medical advice and from whom. Their choices are becoming increasingly restricted as medical practice becomes more organized. The problems of cost control in an insured world are partly met by the increasing use of control of medical services through review by health maintenance organizations and insurance carriers."

"For the voucher system to work, it would be necessary to have informed parents. One cannot be dogmatic without empirical evidence, but I would be surprised if the average parent has the time or patience or competence to digest the relevant information. Indeed, one wonders where the information is to come from and in what form it should exist. Do we use test scores, themselves affected by the selection processes of the students? Impressions of individual teachers or of the physical appearance of the school will tend to dominate."

"Child care has grown up under different circumstances than education and probably for a mixture of reasons, good and bad. There are many systems of child care, some private, some public. As compared with primary and secondary education, there is clearly less need for coordination. The sequencing of classes is much less important. It would appear that the ability of parents to monitor the conduct of the child care activity is much greater because the activity is much closer to everyday experience and knowledge. Most of the informational and structural arguments for the public supply of education are absent in the case of child care. Reputation and experience may suffice for adequate monitoring."

"Krugman's whole attack is directed at a statement made neither by Arthur nor by Cassidy. Krugman has not read Cassidy's piece with any care nor has he bothered to review what Arthur has in fact said."

"There are many unknowns in the creation and use of knowledge as a factor of production. Still, two main lessons stand out: * Every country or firm must have education and training in technology and science, even if the research is not on par with that being conducted elsewhere. Knowledge cannot be absorbed unless some knowledge is already possessed. * Countries and firms must be open to new ideas, have multiple sources of new ideas, and see that ideas are diffused. This point strongly argues for freedom of entry, even when it seems to forgo economies of scale."

"Various medical groups are continually putting out advice as to health-inducing behavior (diet, exercise, and so forth). Individuals who follow this advice will reduce their demand for medical services. An extreme version is the campaign of the American Dental Association for fluoridation of water, a measure designed to reduce cavities and so the demand for dental services. There is also a logical problem. How does the relatively small group of physicians acquire power? In a democratic system, political power derives from numbers or from wealth. While physicians are certainly relatively well off, they do not have the concentration of wealth of many industries. Their power, it seems to me, is derived from moral authority. It is derived from the same professional respect that we are trying to explain. Indeed, when the American Medical Association came into conflict with either the retired or with the business interests that bought medical plans, the weakness of its power base quickly became apparent."

"My own view is that both endogenous and exogenous elements are important in explaining innovation. Incentives certainly play a role, but so does the general state of scientific knowledge, which is not directly produced by profit-making entities."

"The creation of knowledge that constitutes an innovation is in turn dependent on the acquisition and application of existing knowledge; information is an input into the production of information. This background knowledge and the ability to use it are the most important elements of the social context of individually motivated innovation."

"I was a very polite person, though. Paul Samuelson tells these stories how he used to correct his professors. I assume that’s true. But I wasn’t that type."

"The Austrian a priori dogmatism (von Mises, especially; Hayek, to a lesser degree)."

"I don't know which way human psychology will go wrong. We have a world in which there is uncertainty. There are new technologies. And one of the problems is that we do things today with a thought to the future. Any purchase is one for the future. If you buy a refrigerator you are making a commitment to the future, so that you have food to eat for the next ten years. That's a simple theory, one of many simple theories -- theories that people agree on and that don't, in a fundamental way, change. But every once in a while there is unemployment, and wages will drop, and there will be several different interpretations."

"There are information asymmetries in this story. Health insurance is limping along. It's limited in scope, and then you other consequences. Insurance companies have high premiums to protect themselves. The ones who come to the insurance company are sicker and the people have to pay more. You have adverse selection. You have moral hazard. And the doctor does what's on the safe side -- defensive medicine -- without regard to cost. These are fundamental conditions that make health insurance difficult. You have some things that help. Some doctors understand that they shouldn't abuse the system. But you still see problems in the way doctors behave towards patients. They goof off. Sometimes it's too much work. Some things are difficult and risky to diagnose."

"We don't have much time left. We are moving towards temperature increases of around two degrees Celsius, which is going to have consequences in the tropics, and we will lose things like glaciers. That's not a theory; it's happening right now. It's not a prediction; it's happening right now. But you just sightsee near those glaciers. But the glaciers are a big source of water. And on the questions of water, in California we store our water in a snowpack. When that's gone, the rain will be the same but it won't accumulate. With warming temperatures the snowpack will not work. It might be possible to substitute with dams, but that's complicated. This is conjoined with a big energy problem and I think that we really have to encourage development in this area. Just waiting for technological improvement won't work. We need to encourage it."

"I then follow up with four major aspects of economic research in the last 60 years, the period of my scholarly activity. One, econometric methodology and practice, is of such fundamental importance that it cannotgo unnoticed, although I played no role in it. With the other three, general equilibrium, dynamic processes, and uncertainty and information, I was more intimately involved."

"Clearly, information is of the utmost importance in making economic decisions, especially when it comes to securities or other assets whose value depends on events not yet known. Now the distribution of information cannot simply be taken as given. On the contrary, information can be acquired at some cost."

"As we see it, a choice is not something you do today in isolation; it is part of a plan that includes some choices to be made in the future."

"Once individuals are acting to carry out a norm and cannot be fully checked, their natural norm of self-interest will come into play. The rules actually acted upon will therefore move away from any norm that might be acceptable on the basis of general principles."

"We don’t have a laissez-faire system. The intervention of the federal government, as measured by expenditures, is growing. It is not a private system at all. Roughly 50 percent of health costs are paid for by the government, and state governments are spending more and more on health. It’s crowding out education. State budget-support for education, especially higher education, is crowded out by two things: health and prisons. Nobody is prepared for the idea of a laissez-faire system, and we never really had one."

"There’s a famous Churchill quote: “democracy is the worst form of government, except for all the others.” That applies to regulation as well. In the late 1800s, we had a natural monopoly: railroads. The government created a regulatory enterprise – the Interstate Commerce Commission – and of course it was captured. But it still made a difference. I think we just have to accept that capture does occur, but it’s limited. The Federal Trade Commission, for example, is a pretty active body. Monopolies have been broken up. The AT&T telephone monopoly was broken up in 1982 – Stigler was still writing about regulatory capture then. AT&T was a classic monopoly, but a pretty benevolent one. It delivered good service – rates were too high, but not by that much. It didn’t necessarily pass on value to the consumers, but Bell Labs were a source of great innovative function. Nevertheless, it was broken up by antitrust measures, brought on by government. So there is regulatory capture, but it is by no means complete. Regulations do play a role. One example of non-regulatory capture fighting against effective regulation was during the run-up to the 2008 crash, when several officials argued for CDOs to be regulated, which means they would have had to meet certain requirements of transparency. This was not accepted. I’m not saying the crash could have been avoided if that happened, but that would have made a big difference."

"In 1972 American economist Kenneth Arrow, jointly with Sir John Hicks, was awarded the Nobel Prize in economics for “pioneering contributions to general equilibrium theory and welfare theory.” Arrow is probably best known for his Ph.D. dissertation (on which his book Social Choice and Individual Values is based), in which he proved his famous “impossibility theorem.” He showed that under certain assumptions about people’s preferences between options, it is always impossible to find a voting rule under which one option emerges as the most preferred."

"Alchian: Perhaps it might have been more appropriate for the Nobel Prize to have gone to you and Hicks together, and [Kenneth] Arrow and [[Gunnar Myrdal|[Gunnar] Myrdal]] together. Hayek: Oh, surely. [laughter]"

"Then during the early '50s Kenneth Arrow published his book Social Choice and Individual Values (1951). That stirred up a great deal of interest, both in political science and economics. My general reaction was that the people who criticized Arrow, and Arrow himself, really didn't quite get the message in the sense that the concentration was on the fact that majority rule would not give you a political equilibrium, that you get this political cycle and so forth. My criticism basically was, if that's the way the preferences are, that's what you want to have. A democracy should not mean one majority simply ruling. It ought to be a rotation, if that's the way the preferences are. I was kind of an anti-majoritarian then and now. So my critique of Arrow, which not many people paid much attention to, got me further into thinking about these things."

"In technical economics, I see a peak with Paul Samuelson and Kenneth Arrow and some of the core developments in game theory. Since then there are fewer iconic figures being generated in this area of research, even though there are plenty of accomplished papers being published."

"During this period I also came-across Kenneth Arrow's now famous Social Choice and Individual Values. Although I hardly did full justice to that pioneering work, it emboldened me to take a stab at a much more formal presentation than I had encountered in political theory. The form of my two chapters certainly owes something to my having ploughed my way through that book. For better or worse, Arrow's book must also have influenced my decision to present parts of the argument in a formal notational system (though only in footnotes and appendices)."

"I was influenced very early on, my first time at the—I spent a year at the Center at Palo Alto, the Center for Advanced Study there, and I became a good friend of Kenneth Arrow. I think he was not at the Center that year but he lived in Palo Alto. [...] Marvelous man. Both as a person and as a scholar. And I became as I say greatly influenced by the way in which he dealt with phenomena. [...] So I was influenced by that as a model, a way of thinking more abstractly, perhaps, than customary, about democratic theory. Making clear the premises, the epistomological assumptions and matters of that kind, and I think that sort of set the stage. And then once you get in of course, into that field, which was not highly— I don’t know how to put this properly—as a formal field of political science was not highly developed at the time, once you get into it you quickly become aware of how rich the potential subject matter is. One of the enormous changes, perhaps anticipating your question, one of the changes in the world is the extraordinary increase in the number of countries that, by the standards that we use today, can be called democratic—always, I repeat this and repeat this, but, always keeping in mind the difference between the ideal and the threshold at which we now accept a country as democratic, or a polyarchy as I would say. And the enormous increase in the number of those available for study—when I was a graduate student, there were maybe half a dozen countries that you could study: France and Britain and, I’m not quite sure of Canada at that time . . . and then the expansion created out there a field . . . that was both a challenge and an opportunity."

"Ken Arrow was involved with the Santa Fe Institute from its beginning. He is one of my heroes, because he’s a guy who does something, and then moves on. He’s moved on from general equilibrium to complexity."

"The interesting thing is that Ken Arrow was a dove and Bob Solow was then a hawk, in 1963-4. We used to have huge debates. Hahn was very hawkish, Meade was hawkish, only Arrow and what's now the Cambridge left were doves, particularly the Asians, for obvious reasons. After all, it was the Asians who were being napalmed. There were terrible fights going on, and the beginning of huge rifts in the faculty over the Vietnam war. Solow switched, later on, and to his everlasting credit came out and said he'd switched. Arrow was always a dove. That's why, fond as I am of Bob Solow, and much thought I admire him, I've always admired Arrow more, because Arrow, I think, has always had the right instincts. He's a self-declared socialist, he was a dove, he was always active on civil rights, he fought for Sam Bowles at Harvard, and so on. He's always gone out on a limb for the right issues - on the left issues, actually. By that time (1967-8), I was in the thick of moratoria and death threats and bombs and all the rest of it. I wrote the survey in about four months. It was refereed by Arrow, Stiglitz, Samuelson and one other - I've never found out who it was. Samuelson recommended publication 'as is'. Arrow wrote to me and said, 'May I use you brilliant survey for my graduate class at Harvard?', which is the letter I prize most of any I've received in all the world. Stiglitz didn't say anything at the time, but he saved it all up for when he wrote that very critical review article of my book (which he kept calling my article!) in the Journal of Political Economy."

"But the old dilemma between efficiency and fairness was about to be shattered by a young New Yorker called Kenneth Arrow, who knew all about unfairness after watching helplessly as a teenager while his father lost his successful business and all his savings in the Great Depression. The desire for social justice stayed with Arrow, but intellectually he couldn’t just ignore the question of efficiency. The young economist set his logical mind to wrestling with the tension between the unerring efficiency of the free market and the imperative that some kind of fairness should prevail. His solution was brilliant, twisting the traditional thinking about competitive markets and efficiency on its head. He proved that not only are all perfect markets efficient, all efficient outcomes can be achieved using a competitive market, by adjusting the starting position."

"It is not easy to see him. Not because he’s short. Rather because the piles of books and papers scattered around his admittedly relatively narrow office in the Landau Building are so high. ‘They’ve moved us here and now I’m trying to look through all my stuff and see what I can possibly throw out’, says Kenneth J. Arrow, rising swiftly from behind one of the book piles, with an apologetic gesture. In spite of his 86 years, he seems physically quite fit and, no wonder, he prides himself in cycling to the office every day. The room is nice, bright, modern and new, but there is no way Arrow could possibly fit everything into the book shelves along the walls. ‘Never mind’, he says, laughing. He has a great warm open smile, and is eager to talk – which he then does at an amazing speed. Politely, he liberates a chair for me, opens a drawer next to himself for me to place the microphone in since there is no more space on the desk, of course – and off we go."

"And I am glad that you talked to Ken Arrow. But Nobel laureates, who have wide responsibilities and much on their mind, are not necessarily on top of what has been going on in research outside their usual field. I happen to know of one laureate who, circa 1991, was quite unaware that anyone had thought about increasing returns in either growth or trade."

"I’m an optimist, so I am hopeful. I don’t think Samuelsonian economics can be the long-run equilibrium of such an important field such as economics. I think that because of the two secret sins of Samuelsonian economics, the qualitative theorems and significance testing in the absence of the loss function, we can’t make scientific progress. We can do a lot of other stuff. We can take a look at tables and see how large schooling is in the national economy; that kind of thing is science. So I’m sure we can make some progress, off the center of the scientific stage of so-called mainstream Samuelsonian economics. An interesting concrete example of this was a presentation Ken Arrow made when he came to Iowa, where he was trying to make the obvious point that we shouldn’t spend all of our time in undergraduate economics preparing people for graduate school. This is a point that I have made over and over again, that we should be preparing students for life, for business and law school. Arrow said, “Look, the main argument for this is not very complicated: as we all know, half of 1 percent of our students, if that, go on to graduate school in economics, end of argument.” The argument is not special to Arrow, but the fact that it came from Arrow was very interesting. He didn’t come and say there is an existence theorem proof that there doesn’t exist some social welfare function such that blah blah blah. He didn’t do that. He said, “Look, here’s the number that shows obviously that the policy of making undergraduate programs into junior graduate programs is a mistake.”"

"Arrow’s Impossibility Theorem is quite surprising. It shows that three very plausible and desirable features of a social decision mechanism are inconsistent with democracy: there is no “perfect” way to make social decisions. There is no perfect way to “aggregate” individual preferences to make one social preference. If we want to find a way to aggregate individual preferences to form social preferences, we will have to give up one of the properties of a social decision mechanism described in Arrow’s theorem."

"[Arrow's] experience as an Air Force weather forecaster during the Second World War "added the news that the natural world was also unpredictable." ... One incident that occurred while Arrow was forecasting the weather illustrates both uncertainty and the human unwillingness to accept it. Some officers had been assigned the task of forecasting the weather a month ahead, but Arrow and his statisticians found that their long-range forecasts were no better than numbers pulled out of a hat. The forecasters agreed and asked their superiors to be relieved of this duty. The reply was: "The Commanding General is well aware that the forecasts are no good. However, he needs them for planning purposes.""

"[The process of system design is]... consisting of the development of a sequence of mathematical models of systems, each one more detailed than the last."

"[The word system is often defined in a way] that seems the most appropriate for the purpose of any given discussion."

"The problem of the design of a system must be stated strictly in terms of its requirements, not in terms of a solution or a class of solutions."

"Every author has several motivations for writing, and authors of technical books always have, as one motivation, the personal need to understand; that is, they write because they want to learn, or to understand a phenomenon, or to think through a set of ideas."

"If all the theories pertinent to systems engineering could be discussed within a common framework by means of a standard set of nomenclature and definitions, many separate courses might not be required."

"Only if mathematical rigor is adhered to, can systems problems be dealt with effectively, and so it is that the systems engineer must, at least, develop an appreciation for mathematical rigor if not also considerable mathematical competence."

"All that can be done pedagogically is to show the student how some phenomena have been modeled, let him model some phenomena under supervision, and then hope he will be successful on his own—or know enough to secure assistance."

"In the minds of many writers systems engineering is synonomous with component selection and interface design; that is, the systems engineer does not design hardware but decides what types of existing hardware shall be coupled and how they shall be coupled. Complete agreement that this function is the essence of systems engineering will not be found here, for, besides the very important function of systems engineering in systems analysis, there is the role played by systems engineering in providing boundary conditions for hardware design."

"Over 80 million people have participated in Cub Scout Pinewood Derbies. Pinewood is a case study of the design of a Cub Scout Pinewood Derby for one particular scout pack. The system helps manage the entire race from initial entry through final results. Many alternatives for race format, scoring, and judging are presented."

"After earning the PhD degree and acquiring some relatively extensive experience in digital computers… It was time to leave the University. The result of an extensive search for the right job was a family move to Arlington Heights, Illinois, where it was a short commute to the Research Laboratories of the Pure Oil Company at Crystal Lake. I was given the title of Mathematical and Computer Consultant. The Labs were set in a beautiful campus, the professional personnel were eager to learn what I had to teach and to include me in many interesting projects where my knowledge and skills could be put to good use. I was encouraged to initiate my own program of research. I went to work with enthusiasm. The corporate headquarters of Pure Oil were located in down town Chicago. Pure Oil had been trying to install an IBM 705 computer system for all their accounting needs including calculation of all data necessary for the management of exploration, drilling, refining and distribution of oil products and even royalties to shareholders in oil wells. Typical for those early days, the programming team was in deep difficulties and needed help; they lacked adequate resources and suitable training. The Executive Vice President of Pure Oil, when he heard that there was a computer expert already on the payroll at the Crystal Lake lab, ended our family blissful dream and I was reassigned to the down town office."

"During this period I was able to carry out only one project of real interest to me. Pure Oil was a fully integrated oil company in the sense that they engaged in exploration for oil, construction of oil wells, production of crude oil, transportation to refineries, distribution of refinery products to company owned storage facilities and to gas stations. We developed a linear programming model of the whole network hoping to discover the optimum allocation to and from connected nodes in order to meet required deliveries at minimum cost. Then we collected all the data needed by our model and ran the model. The computations took several days and the results were disappointing: The optimum allocations were not significantly different from their current practices. Is it possible that we had discovered a system of human beings in which everyone knew the payoff functions and constraints, and, over time, had evolved behavior patterns that enabled them to achieve near optimum performance? Or was it possible that our model was not detailed enough as it was based so closely on current practice that no new behavior could emerge? Or was our data incorrect? This was disappointing but great experience."

"[In the year 1957] I have just returned from an exciting meeting of the American Society for Engineering Education where I heard a paper on the new discipline of systems engineering. It is no longer sufficient for engineers merely to design boxes such as computers with the expectation that they would become components of larger, more complex systems. That is wasteful because frequently the box component is a bad fit in the system and has to be redesigned or worse, can lead to system failure. We must learn how to design large-scale, complex systems from the top down so that the specification for each component is derivable from the requirements for the overall system. We must also take a much larger view of systems. We must design the man-machine interfaces and even the system-society interfaces. Systems engineers must be trained for the design of large-scale, complex, man-machine-social systems."

"In the folklore of systems engineering, there are sayings, “If it isn't testable, it isn't a requirement,” and, “If it is not quantifiable, it is not testable.” I had always tended to subscribe to the particle of wisdom in these sayings. One of the many lessons that I learned from the CATIE experience, however, was that systems engineering had to be able to deal directly and purposively with what are usually considered to be strictly qualitative (unquantifiable) aspect of systems, such as quality of life, for example. The agricultural practices of these small farmers in Central America is such a large part of their lives that to change any part of their agricultural practices might be seen as diminishing their quality of life - even with respect to the color of the beans that the new practices might require. But even if we cannot deal directly with quality of life or user friendliness or enmity/sympathy, we can identify quantifiable figures of merit relating to these qualitative aspects and if we find enough figures of merit and combine them suitably, we might eventually obtain agreement that we have captured the essence of the qualitative aspect, at least as far as this particular set of stakeholders is concerned."

"General systems theory is considered as a formal theory (Mesarovic, Wymore), a methodology (Ashby, Klir), a way of thinking (Bertalanffy, Churchman), a way of looking at the world (Weinberg), a search for an optimal simplification (Ashby, Weinberg), didactic method (Boulding, Klir, Weinberg), metalanguage (Logren), and profession (Klir)."

"Wayne Wymore is now well established as an important leader in systems engineering and a founder of a highly original "school of thought" in the area of systems design. His contribution to this area, which will be the subject of a special issue of this journal in the near future, is best exposed in a trilogy consisting of this book and its two predecessors [Wymore, 1967, 1976]. Wymore's approach to systems design is characterized by mathematical rigor, comprehensiveness, and broad applicability."

"A. Wayne Wymore founded the first academic department of Systems Engineering in the world at the University of Arizona in 1960. He pioneered Mathematical-based Systems Engineering and later led Model-based Systems Engineering. He was an early and ardent supporter of the fomenting of INCOSE. He has led self-evaluation of Systems Engineering education, and continues to be one of the most prominent theoreticians of the Systems Engineering community. In addition to his teaching, writing, and consulting, he has participated in pro bono projects to bring a Systems Engineering approach to social service organizations."

"System design can be requirements based, function based, or model based. Model based system engineering and design has an advantage of executable models that improve efficiency and rigor. One of the earliest developments of this technique was Wymore’s (1993) book entitled Model-based System Engineering, although the phrase “model-based system design” was in the title and topics of Rosenblit’s (1985) PhD dissertation. Model-based systems engineering depends on having and using well-structured models that are appropriate for the given problem domain."

"Wayne’s book, A Mathematical Theory of Systems Engineering: The Elements, John Wiley, New York [1967] appeared in an era that spawned the concept of a mathematical system as a generalization of the control systems of engineers and the automata theories of computer scientists. Wymore employed the unusual term “Tricotyledon Theory of System Design” to portray the tri-partite nature of his theory. Tricotyledon, or three leaved seed, pictures a leaf for the class of models of the behavior of the system being designed, a second leaf for the technologies that are available to implement the system, and a leaf for the intersection of the two previous classes, namely, the technologies that can implement the models according to specified evaluation criteria. In subsequent work over three decades, he deepened the theory and applied it to numerous system engineering problems. The theory became the basis for his book, Model-based System Engineering, CRC Press, Inc. Boca Raton, FL, USA © 1993 and helped to spawn the trend toward use of systems modeling tools for systems design. However, Wayne himself did not emphasize the use of modeling and simulation as essential tools in systems engineering practice."

"Professor Sylvester's first high class at the new university Johns Hopkins consisted of only one student, G. B. Halsted, who had persisted in urging Sylvester to lecture on the modern algebra. The attempt to lecture on this subject led him into new investigations in quantics."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"Our so-called "Arabic" notation owes its excellence to the application of the principle of local value and the use of a symbol for zero. It is now conclusively established that the principle of local value was used by the ns much earlier than by the Hindus and that the Maya of Central America used the principle and symbols for zero in a well-developed numeral system of their own. The notation of Babylonia used the scale of 60, that of the Maya, the scale 20 (except in one step). It follows, therefore, that the present controversy on the origin of our numerals does not involve the question of the first use of local value and symbols for zero; it concerns itself only with the time and place of the first application of local value to the decimal scale and with the origin of the forms or shapes of our ten numerals. ... Hurt by the alleged arrogance of certain Greek scholars, Sebokht praises the science of the Hindus and speaks of "their valuable methods of computation. . . . I wish only to say that this computation is done by means of nine signs." Unfortunately, he leaves it to us to guess whether or not he used the zero. The passage, written about 662 A.D., is the earliest reference that has been found outside of India to our numerals. ...The form of the symbols with the zero, used in India, differed so widely from the old forms without the zero used there, that the former seem to have had an independent origin and to have been imported into India. ...The following are outstanding facts: 1. The earliest reliable record of the use of our numerals with zero is an inscription of 867 A.D. in India. 2. The validity of the testimony of early Arabic writers ascribing to India the numerals with zero is shaken, but not destroyed. 3. There is not a scintilla of evidence in the form of old manuscripts or numeral inscriptions to support the Greek origin of our numerals. 4. At present the hypothesis of the Hindu origin of our numerals stands without serious rival. But this hypothesis is by no means firmly established."

"My quotations from Newton suggest the motive which induced him to take a stand against the use of hypotheses, namely, the danger of becoming involved in disagreeable controversies. ...Newton could no more dispense with hypotheses in his own cogitations than an eagle can dispense with flight. Nor did Newton succeed in avoiding controversy."

"As regards algebra, the early Arabs failed to adopt either the Diophantine or the Hindu notations. An examination of [the algebra of Al-Khwarizmi] shows that the exposition was altogether rhetorical, i.e., devoid of all symbolism."

"The history of mathematics may be instructive as well as agreeable ; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, "The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics." It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoitre and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken."

"The history of mathematics is important also as a valuable contribution to the history of civilization. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress."

"It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences."

"Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him."

"The Elements has been considered as offering models of scrupulously rigorous demonstrations. It is certainly true that in point of rigour it compares favourably with its modern rivals; but when examined in the light of strict mathematical logic, it has been pronounced by C.S. Peirce to be "riddled with fallacies." The results are correct only because the writer's experience keeps him on his guard."

"The miraculous powers of modern calculation are due to three inventions : the Arabic Notation, Decimal Fractions and Logarithms."

"Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula 2^{2^n} + 1 = a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example 2^{2^5} + 1 = 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation."

"In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded several months' time, was achieved in three days by Euler with aid of improved methods of his own... With still superior methods this same problem was solved by the illustrious Gauss in one hour."

"Most of his [Euler's] memoirs are contained in the transactions of the Academy of Sciences at St. Petersburg, and in those of the Academy at Berlin. From 1728 to 1783 a large portion of the Petropolitan transactions were filled by his writings. He had engaged to furnish the Petersburg Academy with memoirs in sufficient number to enrich its acts for twenty years a promise more than fulfilled, for down to 1818 [Euler died in 1793] the volumes usually contained one or more papers of his. It has been said that an edition of Euler's complete works would fill 16,000 quarto pages."

"J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid "deeper than e'er plummet sounded" out of the schoolboy's reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson's Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson's additions and keeping strictly to the original treatise."

"The grandest achievement of the Hindus and the one which, of all mathematical inventions, has contributed most to the general progress of intelligence, is the invention of the principle of position in writing numbers. Generally we speak of our notation as the “Arabic” notation, but it should be called the “Hindu” notation, for the Arabs borrowed it from the Hindus. That the invention of this notation was not so easy as we might suppose at first thought, may be inferred from the fact that, of other nations, not even the keen-minded Greeks possessed one like it."

"What is perhaps the greatest blow that has ever come to the student body of Colorado College came last Friday when it was announced that Dean Florian Cajori, for about thirty years the best-known and best-liked professor in the College, had resigned and will not be back with us next year. It was not only on account of the value of his service as an instructor that the students felt such a sense of loss at the announcement, but more on account of the friendship and intimate relationship which he has shown to us. "Caj"… has been closer to this student body than any other one man. It was usually "Caj" who made the speech at the Barbecue, it was "Caj" who talked upcoming events in chapel, it was "Caj" who was always out there at the picnic or the Festival or the ball game. No form of student activity has seemed entirely complete unless our "Caj" has been there or has had something to do with it."

"They [the students] looked upon "Caj" as one of their best friends in all the College, and thought of him as the one responsible for their later success. He has had a personal appeal to a great many students... It was the appeal of the one with a human interest in what somebody else is doing, the appeal of the true friend and the hearty well-wisher. It was the appeal of "Caj"."

"As a mathematician Dean Cajori has achieved a name which very few in this world can equal, a name which is respected all over the globe. His text books and his writings have been published all over the world. We are proud of all the achievements of our "Caj", of course, but we are especially proud of what he has done for us here, and it is for this reason that we shall always hold him in our memory. As a friend and as an instructor he has been more to us than we can ever measure, and we shall always look back upon the days when we had "Caj"."

"Professor Florian Cajori died August 14, 1934. In May of the following year I was invited by the University of California Press to edit this work. ...this is a revision of Motte's translation of the Principia. From many conversations with Professor Cajori, I know that he had long cherished the idea of revising Newton's immortal work by rendering certain parts into modern phraseology (e.g., to change the reading of "reciprocally in the subduplicate ratio of " to "inversely as the square root of") and to append historical and critical notes which would provide instruction to some readers and interest to all. This is his last work; one of the most fitting to crown a life devoted to investigation and to the history of the sciences in his chosen field."

"An object in OOA represents a single typical but unspecified instance of something in the real world - any airplane, I don't care which one, as long as it is typical. The object-oriented analyst distinguishes this concept from that of a specified instance: Airplane number N2713A, Air Force One, or The Spirit of St. Louis, for example."

"While a small domain (consisting of fifty or fewer objects) can generally be analyzed as a unit, large domains must be partitioned to make the analysis a manageable task. To make such a partitioning, we take advantage of the fact that objects on an information model tend to fall into clusters: groups of objects that are interconnected with one another by many relationships. By contrast, relatively few relationships connect objects in different clusters. When partitioning a domain, we divide the information model so that the clusters remain intact... Each section of the information model then becomes a separate subsystem. Note that when the information model is partitioned into subsystems, each object is assigned to exactly one subsystem."

"The key books about object-oriented graphical modeling languages appeared between 1988 and 1992. Leading figures included Grady Booch [Booch,OOAD]; Peter Coad [Coad, OOA], [Coad, OOD]; Ivar Jacobson (Objectory) [Jacobson, OOSE]; Jim Odell [Odell]; Jim Rumbaugh (OMT) [Rumbaugh, insights], [Rumbaugh, OMT]; Sally Shlaer and Steve Mellor [Shlaer and Mellor, data], [Shlaer and Mellor, states] ; and Rebecca Wirfs-Brock (Responsibility Driven Design) [Wirfs-Brock]."

"While it was long possible and sometimes tempting for physicists to deny the usefulness of the molecular hypothesis, we economists have the good luck of being some of the ‘molecules’ of economic life ourselves, and of having the possibility through human contacts to study the behavior of other ‘molecules’."

"Econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference."

"Optimizing responses of economic agents are simultaneously feasible only if the proper prices are already known to them. But these prices must somehow themselves be the result of the same responses."

"The early thirties brought what liberal economists called the Great Depression and Marxist economists described as the great crisis of capitalism. It dawned on me that the economic world order was unreliable, unstable, and, most of all, iniquitous. I sought intellectual contacts and friendship with a group of socialist students and also with a small handful of communist-oriented students and unemployed workers."

"[This work urges] a clearer separation, in the construction of economic knowledge, between reasoning and recognition of facts, for the better protection of both."

"One can in particular interpret the proposition as a statement conditions under which the simplicity of incentive structure and the economies of information handling characteristic of a competitive market organization can be secured without loss of efficiency of allocation... The price system carries to each producer, resource holder, or consumer a summary of information about the production possibilities, resource availabilities and preferences of all other decision makers. Under the conditions postulated, this summary is all that is needed to keep all decision makers reconciled with a Pareto optimal state once it has been established."

"It is worth pointing out that in this particular study our authors have abandoned demand and supply functions as a tool for analysis, even as applied to individuals... [The problem] has been reformulated as one of proving that a number of maximizations of individual goals under interdependent restraints can be simultaneously carried out."

"If evolutionary selection is the basis for a belief in profit maximization, 'then we should postulate that basis itself and not the profit maximization which it implies in certain circumstances."

"One is led to conclude that economics as a scientific discipline is still somewhat hanging in the air."

"We look upon economic theory as a sequence of conceptual models that seek to express in simplified form different aspects of an always more complicated reality."

"Without recognising indivisibilities — in human person, in residences, plants, equipment, and in transportation — location patterns, down to those of the smallest village, cannot be understood"

"Decisions and plans made by others... [can be judged to be] quantitatively at least as important as the primary uncertainty arising from random acts of nature and unpredictable changes in consumers' preferences."

"The solution of important problems may be delayed because the requisite tools are not perceived. Or the availability of certain tools may lead to an awareness of problems, important or not, that can be solved with their help."

"According to a frequently cited definition, economics is the study of “best use of scarce resources.” The definition is incomplete. “Second best” use of resources, and outright wasteful uses, have equal claim to attention. They are the other side of the coin."

"… a rather different class of applications of the idea of best allocation of scarce resources... usually referred to as the theory of optimal economic growth. In most studies of this kind made in the countries with market economies there is not an identifiable client to whom the findings are submitted as policy recommendations. Nor is there an obvious choice of objective function, such as cost minimization or profit maximization in the studies addressed to individual enterprises. The field has more of a speculative character. The models studied usually contain only a few highly aggregated variables. One considers alternative objective functions that incorporate or emphasize various strands of ethical, political, or social thought. These objectives are then tried out to see what future paths of the economy they imply under equally simplified assumptions of technology or resource availability."

"The principal customers aimed for are other economists or members of other professions, who are somewhat closer to the making of policy recommendations... The question of the clientèle is even more baffling when the problem concerns growth paths for time spans covering several generations. What can at best be recommended in that case is the signal the present generation gives, the tradition it seeks to strengthen or establish, for succeeding generations to take off from."

"Linear programming was developed as a discipline in the 1940's, motivated initially by the need to solve complex planning problems in wartime operations. Its development accelerated rapidly in the postwar period as many industries found valuable uses for linear programming. The founders of the subject are generally regarded as George B. Dantzig, who devised the simplex method in 1947, and John von Neumann, who established the theory of duality that same year. The Nobel prize in econonmics was awarded in 1975 to the mathematician Leonid Kantorovich (USSR) and the economist Tjalling Koopmans (USA) for their contributions to the theory of optimal allocation of resources, in which linear programming played a key role. Many industries use linear programming as a standard tool, e.g. to allocate a finite set of resources in an optimal way."

"Koopmans complained that macroeconomic models weren't satisfactory because they didn't handle randomness. He talked about building models in continuous time, which is something we're trying to do now."

"Koopmans was also like Kantorovich in generalizing his approach from one sector of the economy to the economy as a whole. Koopmans showed the conditions required for economy-wide efficiency in allocating resources. He also, again like Kantorovich, used his activity analysis techniques to derive efficient criteria for allocating between the present and the future."

"A forthcoming book by Harry Markowitz, Techniques of Portfolio Selection, will treat the general problem of finding dominant sets and computing the corresponding opportunity locus, for sets of securities all of which involve risk. Markowitz's main interest is prescription of rules of rational behaviour for investors; the main concern of this paper is the implications for economic theory, mainly , that can be derived from assuming that investors do in fact follow such rules."

"In economic surveys of households, many variables have the following characteristics: The variable has a lower, or upper, limit and takes on the limiting value for a substantial number of respondents. For the remaining respondents, the variable takes on a wide range of values above, or below, the limit."

"I... set forth and illustrate a general framework for monetary analysis. It is not... new... but... shared... in spirit with many monetary economists. My purpose... is exposition and recapitulation."

"[M]onetary assets fall into place as a part, but not the whole, of the menu of s; and the ing system is one sector, but not the only one, whose behavior must be specified."

"Treatment of the capital account separately from the production and income account of the economy is... a first step, a simplification... justified by convenience... The strategy is to regard income account variables as tentatively exogenous... and to find equilibrium in the markets for stocks of assets conditional upon assumed... outputs, incomes, and other flows."

"In a complete equilibrium... financial inputs to the real side must reproduce the assumed values of the real inputs to the financial side."

"A[n]... example of this strategy is the "LM curve." Macroeconomics... immortalized Hick's decomposition of the Keynesian system into sub-models. One... tells what asset stock equilibrium corresponds to... tentative... aggregate real income and the commodity price level. ..."[T]he" interest rate equates... demand and supply of money and clears... markets for other assets."

"The key behavioral assumption... spending... and portfolio decisions are independent... [A]ccumulation of wealth... [is] separable from... its allocation. As savers, people... add to their wealth; as portfolio managers, they... distribute among... assets and debts the net worth... The propensity to consume may depend upon interest rates, but... not... directly on the... mix of asset supplies or... rates... these... are growing."

"The general accounting framework for... the capital account... Rows represent assets or debts. ...Columns represent sectors of the economy ...Entries in cells ...can be postive, negative, or zero. A negative entry means... the sector... is a debtor in the... asset indicated by the row. ...The sum across the row is the net exogenous supply of the asset to the economy ...For stocks of goods, this ...is the economy's inheritance from the past. For internally generated financial assets the net... supply... is zero. If from the sums in the final column the... government's holdings of an asset are subtracted (or its debt added), the net holdings of the private economy result. The sum of a column represents the net worth of a sector. The sum of the final column is the national wealth. ...[P]rivate wealth differs from this total by the amount of the government's net worth. If government is a net debtor... if its stocks of goods are ignored, then private wealth exceeds national wealth."

"[F]or monetary analysis... assign... to each asset a rate of return r_i (i=1,2,... n) and... [imagine] each sector j (j=1,2,... m) to have a net demand for each asset, f_{ij}, which is a function of the vector r_i and possibly of other variables... [I]n practice, many of the cells are empty..."

"Each sector is... constrained by its own net worth... The individual economic unit can neither change the legacy of the past nor... affect by... portfolio choices... market valuations of his assets."

"[C]onsider an economy with only one private sector and only two assets: money issued by the government to finance its budget deficits, and homogeneous physical capital. Let p be the price of currently produced... consumer goods and capital goods. ...[A]llow the value of existing capital goods ...to diverge from their current reproduction cost—let qp be the market price of existing capital goods."

"The rate of investment – the speed at which investors wish to increase the capital stock – should be related, if to anything, to q, the value of capital relative to its replacement cost."

"According to [the general equilibrium approach to monetary theory], the principal way in which financial policies and events affect aggregate demand is by changing the valuations of physical assets relative to their replacement costs."

"There is no reason to think that the impact [of monetary policy] will be captured in any single [variable]... , whether it is a monetary stock or a market interest rate."

"A long decade ago economic growth was the reigning fashion of political economy. It was simultaneously the hottest subject of economic theory and research, a slogan eagerly claimed by politicians of all stripes, and a serious objective of the policies of governments. The climate of opinion has changed dramatically. Disillusioned critics indict both economic science and economic policy for blind obeisance to aggregate material "progress," and for neglect of its costly side effects. Growth, it is charged, distorts national priorities, worsens the distribution of income, and irreparably damages the environment. Paul Erlich speaks for a multitude when he says, "We must acquire a life style which has as its goal maximum freedom and happiness for the individual, not a maximum Gross National Product.""

"Economics has always flourished and acquired energy from controversies generated by practical policy questions of the day. That was true in the times of Smith, and Ricardo, and Keynes, and it is true today. These periods of division and revolution and counterrevolution are generally followed by periods of synthesis and consolidation from which the science emerges stronger. i am optimistic that this will happen again, and that the best of the insights of the new clasicals will be absorbed in a mainstream, in which the essential insights of Keynesian economists also survive."

"Monetarism—both of the older Friedman version stressing adherence to money stock targets and of the newer rational expectations variety—has been badly discredited. The stage has been set for recovery in the popularity of Keynesian diagnoses and remedies. I do not mean to imply, of course, that there is some Keynesian truth, vintage 1936 or 1961, to which economists and policymakers will or should now return, ignoring the lessons of economic events and of developments in economics itself over these last turbulent fifteen years. I do mean that in the new intellectual synthesis which I hope and expect will emerge to replace the divisive controversies and chaotic debates on macroeconomic policies, Keynesian ideas will have a prominent place."

"Keynesian economics at a minimum provides a license for welfare state measures and other government efforts towards redistribution of wealth. The license is the faith that macroeconomic stabilization and prosperity are compatible with a wide range of social policies, that modern capitalism and democracy are robust enough to prosper and progress while being humane and equitable. That faith conflicts with the visions of extreme Right and Left, which agree that extremes of wealth and poverty, of security and insecurity, are indispensable to the functioning of capitalism. Keynesian policies helped to confound those dismal prophecies in the past; I think they will do so again."

"Keynesian economics was, in the context of those times, essentially conservative. The message was that capitalism was not doomed; its major failing, chronic large-scale unemployment, could be remedied fairly easily, by intelligent use of the fiscal and monetary instruments governments already had at their disposal. This message was not welcome news to Marxists committed to the view that the system was no longer structurally capable of prosperity and progress."

"I studied economics and made it my career for two reasons. The subject was and is intellectually fascinating and challenging, particularly to someone with taste and talent for theoretical reasoning and quantitative analysis. At the same time it offered the hope, as it still does, that improved understanding could better the lot of mankind."

"For me, growing up in the 1930s, the two motivations powerfully reinforced each other. The miserable failures of capitalist economies in the Great Depression were root causes of worldwide social and political disasters. The crisis triggered a fertile period of scientific ferment and revolution in economic theory."

"The historic terrain of macro-economic theory is the explanation of the levels and fluctuations of overall economic activity. Macro-economists have been especially interested in the effects of alternative fiscal, financial, and monetary policies."

"With the publication of J. M. Keynes’s General Theory in 1936 and the mathematical formalizations of his theory by J. R. Hicks (1937) and others, the language of macro-economic theory became systems of simultaneous equations. These are general equilibrium systems of interdependence in the sense that the relationships describe an entire national economy, not just a particular industry or sector. The systems are usually not completely closed; they depend on exogenous parameters including instruments controlled by policy-makers. Seeking definite relationships of economic outcomes to policies and other exogenous variables, qualitative and quantitative, these models sacrifice detail and generality, limiting the number of variables and equations by aggregations over agents, commodities, assets, and time."

"I had, to be sure, been drawn into economics when the General Theory was an exciting revelation for students hungry for explanation and remedy of the Great Depression. At the same time, I was uncomfortable with several aspects of Keynes’ theory, and I sought to improve what would now be called the microfoundations of his macroeconomic relations."

"I shall argue that Keynesian macroeconomics neither asserts nor requires nominal wage and/or price rigidity. It does assert and require that markets not be instantaneously and continuously cleared by prices."

"Ball, Mankiw, Romer and others style themselves as New Keynesians. Their program is to develop improved microeconomic foundations for imperfectly flexible prices. In the process, they hope to illuminate the paradox that individually rational or near-rational behavior can result in significant collective market failures. These are certainly laudable objectives. In the end, I suspect, the program will not change the essential substance of Keynesian macroeconomics. But it will make Keynes more palatable to theorists."

"Keynes did not challenge the efficacy of price adjustment mechanisms in clearing particular markets in the Marshallian partial equilibrium theory on which he had been reared. He did challenge the mindless application of those mechanisms to economy-wide markets. Founding what came to be known as macroeconomics, he was modeling a whole economy as a closed system. He knew he could not use the Marshallian assumption that the clearing of one market could be safely described on the assumption that the rest of the economy was unaffected."

"I probably always say the same things; I hope people don't remember. One of the same things I say is that Japanese macroeconomic policy is perversely and inexcusably incompetent, and I surely would say that again. It's true-as Paul Krugman, a fellow participant in this program, has been saying and as I have said here in previous years-that Japan has reinvented the Keynesian liquidity trap. It can now reappear in classrooms where it had been long ignored or at best barely mentioned as a curiosum of the Great Depression."

"The central message is still that, as Keynes argued, fiscal policy is the answer to liquidity traps, financial or political. The arguments against fiscal policy in Japan, so far as I understand them are intellectually fallacious; they would receive failing grades in an undergraduate macro exam."

"The important Keynesian insight is that a high propensity to save will not generate high national saving unless it goes into investment, into accumulation of real capital. The "paradox of thrift" makes this point in an extreme way. In certain circumstances, when there is no demand for investment around, the economy can be no better off, or even worse off, if a thrifty public cuts consumption."

"I suspect that many of the world's financial lords are somewhat embarrassed to tell Japan repeatedly at G-7 meetings and elsewhere to adopt a Keynesian solution. Within Europe, central banks and governments think Keynesian theories and policies are absolutely wrong. Despite the remarkable success of pragmatic policies in the United States, true believers in the Invisible Hand reject Keynesian diagnoses and prescriptions. Many observers of Japan have found it intellectually comforting to blame the slump on the plight of the banks, flooded with bad loans dated from the land and equity bubbles and their collapse. They hope that a governmentmanaged and -subsidized rectification of bank balance sheets will trigger overall economic recovery. I think this is a false hope. The bank problem is only a small part of the macroeconomic disaster. It has to be resolved, of course, but resolution that is no substitute for the needed fiscal and monetary stimuli."

"Back in 1982, a brief but brusque exchange … took place between James Tobin … and Robert Nozick … Tobin exclaimed at Nozick: ‘There is nothing more dangerous than a philosopher who’s learned a little bit of economics.’ To which Nozick immediately responded: ‘Unless it’s an economist who hasn’t learned any philosophy.’"

"The other economic camp made for quite a different story. James Tobin (an east-coast Ivy League policy advisor) had already won the Nobel Prize when I spoke with him. A true gentleman, he spoke softly about his life and his Keynesian approach to economics. With due respect, I worried after a time that the interview sounded so automatic, so “done” before, that it would add little to the book. Then I brought up Lucas’s criticism. Tobin began to speak much louder and faster (on transcribing the tape I actually had to adjust the volume). He remained reasonable and gentlemanly but his voice betrayed his indignation toward Lucas and his camp, about how they were misleading sensible Keynesian economic thought."

"When I tried to sort out the pernicious disagreements between new classical and new Keynesian economists, I conducted a series of conversations with the protagonists (Klamer 1983). The personal differences were revealing. The viva cious Robert Solow (with a taste for the quick quip), the serious Robert Lucas (never less than self-composed), the chatty Franco Modigliani (not shy of self promotion), and the unassuming James Tobin (wanting an interview at least as long as Lucas’s) quickly taught me how trenchant the rhetorical differences were."

"Tobin asked me to come and talk at Yale in 1977, and I was there for a couple of days. He was really nice in a personal way. He made it clear that he respected my work as a professional, so I didn't feel my professional standing was at risk. When I got there he gave me a nice introduction. It wasn't a question of whether I was a competent economist or not; there was nothing personal involved. These guys, however, had lots of disagreements and criticisms. I'd been thinking along these lines for many years, so I thought I did a pretty good job of taking care of the questions, but I don't know how it looked from the other side. It left me with a feeling of being way ahead of the game. It was an exciting feeling."

"I want to tell you a story about Tobin. There was a conference at the Minnesota Fed in honor of Walter Heller, and all the old people, the heroes of my youth in economics, were there. It was a really nice occasion. Gardner Ackley was giving a talk; it was very negative about the direction of modern macro. saying that there was too much mathematics and that too many assumptions were unrealistic. He also was very critical of rational expectations and of all sorts of modern theorizing. It occurred after two days of really negative things being said about rational expectations. Nobody on our side said anything, in deference to Heller, I suppose. Then Tobin stood up and said that listening to Ackley's talk reminded him of going to the AEA meetings, after the war in 1946, at which the most-prominent old members of the profession were criticizing the young Keynesians for being unrealistic and too mathematical. Tobin said "We've had our chance, we haven't solved all the problems. There are a lot of problems left, there are unsatisfactory things about our models, and it's time to give these guys a chance." It was very gracious."

"Tobin was a person who really impressed me, because he had a passion for social justice and for public policy (...) for Tobin it was always something that was about making the lives of people better."

"When James Tobin, a Nobel Prize winner in economics, was on the US Council of Economic Advisors some years ago, I asked him if he used complicated macroeconometric models in his work for the Council. He responded that he didn’t because he and others could not understand the workings and output of such models and thus did not have much confidence in them. When I asked what he actually did use to analyse problems, he remarked that he used a simple multiplier–accelerator model on the back of an envelope and even though he didn’t have too much confidence in it, he said at least he understood what he was doing."

"Heinz performs the magic trick of convincing us that the familiar objects of our existence can be seen to be nothing more than tokens for the behaviors of the organism that apparently create stable forms. These stabilities persist, for that organism, as an observing system. This is not to deny an underlying reality that is the source of objects, but rather to emphasize the role of process, and the role of the organism in the production of a living map, a map that is so sensitive that map and territory are conjoined."

"Cybernetics is the study of systems and processes that interact with themselves and produce themselves from themselves."

"This is the Unix philosophy: Write programs that do one thing and do it well. Write programs to work together. Write programs to handle text streams, because that is a universal interface."

"The notion of "intricate and beautiful complexities" is almost an oxymoron. Unix programmers vie with each other for "simple and beautiful" honors — a point that's implicit in these rules, but is well worth making overt."

"Word and Excel and PowerPoint and other Microsoft programs have intimate — one might say promiscuous — knowledge of each others' internals. In Unix, one tries to design programs to operate not specifically with each other, but with programs as yet unthought of."

"Everything was small... and my heart sinks for Linux when I see the size of it. [...] The manual page, which really used to be a manual page, is now a small volume, with a thousand options... We used to sit around in the Unix Room saying, 'What can we throw out? Why is there this option?' It's often because there is some deficiency in the basic design — you didn't really hit the right design point. Instead of adding an option, think about what was forcing you to add that option."

"Ritchie and Thompson made an amazing team; and they played Unix and C like a fine instrument. They sometimes divided up work almost on a subroutine-by-subroutine basis with such rapport that it almost seemed like the work of a single person. In fact, as Dennis has recounted, they once got their signals crossed and both wrote the same subroutine. The two versions did not merely compute the same result, they did it with identical source code! Their output was prodigious. Once I counted how much production code they had written in the preceding year − 100,000 lines! Prodigious didn’t mean slapdash. Ken and Dennis have unerring design sense. They write code that works, code that can be read, code that can evolve."

"I don't know the counts of Unix and Linux servers. I do know that my heart sinks whenever I look under the hood in Linux. It is has been so overfed by loving hands. Over 240 system calls! Gigabytes of source! A C compiler with a 250-page user manual (not counting the language definition)! A simple page turner, 'less,' has over 40 options and 60 commands! It's proof that open-source can breed monsters just like the commercial pros. Miraculously, though, this monster works."

"... speaking of Doug, he's the unsung hero of Unix. He was manager of the group that produced it and a huge creative force in the group, but he's almost unknown in the Unix community. He invented a couple of things you might have heard of: pipes and — get this — macros. Well, someone had to do it and that someone was Doug. As Ken once said when we were talking one day in the Unix room, "There's no one smarter than Doug.""

"McIlroy ... is the smartest of all of us and the least remembered or written down of all of us [programmers at Bell Labs' Computing Techniques Research Department]."

"Doug McIlroy's influence on the development of both C and C++ cannot be overestimated. I cannot remember a single critical design decision in C++ that I have not discussed at length with Doug."

"A time series is a sequence of observations, usually ordered in time, although in some cases the ordering may be according to another dimension. The feature of time series analysis which distinguishes it from other statistical analysis is the explicit recognition of the importance of the order in which the observations are made. While in many problems the observations are statistically independent, in time series successive observations may be dependent, and the dependence may depend on the positions in the sequence. The nature of a series and the structure of its generating process also may involve in other ways the sequence in which the observations are taken."

"[At Princeton Samuel Wilks...] was the major interest for me... I did have a contact with Oscar Morgenstern... Von Neumann was developing theory of games at the time... but I must say, I really didn't understand it very well when he lectured it."

"Early in 1943 I got full time war research work... My first project was to evaluate long term weather forecast. Longe range, in that time, meant three to four days."

"In mathematical statistics, as well as econometrics, Ted Anderson is a scholar of immense stature. The scope and diversity of his research in statistical theory is almost a phenomenon in itself. Sometimes it seems that wherever one turns the subject, Ted's mark and influence is already firmly established. His books on multivariate analysis and time series rapidly became accepted as major treatises and are now integral parts of the bookshelves of every statistician."

"Much of T. W. Anderson's work in statistical theory has had an important influence on econometrics. But it is his work on structural estimation that has had the greatest impact on subsequent developments in the subject."

"The Introductio does not boast an impressive number of editions, yet its influence was pervasive. In originality and in the richness of its scope it ranks among the greatest of textbooks; but it is outstanding also for clarity of exposition. Published two hundred and two years ago, it nevertheless possesses a remarkable modernity of terminology and notation, as well as of viewpoint. Imitation is indeed the sincerest form of flattery."

"But what, after all, are the integers? Everyone thinks that he or she knows, for example, what the number three is — until he or she tries to define or explain it."

"It should be mentioned also that the Hindus, unlike the Greeks, regarded irrational roots of numbers as numbers. This was of enormous help in algebra, and Indian mathematicians have been much praised for taking this step; but one must remember that the Hindu contribution in this case was the result of logical innocence rather than of mathematical insight. We have seen the lack of nice distinction on the part of Hindu mathematicians between exact and inexact results, and it was only natural that they should not have taken seriously the difference between commensurable and incommensurable magnitudes. For them there was no impediment to the acceptance of irrational numbers, and later generations followed their lead uncritically until in the nineteenth century mathematicians established the real number system on a sound basis."

"A Hebrew belief asserted that if Yahweh lays aside his bow and hangs it in the clouds, this is a sign that his anger has subsided. Other peoples have had similar ideas, based upon the tradition that an archer carries his bow with the ends pointing downward when he wishes to indicate his peaceful intentions."

"In ancient classical literature the rainbow sometimes was deified as Iris; at other times it was regarded merely as the route traversed by the messenger of Hera. The conception of the rainbow as a pathway or bridge has been widespread. For some it has been the best of all bridges, built out of three colors; for others the phrase "building on the rainbow" has meant a bootless enterprise. North American Indians were among those who thought of the rainbow as the Pathway of Souls, an interpretation found in many other places. Among the Japanese the rainbow is identified as the "Floating Bridge of Heaven"; and Hawaiian and Polynesian myths allude to the bow as the path to the upper world. In the Austrian Alps the souls of the righteous are said to ascend the bow to heaven; and in New Zealand the dead chieftains are believed to pass along it to reach their new home. In parts of France the rainbow is called the pont du St. Esprit, and in many places it is the bridge of St. Bernard or of St. Martin or of St. Peter. Basque pilgrims knew it as the 'puente de Roma'. Sometimes it is called instead the Croy de St. Denis (or of St. Leonard or of St. Bernard or of St. Martin). In Italy the name arcu de Santa Marina is relatively familiar. Associations of the rainbow and the milky way are frequent. The Arabic name for the milky way is equivalent to Gate of Heaven, and in Russia the analogous role was played by the rainbow. Elsewhere also the bow has been called the Gate of Paradise; and by some the rainbow has been thought to be a ray of light which falls on the earth when Peter opens the heavenly gate. In parts of France the rainbow is known as the porte de St. Jacques, while the milky way is called chemin de St. Jacques. In Swabia and Bavaria saints pass by the rainbow from heaven to earth; while in Polynesia this is the route of the gods themselves. In Eddic literature the bow served as a link between the gods and man — the Bifrost bridge, guarded by Heimdel, over which the gods passed daily. At the time of the Gotterdamerung the sons of Muspell will cross the bridge and then demolish it. Sometimes also in the Eddas the rainbow is interpreted as a necklace worn by Freyja, the "necklace of the Brisings," alluded to in Beowulf; again it is the bow of Thor from which he shoots arrows at evil spirits. Among the Finns it has been an arc which hurls arrows of fire, in Mozambique it is the arm of a conquering god. In the Japanese Ko-Ji-Ki (or Records of Ancient Matters), compiled presumably in 712, the creation of the island of Onogoro is related to the rainbow. Deities, standing upon the "floating bridge of heaven," thrust down a jeweled spear into the brine and stirred with it. When the spear was withdrawn, the brine that dripped down from the end was piled up in the form of the island. In myth and legend the rainbow has been regarded variously as a harbinger of misfortune and as a sign of good luck. Some have held it to be a bad sign if the feet of the bow rest on water, whereas a rainbow arching from dry land to dry land is a good augury. Dreambooks held that when one dreams of seeing a rainbow, he will give or receive a gift according as the bow is seen in the west or the east. The Crown-prince Frederick August took it as a good omen when, upon his receiving the kingdom form Napoleon in 1806, a rainbow appeared; but others interpreted it as boding ill, a view confirmed by the war and destruction of Saxony which ensued. By many, a rainbow appearing at the birth of a child is taken to be a favorable sign; but in Slavonic accounts a glance from the fay who sits at the foot of the rainbow, combing herself, brings death."

"Ptolemy left in his Optics, the earliest surviving table of angles of refraction from air to water. … This table, quoted and requoted until modern times, has been admired … A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order … As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience."

"Robert Grosseteste … was born at the decisive moment when Greek and Arabic science became accessible in Latin versions."

"Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i.e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle ..."

"Descartes maintained his confidence in the instantaneity of light. … Yet in his derivation of the law of refraction, Descartes reasoned that light travelled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!"

"Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite."

"Carl B. Boyer … is more or less the Gibbon of math history."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"Number is that property of a group of distinct things which remains unchanged during any change to which the group may be subjected which does not destroy the distinctness of the individual things."

"Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the fraction, and the irrational, but in no other sense; all are alike mere symbols devised for the sake of representing the results of operations even when these results are not numbers (positive integers)."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"Is the Airship Possible? That depends, first of all, on whether we are to make the requisite scientific discoveries... the construction of an aerial vehicle ... which could carry even a single man from place-to-place at pleasure requires the discovery of some new metal or some new force."

"One of the most curious of these cases [geometrical paradoxers] was that of a student, I am not sure but a graduate, of the University of Virginia, who claimed that geometers were in error in assuming that a line had no thickness. He published a school geometry based on his views, which received the endorsement of a well-known New York school official and, on the basis of this, was actually endorsed, or came very near being endorsed, as a text-book hi the public schools of New York."

"I knew that flying machines were impossible; in engineering school I had studied Professor Simon Newcomb's well-known mathematical proof that the efforts of Professor Langley and others to build an aerodyne capable of carrying a man were doomed, useless, because scale theory proved that no such contraption large enough to carry a man could carry a heat-energy plant large enough to lift it off the ground — much less a passenger. That was science's final word on a folly and it put a stop to wasting public monies on a will-o'-the-wisp. Research and development money went into airships, where it belonged, with enormous success. However, in the past few days I had gained a new angle on the idea of "impossible". When a veritable flying machine showed up in our sky, I was not greatly surprised."

"Professor Fisher's The Purchasing Power of Money is dedicated to Simon Newcomb, from whom vid Professor Kemmerer the PT = MV formula ultimately derives. Newcomb was not a professional economist but a mathematician (Professor of Mathematics in the U.S. Navy and at Johns Hopkins). His Principles of Political Economy, published in 1886, is one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half -formed subject like economics."

"It is a matter of historical record that Newcomb, one of the most eminent American mathematicians of his day, published on the topic of four-dimensional space from 1877, and he spoke about it to the New York Mathematical Society in 1893. Four dimensions (and more) were important research topics in mathematics and physics."

"There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it. ...space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to these planes, each at right angle to the others. But some philosophical people have been asking why three dimensions particularly—why not another direction at right angles to the other three?—and have even tried to construct a Four Dimensional geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a Three-Dimensional solid, and similarly they think that by models of three dimensions they could represent one of four—if they could master the perspective of the thing. See?"

"In the late 19th century, Newcomb was one of America’s best known and probably one of its most powerful scientists. He had spent most of his career as a professor at the naval observatory in Washington, D. C. He had served as President of the American Academy of Arts and Science and as President of the Political Economy Club in the 1880s. He eventually received numerous awards for his most important astronomical research more accurately measuring the movements of the moon and the planets in our solar system. In the 1880s, Newcomb joined the faculty of Johns Hopkins University and his views regarding the competence of junior faculty were often communicated to President Daniel Gilman. This was especially the case for Peirce and Ely. Newcomb also confronted America’s most prominent theologians on the relationship between theology and science and of course evolution and Christianity. For the nation’s centennial, Newcomb also had offered his harsh appraisals of American science and political economy maintaining that they were way behind European science and British political economy. Newcomb also thwarted Peirce’s career progress on numerous occasions playing a pivotal role in his exclusion from academia after 1885."

"James R. Wible. "Economics, Christianity, and Creative Evolution: Peirce, Newcomb, and Ely and the Issues Surrounding the Creation of the American Economic Association in the 1880s," 2009."

"My sense is that, in the long run, Mother Nature always wins. Cautionary note: Mother Nature's win may not include the survival of the pesky human race!"

"Even with omnividence and telepathy, I expect that, day in and day out, people won't actually change that much—not even in a million years. That's a lesson history teaches us. Yes, we've utterly changed our tech since the end of the Middle Ages, but the paintings of Hieronymus Bosch or Peter Bruegel show that people back then were much like us, perennially entangled with the seven deadly sins."

"Will molecular manufacture give all of us the luxuries we want? No. Skewed inverse power-law distribution of valued qualities is an intrinsic property of the natural world. That is, roughly speaking, if there are a thousand people at the bottom of the heap, and a hundred immediately above them, there will only be ten farther up, and just one perched on the top in possession of a large proportion of the goodies. Even if we become glowing clouds of ectoplasm, there's going to be something that we’re competing for—and most of us will feel as though we're getting screwed."

"I think computronium is a spurious concept. Matter, just as it is, conducts outlandishly complex chaotic quantum computations by dint of sitting around. Matter isn't dumb. Every particle everywhere and every when computes at the maximum possible flop. I think we tend to very seriously undervalue quotidian reality. Turning an inhabited planet into a computronium Dyson shell is comparable to filling in wetlands to make a mall, clear-cutting a rain forest to make a destination golf resort, or killing a whale to whittle its teeth into religious icons of a whale god."

"But, come on, if you want to smoothly transmogrify a blade of grass into some nanomachines simulating a blade of grass, then why bother grinding up the blade of grass at all? After all, any object at all can be viewed as a quantum computation! The blade of grass already is an assemblage of nanomachines emulating a blade of grass. Nature embodies superhuman intelligence just as she is."

"In short, a gnarly process is complex and unpredictable without being random. If a story hews to some very familiar pattern, it feels stale. But if absolutely anything can happen, a story becomes as unengaging as someone else’s dream. The gnarly zone lies at the interface between logic and fantasy."

"Wit involves describing the world as it actually is. You experience a release of tension when you notice a glitch. Something was off-kilter, and now you see what it was. The elephant in the room has been named. The evil spirit has been incanted. Perceiving an incongruity in our supposedly smooth-running society provokes a shock of recognition and a concomitant burst of laughter. Wit is a critical-satirical process that can be more serious than the “humorous” label suggests."

"Old age is all about killing time."

"“That’s the problem with immortality,” mused Jack. “You never live long enough to get there.”"

"“How do you remember these things?” “Mathematicians don’t get senile,” he said. “They just go nuts,” I muttered."

"As he mentions this last sin, he looks down my nightgown, which I’m just loving. I press his hand against my warm thigh. “Don’t worry, sweetie. I don’t live in Hell. I live in San Jose.”"

"It would take a supercomputer to simulate this puddle in real time—maybe even all the computers in the world. Especially if you included the air currents pushing the raindrops this way and that. Computable or not, it kept happening."

"It was good to be outside, away from the TV and the computer. The natural world had such high bandwidth."

"But Charles was the one who finally realized it was nuts to be walking around inside a sewer with a tweaker leading the way. The fact that Charles figured this out before me makes me wonder about myself. I think I’m spending too much time on my computer."

"“Relax, Wag.” “Relaxing makes me tense!” I scream."

"Thanks to environmental decline, kids of Janna’s age had never seen authentic wildlife. So they flipped for the Goob menagerie: marmosets with butterfly wings, starfish that scuttled like earwigs, long, furry frankfurter cat-snakes."

"He’ll be back. Men always come back when they see you making money."

"Kelso had the kind of slit-eyed street smarts that came only from Berkeley law classes."

"The public revealed its single most predictable trait: fickleness."

"Janna knew full well that the classic dot-com move was to grab that golden parachute and bail like crazy before the investors and employees caught on."

"Tug was fascinated, and not by the money involved. Like many mathematicians, Mesoglea considered money to be one boring, merely bookkeeping subset of the vast mental universe of general computation."

"“Security always soars along with unemployment,” said Pullen, nodding his head at his own wisdom. “We are in a major downturn. I’ve seen this before, so I know the drill. Locks, bolts, Dobermans, they’re all market leaders this quarter. That’s Capitalism 301, girls.”"

"I think of consciousness as a point, an "eye," that moves about in a sort of mental space. All thoughts are already there in this multi-dimensional space, which we might as well call the Mindscape. Our bodies move about in the physical space called the Universe; our consciousnesses move about in the mental space called the Mindscape."

"Just as we all share the same Universe, we all share the same Mindscape. For just as you can physically occupy the same position in the Universe that anyone else does, you can, in principle, mentally occupy the same state of mind or position in the Mindscape that anyone else does."

"Just as a rock is already in the Universe, whether or not someone is handling it, an idea is already in the Mindscape, whether or not someone is thinking it. A person who does mathematical research, writes stories, or meditates is an explorer of the Mindscape in much the same way that Armstrong, Livingstone, or Cousteau are explorers of the physical features of our Universe. The rocks on the Moon were there before the lunar module landed; and all the possible thoughts are already out there in the Mindscape. The mind of an individual would seem to be analogous to the room or to the neighborhood in which that person lives. One is never in touch with the whole Universe through one’s physical perceptions, and it is doubtful whether one’s mind is ever able to fill the entire Mindscape."

"In more familiar terms, it is not hard to prove that God is infinite ... but what if you don’t believe that God exists? It may seem hard to doubt that the more impersonal Absolutes–such as “everything,” or the Mindscape–exist, but there are those who do doubt this. The issue under consideration is a version of the old philosophical problem of the One and the Many. What is being asked is whether the cosmos exists as an organic One, or merely as a Many with no essential coherence. It is certainly true that the Mindscape, for instance, does not exist as a single rational thought. For if the Mindscape is a One, then it is a member of itself, and thus can only be known through a flash of mystical vision. No rational thought is a member of itself, so no rational thought could tie the Mindscape into a One."

"In one of our conversations I pressed Gödel to explain what he meant by the “other relation to reality” by which he said one could directly see mathematical objects. He made the point that the same possibilities of thought are open to everyone, so that we can take the world of possible forms as objective and absolute. Possibility is observer-independent, and therefore real, because it is not subject to our will."

"Gödel shared with Einstein a certain mystical turn of thought. The word “mystic” is almost pejorative these days. But mysticism does not really have anything to do with incense or encounter groups or demoniac possession. There is a difference between mysticism and occultism. A pure strand of classical mysticism runs from Plato to Plotinus and Eckhart to such great modern thinkers as Aldous Huxley and D. T. Suzuki. The central teaching of mysticism is this: Reality is One. The practice of mysticism consists in finding ways to experience this higher unity directly. The One has variously been called the Good, God, the Cosmos, the Mind, the Void, or (perhaps most neutrally) the Absolute. No door in the labyrinthine castle of science opens directly onto the Absolute. But if one understands the maze well enough, it is possible to jump out of the system and experience the Absolute for oneself."

"Is this all there is? Struggle, loneliness, disease, and death ... Is this all there is? Life can seem so chaotic, so dreary, so grindingly hard. Who among us has not dreamt of some higher reality, some transcendent level of meaning and peace? There actually is such a higher reality ... And it is not so very hard to reach. For many, the fourth dimension has served as a gateway into it. But what is the fourth dimension? No one can point to the fourth dimension, yet it is all around us. Philosophers and mystics meditate upon it; physicists and mathematicians calculate with it. The fourth dimension is part and parcel of many respected scientific theories, yet it is also of great use in such disreputable fields as spiritualism and science fiction."

"The fourth dimension is a direction different from all the directions in normal space. Some say that time is the fourth dimension ... And this is, in a sense, true. Others say that the fourth dimension is a hyperspace direction quite different from time ... This is also true. There are, in fact, many higher dimensions. One of these higher dimensions is time, another higher dimension is the direction m which space is curved, and still another higher dimension may lead toward some utterly different universes existing parallel to our own. At the deepest level, our world can be regarded as a pattern in infinite-dimensional space, a space in which we and our minds move like fish in water."

"Starting with no preconceptions at all, what is the most reasonable model of the world that we can build up? Only two things seem really certain: one exists, and one has perceptions. I may be a meat machine, a soul, an eye of God, a collection of ideas, or who knows what — but I am certain that I exist. I am the thing that writes these words. Of course, you may doubt whether I am real — perhaps you are only dreaming that you read this book — but you do know for certain that you yourself exist. The fact that one has experiences is equally certain; to put it more neutrally, one cannot doubt that perceptions occur."

"What is reality? Take all your perceptions and all of mine, take everyone’s thoughts and all the visions. In an infinite-dimensional space there is room to fit them all together; each is a piece of the infinite-dimensional One, and this One is reality."

"Reality is indescribably rich and complex. Sometimes I forget this, and life goes gray. But the world is alive, and we are living parts of it. Thoughts are as real and important as objects. Every object is an endless source of wonder. We don’t know why we’re here — we don’t even know what we are. But we exist, and the world is going on. Our ordinary notions of space and time are just a convenient fiction. Higher dimensions are everywhere. There’s no need to work for enlightenment; enlightenment is here and now, as close as the fourth dimension."

"The patterns of mathematics can be roughly grouped into five archetypes: Number, Space, Logic, Infinity, and Information."

"People sometimes say, “If the world really has a simple explanation, then where did all the randomness and information come from?” We can think of the information as coming in with the passage of time. Each tick of time increases the depth of the world computer’s output."

"My purpose in writing Mind Tools has been to see what follows if one believes that everything is information. I have reached the following (debatable) conclusions."

"So what is reality, one more time? An incompressible computation by a fractal CA of inconceivable dimensions. And where is this huge computation taking place? Everywhere; it’s what we’re made of."

"I'm not a brave man. My self-image is of a very small and weak person. In point of fact, I'm almost six feet, and solidly built. But I was a late bloomer. I spent those formative early high-school years as a pudgy little science whimp. I'm still scared of big men with deep voices."

"My real speciality is the mathematical analysis of Hilbert Space operators. But this was no time to come on like an ivory-tower idealist."

"Not only am I scared of big, strong men, I'm scared of mean little women. It's just little skinny men and nice big women that I get along with."

"I stared down at the object in my lap. A skin-colored sphere the size of a giant beach ball, with breasts on top and a mouth between the breasts. At the bottom were the generous buttocks, a crinkly anus and a vaginal passage containing my rapidly limpening penis. Was this safe?"

"It was funny. I knew I didn't want the bomb to be a success. But yet I'd spent so many years working around physics labs that I couldn't stand not to do it right."

"This brought back the sick, ashamed feeling I'd woken up with. I was no better than some geek with a foam-rubber woman's torso like they advertise in Hustler. What a pathetic, twisted version of womanhood: all the "inessential" parts lopped off, nothing left behind but tits and ass and holes. Lifelike washable plastic skin. Greek and French features. But yet, in a way, wasn't the sex sphere always what I'd wanted in a woman? An ugly truth there. "Shut up and spread!" How many times had I told Sybil that, if not in so many words?"

"Amazing, the respect that nuclear weapons bring."

"I had formed a vague idea that the sex sphere was a hypersphere extending into the fourth dimension. Which meant that if the sphere's giant cunt swallowed me I could end up somewhere very . . . different."

"Sybil had an unreal, larger-than-life feeling . . . as if she were a person in a book."

"At first the tumbling had me totally disoriented. With each degree that I turned, the images around me would deform and change. Three given blobs might split or merge to two or five, while some other shape's angular facets would sprout interlocking crystals. It was a little like trying to make out a human body by watching a Carousel slideshow of three hundred sixty microtomed cross sections."

"But after a while, some higher brain-center cut in, and I began being mentally able to fit the wildly changing scenery into a coherent four-dimensional whole. The process was really no more devious than the process by which one integrates the two hundred lines of a TV screen into a single two-dimensional image . . . which in turn is interpreted as a three-dimensional scene. It's just a matter of processing information. Impossible? I saw."

"The space of our universe is the hypersurface of a vast expanding hypersphere."

"A person's lifeworm is a tangle of atomic worldlines. A braid. The dotty little atoms trace out smooth lines in spacetime: you are the pattern that these lines make up. there is no one single atom that is exclusively yours. I breathe an atom out, you breathe it in. Your garbage helps my tomatoes grow. And so the little spacetime threads weave us all together. The human race is a single vast tapestry, linked by our shared food and air. There are larger links as well: sperm, egg and umblilicus. Each family tree is an organic whole. Your spacetime body tapers back to the threads of mother's egg and father's sperm. And children, if you have them, are forever rooted in your flesh."

"This is just so typical of you, Alwin, to be in love with a giant ass."

"The fifties were supposed to be a golden age when the pig had everything his way. That's what TV and the government wants us to believe: there was a time when no one made trouble. What about Kerouac, you assholes? What about Neal?"

"Was I to be Earth's first casualty in the Attack of the Giant Ass From Hilbert Space?"

"At the most elemental level, reality evanesces into something called Schröedinger's Wave Function: a mathematical abstraction which is best represented as a pattern in an infinite-dimensional space, Hilbert Space. Each point of the Hilbert Space represents a possible state of affairs. The wave function for some one physical or mental system takes the form of, let us say, a coloring in of Hilbert Space. The brightly colored parts represent likely states for the system, the dim parts represent less probable states of affairs."

"The matter of color is more confusing. Not every property of a system can be stated as a definite spatio-temporal state of affairs. A system's tendency, for instance, to move from State A to State B, but not from State B to State A . . . a tendency like this is not any specific event which you can point to in space and time. These nonspecific properties correspond to overall gestalts in the Hilbert Space coloring. Alternating bands of red and green light might, for example, represent a particle which is moving from left to right but which has no specific location. A good mood could be a golden haze not tied to any particular cause."

"For whatever reason, we find it easier to "read" Hilbert Space patterns in terms of time. Yet the patterns exist outside of time. Thinking timelessly is not some unusual skill; when you remember last night's supper you sense a whole and not a chew-by-chew replay. To know a novel's action is to grasp the four-dimensional spacetime whole described."

"Don't you think women would like a man's head that always listens to them and agrees?"

"Women care about specifics, about details. Men care about generalities, about abstract principles."

"There are many possible realities, infinitely many. Yet most of them are not . . . alive. Most of them are like books that no one ever actually wrote. A group-mind, like humanity's, lights up one given world. What makes this world different from some ghostly alternative universe is that we actually live here."

"I knew you’d say that. You’re so anal, Fletcher. Too much math."

"The government had recently repealed all speed limits in an attempt to boost oil consumption."

"Oh, yeah, she told me about that. I think mysticism’s a bunch of crap. All religions are a bunch of crap."

"I wished she would go away and let us destroy the universe in peace."

"This provender was at a double remove from reality; it was artificially made food that had been further treated in an attempt to make it healthy."

"I’ve never seen a religion that wasn’t basically evil."

"“Now that’s a fib, I know,” said the black woman. “Is you folks preachers?”"

"It’s perfect, isn’t it? It just goes to show that everything I’ve ever said about religion is true. The sky’s the limit when it comes to religious stupidity. Here we have a race of alien invaders, and the evangelical true believers are flocking here to get taken over."

"Anyone who’d volunteer for alien domination doesn’t really deserve to have his or her freedom."

"“I’ll wish for ten million more bucks while I’m at it.” “And immortality?” “No, no. I don’t want to live forever. Death’s the only thing that keeps me going.”"

"The surest way to be unhappy is try to be happy all the time."

"“What’s superspace?” I felt around for my body and couldn’t find it. “Thoughtland, Fletch, the cosmos. Pure mentation. Abstract possibility. Infinite dimensions. The class of all sets. God’s mind. The pre-geometric substratum. Hilbert space. Penultimate reality. White...” “Cut the crap, Harry.”"

"My roommate says anyone who mails bombs to computer scientists can’t be all bad."

"Mother Nature doesn’t want power-tripping greedheads looking up her skirts."

"People always have bad news for you when they call you “sir.”"

"“Do you know computer science?” “I know it’s for lamers who can’t handle real math.”"

"Although my mood swings were the logical and deterministic results of my inputs, they were dismayingly hard for me to foresee, let alone control."

"There’s only one way that people change the past, Bela. They stop thinking about it. They move on."

"In a sense mathematics is quite objective: the same deductions can become known to everyone who starts with the same axioms and definitions; the same abstract forms can be universally perceived. So it’s perfectly possible to talk math with a cockroach from Galaxy Z."

"It was odd, odd, odd to see people die. The world rolled on the same as before, as heedlessly as if a person were an ant or a wildflower or a puff of wind. Nature kept on making more and more of everything, and never mind that birth is a death sentence. And now that I’d been to La Hampa, I knew that creation was even more prodigal than I’d ever imagined. There were worlds upon worlds filled with people struggling and swarming like fretful gnats, all of them doomed to vanish into dust while the cosmic dance spun on."

"In the 1970s I even got to meet Kurt Gödel a few times. The king of the logicians. Gödel once told me, “The a priori is very powerful.” By this he meant that pure logic can take you farther than you might believe possible."

"So, okay, I’ll go for the universal-automatist answer to “What is reality?” Reality is made of gnarly computations."

"The meaning of life is beauty and love."

"See the gnarl. The air is a gnarly ocean; the leaves dance on the trees. I’ve always enjoyed watching clouds and water; and now I realize that the computations they’re carrying out are fully as complex as anything in any book I might read. Each flickering shadow is a reminder of the world’s unsolvable and unpredictable richness."

"One last thought: perhaps our universe is perfect."

"Our goal is to build a broad-based model of key components of the economy: households, firms, banks and government... The failure to embrace things like simulation has inhibited progress in economics."

"Rational adventure in a physical setting is becoming increasingly rarer in the world. The evolution of technology and infrastructure has altered the kind of adventures that we can have, so that people with adventurous spirits either take on risk for its own sake, or they embark on rational adventures in the mental domain."

"In a world of superintelligent humans, the account of a quest to prove a theorem may take on a universality in its drama that seems inconceivable to us now. I believe that rational adventure is fundamental to the human spirit, and that it won't go away. But it will evolve of necessity to take place in the increasingly abstract domains that characterize the boundaries and frontiers of an evolving and ever more complex and abstract world. As a result, it will evolve into forms that are difficult for us to even think about at this point in time."

"On learning more astronomy, in the phenomenon of "averted vision," I found a justification for my rationale about the roundabout path to metaphysics via physics: to see a faint star, it's necessary to look away from it; as soon as one looks at it directly, it vanishes."

"It seemed that fundamental physics was stuck. The particle physicists were smashing particles into each other with ever increasing force, trying to figure out how many quarks could dance on the head of a pin. The cosmologists were working with very few facts... on what seemed to me to be mainly religious grounds. And most of physics was still focused on pushing and pulling, on the material properties... rather than on its informational properties. ...those that relate to order and disorder."

"Speaking crudely, a living system—an organism—consists of a symbiotic relationship between a metabolism and a replicator. ...the replicator contains the blueprint of the organism, with the information needed to grow, make repairs, and reproduce. ...the metabolism provides the energy and raw materials needed to build and run the replicator."

"The basic principle of an autocatalytic network is that even though nothing can make itself, everything in the pot has at least one reaction that makes it, involving only other things in the pot. It's a symbiotic system in which everything cooperates to make the metabolism work—the whole is greater than the sum of the parts."

"The paradox that immediately bothers everyone who learns about the second law is this: If systems tend to become more disordered, why, then, do we see so much order around us? ...It seems to conflict with our "creation myth": In the beginning, there was a big bang. ...no one is saying that the second law of thermodynamics is wrong, just that there is a contrapuntal process organizing things at a higher level."

"Complex adaptive systems have the property that if you run them—by just letting the mathematical variable of "time" go forward—they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously... A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life."

"Even though something like Danny Hillis' "connection machine" is big, it's nothing compared with Avogadro's number of processors that nature has at her disposal."

"We don't know what organization is. ...We do know that complex adaptive systems have to be nonlinear and capable of storing information. ...We know a little bit about what distinguishes an adaptive complex system from a nonadaptive system, such as turbulent fluid flow."

"One of the factors that caused Spencer's ideas to lose popularity was social Darwinism... Social evolution is different from biological evolution: it's faster, it's Lamarckian, and it makes even heavier use of altruism and cooperation than biological evolution does. None of this was well understood at the time."

"If we choose, we can use genetic engineering to alter the character of our offspring. ...the motivation to do this will eventually become overwhelming."

"We're rapidly creating an extraordinary silicon-based petri dish for evolution of intelligence. By the year 2025... we're likely to have computers whose raw processing power exceeds that of the human brain. Also, we're likely to have more computers than people..."

"Once we can manipulate our genome, Lamarckian fashion, the rate of change will be staggering."

"The fact that the tragic story of Évariste Galois, the mathematical genius who burned brightly but all too briefly, is not as unusual as one might think among mathematicians of his and subsequent generations. It is, rather, the most famous and dramatic of an entire genre of mathematical stories that originated in the early decades of the nineteenth century but is still going strong today. Consider, for example... Niels Henrik Abel.. János Bolyai... Srinivasa Ramanujan... John Nash... Kurt Gödel... Alexander Grothendieck... Grigory Perelman... Among modern mathematicians, it seems, extreme eccentricity, mental illness, and even solitary death are not a matter of random misfortune. They are, rather... reserved only for the most outstanding members of the field."

"Catholics... believed that the grace of God was bestowed upon sinners only through the holy Church and its sacraments, enacted by an ordained priest. Protestants, conversely, believed in a "priesthood of all believers," meaning that God would bestow his grace directly upon them. Catholics believed that Christ was physically present in the bread and wine during the sacrament of the Mass. Protestants believed that Christ was either present everywhere (Luther) or that the Mass was a mere commemoration of his sufferings (Zwingli). Catholics believed that God would take into account a man's good works in this world in determining whether be saved or lost. Protestants believed that only faith and divine grace mattered. Catholics believed that the Bible required interpretation by the hierarchy and the traditions of the Church. Protestants believed that the Bible was a clear guide for righteous behavior, accessible to anyone. What these arguments had in common were that they were entirely inconclusive."

"Theological and philosophical disputes could rage forever, he Christopher Clavius] believed, because there was no universally accepted way to decide who was right and who was wrong. ...But mathematics was different: with mathematics, the truth forces itself upon its audience whether they like it or not. One could dispute the Catholic doctrine of the sacraments, but one could not deny the Pythagorean theorem; and no one could deny the correctness of the new calendar, based as it was on the detailed mathematical calculations."

"It was clear to Clavius that Euclid's method was successful in doing precisely what the Jesuits were struggling so hard to accomplish: imposing a true, eternal, and unchallengeable order upon a seemingly chaotic reality."

"...the whole point of studying and teaching mathematics was that it demonstrated how universal truth imposed itself upon the world—rationally, hierarchically, and inescapably. Ideally, the Jesuits believed, the truths of religion would be imposed on the world just like geometrical theorems, leaving no room for avoidance or denial by Protestant or other heretics and leading to the inevitable triumph of the Church."

"Where the Jesuits insisted on clear and simple postulates, the new mathematicians relied on a vague intuition of the inner structure of matter, whereas the Jesuits celebrated absolute certainty, the new mathematicians proposed a method rife with paradoxes, and seemed to revel in them; and whereas the Jesuits sought to avoid controversy at all cost, the new method was mired in intractable controversies... It was everything that the Jesuits thought mathematics must never be, and yet it flourished... It was known as the method of indivisibles."

"Number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"

"Sometimes the mathematical anti-Platonist believes that headway is made by showing Platonism to be unsupportable by rational means, and that it is an incoherent position to take when formulated in a propositional vocabulary. It is easy enough to throw together propositional sentences. But it is a good deal more difficult to capture a Platonic disposition in a propositional formulation that is a full and honest expression of some flesh-and-blood mathematician’s view of things. There is, of course, no harm in trying—and maybe its a good exercise. But even if we cleverly came up with a proposition that is up to the task of expressing Platonism formally, the mere fact that the proposition cannot be demonstrated to be true won’t necessarily make it vanish. There are many things—some true, some false— unsupportable by rational means."

"Hodge cohomology, algebraic de Rham cohomology, crystalline cohomology, the étale ℓ-adic cohomology theories for each prime number ℓ ... A strategy to encapsulate all the different cohomology theories in algebraic geometry was formulated initially by Alexandre Grothendieck, who is responsible for setting up much of this marvelous cohomological machinery in the first place. Grothendieck sought a single theory that is cohomological in nature that acts as a gateway between algebraic geometry and the assortment of special cohomological theories, such as the ones listed above—that acts as the motive behind all this cohomological apparatus. ..."

"Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category (of sheaves relative to an extraordinarily fine Grothendieck-style topology on the category of schemes) which in some intuitive sense “softens algebraic geometry” so as to allow for a good notion of homotopy in an algebro-geometric setup and is sufficiently directly connected to concrete algebraic geometry to have already yielded some extraordinary applications. The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so throughout the current century."

"Mazur suggests that it’s possible to glimpse the essence of Grothendieck’s approach to mathematics by looking at two concepts—categories and functors. A category can be thought of almost as a grammar: take triangles, perhaps, and understand them in terms of their relationship to all other triangles. The category consists of objects, and relationships between objects. The objects are nouns and the relationships are verbs, and the category is all the ways in which they can interact. Grothendieck’s discoveries opened up mathematics in a way that was analogous to how Wittgenstein (and Saussure) changed our views of language."

"A number of statistical assumptions are made in the application of his (Thurstone's) attitude scale e.g. that the scale values of the statements are independent of the attitude distribution of the readers who sort the statements assumptions which as Thurstone points out, cannot always be verified. The method is more over laborious. It seems legitimate to enquire whether it actually does its work better than the simple scales which may be employed and the same breath to ask also whether it is not possible to construct equally reliable scales without making unnecessary statistical assumptions."

"Conflict is viewed as the active striving for one's own preferred outcome which, if attained, precludes the attainment by others of their own preferred outcome, thereby producing hostility."

"As people acquire more education, their expectations rise as to the amount of responsibility, authority, and income they receive."

"Research reveal that managers achieving better performance (i.e., greater productivity, higher earnings, lower costs, etc. ) differ in leadership principles and practices from those achieving poorer performance."

"[It remains to be seen whether the newer management theories, based as they are on research in industrial concerns, will be] equally applicable to other kinds of organized human activity, such as schools, voluntary organizations, unions, hospitals, governmental agencies, scientific and professional organizations, and the like."

"How best to organize the efforts of individuals to achieve desired objectives has long been one of the world's most important, difficult, and controversial problems."

"As tasks become more varied and require greater training and skill, the relationship (between job attitudes and performance) appears to change progressively from the negative to positive."

"The leadership and other processes of the organization must be such as to ensure a maximum probability that in all interactions and all interactions and all relationships with the organization each member will, in the light of his background, values, and expectations, view the experience as supportive and one which builds and maintains his sense of personal worth and importance."

"[Each person] is a member of one or more functioning workgroups that have a high degree of group loyalty, effective skills of interaction and high performance goals."

"The superior in one group is a subordinate in the next group, and so on through the organization."

"To be effective in leading his own work group, a superior must be able to influence his own boss, that is he needs to be skilled both as a superior and as a subordinate."

"All component parts of any system of management must be consistent with each of the other parts and reflect the system's basic philosophy."

"A variety of studies in widely different fields show that supervisors who are getting the best production, the best motivation, and the highest levels of worker satisfaction are employee-centred appreciably more often than production-centred."

"Interaction and decision making rely heavily on group processes."

"The preceding analysis shows that a manager who has high performance goals and excellent job organization but who relies solely on economic needs and direct pressure to motivate his men is very likely to be to be disappointed by their achievements. The noneconomic motives must be used fully, along with the economic needs, to create high performance goals and establish the level of motivational forces which yield high productivity. Since the principle of supportive relationships and group methods of supervision enable a manager to make effective use of the noneconomic motives, some valuable insights can be obtained by examining how these managerial principles appear to affect the motivations, satisfactions, and behavior of the members of an enterprise. A substantial body of research findings demonstrates that the greater the loyalty of the members of a group toward the group, the greater is the motivation among the members to achieve the goals of the group, and the greater is the probability that the group will achieve its goals."

"The management system of an organization must have compatible component parts if it is to function effectively. This conclusion has a very important implication; experiments in organizations must involve internally consistent changes. The traditional atomistic research design is not appropriate for experiments involving organizational theory or management systems. Every aspect of a management system is related to every other part and interacts with it. The results obtained by altering a single variable or procedure while keeping all others the same usually will yield quite different results from those obtained when that variable is changed along with simultaneous and compatible changes in all other aspects of the management system. The true influence of altering one aspect of the system cannot be determined by varying it and it alone... In experiments involving organizational theory and management systems, therefore, a systems approach must be used. The organic integrity of each system must be maintained while experimental variations are being made."

"Molecular dynamics is not primarily about making movies of molecules. More often it is about developing quantitative predictions of molecular size and shape, flexibilities, interactions with other molecules, behavior under pressure, and the relative frequency of one state or conformation compared to another."

"Understand the problem. What kind of problem is it? There are three main types of problems: ‘Show that ...’ or ‘Evaluate ...’ questions, in which a certain statement has to be proved true, or a certain expression has to be worked out; ‘Find a...’ or ‘Find all...’ questions, which requires one to find something (or everything) that satisfies certain requirements; ‘Is there a ...’ questions, which either require you to prove a statement or provide a counterexample (and thus is one of the previous two types of problem)."

"Relying on intelligence alone to pull things off at the last minute may work for a while, but generally speaking at the graduate level or higher it doesn't. One needs to do a serious amount of reading and writing, and not just thinking, in order to get anywhere serious in mathematics."

"[P]rofessional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest score, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications."

"For the third law.., Kepler had... 6 data points..: every planet.., the length of the orbit and the distance to the sun.., and he did... regression. ...He could fit a curve to these 6 data points and he got a square cube law. Amazing, but he was... lucky. That's not enough data to be... reliable."

"There was a later astronomer, Johann Bode who took the same data... and... had a prediction that the distances to the planets formed a shifted ... He also fit a curve, except there was one point missing, a... gap... His law predicted... a missing planet. ...[W]hen Uranus was discovered by Herschel, the distance fit... this pattern. Then Ceres was discovered... in the astroid belt, and it also fit the pattern. ...But then Neptune was discovered, and it was... way off. ...[I]t was a numerical fluke."

"Gauss... created one of the first mathematical data sets. He computed the first [~]100,000 prime numbers. ...He found a statistical pattern ...they get sparser and sparser, but the drop-off in the density was inversely proportional to the of the range of numbers. So he conjectured... the the number of primes up to x is... x divided by the natural log of x, and he had no way to prove this. It was a conjecture. It was revolutionary because it was maybe the first important conjecture of math that was statistical in nature. ...It just gave you an approximation that got better... as you went further... out. ...It started the field of... . ...[I]t was the first of many ...which ...started consolidating the idea that the prime numbers ...really didn't have a pattern, that they behaved like random sets of numbers with a certain density. They have some patterns. They're almost all odd. ...They're not actually random. They're... pseudorandom."

"Over time it became more... productive to think of the primes as if they were generated by some... random set, and this allowed us to make... other predictions. ...[B]ecause of this statistical random model.., we are ...absolutely convinced it's true. ...[W]e have, over time, developed this very accurate conceptual model of what primes should behave like.., but it's mostly and non-rigorous, but extremely accurate. It's the same reason we believe the Riemann hypothesis is true, and why we believe that cryptography based on the primes is... mathematically secure."

"[O]ne reason why we care about the Riemann hypothesis is that if... we knew it was false, ...it would mean there was a secret pattern to the primes that we were not aware of, and I think we would very rapidly abandon any cryptography based on the primes, because if there was one pattern... there are probably more, and these... can lead to exploits in crypto."

"what looks like a permanently high plateau"

"Professor Fisher's The Purchasing Power of Money is dedicated to Simon Newcomb, from whom vid Professor Kemmerer the PT = MV formula ultimately derives. Newcomb was not a professional economist but a mathematician (Professor of Mathematics in the U.S. Navy and at Johns Hopkins). His Principles of Political Economy, published in 1886, is one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half -formed subject like economics."

"THE great American who has departed from us was much more than an economist. But the vast realm over which he held sway and the intellectual climate of the epoch that nourished his thought have been admirably surveyed in Econometrica, and I shall confine myself to Fisher’s purely scientific work in our field. This will restrict our subject. But it will not lower it — at least, it could do so only through my own fault. For whatever else Fisher may have been—social philosopher, economic engineer, passionate crusader in many causes that he believed to be essential to the welfare of humanity, teacher, inventor, businessman — I venture to predict that his name will stand in history principally as the name of this country’s greatest scientific economist."

"I think I’m starting to resolve a puzzle that’s been bugging me for awhile. Pop economists (or, at least, pop micro-economists) are often making one of two arguments:1. People are rational and respond to incentives. Behavior that looks irrational is actually completely rational once you think like an economist. 2. People are irrational and they need economists, with their open minds, to show them how to be rational and efficient. Argument 1 is associated with “why do they do that?” sorts of puzzles. Why do they charge so much for candy at the movie theater, why are airline ticket prices such a mess, why are people drug addicts, etc. The usual answer is that there’s some rational reason for what seems like silly or self-destructive behavior. Argument 2 is associated with “we can do better” claims such as why we should fire 80% of public-schools teachers or Moneyball-style stories about how some clever entrepreneur has made a zillion dollars by exploiting some inefficiency in the market. The trick is knowing whether you’re gonna get 1 or 2 above. They’re complete opposites!"

"I’m not saying that arguments based on rationality are necessarily wrong in particular cases. (I can’t very well say that, given that I wrote an article on why it can be rational to vote.) I’m just trying to understand how pop-economics can so rapidly swing back and forth between opposing positions. And I think it’s coming from the comforting presence of rationality and efficiency in both formulations. It’s ok to distinguish economists from ordinary people (economists are rational and think the unthinkable, ordinary people don’t) and it’s also ok to distinguish economists from other social scientists (economists think ordinary people are rational, other social scientists believe in “culture”). You just have to be careful not to make both arguments in the same paragraph."

"One does not have to have experience raising children through school, dealing with family tragedies, and so forth, to be able to find three numbers whose fourth powers add up to another one."

"One of the things about math and chess is that we’re better at doing it than philosophizing about it."

"Indeed, Elkies admits he can improvise fugues, "at least on reasonable themes in a slow enough tempo.""

"Among students and faculty alike, any mention of his name is usually accompanied by a quick glance around, a devious smile, and hunched-over, half-whispered anecdotes about the man."

"Noam is unlike anyone we've ever had."

"In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy."

"Greek thought was essentially non-algebraic, because it was so concrete. The abstract operations of algebra, which deal with objects that have been purposely stripped of their physical content, could not occur to minds which were so intently interested in the objects themselves. The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations."

"The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections...There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being... L. ...the Greeks named these curves and many others... loci... Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve..."

"The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. ...The conic sections, invented in an attempt to solve the problem of doubling the alter of an oracle, ended by becoming the orbits followed by the planets... The imaginary magnitudes invented by Cardan and Bombelli describe... the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Riemann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the... quantum of the atom."

"The arithmetization of mathematics... which began with Weierstrass... had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought."

"But how can we avoid the use of human language? The... symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic."

"The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it. ...It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth in had no part. ...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied."

"Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic."

"There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, nor 20 for base. It is a binary system, i.e., of base two. These savages have not yet reached finger counting. They have independent numbers for one and two, and composite numbers up to six. Beyond six everything is denoted by “heap.”"

"‘…the transition [to the Hindu number system], far from being immediate, extended over long centuries. The struggle between the Abacists, who defended the old traditions, and the Algorists, who advocated the reform, lasted from the eleventh to the fifteenth century and went through all the usual stages of obscurantism and reaction. In some places, Arabic numerals [more precisely, Hindu numerals] were banned from official documents; in others, the art was prohibited altogether. And, as usual, prohibition did not succeed in abolishing, but merely served to spread bootlegging, ample evidence of which is found in the thirteenth century archives of Italy, where, it appears, merchants were using the Arabic numerals as a sort of secret code.’"

"The preface to the French edition of that work contains the following passage: "To me the French edition of my work is not a mere translation, but a transcription of ideas into a language in which it should have been written in the first place... I proudly acknowledge... my master. His words are among the most brilliant recollections of my youth; his piercing wisdom and potent prose have inspired my efforts of a riper age. To the memory of Henri Poincaré, the intellectual giant who was the first to recognize the role which the idiosyncrasies of the race play in the evolution of scientific ideas, I dedicate this book."

"To describe means to classify, and the man Poincaré defies classification, as does indeed his philosophy."

"His essays on the foundations of science are cases in point. They strike one as extemporaneous speeches rather than edited articles. ...those who knew him best insisted that he rarely, if ever, would revise a manuscript, even if he was fully aware of its stylistic shortcomings."

"Poincaré was an artist par excellence. Estheticism with him was not a mere creed: it was a way of life."

"Poincaré's mind was not subject to hysteresis or hibernation. He had the unique faculty of dismissing an idea from his mind, the instant the stimulus was gone, and to supplant it immediately with another creative idea."

"He was an iconoclast. But even in this category he defies classification. For, he fits no pattern, and is beyond all norm. He sought no followers, he shunned confederates, he hewed no tablets to replace those which he had shattered."

"The evolution of scientific thought is inseparable from the history of man's efforts to resolve the perplexities of his own existence."

"Science... may be viewed as man's supreme effort to find himself in that perplexing pattern which he calls Nature. ...Has he succeeded in achieving some measure of harmony with Nature? Or has he merely managed to transfer to Nature the irreconcilable duality within himself?"

"d'Alembert, who wrote the introduction to the Encyclopédie, resigned his editorship with the scathing remark that the work was like a harlequin's coat: some good stuff, but mostly rags."

"Barely a hundred and fifty years had passed since Galileo's experiment at Pisa had ushered in the new order of things; a mere instant as compared with the previous life of the race. Yet, this brief span had witnessed a complete shift in the outlook of the intellectual leaders of humanity: from blind adherence to authority and dogma towards a healthy habit of facing facts and an enlightened faith in the efficacy of reason. Few doubted that this buoyancy and self-reliance of the leaders would eventually reach the masses, thus causing a profound metamorphosis in the attitude of the common man towards his own life and the destinies of his race. ...Led by thinkers, and under the banners of liberty, happiness, and truth, humanity was to emerge into a Golden Age, free from oppression and strife. Alas! The French Revolution... resembled more a convention of inquisitors and hangmen than it did an assembly of enlightened emancipators. ...After twenty years of adventure, the humanitarian aspirations bequeathed by the Encyclopedists, tattered and trampled first by a bloody republic, then by a still bloodier empire, were finally declared dead by the Holy Alliance."

"The Industrial Revolution, too, failed to introduce a reign of freedom and happiness: it converted the medieval serf into an industrial slave; replaced the feudal baron by the industrial mogul, created in its wake an ever-growing, ever-shifting class of declassés, who had neither pride of ancestry nor love of tradition... The age of machine and competition, of capital, class-struggle, and demagogy was upon man."

"One part of the dreams of the eighteenth century intellectuals was realized: the resources of nature did yield a magnificent harvest. But the thinkers who helped to tap these resources... failed to attend, detained in their studies and laboratories, lost in their dreams and calculations, seeking new fields, co-ordinating old and new, spinning abstract theories... the thinkers were unequal to the task of developing these vast resources, most of which they had themselves uncovered. The shrewd declassés, who had... the world to gain, pioneered this development and took possession of the earth."

"The mathematical activity of Ancient Greece reached its peak during the glorious era of Euclid, Eratosthenes, Archimedes and Apollonius, a time when Greek letters, art and philosophy were already on the decline. ...it was not Greece proper but its outposts in Asia Minor, in Lower Italy, in Africa that had contributed most to the development of mathematics."

"Mathematics fluourished as long as freedom of thought prevailed; it decayed when creative joy gave way to blind faith and fanatical frenzy."

"Despite the vociferous claims of the Platonists and Neoplatonists, Plato was not a mathematician. To Plato and his followers mathematics was largely a means to an end... they viewed the technical aspects of mathematics as a mere device for sharpening one's wits, or at most a course of training peparatory to handling the larger issues of philosophy. This is reflected in the very name "mathematics,"... a course of studies or... a curriculum. ...in the Dialogues... such topics as harmony, triangular numbers, figurate numbers... which we view today as more or less irrelevant, if not trivial, were taken up at length. ...the guiding motive behind the... Pythagoreans and Platonists was... metaphysical ...which for the nonprofessional have all the earmarks of the occult. ...We also discover in the Pythagorean speculations more than a mere germ of... the scientific attitude."

"It has the very commendable aim of contributing towards stressing the cultural side of mathematics. ...there appears the widespread interchange of the definitions of excessive and defective numbers. ...it is stated that Euclid contended that every perfect number is of the form 2n-1(2n -1). It is true that Euclid proved that such numbers are perfect whenever 2n - 1 is a prime number but there seems to be no evidence to support the statement that he contended that no other such numbers exist. ...it is stated that the arithmetization of mathematics began with Weierstrass in the sixties of the last century. The fact that this movement is much older was recently emphasized by H. Wieleitner... it is stated that the arithmos of Diophantus and the res of Fibonacci meant whole numbers, and... we find the statement that in the pre-Vieta period they were committed to natural numbers as the exclusive field for all arithmetic operations. On the contrary, operations with common fractions appear on some of the most ancient mathematical records."

"In the winter of 2008, Jenifer and I visited Chennai Mathematical Institute. This remarkable Institute is the creation of Seshadri. It is a unique blend of an American style liberal arts college with traditional Indian guru one-on-one teaching, adding physics, computer science, history and music to its maths curriculum. Only in India could an intellectual with no business or management experience, who spends all his spare time singing classical south Indian music, have been the catalyst for such a unique educational experiment."

"On a more personal note, I see many similarities between India's Dalit problems and the African-American problems that have rocked the US since its beginnings. For this reason, I personally take Dr. Ambedkar as one of my heroes."

"There is only one other survey, Datta and Singh’s 1938 History of Hindu Mathematics, recently reprinted but very hard to obtain in the West (I found a copy in a small specialized bookstore in Chennai). They describe in some detail the Indian work in arithmetic and algebra and, supplemented by the equally hard to find Geometry in Ancient and Medieval India by Sarasvati Amma (1979), one can get an overview of most topics."

"John Tate and I were asked by Nature magazine to write an obituary for Alexander Grothendieck. Now he is a hero of mine, the person that I met most deserving of the adjective "genius". I got to know him when he visited Harvard and John, Shurik (as he was known) and I ran a seminar on "s". His devotion to math, his disdain for formality and convention, his openness and what John and others call his naiveté struck a chord with me."

"I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate."

"My dissertation for the Ph.D. degree at the University of Michigan was on applications of vectorial methods to metric geometry (in the sense of the Menger school), especially with a view to the merging of metric geometry in that sense with differential geometry. Professor S B Myers at the University of Michigan sponsored my dissertation, but I was particularly close to R L Wilder there."

"For a person who wants to do original, realistic, and critical work in statistics there is no atmosphere anywhere in the world today to compare with this Department."

"[The George E. P. Box paper Fitting empirical data (1960) is] a mature exposition of an important branch of statistics, to which the author has made great contributions. One feature of particular interest is practical discussion of genuinely nonlinear fitting problems and their solution with the help of tact and a special, publicly available, IBM-704 program. Another is insightful comments on the role of prior distributions in statistics."

"[Leonard Jimmie Savage is] one of the few people I have met whom I would unhesitatingly call a genius."

"R. A. Fisher, J. Neyman, R. von Mises, W. Feller, and L. J. Savage denied vehemently that probability theory is an extension of logic, and accused Laplace and Jeffreys of committing metaphysical nonsense for thinking that it is."

"It was only when L. J. Savage arrived on the scene, and championed the work of Ramsey and de Finetti that the work of these two pioneers in subjective probability first received serious philosophical attention."

"Alan Turing was the first to make a careful analysis of the potential capabilities of machines, inventing his famous "Turing machines" for the purpose. He argued that if any machine could perform a computation, then some Turing machine could perform it. The argument focuses on the assertion that any machine's operations could be simulated, one step at a time, by certain simple operations, and that Turing machines were capable of those simple operations. Turing's first fame resulted from applying this analysis to a problem posed earlier by Hilbert, which concerned the possibility of mechanizing mathematics. Turing showed that in a certain sense, it is impossible to mechanize mathematics: We shall never be able to build an "oracle" machine that can correctly answer all mathematical questions presented to it with a "yes" or "no" answer. In another famous paper Turing went on to consider the somewhat different question, "Can machines think?." It is a different question, because perhaps machines can think, but they might not be any better at mathematics than humans are; or perhaps they might be better at mathematics than humans are, but not by thinking, just by brute-force calculation power. These two papers of Turing lie near the roots of the subjects today known as automated deduction and artificial intelligence."

"Gottfried Leibniz is famous... for his slogan Calculemus, which means "Let us calculate." He envisioned a formal language to reduce reasoning to calculation, and he said that reasonable men, faced with a difficult question of philosophy or policy, would express the question in a precise language and use rules of calculation to carry out precise reasoning. This is the first reduction of reasoning to calculation ever envisioned. ...he actually designed and built a working calculating machine, the Stepped Reckoner ...inspired by the somewhat earlier work of Pascal, who built a machine that could add and subtract. Leibniz's machine could add, subtract, divide, and multiply, and was apparently the first machine with all four arithmetic capabilities."

"George Boole took up Leibniz's idea, and wrote a book he called '. The laws he formulated are now called ... Boole seems to have had a grandiose vision about the applicability of his algebraic methods to practical problems—his book makes it clear that he hoped these laws would be used to settle practical questions. William Stanley Jevons heard of Boole's work, and undertook to build a machine to make calculations in Boolean algebra. He successfully designed and built... the Logical Piano... the first machine to do mechanical inference."

"Gottlob Frege created modern logic including "for all," "there exists," and rules of proof. Leibniz and Boole had dealt only with what we now call "propositional logic" (that is, no "for all" or "there exists"). They also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number."

"Bertrand Russell found Frege's famous error: Frege had overlooked what is now known as the Russell paradox. Namely, Frege's rules allowed one to define the class of x such that P(x) is true for any "concept" P. Frege's idea was that such a class was an object itself, the class of objects "falling under the concept P." Russel used this principle to define the class R of concepts that do not fall under themselves. This concept leads to a contradiction... argument: (1) if R falls under itself then it does not fall under itself; (2) this contradiction shows that it does not fall under itself; (3) therefore by definition it does fall under itself after all."

"This theory maintains that the objectives of the firm should be derived by balancing the conflicting claims of the various 'stakeholders' in the firm: managers, workers, stockholders, suppliers, vendors. The firm has a responsibility to all of these and must configure its objectives so as to give each a measure of satisfaction. Profit which is a return on investment to the stockholder is one of such satisfactions, but does not receive special predominance in the objective structure,"

"We shall approach practical objectives through a series of approximations. Keeping the maximization of the rate of return as the central theoretical objective, we shall develop a number of subsidiary objectives (which the economists call proxy variables) which contribute in different ways to improvement in the return and which are also measurable in business practice. A firm which meets high performance in most of its subsidiary objectives will substantially enhance its long-term rate of return. (The defect in our approach is that we cannot prove that the result will be a ‘‘maximum’’ possible overall return.) As will be seen, this road has its own obstacles: the difficulties of long term maximization are replaced by the problem of reconciling claims of conflicting objectives."

"By searching out opportunities which match its strengths the firm can optimize the synergistic effects."

"The triplet of specifications - the product-market scope, the growth vector and the competitive advantage - describes the firm's product-market path in the external environment."

"A natural companion to the competitive advantage is the synergy component of strategy. This requires that opportunities within the scope possess characteristics which will enhance synergy."

"Ansoff (1965) gives only some indication of what he means by environment. This can be explained by Ansoff's classification of decisions into strategic. administrative and operating decisions. He (1965, p. 8) defines these types of decision as follows:"

"The publication of the book, Corporate Strategy, by H. Igor Ansoff was a major event in the 1965 world of management. As early as it came in this literature, the book represented a kind of crescendo in the development of strategic planning theory, offering a degree of elaboration seldom attempted since."

"The stakeholder concept was originally defined as "those groups without whose support the organization would cease to exist." The list of stakeholders originally included shareowners, employees, customers, suppliers, lenders and society. Stemming from the work of Igor Ansoff and Robert Stewart (in the planning department at Lockheed) and, later Marion Doscher and Stewart at SRI, the original approach served an important information function in the SRI corporate planning."

"The present article is almost wholly devoted to a single problem—the definition of truth. Its task is to construct—with reference to a given language—a materially adequate and formally correct definition of the term 'true sentence. This problem, which belongs to the classical problems of philosophy, raises considerable difficulties. For although the meaning of the term 'true sentence' in colloquial language seems to be quite clear and intelligible, all attempts to define this meaning more precisely have hitherto been fruitless, and many investigations in which this term has been used and which started with apparently evident premisses have often led to paradoxes and antinomies (for which, however, a more or less satisfactory solution has been found). The concept of truth shares in this respect the fate of other analogous concepts in the domain of the semantics of language."

"Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws."

"There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly."

"It is perhaps worth while saying that semantics as conceived in this paper (and in former papers of the author) is a sober and modest discipline which has no pretensions to being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflicts. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense."

"If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes."

"For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category."

"Tarski tried to publish his theorem (the equivalence between AC and "every infinite set A has the same cardinality as A × A") in Comptes Rendus, but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known (true) propositions is not a new result, and Lebesgue wrote that an implication between two false propositions is of no interest. And Tarski said that after this misadventure he never tried to publish in the Comptes Rendus."

"It's interesting... Tarski, although his English was weak, had a very good sense of language and he kept on asking me "Is that really good English?" Not in the sense of being grammatically correct, but, well for example, Helmer was very fond of using the word "tantamount" and Tarski got the feeling that somehow it's not a word used very often. Actually his instincts for language were extremely good. I suppose that was connected with his general work on formalizations and metalanguages. Anyway, I was just a proofreader."

"In 1931, Tarski proved quite simply that... there is no complete language of science. ...Tarski's proof... essentially consists in showing that, as soon as you not only exhibit the statements but add to them the statement, "is true," you are in trouble because you are bound to be landed in contradictions like the one which arises in the ."

"I think that I have learned more from you than from any other living thinker, except perhaps Alfred Tarski... but not even excepting Russell."

"His mathematical prose is simple, spare, and exceedingly beautiful. His prose style is to mathematics what Hemingway's is to English or Simenon's to French."

"I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naiveté, unburdened by conventional wisdom, can sometimes be a positive asset."

"In mathematics we agree that clear thinking is very important, but fuzzy thinking is just as important."

"Another project which keeps the Bourbaki name alive is the Seminaire Nicolas Bourbaki, which is a series of seminars, about 12–20 per year, on contemporary mathematics started in 1948. It is considered an honour to be invited to give a seminary in this seminar in this series; the only Indian to figure in the seminar so far is Harish Chandra, who gave a talk in the 1957–58 series and, apparently, thus lost the chance of winning the Fields medal in 1958! (Siegel was the chairman of the Fields medal committee in the ICM 1958!)"

"Henri Poincaré thought the theory of infinite sets a grave malady and pathologic. "Later generations," he said in 1908, "will regard set theory as a disease from which one has recovered."

"As our survey indicates, the Hindus were interested in and contributed to the arithmetical and computational activities of mathematics rather than to the deductive patterns. Their name for mathematics was ganita, which means “the science of calculation”. There is much good procedure and technical facility, but no evidence that they considered proof at all. They had rules, but apparently no logical scruples. Moreover, no general methods or new viewpoints were arrived at in any area of mathematics."

"While the mathematicians were still looking askance at the Greek gift of the irrational number, the Hindus of India were preparing another brain-teaser, the negative number, which they introduced about A.D. 700. The Hindus saw that when the usual, positive numbers were used to represent assets, it was helpful to have other number represent debts."

"The Hindus saw clearly that if the arithmetic operations... were properly defined for negative numbers, these numbers could be employed to as good advantage as people had previously derived from positive numbers. ...To people to whom the word number had always meant positive whole numbers and positive fractions, the very idea that there could be other numbers came hard. For many centuries negative numbers were either rejected or treated as second-class citizens. What was especially difficult for mathematicians to swallow was that negative numbers could be acceptable roots of equations."

"The famous sixteenth-century algebraist Jerome Cardan called negative roots fictitious, and the founder of modern symbolic algebra, François Viète, discarded negative roots entirely. Descartes, called them false on the ground that they represented numbers less than nothing and so were meaningless."

"The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. ...on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries..."

"The chief innovator of symbolism in algebra was François Viète... an amateur in the sense that his professional life was devoted to the law... John Wallis... says that Viète, in denoting a class of numbers by a letter, followed the custom of lawyers who discussed legal cases by using arbitrary names [for the litigants]... and later the abbreviations... and still more briefly A, B, and C. Actually, letters had been used occasionally by the Greek Diophantus and by the Hindus. However, in these cases letters were confined to designating a fixed unknown number, powers of that number, and some operations. Viète recognized that a more extensive use of letters, and, in particular, the use of letters to denote classes of numbers, would permit the development of a new kind of mathematics; this he called logistica speciosa in distinction from logistica numerosa. ...the growth of symbolism was slow. Even simple ideas take hold slowly. Only in the last few centuries has the use of symbolism become widespread and effective."

"The historical associations of the word algebra almost substantiate the sordid character of the subject. The word comes from the title of a book written by... Al Khowarizmi. In this title, al-jebr w' almuqabala, the word al-jebr meant transposing a quantity from one side of an equation to another and muqabala meant simplification of the resulting expressions. Figuratively, al-jebr meant restoring the balance of an equation... When the Moors reached Spain... algebrista... came to mean a bonesetter... and signs reading Algebrista y Sangrador (bonesetter and bloodletter) were found over Spanish barber shops. Thus it might be said that there is a good historical basis for the fact that the word algebra stirs up disagreeable thoughts."

"Historically, it was Euclidean geometry that, developed to a large extent as a votive offering to the God of Reason, opened men's eyes to the possibility of design and to the possibility of uncovering it by the pursuit of mathematics."

"The use of canon raised numerous questions concerning the paths of projectiles. ...One might determine... what type of curve a projectile follows and.... prove some geometrical facts about this curve, but geometry could never answer such questions as how high the projectile would go or how far from the starting point it would land. The seventeenth century sought the quantitative or numerical information needed for practical applications, and such information is provided by algebra."

"Galileo had provided the methodology for the analysis of motions on and near the earth and had applied it successfully. Copernicus and Kepler had previously obtained the laws of motion of the planets and their satellites. ...But Galileo had succeeded in deriving numerous laws from a few physical principles and... the axioms and theorems of mathematics. ...The Keplerian laws ...were not logically related to each other. Each was an independent inference from observations. ...They seemed to be suspended in the same vacuum in which the planets moved. Galileo's laws had the additional advantage of supplying physical insight. The first law of motion and the law that the force of graviation gives... a downward acceleration of 32 ft/sec2... explain the vertrical rise and fall of bodies, motion on slopes, and projectile motion. Kepler's laws... had no physical basis. ...Kepler tried to introduce the idea of a magnetic force which the sun exerted... But he failed to related the behavior of the planets to the precise laws of planetary motion. ... The new astronomical theory was completely isolated from the theory of motion on earth. ...it bothered mathematicians and scientists who believed that all the phenomena of the universe were governed by one master plan instituted by the master planner—God."

"The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo... In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens... Kepler... had found the ellipse to be the basic curve. Why this difference? ...since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. ... It has often happened in the history of mathematics and science that major problems remained outstanding... great minds... succeeded only in revealing the true difficulties... and in generating an atmosphere of dispair... Then a genius appeared... with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who... picked up the torch of science dropped by Galileo, was Isaac Newton."

"The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making."

"Descartes... complained that Greek geometry was so much tied to figures "that is can exercise the understanding only on condition of greatly fatiguing the imagination." Descartes also deplored that the methods of Euclidean geometry were exceedingly diverse and specialized and did not allow for general applicability. Each theorem required a new kind of proof... What impressed Descartes especially was that algebra enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish. ...historically it was Descartes who clearly perceived and called attention to this feature. Whereas geometry contained the truth about the universe, algebra offered the science of method. It is... paradoxical that great thinkers should be enamored with ideas that mechanize thought. Of course, their goal is to get at more difficult problems, as indeed they do."

"The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces.""

"When an equation...clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. ...Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions."

"Another feature of Alexandrian algebra is the absence of any explicit deductive structure. The various types of numbers... were not defined. Nor was there any axiomatic basis on which a deductive structure could be erected. The work of Heron, Nichomachus, and Diophantus, and of Archimedes as far as his arithmetic is concerned, reads like the procedural texts of the Egyptians and Babylonians... The deductive, orderly proof of Euclid and Apollonius, and of Archimedes' geometry is gone. The problems are inductive in spirit, in that they show methods for concrete problems that presumably apply to general classes whose extent is not specified. In view of the fact that as a consequence of the work of the classical Greeks mathematical results were supposed to be derived deductively from an explicit axiomatic basis, the emergence of an independent arithmetic and algebra with no logical structure of its own raised what became one of the great problems of the history of mathematics. This approach to arithmetic and algebra is the clearest indication of the Egyptian and Babylonian influences... Though the Alexandrian Greek algebraists did not seem to be concerned about this deficiency... it did trouble deeply the European mathematicians."

"The Pythagoreans associated good and evil with the limited and unlimited, respectively."

"Aristotle says the infinite is imperfect, unfinished, and therefore unthinkable; it is formless and confused. Only as objects are delimited and distinct do they have a nature."

"To avoid any assertion about the infinitude of the straight line, Euclid says a line segment (he uses the word "line" in this sense) can be extended as far as necessary. Unwillingness to involve the infinitely large is seen also in Euclid's statement of the parallel axiom. Instead of considering two lines that extend to infinity and giving a direct condition or assumption under which parallel lines might exist, his parallel axiom gives a condition under which two lines will meet at some finite point."

"The concept of the infinitely small is involved in the relation of points to a line or the relation of the discrete to the continuous, and Zeno's paradoxes may have caused the Greeks to shy away from this subject."

"The relationship of point to line bothered the Greeks and led Aristotle to separate the two. Though he admits points are on lines, he says that a line is not made up of points and that the continuous cannot be made up of the discrete. This distinction contributed also to the presumed need for separating number from geometry, since to the Greeks numbers were discrete and geometry dealt with continuous magnitudes."

"Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small."

"The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius cites others who worked on the problem and says further that people "in ancient times" objected to the use of the parallel postulate."

"Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension."

"Aristotle had considered the question of whether space is infinite and gave six nonmathematical arguments to prove that it is finite; he foresaw that this question would be troublesome."

"The theory of perspective was taught in painting schools from the sixteenth century onward according to principles laid down by the masters... However, their treatises on perspective had on the whole been precept, rule, and ad hoc procedure; they lacked a solid mathematical basis. In the period from 1500 to 1600 artists and subsequently mathematicians put the subject on a satisfactory deductive basis, and it passed from quasi-empirical art to a true science. Definitive works on perspective were written much later by eighteenth-century mathematicians Brook Taylor and J. H. Lambert."

"The Hindus introduced negative numbers... The first known use is about 628; he also states the rules for the four operations with negative numbers. Bhāskara points out that the square root of a positive number is twofold, positive and negative. He brings up the matter of the square root of a negative number but says that there is no square root because a negative number is not a square. No definitions, axioms, or theorems are given. The Hindus did not unreservedly accept negative numbers. Even Bhāskara, while giving 50 and -5 as two solutions of a problem, says, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative solutions." However, negative numbers gained acceptance slowly."

"In arithmetic the Arabs took one step backward. Though they were familiar with negative numbers and the rules for operating with them through the work of the Hindus, they rejected negative numbers."

"As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense."

"One of the first algebraists to accept negative numbers was ... who occasionally placed a negative number by itself on one side of an equation. But he did not accept negative roots. ... gave clear definitions for negative numbers. Stevin used positive and negative coefficients in equations and also accepted negative roots. In his L'Invention nouvelle en l'algèbre (1629), ... placed negative numbers on a par with positive numbers and gave both roots of a quadratic equation, even when both were negative. Both Girard and Harriot used the minus sign for the operation of subtraction and for negative numbers."

"Though Wallis was advanced for his times and accepted negative numbers, he thought they were larger than infinity but not less than zero. In his Arithmetica Infinitorum (1655), he argued that since the ratio a/0, when a is positive, is infinite, then, when the denominator is changed to a negative number, as in a/b with b negative, the ratio must be greater than infinity."

"Over and above the specific theorems created by men such as Desargues, Pascal and La Hire, several new ideas and outlooks were beginning to appear. The first is the idea of continuous change of a mathematical entity from one state to another... [i.e., of a] a geometrical figure. It was Kepler, in his Astronomiae Optica of 1604, who first seemed to grasp the fact that parabola, ellipse, hyperbola, circle, and the degenerate conic consisting of a pair of lines are continuously derivable from each other. ...The notion of a continuous change in a figure was also employed by Pascal. He allowed two consecutive vertices of his hexagon to approach each other so that the figure became a pentagon. In the same manner he passed from pentagons to quadrilaterals. The second idea to emerge from the work of the projective geometers is that of transformation and invariance. To project a figure from some point and then take a section of that projection is to transform the figure to a new one. The properties... of interest are those that remain invariant under transformation. Other geometers of the seventeenth century, for example, Gregory of St. Vincent... and Newton, introduced transformations other than projection and section."

"Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method of differential calculus, though it begs entirely the difficult theory of limits."

"Brook Taylor... in his Methodus Incrementorum Directa et Inversa (1715), sought to clarify the ideas of the calculus but limited himself to algebraic functions and algebraic differential equations. ...Taylor's exposition, based on what we would call finite differences, failed to obtain many backers because it was arithmetical in nature when the British were trying to tie the calculus to geometry or to the physical notion of velocity."

"To the scientists of 1850, Hamilton's principle was the realization of a dream. ...from the time of Galileo scientists had been striving to deduce as many phenomena of nature as possible from a few fundamental physical principles. ...they made striking progress ...But even before these successes were achieved Descartes had already expressed the hope and expectation that all the laws of science would be derivable from a single basic law of the universe. This hope became a driving force in the late eighteenth century after Maupertuis's and Euler's work showed that optics and mechanics could very likely be unified under one principle. Hamilton's achievement in encompassing the most developed and largest branches of physical science, mechanics, optics, electricity, and magnetism under one principle was therefore regarded as the pinnacle of mathematical physics."

"The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics... but these are not only restricted... but seem to be contrived... A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations."

"In the field of non-Euclidean geometry, Riemann... began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length. ...he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom... In brief, there are no parallel lines. This ... had been tried... in conjunction with the infiniteness of the straight line and had led to contradictions. However... Riemann found that he could construct another consistent non-Euclidean geometry."

"Laplace made many important discoveries in mathematical physics... Indeed, he was interested in anything that helped to interpret nature. He worked on hydrodynamics, the wave propagation of sound, and the tides. In the field of chemistry, his work on the liquid state of matter is classic. His studies of the tension in the surface layer of water, which accounts for the rise of liquids inside a capillary tube, and of the cohesive forces in liquids, are fundamental. Laplace and Lavoisier designed an ice calorimeter (1784) to measure heat and measured the specific heat of numerous substances; heat, to them, was still a special kind of matter. Most of Laplace's life was, however, devoted to celestial mechanics."

"Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature."

"Fermat knew that under reflection light takes the path requiring least time and, convinced that nature does indeed act simply and economically, affirmed in letters of 1657 and 1662 his Principle of Least Time, which states that light always takes the path requiring least time. He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct. ...Huygens, who had at first objected to Fermat's Principle, showed that it does hold for the propagation of light in media with variable indices of refraction. Even Newton's first law of motion, which states that the straight line or shortest distance is the natural motion of a body, showed nature's desire to economize. These examples suggested that there might be a more general principle. The search for such a principle was undertaken by Maupertuis."

"By 1700 all of the familiar members of the [number] system... were known. However, opposition to the newer types of numbers was expressed throughout the century. Typical are the objections of... Baron Francis Masères... in 1759 his Dissertation on the Use of the Negative Sign in Algebra... shows how to avoid negative numbers... and especially negative roots, by carefully segregating the types of quadratic equations so that those with negative roots are considered separately; and... the negative roots are to be rejected."

"The field of mathematics is now so extensive that no one can [any] longer pretend to cover it, least of all the specialist in any one department. Furthermore it takes a century or more to weigh men and their discoveries, thus making the judgment of contemporaries often quite worthless."

"1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves. 2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra. 3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry. Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics."

"The fact that arithmetic and geometry took such a notable step forward... was due in no small measure to the introduction of Egyptian papyrus into Greece. This event occurred about 650 B.C., and the invention of printing in the 15th century did not more surely effect a revolution in thought than did this introduction of writing material on the northern shores of the Mediterranean Sea just before the time of Thales."

"The excellent work of Tropfke is an example of the tendency to break away from the mere chronological recital of facts."

"More than any of his predecessors Plato appreciated the scientific possibilities of geometry. .. By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is... clear. ...That Plato should hold the view... is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought."

"Grégoire de Saint-Vincent... was a Jesuit, taught mathematics in Rome and Prag (1629-1631), and was afterwards called to Spain by Phillip IV as tutor to his son... He wrote two works on geometry [Principia Matheseos Univerales (1651); Exercitationum Mathematicarum Libri quinque (1657)], giving in one of them the quadrature of the hyperbola referred to its asymptotes, and showing that as the area increased in arithmetic series the abscissas increased in geometric series."

"Of the contemporaries of Newton one of the most prominent was John Wallis. ...Wallis was a voluminous writer, and not only are his writings erudite, but they show a genius in mathematics... He was one of the first to recognize the significance of the generalization of exponents to include negative and fractional as well as positive and integral numbers. He recognized also the importance of Cavalieri's method of indivisibles, and employed it in the quadrature of such curves as y=xn, y=x1/n, and y=x0 + x1 + x2 +... He failed in his attempts at the approximate quadrature of the circle by means of series because he was not in possession of the general form of the binomial theorem. He reached the result, however, by another method. He also obtained the equivalent of ds = \!dx \sqrt{1+(\frac{dy}{dx})^2} for the length of an element of a curve, thus connecting the problem of rectification with that of quadrature."

"In 1673 he wrote his great work De Algebra Tractatus; Historicus & Practicus, of which an English edition appeared in 1685. In this there is seen the first serious attempt in England to write on the history of mathematics, and the result shows a wide range of reading of classical literature of the science. This work is also noteworthy because it contains the first of an effort to represent the imaginary number graphically by the method now used. The effort stopped short of success but was an ingenious beginning."

"Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates."

"His writings include works on mechanics, sound, astronomy, the tides, the laws of motion, the Torricellian tube, botany, physiology, music, the calendar (in opposition to the Gregorian reform), geology, and the compass,—a range too wide to allow of the greatest success in any of the lines of his activity. He was also an ingenious cryptologist and assisted the government in deciphering diplomatic messages."

"Among his [John Wallis'] interesting discoveries was the relation \frac{4}{\pi} = \frac32\cdot\frac34\cdot\frac54\cdot\frac56\cdot\frac76\cdot\frac78\cdots one of the early values of π involving infinite products."

"The Arabs contributed nothing new to the theory, but al-Khowârizmî (c. 825) states the usual rules, and the same is true of his successors."

"When we speak of the early history of algebra it is necessary to consider... the meaning of the term. If... we mean the science that allows us to solve the equation ax^2 + bx + c = 0, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the science was known about 1800 B.C., and probably still earlier.<"

"The first writer on algebra whose works have come down to us is . He has certain problems in linear equations and in series, and these form the essentially new feature in his work. His treatment of the subject is largely rhetorical."

"There are only four Hindu writers on algebra whose names are particularly noteworthy. These are Āryabhata, whose Āryabhatiyam (c. 510) included problems in series, permutations, and linear and quadratic equations; , whose Brahmasiddhānta (c. 628) contains a satisfactory rule for solving the quadratic... Mahāvīra, whose Ganita-Sāra Sangraha (c. 850) contains a large number of problems involving series, radicals, and equations; and Bhāskara, whose Bija Ganita (c. 1150)... extends the work through quadratic equations."

"It is difficult to say when algebra as a science began in China. Problems which we should solve by equations appear in works as early as the Nine Sections (K'iu-ch'ang Suan-shu) and so may have been known by the year 1000 B.C. In 's commentary on this work (c. 250) there are problems of pursuit, the Rule of False Position... and an arrangement of terms in a kind of notation. The rules given by Liu Hui form a kind of rhetorical algebra. The work of Sun-tzï contains various problems which would today be considered algebraic. These include questions involving s. ...Sun-tzï solved such problems by analysis and was content with a single result... The Chinese certainly knew how to solve quadratics as early as the 1st century B.C., and rules given even as early as the K'iu-ch'ang Suan-shu... involve the solution of such equations. Liu Hui (c. 250) gave various rules which would now be stated as algebraic formulas and seems to have deduced these from other rules in much the same way as we should... By the 7th century the cubic equation had begun to attract attention, as is evident from the Ch'i-ku Suan-king of Wang Hs'iao-t'ung (c. 625). The culmination of Chinese is found in the 13th century. ...numerical higher equations attracted the special attention of scholars like Ch'in Kiu-shao (c.1250), Li Yeh (c. 1250), and Chu-Shï-kié (c. 1300), the result being the perfecting of an ancient method which resembles the one later developed by W. G. Horner (1819)."

"With the coming of the Jesuits in the 16th century, and the consequent introduction of Western science, China lost interest in her native algebra..."

"Algebra in the Renaissance period received its first serious consideration in Pacioli's Sūma (1494)... which characterized in a careless way the knowledge... thus far accumulated. By the aid of the crude symbolism then in use it gave a considerable amount of work in equations. The noteworthy work... and the first to be devoted entirely to the subject, was Rudolff's Coss (1525). This work made no decided advance in the theory, but it improved the symbolism for radicals and made the science better known in Germany. Stiffel's edition of this work (1553-1554) gave the subject still more prominence. The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). The next great work... to appear in print was the General Trattato of Tartaglia..."

"The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra."

"The first noteworthy attempt to write an algebra in England was made by , whose Whetstone of witte (1557) was an excellent textbook for its time. The next important contribution was Masterson's incomplete treatise of 1592-1595, but the work was not up to the standard set by Recorde. The first Italian textbook to bear the title of algebra was Bombelli's work of 1572. By this time elementary algebra was fairly well perfected, and it only remained to develop a good symbolism. ...this was worked out largely by Vieta (c. 1590), Harriot (c. 1610), Oughtred (c. 1628), Descartes (1637), and the British school of Newton's time (c. 1675). So far as the great body of elementary algebra is concerned, therefore, it was completed in the 17th century."

"Vieta (c. 1590) rejected the name "algebra" as having no significance in the European languages, and proposed to use the word "analysis," and it is probably to his influence that the popularity of this term in connection with higher algebra is due."

"Vieta: 1QC - 15QQ + 85C - 225Q + 274N, aequator 120. Modern form:x^6 - 15x^4 + 85x^3 - 225x^2 + 274x = 120"

"He used capital vowels for the unknown quantities and capital consonants for the known, thus being able to express several unknowns and several knowns."

"In the work of Vieta the analytic methods replaced the geometric, and his solutions of the quadratic equation were therefore a distinct advance upon those of his predecessors. For example, to solve the equation x^2 + ax + b = 0 he placed u + z for x. He then hadu^2 + (2z + a)u +(z^2 + az + b) = 0.He now let 2z + a = 0, whence z = -\frac{1}{2}a,and this gaveu^2 - \frac{1}{4}(a^2 - 4b) = 0. u = \pm \frac{1}{2} \sqrt{a^2 - 4b}.andx = u + z = -\frac{1}{2}a \pm \sqrt{a^2 - 4b}."

"[Zuanne de Tonini] da Coi... impuned Tartaglia to publish his method, but the latter declined to do so. In 1539 Cardan wrote to Tartaglia, and a meeting was arranged at which, Tartaglia says, having pledged Cardan to secrecy, he revealed the method in cryptic verse and later with a full explanation. Cardan admits that he received the solution from Tartaglia, but... without any explanation. At any rate, the two cubics x^3 + ax^2 = c and x^3 + bx = c could now be solved. The reduction of the general cubic x^3 + ax^2 + bx = c to the second of these forms does not seem to have been considered by Tartaglia at the time of the controversy. When Cardan published his Ars Magna however, he transformed the types x^3 = ax^2 + c and x^3 + ax^2 = c by substituting x = y + \frac{1}{3}a and x = y - \frac{1}{3}a respectively, and transformed the type x^3 + c = ax^2 by the substitution x = \sqrt[3]{c^2/y}, thus freeing the equations of the term x^2. This completed the general solution, and he applied the method to the complete cubic in his later problems."

"Cardan's originality in the matter seems to have been shown chiefly in four respects. First, he reduced the general equation to the type x^3 + bx = c; second, in a letter written August 4, 1539, he discussed the question of the irreducible case; third, he had the idea of the number of roots to be expected in the cubic; and, fourth, he made a beginning in the theory of symmetric functions. ...With respect to the irreducible case... we have the cube root of a complex number, thus reaching an expression that is irreducible even though all three values of x turn out to be real. With respect to the number of roots to be expected in the cubic... before this time only two roots were ever found, negative roots being rejected. As to the question of symmetric functions, he stated that the sum of the roots is minus the coefficient of x2"

"He states that the root of x^3 + 6x = 20 isx = \sqrt[3]{\sqrt{108} + 10} - \sqrt[3]{\sqrt{108} - 10}."

"He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam."

"Although Cardan reduced his particular equations to forms lacking a term in x^2, it was Vieta who began with the general formx^3 + px^2 + qx + r = 0and made the substitution x = y -\frac{1}{3}p, thus reducing the equation to the formy^3 + 3by = 2c.He then made the substitutionz^3 + yz = b, or y = \frac{b - z^2}{z},which led to the formz^6 + 2cz^2 = b^2,a sextic which he solved as a quadratic."

"The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed. ...This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri [of Deventer]."

"The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes."

"Vieta was the first algebraist after Ferrari to make any noteworthy advance in the solution of the biquadratic. He began with the type x^4 + 2gx^2 + bx = c, wrote it as x^4 + 2gx^2 = c - bx, added gx^2 + \frac{1}{4}y^2 + yx^2 + gy to both sides, and then made the right side a square after the manner of Ferrari. This method... requires the solution of a cubic resolvent. Descartes (1637) next took up the question and succeeded in effecting a simple solution... a method considerably improved (1649) by his commentator Van Schooten. The method was brought to its final form by Simpson (1745)."

"It is difficult to say who it is who first recognized the advantage of always equating to zero in the study of the general equation. It may very likely have been Napier, for he wrote his De Arte Logistica before 1594, and in this there is evidence that he understood the advantage of this procedure. Bürgi also recognized the value of making the second member zero, Harriot may have done the same, and the influence of Descartes was such that the usage became fairly general."

"Aside from Cauchy, the greatest contributory to the theory [of determinants] was Carl Gustav Jacob Jacobi. With him the word "determinant" received its final acceptance. He early used the functional determinant which Sylvester has called the Jacobian, and in his famous memoirs in Crelle's Journal for 1841 he considered these forms as well as that class of alternating functions which Sylvester has called alternants."

"Johannes Tropfke... described the history of those individual parts of mathematics that he believed were most important for mathematics as taught in secondary schools. He intended his history to inform teachers about the origin of special problems, terms, and methods in school mathematics. ...Tropfke's approach to the history of mathematics at this time was new and even now is not yet out of date. The only comparable work is the second volume of D.E Smith's History of Mathematics... which gives far less detailed information."

"The numerical relations existing between ordinary or so-called Plückerian singularities of a plane curve were determined as early as 1834 by P, but the inverse question has been left almost untouched. It may be stated thus: To show the existence of a curve having assigned Plückerian characters; and is equivalent to the determination of the maximum of cusps κM that a curve of order m and genus p may have. V ... has solved the question for rational curves."

"In the development of the theory of algebraic functions of one variable the introduction by Riemann of the surfaces that bear his name has played a well-known part. Owing to the partial failure of space intuition with the increase in dimensionality, the introduction of similar ideas into the field of algebraic functions of several variables has been of necessity slow. It was first done by Emile Picard, whose work along this line will remain a classic. A little later came the capital writings of Poincaré in which he laid down the foundations of Analysis Situs, thus providing the needed tools to obviate the failure of space intuition."

"It will be remembered that the positions on a Riemann surface are treated by Hensel, Landsberg, and Jung as arithmetical divisors. At bottom the associated symbolical operations are in no sense different from those that occur in connection with the Noether-Brill theory of groups of points, elements being merely multiplied instead of added."

"As is well known, when one endeavors to pass from one-dimensional birational geometry to the higher dimensions, the difficulties multiply enormously. Many results do not extend at all, or if they do, they are apt to assume a far more complicated aspect or else to demand most difficult proofs."

"It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry."

"In its early phase (Abel, Riemann, Weierstrass), algebraic geometry was just a chapter in analytic function theory. ... A new current appeared however (1870) under the powerful influence of Max Noether who really put "geometry" and more "birational geometry" into algebraic geometry. In the classical mémoire of Brill-Noether (Math. Ann., 1874), the foundations of "geometry on an algebraic curve" were laid down centered upon the study of linear series cut out by linear systems of curves upon a fixed curve ƒ{x, y) = 0. This produced birational invariance (for example of the genus p) by essentially algebraic methods."

"It is quite obvious that he was strongly influenced by the similar problems in algebraic geometry, and in particular by the theory of correspondences, studied since the middle of the nineteenth century by Chasles and the school of “enumerative geometry” (de Jonquières, Zeuthen, Schubert), then by Hurwitz in the theory of Riemann surfaces, and which had been thoroughly investigated by Severi in the first years of the twentieth century; this influence explains the rather unusual frame within which Lefschetz developed his theory."

"Solomon Lefschetz had a reputation for “kibitzing” during the lectures of colleagues; at perhaps the first public talk on computing that von Neumann ever gave, von Neumann said, halfway in, “Well, so far so good” — and Lefschetz added, “and so trivial.” (The students passed down an impious faculty song about their elders; the verse for Lefschetz ended, “When he’s at last beneath the sod, he’ll then begin to heckle God.”)"

"Lefschetz made a brief trip to Rome, and I asked Severi what he thought of Lefschetz's work. È bravo,' Severi told me, meaning more or less 'he is talented.' The word bravo,' as far as I can tell, has no equivalent in other languages. 'He is no Poincaré,' Severi added. Poincaré was an eagle, un'aquila—and at this, he raised his hand high. Lefschetz was a sparrow, un passero,' and he lowered his hand halfway. But Lefschetz was talented, è bravo però, è bravo."

"I would read Lefschetz's book on analysis situs and algebraic geometry - the book about which Hodge used to say that all the important statements were true and all the others false."

"Since I was a teenager I had an interest in number theory. Fortunately, I came across a good number theory book by L. E. Dickson, so I knew a little number theory. Also I had been reading Bell’s histories of people like Gauss. I liked number theory. It’s natural, in a way, because many wonderful problems and theorems in number theory can be explained to any interested high-school student. Number theory is easier to get into in that sense. But of course it depends on one’s intuition and taste also."

"It doesn't matter how long it takes, if the end result is a good theorem."

"A “good theorem,” as Tate puts it, lasts forever. Once proved, it will always stay proved, and other mathematicians are free to use it and build on it as they please, sometimes to great effect."

"Langlands and Grothendieck are both (at least) Giants by any measure, and both were consciously successors of Galois."

"Langlands' life has been by no means as extravagant as Grothendieck's, but his romanticism is evident to anyone who reads his prose; the audacity of his program, one of the most elaborate syntheses of conjectures and theorems ever undertaken, has few equivalents in any field of scholarship."

"Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is known to be finite, the BSD conjecture concerns the simplest class of polynomial equations—elliptic curves—for which there is no simple way to decide whether the number of solutions is finite or infinite."

"Moreover, according to Alexander, the “troubled mathematical martyr,” exemplified not only by Galois but also by Abel, János Bolyai, Riemann, Cantor, Gödel, Turing, John Nash, Grothendieck, Perelman, and even, in a certain sense, Cauchy, remains to this day the dominant image of the “ideal mathematician,” long after the romantic paradigm was exhausted in the arts."

"Within mathematics itself, Voevodsky's proposal, if adopted, will create a new paradigm. In his “fairy tale” and some of his other papers, Langlands made deft use of categories and even 2-categories, but number theory is only superficially categorical, and so is the Langlands program. In the event that Univalent Foundations could shed light on a guiding problem in number theory — the Riemann hypothesis or the Birch Swinnerton-Dyer conjecture, which is not so far removed from Voevodsky's motives — then we could easily see Grothendieck's program absorbing the Langlands program within Voevodsky's new paradigm."

"Literametrics' may become to philology, what 'Biometrics' has already become to the biological sciences."

"Every one knows that the fine phrase "God geometrizes" is attributed to Plato, but few know where this famous passage is found, or the exact words in which it was first expressed. Those who, like the author, have spent hours and even days in the search of the exact statements, or the exact references, of similar famous passages, will not question the timeliness and usefulness of a book whose distinct purpose it is to bring together into a single volume exact quotations, with their exact references, bearing on one of the most time-honored, and even today the most active and most fruitful of all the sciences, the queen-mother of all the sciences, that is, mathematics."

"We should, of course, expect that any universe which expands without limit will approach the empty de Sitter case, and that its ultimate fate is a state in which each physical unit—perhaps each nebula or intimate group of nebulae—is the only thing which exists within its own observable universe."

"The general theory of relativity considers physical space-time as a four-dimensional manifold whose line element coefficients g_{\mu \nu} satisfy the differential equationsG_{\mu \nu} = \lambda g_{\mu \nu} \qquad .\;.\;.\;.\;.\;.\; (1)in all regions free from matter and electromagnetic field, where G_{\mu \nu} is the contracted Riemann-Christoffel tensor associated with the fundamental tensor g_{\mu \nu}, and \lambda is the ."

"An "empty world," i.e., a homogeneous manifold at all points at which equations (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy."

"In considerations involving the nature of the world as a whole the irregularities caused by the aggregation of matter into stars and stellar systems may be ignored; and if we further assume that the total matter in the world has but little effect on its macroscopic properties, we may consider them as being determined by the solution of an empty world."

"The solution of (1), which represents a homogeneous manifold, may be written in the form:ds^2 = \frac{d\rho^2}{1 - \kappa^2\rho^2} - \rho^2 (d\theta^2 + sin^2 \theta \; d\phi^2) + (1 - \kappa^2 \rho^2)\; c^2 d\tau^2, \qquad (2)where \kappa = \sqrt \frac{\lambda}{3}. If we consider \rho as determining distance from the origin... and \tau as measuring the proper-time of a clock at the origin, we are led to the de Sitter spherical world..."

"is a congruence geometry, or equivalently the space comprising its elements is homogeneous and isotropic; the intrinsic relations between... elements of a configuration are unaffected by the position or orientation of the configuration. ...[M]otions of are the familiar translations and rotations... made in proving the theorems of Euclid."

"[O]nly in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained."

"That the existence of these motions (the "axiom of free mobility") is a desideratum, if not... a necessity, for a geometry applicable to physical space, has been forcefully argued on a priori grounds by von Helmholtz, Whitehead, Russell and others; for only in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained."

"Euclidean geometry is only one of several congruence geometries... Each of these geometries is characterized by a real number K, which for Euclidean geometry is 0, for the hyperbolic negative, and for the spherical and elliptic geometries, positive. In the case of 2-dimensional congruence spaces... K may be interpreted as the ' of the surface into the third dimension—whence it derives its name..."

"[W]e propose... to deal exclusively with properties intrinsic to the space... measured within the space itself... in terms of... inner properties."

"Measurements which may be made on the surface of the earth... is an example of a 2-dimensional congruence space of positive curvature K = \frac{1}{R^2}... [C]onsider... a "small circle" of radius r (measured on the surface!)... its perimeter L and area A... are clearly less than the corresponding measures 2\pi r and \pi r^2... in the Euclidean plane. ...for sufficiently small r (i.e., small compared with R) these quantities on the sphere are given by 1):L = 2 \pi r (1 - \frac{Kr^2}{6} + ...), A = \pi r^2 (1 - \frac{Kr^2}{12} + ...)"

"In the sum \sigma of the three angles of a triangle (whose sides are arcs of s) is greater than two right angles [180&deg;]; it can... be shown that this "spherical excess" is given by 2)\sigma - \pi = K \deltawhere \delta is the area of the spherical triangle and the angles are measured in s (in which 180&deg; = \pi [radians]). Further, each full line (great circle) is of finite length 2 \pi R, and any two full lines meet in two points—there are no parallels!"

"[T]he space constant K... "" may in principle at least be determined by measurement on the surface, without recourse to its embodiment in a higher dimensional space."

"These formulae [in (1) and (2) above] may be shown to be valid for a circle or a triangle in the hyperbolic plane... for which K < 0. Accordingly here the perimeter and area of a circle are greater, and the sum of the three angles of a triangle are less, than the corresponding quantities in the Euclidean plane. It can also be shown that each full line is of infinite length, that through a given point outside a given line an infinity of full lines may be drawn which do not meet the given line (the two lines bounding the family are said to be "parallel" to the given line), and that two full lines which meet do so in but one point."

"The value of the intrinsic approach is especially apparent in considering 3-dimensional congruence spaces... The intrinsic geometry of such a space of curvature K provides formulae for the surface area S and the volume V of a "small sphere" of radius r, whose leading terms are 3)S = 4 \pi r^2 (1 - \frac{Kr^2}{3} + ...), V = \frac{4}{3} \pi r^3 (1 - \frac{Kr^2}{5} + ...)."

"In all these congruence geometries, except the Euclidean, there is at hand a natural unit of length R = \frac{1}{K^\frac{1}{2}}; this length we shall, without prejudice, call the "radius of curvature" of the space."

"We have merely (!) to measure the volume V of a sphere of radius r or the sum \sigma of the angles of a triangle of measured are \delta, and from the results to compute the value of K."

"What is needed is a homely experiment which could be carried out in the basement with parts from an old sewing machine and an Ingersoll watch, with an old file of Popular Mechanics standing by for reference! This I am, alas, afraid we have not achieved, but I do believe that the following example... is adequate to expose the principles..."

"Let a thin, flat metal plate be heated... so that the temperature T is not uniform... clamp or otherwise constrain the plate to keep it from buckling... [and] remain [reasonably] flat... Make simple geometric measurements... with a short metal rule, which has a certain coefficient of expansion c... What is the geometry of the plate as revealed by the results of those measurements? ...[T]he geometry will not turn out to be Euclidean, for the rule will expand more in the hotter regions... [T]he plate will seem to have a negative curvature K... the kind of structure exhibited... in the neighborhood of a ".""

"What is the true geometry of the plate? ...Anyone examining the situation will prefer Poincaré's common-sense solution... to attribute it Euclidean geometry, and to consider the measured deviations... as due to the actions of a force (thermal stresses in the rule). ...On employing a brass rule in place of one of steel we would find that the local curvature is trebled—and an ideal rule (c = 0) would... lead to Euclidean geometry."

"In what respect... does the general theory of relativity differ...? The answer is: in its universality; the force of gravitation in the geometrical structure acts equally on all matter. There is here a close analogy between the gravitational mass M...(Sun) and the inertial mass m... (Earth) on the one hand, and the heat conduction k of the field (plate)... and the coefficient of expansion c... on the other. ...The success of the general relativity theory... is attributable to the fact that the gravitational and inertial masses of any body are... rigorously proportional for all matter."

"The field equation may... be given a geometrical foundation, at least to a first approximation, by replacing it with the requirement that the mean curvature of the space vanish at any point at which no heat is being applied to the medium—in complete analogy with... the general theory of relativity by which classical field equations are replaced by the requirement that the Ricci contracted curvature tensor vanish."

"Now it is the practice of astronomers to assume that brightness falls off inversely with the square of the "distance" of an object—as it would do in Euclidean space, if there were no absorption... We must therefore examine the relation between this astronomer's "distance" d... and the distance r which appears as an element of the geometry."

"All the light which is radiated... will, after it has traveled a distance r, lie on the surface of a sphere whose area S is given by the first of the formulae (3). And since the practical procedure... in determining d is equivalent to assuming that all this light lies on the surface of a Euclidean sphere of radius d, it follows...4 \pi d^2 = S = 4 \pi r^2 (1 - \frac{K r^2}{3} + ...);whence, to our approximation 4)d = r (1- \frac{K r^2}{6} + ...), or r = d (1 + \frac{K d^2}{6} + ...)."

"[T]he astronomical data give the number N of nebulae counted out to a given inferred "distance" d, and in order to determine the curvature... we must express N, or equivalently V, to which it is assumed proportional, in terms of d. ...from the second of formulae (3) and... (4)... to the approximation here adopted, 5)V = \frac{4}{3} \pi d^2 (1 + \frac{3}{10} K d^2 + ...);...plotting N against... d and comparing... with the formula (5), it should be possible operationally to determine the "curvature" K."

"This... is an outrageously over-simplified account of the assumptions and procedures..."

"The search for the curvature K indicates that, after making all known corrections, the number N seems to increase faster with d than the third power, which would be expected in a Euclidean space, hence K is positive. The space implied thereby is therefore bounded, of finite total volume, and of a present "radius of curvature" R = \frac{1}{K^\frac{1}{2}} which is found to be of the order of 500 million light years. Other observations, on the "red shift" of light from these distant objects, enable us to conclude with perhaps more assurance that this radius is increasing..."

"It was the work of... Friedmann, Robertson and Walker, which resulted in the general mathematical framework that is still used today when discussing relativistic cosmological models of a homogeneous and isotropic universe."

"[I]nvestigations of cosmological issues, whose only observational basis was the observations. ...involved ...mostly of mathematicians like Howard Robertson and and astronomers with strong mathematical training such as Eddington, Lemaître, George McVittie, and William McCrea. They were mainly interested in how to apply general relativity to cosmological problems, which involved not only understanding cosmic dynamics but also solving the intricate problem of interpreting cosmological solutions to the Einstein equations, in particular separating time (which determined the evolution of the universe) from space (to which simplified assumptions concerning the structure of the universe, such as homogeneity and , were to be applied)."

"Distinguished scientist, selfless servant of the national interest, courageous champion of the good and the right, warm human being, he gave richly to us and to all from his own great gifts. We are grateful for the years with him. We mourn the loss of his presence but rejoice in the legacy of his wisdom and strength."

"Weyl published a third appendix to his Raum, Zeit, Materie, and an accompanying paper], where he calculated the redshift for the ‘de Sitter cosmology’,ds^2 = -dt^2 + e^{2{\sqrt{\frac{\Lambda}{3}t}}} (dx^2+dy^2+dz^2),the explicit form of which would only be found later, independently by Lemaître and Robertson."

"The basic cause and nature of cosmic expansion, along with its recently-observed acceleration, are significant problems of the standard model; so, condisering the evidence that the acceleration is best described by pure \Lambda, there is strong motivation to search for an alternative big bang model that would respect the pioneering concept of expansion, as a direct consequence of the ‘de Sitter effect’ in the modified . It is therefore worth investigating the axiomatic basis of the Robertson-Walker (RW) line-element."

"[I]n deriving the general line-element for the background geometry of FLRW [Friedmann–Lemaître–Robertson–Walker, sometimes called the Standard Model] cosmology, Robertson required four basic assumptions: i. a congruence of s, ii. , iii. homogeneity, and iv. . i. and ii. are required to satisfy of a causal coherence amongst s in the entire Universe, by which every single event in the bundle of fundamental world lines is associated with a well-defined three-dimensional set of others with which it ‘really’ occurs simultaneously. However, it seems that ii. is therefore mostly required to satisfy the concept that synchronous events in a given inertial frame should have occurred simultaneously, against which I’ve argued..."

"Note.—The second part of this paper was considerably altered by me after the departure of Mr. Rosen for Russia since we had originally interpreted our results erroneously. I wish to thank my colleague Professor Robertson for his friendly in his assistance in the clarification of the original error."

"Important contributions to what would later appear as mainstream big bang cosmology were made by Americans Howard P. Robertson and Richard Tolman... Robertson (and independently, A. G. Walker in England) deduced in 1935 the most general form of the metric for a space-time satisfying the : the postulate that the universe is spatially homogeneous in its large scale appearance. This metric became generally known as the Robertson-Walker metric. Together with Tolman, Robertson pioneered the study of thermodynamics in the theory of the expanding universe."

"Many of the theoretical investigations of cosmology in the 1920s were examinations of De Sitter's model, which is particular because it can be understood both as a static model (as De Sitter did) and as an expanding model (as became the view after 1930). It is clearly problematic to read the pre-1930 literature in light of later knowledge. 'Expanding' versions of the De Sitter universe were found by in 1922, Hermann Weyl in 1923, and Lemaître in 1925, but were not conceived as expanding in any real sense. These works, as well as later works by Howard Percy Robertson and Richard Chase Tolman in the United States, consisted in transforming De Sitter's line element in such a way that it formally became static, that is, included a term F(t) referring to the time parameter. The metric, giving the distance in space-time between two neighboring points, would then be in the form ds^2 = c^2 dt^2 - F(t)(dx^2 = dy^2 +dz^2)."

"In 1928 Robertson found a non-static line element similar to the one Lemaître had found three years earlier. Also like Lemaître, he derived a linear relationship between apparent recessional velocities and distances, and he discussed it in relation to observation data. Within the same tradition was Tolman's 1929 derivation of a 'Hubble law', that is, a relationship of the form v = kr, with v = \frac{d\lambda}{\lambda}. Robertson and Tolman generalized the De Sitter model to an arbitrary scale factor F(t), but they remained within the static paradigm and did not realize the significance of F(t). In a paper of 1929, Robertson wrote the general line element of what would later be known as the Robertson-Walker models and he even referred to Friedmann's work. And yet, although he had evidently studied Friedmann, he 'misread' him and failed to realize the significance of the expanding metric."

"Robertson and Tolman developed much of the mathematics of the expanding universe, but without concluding or predicting prior to 1930 that the universe actually expands. They were not discoverers or codiscoverers of the expanding universe (and never claimed that they were)."

"Howard Percy Robertson was a postdoctorate student at Göttingen and Munich from 1925 to 1927. While in Göttingen he completed an important paper on relativistic cosmology in which he derived a relation between the velocity of nebulae and their distances. For the radius of the observable world he calculated R = 2 \times 10^{25} m. Although he had a velocity-distance relation and referred to Slipher's s, he did not conclude that the universe was in a state of expansion."

"Robertson wrote an influential [1933] review of relativistic world models in which he specifically excluded those which have "arisen in finite time from the singular state R = 0." Although he included the Einstein-de Sitter paper in his bibliography, he did not mention it in the review. He also did not mention Lemaître's primeval-atom hypothesis."

"Howard P. Robertson showed that the uncertainty relation follows from the commutation rule."

"As Daniel Dennefink explains in his article on the story behind the writings of the Einstein-Rosen gravitational paper, the singularity that Einstein and Rosen had encountered was an apparent singularity introduced by their choice of coordinate system, similar to the singularity one encounters when attempting to find the longitude of the North Pole. In fact, in his referee report Robertson had indicated that the singularity was removed by a change to a cylindrical coordinate system."

"In June 1936, Einstein and Rosen sent the paper... "Do Gravitational Waves Exist?" to The Physical Review... [which] rejected the paper, provoking Einstein's furious reaction. Einstein told the editor he... saw no reason to address the erroneous comments of his anonymous expert [Howard Percy Robertson] and... preferred to publish the paper elsewhere. ...Leopold Infeld arrived in Princeton to replace Rosen as... assistant. Einstein explained to him his proof of the non-existence of gravity waves. ...Infeld told Robertson [then professor of theoretical physics at Princeton] about Einstein's... paper[.] Robertson... found a trivial mistake [by] Infeld [and] clarified... the mistake in Einstein's explanation... The linearized approximation [led] to plane transverse gravitational waves... introduc[ing]... coordinate singularities... not real singularities. ...Robertson ...suggested ...the so-called Einstein-Rosen metric... be transformed... to cylindrical coordinates. ...the singularity can be regarded as describing a material source. The solution describe[s]...cylindrical... rather than plane gravitational waves. ...with Robertson's help (still not knowing it was Robertson who had [refereed] The Physical Review) ...Einstein ...revis[ed the] ...paper and added a section: "Rigorous Solution for Cylindrical Waves"... The new version of the paper was re-titled "On Gravitational Waves"..."

"Maybe so, but something is going on with the primes."

"You can ask the question about these ancient topics, such as s and ... and ask, are these good problems... I'd like to give a small amount of evidence... that they are... [S]tudying them helped us develop all of elementary number theory and from elementary number theory we developed the rest of number theory, and also you can argue that from elementary number theory came algebra.."

"The subject matter of mathematics is the expressions themselves together with the rules for manipulating them—nothing more."

"Intellectual property is an oxymoron."

"Nelson rejected the prevailing views to the effect that nonstandard analysis operates with some fictional elements that extend the standard world of mathematical entities. In his approach, nonstandard objects inhabit the realm of the most ordinary mathematical objects. Nelson emphasized the creative syntactic contribution of the new approach in the following terms: “Really new in nonstandard analysis are not theorems but the notions, i.e., external predicates.” (Nelson 1988 ...)"

"Why do I paint? In my work as a mathematician, form, structure, and economy of expression are important. In music, add tone quality, balance and harmony. And now in painting, these aesthetic values are enhanced by color, contrast, and composition."

"Algebraic geometry has developed in waves, each with its own language and point of view. The late nineteenth century saw the function-theoretic approach of Riemann, the more geometric approach of Brill and Noether, and the purely algebraic approach of Kronecker, Dedekind, and Weber. The Italian school followed with Castelnuovo, Enriques, and Severi, culminating in the classification of algebraic surfaces. Then came the twentieth-century "American" school of Chow, Weil, and Zariski, which gave firm algebraic foundations to the Italian intuition. Most recently, Serre and Grothendieck initiated the French school, which has rewritten the foundations of algebraic geometry in terms of schemes and cohomology, and which has an impressive record of solving old problems with new techniques. Each of these schools has introduced new concepts and methods."

"The predecessors of Newton and Leibnitz knew perfectly well how to determine tangents and areas, but they had to approach each problem from first principles. The great contribution of Newton and Leibnitz was precisely to make the procedures for finding tangents, areas, etc. into a calculus, that is, a systematic way of calculating—a collection of algorithms, to use the currently fashionable word."

"Suppose you want to teach the "cat" concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying "kitty" each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits."

"The fact that N Bourbaki was not a real person and represented a group of mathematicians was known to very few, for example, Ralph Boas, but the world of mathematics had come to believe in his existence. In an article for the Encyclopaedia Britannica, Boas revealed the truth; he was severely reprimanded in a letter to him "From my ashram in the Himalayas", beginning with "You miserable worm, how dare you say that I do not exist?" and signed 'Nicolas Bourbaki'!"

"It is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind."

"In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature."

"Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. Santaló, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety."

"Not all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan."

"The main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves."

"The treatises of Darboux (1842–1917) and Bianchi (1856–1928) on surface theory are among the great works in the mathematical literature. They are: G. Darboux, Théorie générale des surfaces, Tome 1 (1887), 2 (1888), 3 (1894), 4 (1896), and later editions and reprints. L. Bianchi. Lezioni di Geometria Differenziale, Pisa 1894; German translation by Lukat, Lehrbuch der Differentialgeometrie, 1899. The subject is basically local surface theory."

"I have no doubt that future historians of differential geometry will rank Chern as the worthly successor of Elie Cartan in that field."

"Recently, having refreshed my understanding of the mathematics of relativity theory, I called one of my old Berkeley professors to ask him some questions about the geometry of general relativity. S. S. Chern is arguably the greatest living geometer. We spoke on the phone for a long time, and he patiently answered all my questions. When I told him I was contemplating writing a book about relativity, cosmology, and geometry and how they interconnect to explain the universe, he said, "It's a wonderful idea for a book, but writing it will surely take too many years of your life ... I wouldn't do it." Then he hung up."

"S. S. Chern revolutionized differential geometry with the use of moving frames, the invention of characteristic classes, the modern concept of a connection and so much more, but he’ll probably always be most remembered for the yellowing University of Chicago mimeographed lecture notes from the 1950s. An entire generation of geometers learned the elements of differentiable manifolds from those notes."

"One respectful question will be addressed to Jews who plan to continue to eat meat: In view of strong Jewish mandates to be compassionate to animals, preserve our health, help feed the hungry, preserve and protect the environment, conserve resources, and seek and pursue peace, and the very negative effects animal-centered diets have in each of these areas, will you now become a vegetarian, or at least sharply reduce your consumption of animal products?"

"THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension."

"A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known."

"Others have spoken and written about his solution of Hilbert's fifth problem, but perhaps not enough is said about his later work, especially his joint work with C. T. Yang. In a long series of papers written in the late 1960s and early 1970s, they used the study of group actions on homotopy 7-spheres to showcase and test the growing new techniques of differential topology, especially index theory and surgery theory. At a time when much work in topology consisted in building these machines, their papers demonstrated the beauty of applying this theory to unfurl complexities of symmetry and structure."

"...Once you entomb mathematics in an artificial language à la Hilbert, once you set up a completely formal axiomatic system, then you can forget that it has any meaning and just look at it as a game that you play with marks on paper that enable you to deduce theorems from axioms. You can forget about the meaning of the game, the game of mathematical reasoning, it's just combinatorial play with symbols! There are certain rules, and you can study these rules and forget that they have any meaning!"

"At first it might seem that quantum mechanics (QM), which began with Einstein's photon as the explanation for the photoelectric effect in 1905, goes further in the direction of discreteness. But the wave-particle duality discovered by de Broglie in 1925 is at the heart of QM, which means that this theory is profoundly ambiguous regarding the question of discreteness vs. continuity. QM can have its cake and eat it too, because discreteness is modeled via standing waves (eigenfunctions) in a continuous medium."

"Are there mathematical propositions for which there is a considerable amount of computational evidence, evidence that is so persuasive that a physicist would regard them as experimentally verified?"

"Why do I think that Turing's paper "On computable numbers" is so important? Well, in my opinion it's a paper on epistemology, because we only understand something if we can program it, as I will explain in more detail later. And it's a paper on physics, because what we can actually compute depends on the laws of physics in our particular universe and distinguishes it from other possible universes. And it's a paper on ontology, because it shows that some real numbers are uncomputable, which I shall argue calls into question their very existence, their mathematical and physical existence."

"I'm interested in the computer as a new idea, a new and fundamental philosophical concept that changes mathematics, that solves old problems better and suggests new problems, that changes our way of thinking and helps us to understand things better, that gives us radically new insights..."

"[A]ccording to Weyl, complexity is essential in understanding the concept of a law of nature. If laws of nature may be arbitrarily complex, he argued, the very concept... becomes vacuous. What difference would remain... if the laws meant to explain them were as complex as the phenomena they are meant to explain? Laws of nature must be simple."

"Mathematicians are coming up with s that they use in their actual mathematical research. And these, like , I think is the name of one of them ... these are actually like s that have been engineered in a way that they can actually be used by working mathematicians to check the work they're doing."

"Problem: Name a book that combines mathematical history, philosophy, more than a whiff of theology, personal palaver, and brilliant insights, along with evidence of a Borges-like imagination, eyebrow-raising mathematical constructions, breathtaking excitement, grandiose ruminations, and some bosh. Solution: The book under review. ...Ω leads me to turn 180 degrees away from these classical philosophical questions—discussed ad nauseam and with diminishing profit—of why mathematics is true, whether its objects and constructs have ontological validity, whether it is the only mode of inference, what its limitations are, whether it is the unique language in which theoretical physics must be formulated. If we could focus instead on mathematical pragmatics—why mathematics throughout the millennia has been useful or deleterious to society—then I believe that we might be able to illuminate an aspect of mathematics that is often ignored: mathematics as a enterprise, for that is surely what it is."

"The spinor genus is due to Eichler. His early results (1952) established the theory over the rational field and also, in certain special cases, over a number field. Kneser (1956) extended this to number fields in general. At about the same time Watson obtained Eichler's results by elementary methods over the rational field."

"Class field theory can be divided into two parts, local and global. In each part it is the study of all the abelian extensions of a certain base field. The underlying philosophy is to describe all abelian extensions in terms of objects residing within, or close to, the base field."

"It was not until my second year as a doctoral student that I began to understand that mathematics was an ever-expanding universe. My thesis advisor at Princeton was Emil Artin, one of the great algebraists of the century. Unfortunately, or perhaps fortunately, he offered me no advice in the selection of a thesis topic. I think it was a fluke that I got started at all. But once I did, a whole new world opened up, to which I would devote a vast amount of time and energy for over thirty years."

"To the average mathematician who merely wants to know that his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency."

"However, in all honesty, I must say that one must essentially forget that all proofs are transcribed in this formal language. In order to think productively, one must use all the intuitive and informal methods of reasoning at one's disposal. At the very end one must check that no errors have been committed; but in practice set theory is treated as any other branch of mathematics. The reason that we can do this is that we will never speak about proofs but only about models."

"The theorem of Löwenheim–Skolem was the first truly important discovery about formal systems in general, and it remains probably the most basic. It is not a negative result at all, but plays an important role in many situations. For example, in Gödel's proof of the consistency of the Continuum Hypothesis, the fact that the hypothesis holds in the universe of constructible sets is essentially an application of the theorem."

"It is now known that the truth or falsity of the continuum hypothesis and other related conjectures cannot be determined by set theory as we know it today. This state of affairs regarding a classical and presumably well-posed problem must certainly appear rather unsatisfactory to the average mathematician. One is tempted to look more closely and perhaps more critically at the foundations of mathematics. Although our present "Cantorian" mathematics is highly successful in its treatment of abstractions, one must not overlook the fact that from the very beginning the use of infinite processes was regarded with suspicion by many people."

"The object of mathematics is to discover "true" theorems. We shall use the term "valid" to describe statements formed according to certain rules and then shall discuss how this notion compares with the intuitive idea of "true"."

"When the Löwenheim-Skolem theorem is applied to particular formal systems, we obtain as special cases: Every group, field, ordered field, etc., has a countable subsystem of the same type. A more spectacular result follows from applying the theorem to set theory (a system which we shall later formalize): There is a countable collection of sets, such that if restrict the membership relation to these sets alone, they form a model for set theory (more precisely all the true statements of set theory are true in this model). In particular, within this model which we may denote by M, there must be an uncountable set. This paradox, that a countable model can contain an uncountable set, is explained by noting that to say a set is uncountable merely asserts the nonexistence of a one-one mapping of the set with the set of integers. The "uncountable" set in M set actually has only countably many members in M, but there is no one-one correspondence \underline {within} M of this set with the set of integers."

"In 1963 P. J. Cohen completed Gödel's linguistic attack on set theory by introducing the immensely valuable, syntactic notion of forcing, and by using it to demonstrate that the axioms of set theory were not powerful enough to prove Cantor's continuum hypothesis. Thus the presently existing axioms of set theory leave the most celebrated hypothesis of set theory shrouded in uncertainty."

"To him mathematics was a unified subject that one could master broadly. He had a deep understanding of most areas, and he taught advanced courses in logic, analysis, differential equations, algebra, topology, Lie theory, and number theory on a regular basis. He felt that good mathematics should be easy to understand and that it is always based on simple ideas once you get to the bottom of the issue. This attitude extended to a strong belief that the well-recognized unsolved problems in mathematics are the heart of the subject and have clear and transparent solutions once the right new ideas and viewpoints are found. This belief gave him the courage to work on notoriously difficult problems throughout his career."

"The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions."

"The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative."

"Besides their possible role in physics, the octonions are important because they tie together some algebraic structures that otherwise appear as isolated and inexplicable exceptions."

"The most popular approach to quantum gravity is string theory. Despite decades of hard work by many very smart people, it's far from clear that this theory is successful. It's made no predictions that have been confirmed by experiment. In fact, it's made few predictions that we have any hope of testing anytime soon! Finding certain sorts of particles at the big new particle accelerator near Geneva would count as partial confirmation, but string theory says very little about the details of what we should expect. In fact, thanks to the vast "landscape" of string theory models that researchers are uncovering, it keeps getting harder to squeeze specific predictions out of this theory."

"Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". ... This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics."

"Together the, two ingredients—a perceived incongruity with a point and an appropriate emotional climate—seem to be both necessary and sufficient for humor."

"After all, one must have some grasp of logic even to recognize a non sequitur."

"The necessity of this psychic stepping back (or up) to the metalevel is probably what is meant when people say that a sense of perspective is needed for an appreciation of humor. It also explains why dogmatists, idealogues, and others with one-track minds are often notoriously humorless."

"Appreciating humor—even recognizing it—requires human skills of the highest order (level?); no computer comes close to having them."

"Humor, since it depends on so many emotional, social, and intellectual facets of human beings, is particularly immune to computer simulation."

"All art, in fact, has these two aspects: its content and its frame (or setting), which sets it apart from nonart and which says of itself, “This is not an everyday sort of communication. This is unreal.”"

"Innumerate people characteristically have a strong tendency to personalize—to be misled by their own experiences, or by the media’s focus on individuals and drama."

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence."

"The moral, again, is that some unlikely event is likely to occur, whereas it’s much less likely that a particular one will...The paradoxical conclusion is that it would be very unlikely for unlikely events not to occur. If you don’t specify a predicted event precisely, there are an indeterminate number of ways for an event of that general kind to take place."

"There’s always enough random success to justify almost anything to someone who wants to believe."

"There surely is something to these terms, but too often they’re the result of minds intent on discovering meaning where there is only probability."

"To follow foolish precedents, and wink with both eyes, is easier than to think."

"Any bit of nonsense can be computerized—astrology, biorhythms, the I Ching—but that doesn’t make the nonsense any more valid."

"Disproving a claim that something exists is often quite difficult, and this difficulty is often mistaken for evidence that the claim is true...Presented as I am periodically with these and other fantastical claims, I sometimes feel a little like a formally dressed teetotaler at a drunken orgy for reiterating that not being able to conclusively refute the claims does not constitute evidence for them."

"I remember thinking of mathematics as a kind of omnipotent protector. You could prove things to people and they would have to believe you whether they liked you or not."

"Bad things happen periodically, and they’re going to happen to somebody. Why not you?"

"Too often, this concern for the big picture is simply obscurantist and is put forward by people who prefer vagueness and mystery to (partial) answers. Vagueness is at times necessary and mystery is never in short supply, but I don’t think they’re anything to worship. Genuine science and mathematical precision are more intriguing than are the “facts” published in supermarket tabloids or a romantic innumeracy which fosters credulity, stunts skepticism, and dulls one to real imponderables."

"There is no such thing as free lunch, and even if there were, there’d be no guarantee against indigestion."

"Correlation and causation are two quite different words, and the innumerate are more prone to mistake them than most."

"If we’re not keenly aware of the choices we’re making, we’re not likely to work for better ones."

"It’s time to let the secret out: mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us."

"You can only predict things after they’ve happened."

"Our two most basic political ideals—liberty and equality—are, in their purest forms, incompatible. Complete liberty results in inequality, and mandatory equality leads to a loss of liberty."

"Having been involved in a couple of lawsuits as an expert probability witness and having observed that a prudent skepticism is often less prized than an indefensible certainty, I turned down preliminary requests from both sides to testify."

"In general, any differences between two groups will always be greatly accentuated at the extremes."

"One can and should debate whether the tests in question are appropriate for the purposes at hand, but one shouldn’t be surprised when normal curves behave normally."

"Even the most superficial of a newspaper reveals an important aspect of human psychology: our preoccupation with the short term."

"When the law’s on your side, pound the law. When the facts are on your side, pound the facts. And when neither is on your side, pound the table."

"Two dangers threaten the world—order and disorder."

"Gullible citizens are a demagogue’s dream."

"Rigid distinctions between the deep and the shallow are generally themselves quite superficial."

"The fashion pages have always puzzled me. In my smugly ignorant view, the articles appear to be so full of fluff and nonsense as to make the astrology columns seem insightful by comparison."

"There are, of course, innumerable abuses, countless possible misinterpretations, and depressingly many biased studies, but, done right, the process works; it yields knowledge."

"There is a fine line between public expressions of faith and aggressive declarations thereof, and religious tolerance is inversely proportional to the latter."

"Always be smart; seldom be certain."

"I’ve argued that the set of standard questions journalists ask and readers want answers should be enlarged. Besides Who, What, Where, When, Why, and How, it should include How many? How likely? What fraction? How does the quantity compare with other quantities? What is its rate of growth, and how does that compare? What about the self-referential aspects of the story? Is there an appropriate degree of complexity in it? Are we looking at the right categories and relations? How much of the story is independent of its reporting? Are we especially vulnerable to the availability error or to anchoring effects? If statistics are presented, how were they obtained? How confident can we be of them? Were they derived from a random sample or from a collection of anecdotes? Does the correlation suggest a causal relationship, or is it merely a coincidence? And do we understand how the people and various pieces of an organization reported upon are connected? What is known about the dynamics of the whole system? Are they stable or do they seem sensitive to tiny perturbations? Are there other ways to tally any figures presented? Do such figures measure what they purport to measure? Is the precision recounted meaningful?"

"Almost any bunkum has some partial validity, and we regularly read into the confusing mess what we want to see."

"Those who can make you believe absurdities can make you commit atrocities."

"Define God in a sufficiently nebulous way as beauty, love, mysterious complexity, or the ethereal taste of strawberry shortcake, and most atheists become theists. Still, although one can pose as Humpty Dumpty and aver, “When I use a word, it means just what I choose it to mean, neither more nor less,” others needn’t play along."

"For the record, natural selection is a highly nonrandom process that acts on the genetic variation produced by random mutation and genetic drift and results in those organisms with more adaptive traits differentially surviving and reproducing."

"You would think that the obvious irreligious objection would come to almost anyone’s mind when reading a religious tome or holy book. What if you don’t believe the holy book’s presuppositions and narrative claims and simply ask for independent argument or evidence for God’s existence? What if you’re not persuaded by the argument that God exists because His assertion that He exists and discussion of His various exploits appear in this book about Him that believers say He inspired?"

"Claiming that a holy book’s claims are undeniable because the book itself claims them to be is convincing only to the convinced."

"Confirmation of a person’s unreliable statement by another unreliable person makes the statement even less reliable."

"The whole weight of science is the prima facie evidence against a miracle having occurred."

"It’s become somewhat fashionable to say that religion and science are growing together and are no longer incompatible. This convergence is, in my opinion, illusory. In fact, I don’t believe that any attempt to combine these very disparate bodies of ideas can succeed intellectually."

"The universe acts on us, we adapt to it, and the notions that we develop as a result, including the mathematical ones, are in a sense taught us by the universe. Evolution has selected those of our ancestors (both human and not) whose behavior and thought were consistent with the workings of the universe."

"The connections among morality, prudence, and religion are complicated and beyond my concerns here. I would like to counter, however, the claim regularly made by religious people that atheists and agnostics are somehow less moral or law-abiding than they. There is absolutely no evidence for this, and I suspect whatever average distance there is along the nebulous dimension of morality has the opposite algebraic sign."

"It’s always healthy to recognize facts."

"While not a panacea, candidly recognizing the absence of any good logical arguments for God’s existence, giving up on divine allies and advocates as well as taskmasters and tormentors, and prizing a humane, reasonable, and brave outlook just might help move this world a bit closer to a heaven on earth."

"Our first action that really set us off in a bad direction was when Nato started to expand, bringing in eastern European nations, some of them bordering Russia. At that time we were working closely with Russia and they were beginning to get used to the idea that Nato could be a friend rather than an enemy ... but they were very uncomfortable about having Nato right up on their border and they made a strong appeal for us not to go ahead with that."

"We stand today, I believe, in greater danger of a nuclear catastrophe than we faced during the Cold War. And I can explain why I believe that, but the first point I want to make, though, is that hardly anybody understands that. And because we don’t understand it, our policies are not responsive to those dangers. During the Cold War, at least we had, we understood the danger and were taking action to try to deal with it; we had very serious arms control discussions, for example. Today, it’s so far in the background that people don’t understand it at all, particularly the new generation of people who didn’t live through the Cold War. But it’s a very dangerous situation today. And the headlines, which are about North Korea, just emphasize the danger; but the greater danger, really, is–the ultimate danger–is some sort of an exchange between the United States and Russia today. That would lead not just to a great catastrophe, it would basically lead to the end of civilization. So that’s what’s at stake here: ending our civilization, and the nuclear weapons have the power to do that."

"Any further spread of nuclear weapons multiplies the possibilities of nuclear confrontation and magnifies the danger of diversion. Thus, if proliferation of weapons of mass destruction continues into Iran and remains in North Korea in the face of all ongoing negotiations, the incentives for other countries to follow the same path will become overwhelming. Considerations as these have induced former Senator Sam Nunn, former Secretary of Defense William Perry, former Secretary of State George Shultz, and I -- two Democrats and two Republicans -- to publish recommendations for systematically reducing and eventually eliminating reliance on nuclear weapons. We have a record of strong commitment to national defense and security. We continue to affirm the importance of adequate deterrent forces, and we do not want our recommendations to diminish essentials for the defense of free peoples while a process of adaptation to new realities is going on. At the same time, we reaffirm the objective of a world without nuclear weapons that has been proclaimed by every American President since President Eisenhower."

"In February William Perry let slip that if this reform falls through in Russia, then the West should be ready to strengthen its collective security. What's the connection? Since when can the defense secretary of the U.S. determine the type of economic reform Russia needs? And why are we being threatened with external pressure if Russia changes the direction and tempo of reform?"

"I'd say I am somewhere in between being a libertarian and a liberal. So if I were to vote it would be kind of a Gary Johnson versus Mitt Romney decision, I suppose."

"I've always felt like something of an outsider. I've always had friends, but I've always come from an outside point of view. I think that's important. If you grow up gay, or in a household that's agnostic, when most people are religious, then from the get-go, you are saying that there are things that the majority of society believes that I don't believe."

"There are entire disciplines in which predictions have been failing, often at great cost to society. Consider something like biomedical research. In 2005, an Athens-raised medical researcher named John P. Ioannidis published a controversial paper titled "Why Most Published Research Findings Are False." ... The paper studied positive findings documented in peer-reviewed journals: descriptions of successful predictions of medical hypotheses carried out in laboratory experiments. It concluded that most of these findings were likely to fail when applied in the real world. Bayer Laboratories recently confirmed Ioannidis's hypothesis. They could not replicate about two-thirds of the positive findings in medical journals when they attempted the experiments themselves. ..."

"GOP are so all-in on an "all base mobilization, all the time" strategy that people just take for granted it must be smart politics when it's far from obvious that's the case."

"Bernie Sanders proudly describes himself as a “socialist” (or more commonly, as a “democratic socialist”). To Americans of a certain age, this is a potential liability. I’m just old enough (38) to have grown up during the Cold War, a time when “socialist” did not just mean “far left” but also implied something vaguely un-American. If you’re older than me, you may have even more acutely negative associations with “socialism” and may see it as a step on the road to communism. If you’re a few years younger than me, however, you may instead associate “socialism” with the social democracies of Northern Europe, which have high taxes and large welfare states. Sweden may not be your cup of tea, but it isn’t scary in the way the USSR was to people a generation ago."

"Since December 2015, there have 10 incidents that killed 10 or more people. That’s more than there was in 30 years between 1982 and 2011. And five of the 10 deadliest mass shootings in modern American history have all happened in the last five years."

"Mathematics is a process of staring hard enough with enough perseverence at at the fog of muddle and confusion to eventually break through to improved clarity. I'm happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarrassment that I might reveal ignorance or confusion.Over the years, this has helped me develop clarity in some things, but I remain muddled in many others."

"Mathematics is primarily a tool for human thought."

"The most important thing about mathematics is how it resides in the human brain."

"People can be fooled into thinking of mathematics as logical, formal, symbolic reasoning. But this is far from reality...computers are far better at formal computation and formal reasoning, but humans are far better mathematicians."

"When mathematics is explained, formalized and written down, there is a strong tendency to favor symbolic modes of thought at the expense of everything else, because symbols are easier to write and more standardized than other modes of reasoning. But when mathematics loses its connection to our minds, it dissolves into a haze."

"The term `geometry'...refers to a pattern of processing within our brains related to our spatial and visual senses, more than it refers to a separate content area of mathematics."

"I was really amazed by my first encounters with serious mathematics textbooks...I could appreciate that the mathematics was an impressive intellectual edifice, and I could follow the steps of proofs. I assumed that such an elaborate buildup must be leading to a fantastic denouement, which I eagerly awaited -- and waited, and waited. It was only much later, after much of the mathematics I had studied had come alive for me that I came to appreciate how ineffective and denatured the standard ((definition theorem proof)n remark)m style is for communicating mathematics. When I reread some of these early texts, I was stunned by how well their formalism and indirection hid the motivation, the intuition and the multiple ways to think about their subjects: they were unwelcoming to the full human mind."

"But why did I do it? I confess that I'm an unabashed Old Leftist who never quite understood how deconstruction was supposed to help the working class. And I'm a stodgy old scientist who believes, naively, that there exists an external world, that there exist objective truths about that world, and that my job is to discover some of them."

"Anyone who believes that the laws of physics are mere social conventions is invited to try transgressing those conventions from the windows of my apartment. (I live on the twenty-first floor.)"

"The results of my little experiment [Sokal affair] demonstrate, at the very least, that some fashionable sectors of the American academic Left have been getting intellectually lazy. The editors of Social Text liked my article because they liked its conclusion: that "the content and methodology of postmodern science provide powerful intellectual support for the progressive political project" [sec. 6]. They apparently felt no need to analyze the quality of the evidence, the cogency of the arguments, or even the relevance of the arguments to the purported conclusion."

"When scientific research is increasingly funded by private corporations that have a financial interest in particular outcomes of that research—is the drug effective or not?—scientific objectivity is undermined. When universities are more interested in patent royalties than in the open sharing of scientific information, the public suffers. There are hundreds of important political and economic issues surrounding science and technology. Sociology of science, at its best, has done much to clarify these issues. But sloppy sociology, like sloppy science, is useless or even counterproductive."

"Though there are important differences among species, there is reason to be optimistic that these methods can provide useful interventions for humans...This paper and related studies have the potential for huge clinical impact in Alzheimer's disease and others involving brain inflammation."

"What is the question, to which this is the answer?"

"A distributed system is one in which the failure of a computer you didn't even know existed can render your own computer unusable."

"I think in other things that I've done, I can look back and see: "This idea developed from something else." Sometimes it would lead back to a previous idea of mine, very often it would lead to something somebody else had done. But the Bakery algorithm just seemed to come out of thin air to me. There was nothing like it that preceded it, so perhaps that's why I'm proudest of it."

"The first thing is deciding what the program should do. If you don’t think carefully about that, it’s going to wind up not doing something that it probably should do or you wind up with an ‘absolute bug-free program’. Because to have a bug, you have to have some notion of what it means for the program to be operating correctly. And there is no precise definition of what it means for the program to be correctly operating — so, well, no bugs. Not a very good situation."

"With so many people doing so much writing, great writing is hard to find ... If you succeed in attaining a position that allows you to do something great, if you do something that really is great, and if you realize that it’s great, there’s still one more hurdle: You have to convince others that it’s great. This will require writing."

"Thinking doesn't guarantee that we won't make mistakes. But not thinking guarantees that we will."

"Marine navigation blends both science and art. A good navigator constantly thinks strategically, operationally, and tactically. He plans each voyage carefully. As it proceeds, he gathers navigational information from a variety of sources, evaluates this information, and determines his ship’s position. He then compares that position with his voyage plan, his operational commitments, and his predetermined “dead reckoning” position. A good navigator anticipates dangerous situations well before they arise, and always stays “ahead of the vessel.” He is ready for navigational emergencies at any time. He is increasingly a manager of a variety of resources--electronic, mechanical, and human. Navigation methods and techniques vary with the type of vessel, the conditions, and the navigator’s experience. The navigator uses the methods and techniques best suited to the vessel, its equipment, and conditions at hand. Some important elements of successful navigation cannot be acquired from any book or instructor. The science of navigation can be taught, but the art of navigation must be developed from experience."

"The Earth is an irregular oblate spheroid (a sphere flattened at the poles). Measurements of its dimensions and the amount of its flattening are subjects of geodesy. However, for most navigational purposes, assuming a spherical Earth introduces insignificant error. The Earth’s axis of rotation is the line connecting the north and south geographic poles. A great circle is the line of intersection of a sphere and a plane through its center. This is the largest circle that can be drawn on a sphere. The shortest line on the surface of a sphere between two points on the surface is part of a great circle. On the spheroidal Earth the shortest line is called a geodesic. A great circle is a near enough approximation to a geodesic for most problems of navigation."

"However, Seidenberg was told by the Indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC. But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case: “Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia. And the geometry of Babylonia is already secondary whereas in India it is primary.” [To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics:] “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”"

"By examining the evidence in the Shatapatha Brahmana, we now know that Indian geometry predates Greek geometry by centuries. For example, the earth was represented by a circular altar and the heavens were represented by a square altar and the ritual consisted of converting the circle into a square of an identical area. There we see the beginnings of geometry! Two aspects of the 'Pythagoras' theorem are described in the Vedic literature. One aspect is purely algebraic that presents numbers a, b, c for which the sum of the squares of the first two equals the square of the third. The second is the geometric, according to which the sum of the areas of two square areas of different size is equal to another square. The Babylonians knew the algebraic aspect of this theorem as early as 1700 BCE, but they did not seem to know the geometric aspect. The Shatapatha Brahmana, which precedes the age of Pythagoras, knows both aspects. Therefore, the Indians could not have learnt it from the Old-Babylonians or the Greeks, who claim to have rediscovered the result only with Pythagoras. India is thus the cradle of the knowledge of geometry and mathematics."

"Its mathematics was very much like what we see in the Sulvasutras [szulbasu utras]. In the first place, it was associated with ritual. Second, there was no dichotomy between number and magnitude … In geometry it knew the Theorem of Pythagoras and how to convert a rectangle into a square. It knew the isosceles trapezoid and how to compute its area … [and] some number theory centered on the existence of Pythagorean triplets … [and how] to compute a square root. …The arithmetical tendencies here encountered [ie in the SZulbasuutras] were expanded and in connection with observations on the rectangle led to Babylonian mathematics. A contrary tendency, namely, a concern for exactness of thought … together with a recognition that arithmetic methods are not exact, led to Pythagorean mathematics."

"‘Greece and India have a common heritage that cannot have derived from Old-Babylonia, i.e., the Old-Babylonia of about 1700 B.C.’ (Seidenberg 1978)"

"‘A comparison of Pythagorean and Vedic mathematics together with some chronological consideration showed that the current view [of Greek influence on Vedic thought] is not tenable. A common source for the Pythagorean and Vedic mathematics is to be sought either in the Vedic mathematics [i.e. the Sulbasutras] or in an older mathematics very much like it.’ (Seidenberg 1978)"

"I think its mathematics [of the common source] was very much like what we see in the Sulbasutras. (Seidenberg 1978)"

"I cannot help thinking that it shows battle weariness rather than a considered opinion."

"Yet long before 1937 people had suggested a non-Greek origin to Greek mathematics; and long before 1943 people had pointed out that sacred books of the East contain the ‘Pythagorean numbers’ [and indeed the ‘theorem’]. Such numbers are mentioned in the Sulvasutras; ancient Indian works on altar constructions. […] Neugebauer does not mention the Sulvasutras in his book Vorlesungen über Geschichte der Antiken Mathematischen Wissenschaften, nor does B. L. van der Waerden them in his book Science Awakening. Why this omission?"

"[…] nor did he [Thibaut] formulate the obvious conclusion, namely, that the Greeks were not the inventors of plane geometry, rather it was the Indians. At least this was the message that the Greek scholars saw in Thibaut’s paper. And they didn’t like it."

"If the Indians invented plane geometry, what was to become of Greek ‘genius’ or of the Greek ‘miracle’?"

"‘a number of points in Greek geometry are illuminated by the hypothesis that it started from a tradition of peg-and-cord constructions of the kind we find with the Vedic ritualists’ [45]."

"As N.S. Rajaram has rightly observed, Seidenberg traces Babylonian mathematics and astronomy to Indian models. He suggests the Kassite dynasty (18th-16th century) as the channel of transmission, as the Kassite language has an Indo-Aryan substrate. This is eminently reasonable. Thus, Babylonian astronomy divided the ecliptic in 18, yet by the first millennium it had adopted a division in 12, the same as existed in Vedic culture, where a nightly division into 28 lunar houses was complemented by a daily division of the ecliptic in 12 half-seasons (Madhu, Madhava etc.), and where the rishi Dirghatamas introduced the first-ever division of the circle into 12 and 360. Till today, the division into 360 is explained in textbooks as a Babylonian invention, but the earliest mention is Indian."

"Seidenberg (1983), a historian of science, described the reaction to Thibaut's claim: "Thibaut himself never belabored or elaborated these views, nor did he formulate the obvious conclusion, namely, that it was not the Greeks who invented plane geometry, it was the Indians. At least this was the message that the Greek scholars saw in Thibaut's paper. And they didn't like it" (103). Eventually, Thibaut was pressured into proposing a date for the sutras that would disarm the Greek scholars, but he would not forgo the possibility that the two different peoples could at least have developed the same knowledge independently. The date he offered was the fourth or third century B.C.E. Seidenberg (1978) comments: "A terrible statement! I cannot help thinking that it shows battle- weariness rather than a considered opinion. . . . Anyway, the damage had been done and the Sulvasutras have never taken the position in the history of mathematics that they deserve" (306)"

"Seidenberg (1983), "regard[s] it as certain that knowledge of Pythagoras' Theorem was known to the Satapatha Brahmana, which mentions calculations connected with the purusa bird altar, and to the Taittiriya Samhita, which showed similar geometrical awareness" (106). Since these texts are generally dated to around 1000-800 B.C.E., "Greek geometry did not somehow make its way into Vedic geometry, as Greek geometry is only supposed to have started about 600 B.C." (108). Scholars no longer consider Vedic geometry to have been borrowed from the Greeks, so Seidenberg's more controversial claim in the modern context is his rejection of the possibility that the algebra either of the Indians or the Greeks was derived from Babylonia, since the former were aware of aspects of the theorem to which the Babylonians make no reference. He also rejects the possibility that these aspects could have been discovered by the Indians after receiving the basic theorem from Babylonia and then transforming it, and concludes that either "Old Babylonia got the theorem of Pythagoras from India or that Old Babylonia and India got it from a third source" (Seidenberg 1983, 121)."

"Seidenberg's next steps involve a series of assumptions that need to be laid out. He first states that since the Babylonian sources are dated to 1700 B.C.E., the mathematical knowledge in the Sulvasutras must predate that. His next statement is significant: "Now the Sanskrit scholars do not give a date for the geometric rituals in question as early as 1700 B.C. Therefore I postulate a pre-Babylonian (i.e., pre-1700 B.C.) source for the kind of geometric rituals we see preserved in the Sulvasutras, or at least for the mathematics involved in these rituals" (1983, 121). Seidenberg assigns a date of 2200 B.C.E. for the common source, but upon being told by his Indological colleagues that the Aryans were not even in India in 1700 B.C.E. (1978, 324), let alone 2200 B.C.E., he is forced to postulate that the Aryans and Greeks inherited their mathematics from the joint Indo- European period, and the Indo-Aryans brought the knowledge into the subcontinent with them."

"... the theory of valuations may be viewed as a branch of topological algebra. In fact, historically speaking, it represents the first invasion of topology, more precisely, of early metric topology, into the domains of algebra. The introduction of metric methods into algebra has been so fruitful that today many of the deeper algebraic theories carry their mark. In this regard, one should distinguish between the classical use in algebra of the natural metric of the real or complex number fields, such as in proving the "fundamental theorem of algebra," and the much more recent use of the far less evident metrics which are derived from arithmetic notions of divisibility and which constitute the principal notion of valuation theory. Such a metric occurs for the first time in Hensel's construction of the p-adic numbers ..."

"Let F be a field of characteristic 0, and let F be a finite dimensional vector space over F. Let E denote the algebra of all endomorphisms of V, and let L be any Lie subalgebra of E. Among the algebraic Lie algebras contained in E and containing L, there is one that is contained in all of them, and this is called the algebraic hull of L in E. Here, an algebraic Lie algebra is defined as the Lie algebra of an algebraic group. It is an easy consequence of the definitions that if A and B are algebraic groups of automorphisms of V such that A⊂B then the Lie algebra of A is contained in the Lie algebra of B. Hence the existence of the algebraic hull of L is an immediate consequence of the following basic result: let G be the intersection of all algebraic groups of automorphisms of V whose Lie algebras contain L."

"A Lie algebra is said to be algebraic if it is isomorphic with the Lie algebra of an affine algebraic group. In view of the fact that entirely unrelated affine algebraic groups (typically, vector groups and toroidal groups) may have isomorphic Lie algebras, this notion of algebraic Lie algebra calls for some clarification. The most relevant result in this direction is due to M. Goto. It says that a finite- dimensional Lie algebra L over a field of characteristic 0 is algebraic if and only if the image of L under the adjoint representation is the Lie algebra of an algebraic subgroup of the group of automorphisms of L ..."

"... Lie algebras have a significance reaching beyond the domain of algebra, because they play such an important role in the theory of Lie groups. Thus, classical Lie algebra theory is strongly dominated by the fact that the finite-dimensional analytic representations of a simply connected analytic group are identifiable with the finite-dimensional representations of its Lie algebra. In the theory of infinite-dimensional representations, the connection with Lie algebra representations is somewhat tenuous, but it is nevertheless at the core of the major advances made in that theory during the last 30 years."

"In these days, when the number of papers in mathematics published each year is almost without limit and the ramifications are no less perplexing in their variety, one is delighted to find here and there a digest of the work in a particular field."

"In 1869 Dini solved the problem of geodesic representation of two surfaces upon one another. In 1896 Levi-Civita extended the problem to spaces of any order."

"The layman thinks that mathematics deals with facts and that thus there can possibly be no differences of opinion among mathematicians. We know that this is not the case."

"The well known classical treatise by Krazer on the theory of θ functions contains several beautiful chapters dealing with the applications of this theory to algebraic geometry (in the largest sense of the word), but on the whole this treatise is more analytic than geometric in character. In it, page after page, swarms of complicated formulas and relations follow each other, rarely illuminated by a geometric interpretation. One can say, without fear of exaggeration, that all the geometric applications of this theory to algebraic curves and varieties made since Riemann and Weierstrass (Hurwitz, Poincaré, Schottky, Wirtinger, etc.) are absent in Krazer's treatise, or at most are only mentioned in short historical notes."

"The idea of topologizing an algebraic variety V by choosing as closed sets the algebraic subvarieties of V can be used with good effect in order to topologize the set M* of all homomorphic mappings of any abstract field A into another abstract field K. In this general case we are dealing essentially with a generalization of the concept of the Riemann manifold of a field of algebraic functions ..."

"The Italian geometers have erected, on somewhat shaky foundations, a stupendous edifice: the theory of algebraic surfaces. It is the main object of modern algebraic geometry to strengthen, preserve, and further embellish this edifice, while at the same time building up also the theory of algebraic varieties of higher dimension. The bitter complaint that Poincaré has directed, in his time, against the modern theory of functions of a real variable cannot be deservedly directed against modern algebraic geometry. We are not intent on proving that our fathers were wrong. On the contrary, our whole purpose is to prove that our fathers were right. ... In helping geometry, modern algebra is helping itself above all. We maintain that abstract algebraic geometry is one of the best things that happened to commutative algebra in a long time."

"Minimal surfaces are of interest in various branches of mathematics. In the calculus of variations they appear as surfaces of least area, in differential geometry as surfaces of vanishing mean curvature. In gas dynamics the equation of minimal surfaces,"

"The theory of analytic functions of a complex variable occupies a central place in analysis and it is not surprising that mathematical literature abounds in generalizations. In some generalizations one extends the domain of the functions considered, or their range, or both (functions of several complex variables, analytic functions with values in a vector space or an algebra, analytic functions of hyper-complex variables, analytic operators, etc.) If we restrict ourselves to functions from plane domains to plane domains, or, more generally, from Riemann surfaces to Riemann surfaces, we encounter two well known and very useful generalizations of analytic functions: interior functions and quasi-conformal functions. Interior functions ... have all topological properties of analytic functions and no others. As a matter of fact, they may be defined as functions which can be made analytic by a homeomorphism of the domain of definition. Quasi-conformal functions ... are interior functions subject to an additional metric condition. If the functions are assumed to be continuously differentiable mappings, this additional condition requires that infinitesimal circles be taken into infinitesimal ellipses of uniformly bounded eccentricity."

"Bers' paper [15], in which he shows that a C-linear algebra isomorphism between the rings of holomorphic functions on two surfaces is induced by a conformal map between them, appeared in 1948 and started a whole industry. ..."

"Generally speaking, I favor increased levels of support for mathematics and physical and life science. Aside from the inevitable positive impact on the world’s economy, the advancement of knowledge lifts humanity’s spirits, opening our eyes to the wonders of the universe."

"When you're really thinking hard about mathematics, you're in your own world. And you're cushioned from other things."

"... Be guided by beauty ... Beauty is an aesthetic. There is beauty in things that work really well — the way a company is run, or the way a theorem comes out. … Don’t give up easily. Stick to something. Not to the point where it’s clearly insane, but be persistent. … Getting fired once can be a good experience. You just don’t want to make a habit of it. … Work with the smartest people you can. Hopefully smarter than you even. It amplifies your effect. … Hire the smartest people you possibly can … Work collaboratively, and let everyone know what everyone else is researching, so people aren’t wasting their time. … You never know where good science is going to take you."

"A former math professor, Simons is arguably the most successful trader in the history of modern finance. Since 1988, Renaissance's flagship Medallion hedge fund has generated average annual returns of 66 percent, racking up trading profits of more than $100 billion ... No one in the investment world comes close. Warren Buffett, George Soros, Peter Lynch, Steve Cohen, and Ray Dalio all fall short ..."

"A partially computable function may be thought of as one for which we possess an algorithm which enables us to compute its value for elements of its domain, but which will have us computing forever in attempting to obtain a functional value for an element not in its domain, without ever assuring us that no value is forthcoming. In other words, when an answer is forthcoming, the algorithm provides it; when no answer is forthcoming, the algorithm has one spend an infinite amount of time in a vain search for an answer."

"Nonstandard analysis is a technique rather a subject. Aside from theorems that tell us that nonstandard notions are equivalent to corresponding standard notions, all the results we obtain can be proved by standard methods. Therefore, the subject can only be claimed to be of importance insofar as it leads to simpler, more accessible expositions, or (more important) to mathematical discoveries."

"Takeuti has studied models of axiomatic set theory in which the “truth values” are elements of a complete Boolean algebra of projections on closed subspaces of a Hilbert space, and has found that the real numbers of such a model can be taken to be self-adjoint operators which can be resolved in terms of projections belonging to the Boolean algebra. It is suggested that this is the mathematical source of the replacement of real quantities by operators in quantizing a classical description, and that quantum theory involves a relativity principle with Takeuti's Boolean algebras serving as reference “frames.”"

"The analysis of algorithmic process that emerged from the work of Gödel, Church, Turing, and Post has been of great importance not only for theoretical investigations but also for practice, by providing an expansive framework for computer science. The discussion of computation-like processes that transcend the limits imposed by the Church–Turing thesis can likewise be framed either in terms of theory or of practice."

"Davis became one of the earliest computer programmers when he began programming on the ORDVAC computer at the University of Illinois in the early 1950s. His book Computability and Unsolvability ... first appeared in 1958 and has become a classic in theoretical computer science."

"In this paper, we shall show the validity of an iterative procedure suggested by George W. Brown ... This method corresponds to each player choosing in turn the best pure strategy against the accumulated mixed strategy of his opponent up to then."

"We say a mathematical theory is decidable if there is an effective method of determining the validity of each statement of the theory. If there is no such method, the theory is undecidable. It is clear that if there is a mechanical way of transforming each statement of an undecidable theory into an equivalent statement of another theory, the second theory is also undecidable. This principle, together with the fact that the arithmetic of natural numbers is undecidable, enables us to solve the decision problem for fields of finite degree over the rationals."

"And I continued to struggle with the Tenth Problem. In 1961 Martin Davis, Hilary Putnam, and I published a joint paper, "The undecidability of exponential diophantine equations," which used ideas from the papers Martin and I had presented at the International Congress along with various new results. The paper contains what is sometimes referred to as the Robinson hypothesis (or, as Martin calls it, "J.R.") to the effect that if there were some diophantine relation that grew faster than an exponential but not too terribly fast—less than some function could be expressed in exponentials—then we would be able to define exponentiation. It would follow from the definition that exponential diophantine equations would be equivalent to diophantine equations and that, therefore, the solution to Hilbert's tenth problem would be negative. At the time many people told Martin that this approach was misguided, to say the least. They were more polite to me."

"Notices: Can you tell me your memories of Julia Robinson, what she was like as a person? Davis: Very nice, very straightforward. Broad in her interests, mathematical and otherwise. And great power—there is no question in my mind that she was a much more powerful mathematician than I. We worked together on a problem on which we didn’t get anywhere. We were trying to prove the unsolvability of the decision problem for word equations. It turned out that we wouldn’t have been able to do that because the problem is solvable. Makanin solved it positively."

"In Julia Robinson we find a mathematician who was a heroine in her own time and a role model for all time. It is a story of childhood, illness, love, marriage, disappointment, obsession, and triumph."

"Surface tension is commonly thought of as a fluid phenomenon; the mere mention of the term brings to mind bugs skimming over water, liquids rising or falling in capillary tubes—and soap films and soap bubbles. But there is in fact a notion of surface tension (which is surface energy per unit surface area) for the interface between any two substances, or even between one substance and a vacuum. This surface energy arises from the fact that atoms (or molecules, or ions) of a given substance have a different environment at the interface between that substance and another than those in the bulk of the substance. (Sometimes even the composition of the surface is different from the bulk; this occurs for instance in soapy water having an interface with air.)"

"Grain boundaries and surfaces of crystalline materials have a surface free energy which in general depends on the normal direction of the interface relative to the crystal lattice(s). Determining the surface energy minimizing configurations of such interfaces, for a given surface free energy function, is an interesting mathematical problem; it reduces in the case of isotropic (i.e. constant) surface energy to the minimal surface problem. A first step is to classify minimizing cones, since they can arise as tangent cones to minimizing or asymptotically minimizing surfaces. In the isotropic case for two-dimensional surfaces in R^3, the only minimizing cones are planes. For anisotropic surface energy functions, we give here a catalog of 12 types of embedded minimizing cones, and prove that it is a complete catalog among embedded minimizing crystalline cones ..."

"Item: Retirement party for Joanne Elliott. One of my (male) colleagues reminisced about seeing Joanne as an attractive young woman in the common room at Princeton surrounded by young men eager to be near her. The comment made me very uncomfortable, since it placed emphasis on her attractiveness in a setting where conversations are often mathematical. If only the men had been clustered around her because they were eager to hear her theorems and conjectures! But at least as the story was related, that was not the case."

"The subject of motion by crystalline curvature is of interest for three quite distinct reasons. One is that some physical surface energies and physical models of crystal growth simply do give rise to such motion. Another is its use as a way to approximate motion of curves by curvature, both for computation and possibly for proving theorems. The third is that this motion simply is interesting and beautiful in its own right, having results that sometimes parallel those for ordinary curvature and sometimes are strikingly different."

"A surface free energy function is defined to be crystalline if its Wulff shape (the equilibrium crystal shape) is a polyhedron. All the questions that one considers for the area functional, where the surface free energy per unit area is 1 for all normal directions, can be considered for crystalline surface free energies. Such questions are interesting for both mathematical and physical reasons. Methods from the geometric calculus of variations are useful for studying a number of such questions; a survey of some of the results is given."

"Our knowledge of Babylonian mathematics is derived mainly from tablets in the British Museum, the Prussian State Museum of Berlin, the Ottoman Museum of Constantinople, the University of Strasbourg, the University of Pennsylvania and the Palais du Cinquantenaire of Brussels."

"In yesteryears there were two gloriously inspiring centers of mathematical study in America. One of these was at the University of Chicago, when , and and were in their prime. The other center was at The Johns Hopkins University, 1876–83, where scholars were " Led by soaring-genius'd Sylvester," as has expressed it in his " Ode to The Johns Hopkins University.""

"... in America before the end of 1888 there had been appreciable amount of mathematical research, some of it of first importance, even according to recent standards. There had been centers of mathematical inspiration. Such universities as Yale, The Johns Hopkins, and Harvard, had been sending out doctors in mathematics for a number of years, and many Americans had been getting degrees in Europe. The time was ripe for an organization to draw together many people scattered throughout the country who were especially interested in mathematical pursuits."

"About half a century after Thales came Pythagoras. Under his inspiration geometry was first pursued as a study for its own sake. A man of great ability and a most interesting and magnetic mystic, he finally settled at Crotona on the southeastern coast of Italy."

"The idea of constructing a table in which the logarithm of unity was zero originated with Napier. Napier and Briggs never thought of logarithms as exponents of a base. ... It was not till considerably later that our modern definition of a logarithm as an exponent was put forward by such mathematicians as , 1684; , 1742; , 1748, 1770."

"For more than sixty years after the publication of the Principia astronomers were puzzled to account for the motion of the lunar perigee, simply because they could not conceive that terms of the second and higher orders, with respect to the disturbing force, produced more than half of it. For a similar reason, the great inequalities of Jupiter and Saturn remained a long time unexplained."

"It was not until 1748 that any computation of the perturbations of Jupiter and Saturn, in accordance with the theory of gravitation, was undertaken. This was by . He appears to have limited himself to the terms which have the mean elongation of the planets of the planets from each other as their argument. Later the terms factored by the simple power of the eccentricities were added by himself, , , , and . But these terms not bringing about a reconciliation between observation and theory, and were led to make their notable researches on the possibility of secular equations in the mean motions of the planet. At length the whole difficulty with Jupiter and Saturn was removed by discovery of the great inequalities in 1786. almost immediately constructed tables which far exceeded in accuracy any previously possessed. They are those that appear in the third edition of Astronomie."

"The application of mathematics to the solution of the problems presented by the motion of the heavenly bodies has had a larger degree of success than the same application in the case of the other departments of physics. This is probably due to two causes. The principal objects to be treated in the former case are visible every clear night, consequently the questions connected with them received earlier attention; while, in the latter case, the phenomena to be discussed must ofttimes be produced by artificial means in the laboratory; and the discovery of certain classes of them, as, for instance, the property of magnetism, may justly be attributed to accident. A second cause is undoubtedly to be found in the fact that the application of quantitative reasoning to what is usually denominated as physics generally leads to a more difficult department of mathematics than in the case of the motion of the heavenly bodies. In the latter we have but one independent variable, the time; while in the former generally several are present, which makes the difference of having to integrate ordinary differential equations or those which are partial."

"In the papers published by Hill in the American Journal of Mathematics there is introduced for the first time a very radical and important idea. Up to this time the orbits of the moon and planets were considered as being ellipses which continually change. The problem was to find the changes in the ellipses, or the deviations from the initial ellipses. That is, the ellipse was taken as a first approximation to the orbit of the body under consideration. Hill proposed to take a certain simple type of periodic orbit as a first approximation. He proved the existence of the periodic orbits by numerically integrating the differential equations in numerous special cases by a process known as mechanical quadratures. These were the first periodic orbits of the problem of three bodies having a practical use, and the first ones known to exist beyond the simple ones which were discovered by Lagrange. It should be added that Hill omitted a small part of the disturbing action of the sun, viz., that which is said to depend upon the solar parallax; but his method would have applied without sensible modification to the rigorous problem. In fact, in all his researches, on the problem of three bodies, Darwin used methods which differ from those of Hill only in the variables employed and in inconsequential details."

"The theory of s in approximately one century old, although its origin may be traced back much further. As originally formulated by and subsequently used throughout his work, the theory was intended as a tool to be used in the study of geometric problems. After two periods of theoretical development, one in the 1930s and the other in the 1960s, there has recently been a renewed interest in exterior differential systems as providing a systematic framework for the study of geometric problems. It is my opinion that this development is just beginning, and that exterior differential systems should become a standard tool for geometers, especially for questions where the differential equations expressing the problem are overdetermined systems, and for global questions. When used properly, the theory has a marvelous ability to reveal the underlying geometry in a complicated problem."

"One of the points I have tried to make is that mathematics is extremely useful to our society. If this is true, one would think that we as a society would vigorouly support the research that leads to new uses and that students would be at an all time high. Today that is not the case. The mathematics community has yet to effectvely demonstrate to the public and their elected representatives that our subject is dfferent from the sciences. We do not design widgets or cure diseases, yet our impact on engineering and medicine is enabling and significant. But the community has dwelled so long in splendid isolation that the public poorly understands what we do."

"for a smooth algebraic curve includes both the Hodge structure (period matrix) on cohomology and the use of that Hodge structure to study the geometry of the curve, via the . extended the theory of the period matrix to smooth algebraic varieties of any dimension, defining in general a Hodge structure on the cohomology of the variety. He gave a few applications to the geometry of the variety, but these did not attain the richness of the Jacobian variety. In recent years, Hodge theory has been successfully extended to arbitrary varieties, and to families of varieties."

"The influence on mathematics of its two neighbors, physics and logic, is sometimes opposite or, at least, complementary. Whereas the entropy theorems of probability theory and mathematical physics imply that, in a large universe, disorder is probable, certain combinatorial theorems imply that complete disorder is impossible."

"... Eventually, I became a tenure-track professor at , which had a combined math department with . And then I made a big change. I quit my job and went to work as a quant for , a leading hedge fund. In leaving academia for finance, I carried mathematics from abstract theory into practice. The operations we performed on numbers translated into trillions of dollars sloshing from one account to another. At first I was excited and amazed by working in this new laboratory, the global economy. But in the autumn of 2008, after I'd been there for a bit more than a year, it came crashing down The crash made it all too clear that mathematics, once my refuge, was not only deeply entangled in the also fueling many of them. The housing crisis, the collapse of major financial institutions, the rise of unemployment—all had been aided and abetted by mathematicians wielding magic formulas."

"… techno utopia is this idea that the machine-learning tools, the algorithms, the things that help Google, like, have cars that drive themselves, that these tools are somehow making things objective and fair when, in fact, we really have no idea what's happening to most algorithms under the hood."

"For shame machines, there is nothing more profitable than a painful and intractable scourge shrouded in mystery. False promises sell, and since they don’t work, the market stays strong. Failure, in fact, is central to the dieting business model, fueling earnings for giants like and . They profit from a never-ending stream of shame-addled, self-loathing repeat customers. Weight Watchers’ former chief financial officer, Richard Samber, told ' that 84 percent of the customers failed in their diets and cycled back to the company. “That’s where your business comes from,” he said."

"The tech giants are paying millions of dollars to the operators of clickbait pages, bankrolling the deterioration of information ecosystems around the world. Shame is a potent mechanism to turn a systemic injustice against the targets of the injustice. Someone might say, “This is your fault” (for poor people or people with addictions), or “This is beyond you” (for algorithms), and that label of unworthiness often is sufficient to get the people targeted with that shame to stop asking questions."

"… In her new book, “The Shame Machine,” the writer and data scientist Cathy O’Neil, writing with Stephen Baker, examines how shame has been both commodified and weaponized by a society that is increasingly estranged from real life. Who stands to profit from our ubiquitous shame-driven culture wars? she wonders. And is there anything to be gained from them? … … O’Neil suggests that we enter treacherous waters when we start -ing people online; it is a fantasy to believe that it does anything other than enrich ."

"... She is an academic mathematician turned Wall Street quant turned data scientist who has been involved in and recently started an algorithmic auditing company. She is one of the strongest voices speaking out for limiting the ways we allow algorithms to influence our lives and against the notion that an algorithm, because it is implemented by an unemotional machine, cannot perpetrate bias or injustice."

"Black Lives Matter was a piece of genus called declarative marketing. I don't know if you've ever heard of it via products in the 1970's called "Gee, Your Hair Smells Terrific" or "I Can't Believe It's Not Butter!" was the name of the product. So the name of the product is called Black Lives Matter. How can you disagree with that?"

"Who came up with ethno-nationalism? [Is] swedes caring about Sweden ethno-nationalism? FU! You know, people have a right to be in their country without somebody saying "Oh, that's just blood and soil like from the nazis.""

"There is a jewish strategy. The great part of the jewish strategy is that most of it is pretty much open source. If you want to push your children really, really hard to survive and if you want to tell them "You've got a dragon breathing fire down the back of your neck because you've always been oppressed and you never know when you have to leave very quickly on short notice", you can duplicate the jewish experience. Good luck!"

"It is notoriously difficult to convey the proper impression of the frontiers of mathematics to nonspecialists. Ultimately the difficulty stems from the fact that mathematics is an easier subject than the other sciences. Consequently, many of the important primary problems of the subject‍—‌that is, problems which can be understood by an intelligent outsider‍—‌have either been solved or carried to a point where an indirect approach is clearly required. The great bulk of pure mathematical research is concerned with secondary, tertiary, or higher-order problem, the very statement of which can hardly be understood until one has mastered a great deal of technical mathematics."

"Early in his college days, Minsky had had the good fortune to encounter Andrew Gleason. Gleason was only six years older than Minsky, but he was already recognized as one of the world’s premier problem-solvers in mathematics; he seemed able to solve any well-formulated mathematics problem almost instantly... “I couldn’t understand how anyone that age could know so much mathematics,” Minsky told me. “But the most remarkable thing about him was his plan. When we were talking once, I asked him what he was doing. He told me that he was working on Hilbert’s fifth problem.” Gleason said he had a plan that consisted of three steps, each of which he thought would take him three years to work out. Our conversation must have taken place in 1947, when I was a sophomore. Well, the solution took him only about five more years... I couldn’t understand how anyone that age could understand the subject well enough to have such a plan and to have an estimate of the difficulty in filling in each of the steps. Now that I’m older, I still can’t understand it. Anyway, Gleason made me realize for the first time that mathematics was a landscape with discernible canyons and mountain passes, and things like that. In high school, I had seen mathematics simply as a bunch of skills that were fun to master—but I had never thought of it as a journey and a universe to explore. No one else I knew at that time had that vision, either."

"The ultimate goal of the Hindu was to free himself from the endless cycle of pain found in continual reincarnation and reconnect with the Nothingness that is the source and fundament of the All. For Indians, the void of Sunya was the very font of all- potential; nothingness was liberation. No surprise then that it is from this sophisticated culture that we inherit the mathematical analog of nothing, zero"

"In 1972 announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions."

"A major difficulty in trying to construct a proof of RH through analysis is that the zeros of L-functions behave so much differently from zeros of many of the s we are used to seeing in mathematics and mathematical physics. For example, it is known that the zeta-function does not satisfy any differential equation. The functions which do arise as solutions of some of the classical differential equations, such as s, s, etc., have zeros which are fairly regularly spaced. A similar remark holds for the zeros of solutions of classical differential equations regarded as a function of a parameter in the differential equation."

"The Riemann Hypothesis is a statement about a deep connection between addition and multiplication that we do not yet understand."

"The duality theorems for a manifold will be derived from the corresponding ones for nets and co-nets of group systems ... Of the two types of duality theorems — the and s — the first could be obtained more easily from the corresponding one for a group system and its character system ... But when applied to the Alexander type this method fails. Also in using the net and co-net theory for both types, the less complicated Poincaré theorem serves as an introduction for the Alexander theorem."

"... I think Walther Mayer got a designation that has never been used for anyone else. He was the only associate professor the Institute has ever had. He was called "associate professor." Yes, and the reason was: Einstein wanted him very much. Clearly the mathematicians did not feel that he really should be a full-fledged faculty member. This was at an early stage, so they took a designation that was used in American universities. Only later did it occur to them to create a new thing called "permanent member.""

"Sometimes the bishop risks focusing only on the local dimension. But a bishop should have a much broader vision of the Church and reality, and experience the universality of the Church. He also needs the ability to listen to his neighbour and seek advice, as well as psychological and spiritual maturity. A fundamental element of the portrait of a bishop is being a pastor, capable of being close to the members of the community."

"Q: Can the process for the appointment of new bishops be improved? Praedicate Evangelium states that "members of the people of God" must be involved. Is this happening? A: We had an interesting reflection among the members of the Dicastery on this issue. For some time now, not only some bishops or some priests, but also other members of the people of God are being heard. This is very important, because the bishop is called to serve a particular Church. Therefore, listening to the people of God is also important. If a candidate is not known by anyone among his people, it is difficult—not impossible, but difficult—for him to truly become pastor of a community, of a local Church. So, it is important that the process is a little more open to listening to different members of the community. This does not mean that it is the local Church that has to choose its pastor, as if being called to be a bishop was the result of a democratic vote, of an almost ‘political’ process. A much broader view is needed, and the apostolic nunciatures help a lot in this. I believe that, little by little, we need to open up more, to listen a little more to the religious, the laity."

"Interviewer: You are an Augustinian. How does Augustinian spirituality characterise your ministry? Cardinal Prevost: We could say several things... As my episcopal motto suggests, unity and communion are part of the charism of the Order of Saint Augustine and also of my way of acting and thinking. I think it is very important to promote communion in the Church, and we know well that communion, participation and mission are the three key words of the Synod. So, as an Augustinian, promoting unity and communion is fundamental for me. St Augustine also speaks a lot about unity in the Church and the need to live it, about the fact that there is a certain guarantee of unity in listening to the Bishop of Rome, in being part of the Church of Rome. In this sense too, therefore, I feel that the Pope's new call is a way of living my unity and participation in the Church, in obedience to the Holy Father. This too is very Augustinian. Interviewer: How much does the figure of Augustine inspire your choices, your steps, your service in the Church? Cardinal Prevost: St Augustine is certainly a great figure not only for the order but for everyone. I wish I had more time to study and read him. He has so much to offer the Church, even the Church of today. Then there is what I said before: unity in the Church and fidelity to the Bishop of Rome, always seeking to promote communion. Living unity in the Church, as Augustine recommends, means living united in Christ."

"A bishop must not be a little prince sitting in his kingdom."

"Pope Francis has spoken of four types of closeness: closeness to God, to brother bishops, to priests and to all God's people. One must not give in to the temptation to live isolated, separated in a palace, satisfied with a certain social level or a certain level within the church. And we must not hide behind an idea of authority that no longer makes sense today. The authority we have is to serve, to accompany priests, to be pastors and teachers."

"I always had the impression of a man who wanted to live the Gospel authentically, consistently. In the days when I was Prior General of the Augustinians, several times during visits to my brothers in Argentina, when he was still a cardinal, I had the opportunity to meet him and speak with him, informally and on more institutional matters'."

"Even today, there are many contexts in which the Christian faith is considered absurd, for weak and unintelligent people; contexts in which other forms of security are preferred, such as technology, money, success, power, and pleasure. These are environments where it is not easy to bear witness to and proclaim the Gospel, and where believers are mocked, opposed, despised, or at best tolerated and pitied. Yet, precisely for this reason, they are places where mission is urgent, because the lack of faith often brings with it tragedies such as the loss of the meaning of life, the forgetting of mercy, the violation of human dignity in its most dramatic forms, the crisis of the family and other wounds from which our society suffers greatly."

"(Meeting the cardinals in Vatican) Dear brothers, I would like to conclude this first part of our meeting by making my own – and proposing to you as well – the wish that Saint Paul VI expressed at the beginning of his Petrine Ministry in 1963: ‘May it pass over the whole world like a great flame of faith and love, kindling all people of good will, illuminating the paths of mutual cooperation, and drawing upon humanity, again and always, the abundance of divine favours, the very strength of God, without whose help nothing is valid, nothing is holy.’"

"Trusting in the assistance of the almighty, I pledge to continue and strengthen the Church’s dialogue and cooperation with the Jewish people in the spirit of the Second Vatican Council’s declaration Nostea Aetate."

"The Universal Declaration of Human Rights , approved and proclaimed by the United Nations on 10 December 1948, is now part of humanity’s cultural heritage. That text, which is always relevant, can contribute greatly to placing the human person, in his or her inviolable integrity, at the foundation of the quest for truth, thus restoring dignity to those who do not feel respected in their inmost being and in the dictates of their conscience."

"We continue to follow carefully and with hope the developments in Iran, Israel and Palestine. The words of the prophet Isaiah resound with urgent relevance: “Nation shall not lift up sword against nation, neither shall they learn war any more” (Is 2:4)."

"Today we desolately witness the unjust use of hunger as a weapon of war. Starving the population is a very cheap way of waging war. That is why today, when most conflicts are not fought by regular armies but by groups of armed civilians with few means, burning land, stealing livestock, blocking aid are tactics increasingly used by those who wish to control entire defenceless populations. Thus, in this type of conflict, the first military targets become the water supply networks and communication routes.Farmers cannot sell their produce in contexts threatened by violence and inflation skyrockets. This leads to huge numbers of people succumbing to the scourge of hunger and dying, with the aggravating factor that, while civilians are weakened by misery, the political summits grow fat on corruption and impunity."

"(Concerning Nostra Aetate) And so I, too, confirm that the church does not tolerate antisemitism and fights against it, on the basis of the Gospel itself. We cannot deny that there have been misunderstandings, difficulties and conflicts in this period, but these have never prevented the dialogue from continuing. Even today, we must not allow political circumstances and the injustices of some to divert us from friendship, especially since we have achieved so much so far. Even in these difficult times, marked by conflicts and misunderstandings, it is necessary to continue the momentum of this precious dialogue of ours. Never in the relationship of Catholics and Jews since ‘Nostra Aetate’ has the Jewish people been more in need of friends who commit themselves to combating antisemitism with every fiber of their being. The Catholic Church has one of the largest megaphones available. It has moral suasion that is unparalleled. We hope that they will use all of the tools in their arsenal to double down in that effort."

"Do you know how many stars there are in the observable universe? An impressive and marvellous number: a sextillion stars – a 1 followed by 24 zeros! If we divided them among the 8 billion inhabitants of Earth, each person would have hundreds of billions of stars to themselves. With the naked eye, on clear nights, we can see about five thousand of them. However, they show us a direction, just like when sailing at sea. Travellers have always found their way using the stars. Sailors followed the North Star; Polynesians crossed the ocean by memorising star charts. According to the farmers of the Andes, whom I met as a missionary in Peru, the sky is an open book that marks the seasons of sowing, shearing, and the cycles of life. Even the Magi followed a star to get to Bethlehem and worship the Baby Jesus."

"Being a good shepherd means being able to accompany God's people and live close to them, not being isolated. Pope Francis has said this clearly many times. He does not want bishops who live in palaces. He wants bishops who live in relationship with God, with the rest of the episcopate, with priests and, above all, with the people of God in a way that reflects the compassion and love of Christ, creating community, learning to live what it means to be part of the Church in an integral way that includes much listening and dialogue."

"The priorities of pastoral work will always be different in one place or another, but recognising the great richness of the diversity of the People of God is tremendously helpful because it makes us more sensitive to reaching out and responding better to what is expected of us."

"Ideologies have become more powerful than humanity's real experience, faith, and the different values we live by. Some will misunderstand unity as uniformity: ‘You must be like us.’ No, it cannot be so. Nor can diversity be understood as a way of living without criteria or order. The latter lose sight of the fact that since the very creation of the world, the gift of nature, the gift of human life, the gift of so many different things that we experience and celebrate, cannot be sustained by inventing my own rules and doing things my way. These are ideological positions. When an ideology becomes, so to speak, the master of my life, then I can no longer dialogue with another person because I have already decided how things will be. Therefore, I am closed to encounter and transformation cannot take place. And this can happen anywhere in the world, on any subject. This obviously makes it very difficult to be Church, to be community, to be brothers and sisters."

"One of the things that comes to mind when I think of St Augustine, his vision and his understanding of what it means to belong to the Church, is what he says about not being able to say you are a follower of Christ without being part of the Church. Christ is part of the Church. He is the head. So anyone who thinks they can follow Christ ‘in their own way’ without being part of the body is, unfortunately, a distortion of what is an authentic experience. St Augustine has an omnipresent wisdom that helps us to live in communion. Unity and communion are essential charisms of the life of the Order and a fundamental part of understanding what the Church is and what it means to be in the Church."

"Perseverance is a great gift that the Lord is ready to offer us. But we must learn to welcome it and make it come alive, to be strong. It is one of those gifts that are built up over time, in the small trials of the beginning that help us to be stronger, to be able to carry the Cross when it becomes heavier. It is what enables us and makes us capable of moving forward."

"°I consider myself an amateur tennis player. [...] I really enjoy reading, going for long walks, travelling, seeing new places and enjoying the countryside in a different environment. I like to relax with friends and get to know people who are so different from me, whose gifts I learn from and appreciate greatly."

"Peace be with you all! Dear brothers and sisters, this is the first greeting of the Risen Christ, the good shepherd who gave his life for the flock of God. I too would like this greeting of peace to enter your heart, to reach your families, to all people, wherever they are, to all peoples, to all the earth. Peace be with you! This is the peace of the Risen Christ, an unarmed peace and a disarming, humble and persevering peace. He comes from God, God who loves us all unconditionally."

"We still keep in our ears that weak but always courageous voice of Pope Francis who blessed Rome! The Pope who blessed Rome gave his blessing to the world, to the whole world, that morning of Easter Day. Allow me to follow up that same blessing: God loves us, God loves you all, and evil will not prevail! We are all in God’s hands. Therefore, without fear, united hand in hand with God and we move forward with each other. We are disciples of Christ. Christ is before us. The world needs its light. Humanity needs Him as the bridge to be reached by God and His love. Help us too, then one another to build bridges, with dialogue, with encounter, all by uniting us to be one people always at peace. Thank you to Pope Francis!"

"I also want to thank all my brother cardinals who chose me to be Peter's successor and to walk with you as a united Church, always seeking peace, justice, always trying to work as men and women faithful to Jesus Christ, without fear, to proclaim the Gospel, to be missionaries."

"I am a son of St. Augustine, an Augustinian, who said: “I am a Christian with you and a bishop for you.” In this sense we can all walk together towards that homeland that God has prepared for us. A special greeting to the Church of Rome! We must seek together how to be a missionary Church, a Church that builds bridges, dialogue, always open to receive like this square with open arms. All of them, all those who need our charity, our presence, dialogue and love."

"To all of you, brothers and sisters of Rome, of Italy, of the whole world, we want to be a synodal Church, a Church that walks, a Church that always seeks peace, that always seeks charity, which always seeks to be close especially to those who suffer."

"Today is the day of the Supplication to the Madonna of Pompeii. Our Mother Mary always wants to walk with us, to be close, to help us with her intercession and her love. Then I would like to pray with you. Let us pray together for this new mission, for the whole Church, for peace in the world and let us ask this special grace from Mary, our mother."

"Brother Cardinals, I greet and thank you all for this meeting and for the days that preceded it, days that were painful because of the loss of the Holy Father Francis, demanding because of the responsibilities we face together, and at the same time, according to the promise Jesus himself made to us, rich in grace and consolation in the Spirit. Your presence reminds me that the Lord who entrusted this mission to me does not leave me alone in bearing its responsibility. I know, first of all, that I can always, always count on his help, the help of the Lord, and, by his grace and providence, on your closeness and that of so many brothers and sisters throughout the world who believe in God, love the Church, and support the Vicar of Christ with their prayers and good works."

"God's charity, which makes us brothers and sisters, is at the heart of the Gospel, and with Leo XIII, we can ask ourselves today: if this criterion ‘were to prevail in the world, would not all strife cease and peace return?’ (Encyclical Letter Rerum novarum, 21). With the light and strength of the Holy Spirit, let us build a Church founded on God's love and a sign of unity, a missionary Church that opens its arms to the world, proclaims the Word, allows itself to be unsettled by history, and becomes a leaven of harmony for humanity. Together, as one people, as Fratelli tutti [brothers and sisters], let us walk towards God and love one another."

"With great joy I extend my cordial greetings to all of you, Representatives of other Churches and Ecclesial Communities, as well as of other religions, who participated in the inaugural celebration of my ministry as Bishop of Rome and Successor of Peter. [...] One of the strong emphases of Pope Francis’ pontificate was that of universal fraternity. In this regard the Holy Spirit really “urged” him to advance with great strides the initiatives already undertaken by previous Pontiffs, especially since Saint John XXIII. The Pope of Fratelli Tutti promoted both the ecumenical path and interreligious dialogue. He did so above all by cultivating interpersonal relations, in such a way that, without taking anything away from ecclesial bonds, the human trait of the encounter was always valued. May God help us to treasure his witness! [...]"

"In order to feed the thousands of people who came to listen to him and to ask for healing, Jesus invited the Apostles to bring him what little they had; he then blessed the loaves and fishes, and told them to distribute them to everyone. The result was astonishing: not only did everyone receive enough food, but there was an abundance left over … Beyond being a marvel, the miracle is a "sign" that reminds us that God’s gifts, even the smallest, grow whenever they are shared. Reading this on the day of Corpus Christi, however, leads us to reflect on an even deeper reality. For we know that at the root of every human sharing lies a greater sharing that precedes it, namely God’s sharing with us."

"Let us think of how wonderful it is when we give a gift — even a small one, proportionate to our means — and see that it is appreciated by the recipient; how happy we are when the gift, despite its simplicity, unites us even more to those we love. Indeed, what happens between us and God through the Eucharist is precisely that the Lord welcomes, sanctifies and blesses the bread and wine that we place on the altar, together with the offering of our lives, and he transforms them into the Body and Blood of Christ, the sacrifice of love for the salvation of the world. God unites himself to us by joyfully accepting what we bring, and he invites us to unite ourselves to him by likewise joyfully receiving and sharing his gift of love."

"Alarming news continues to emerge from the Middle East, especially from Iran. Against this tragic backdrop, which includes Israel and Palestine, people’s daily suffering, especially in Gaza and the other territories, where the need for adequate humanitarian aid is becoming increasingly urgent, risks being forgotten."

"Today more than ever, humanity cries out and calls for peace. This is a cry that requires responsibility and reason, and it must not be drowned out by the din of weapons or the rhetoric that incites conflict. Every member of the international community has a moral responsibility to stop the tragedy of war before it becomes an irreparable chasm. There are no "distant" conflicts when human dignity is at stake."

"War does not solve problems; on the contrary, it amplifies them and inflicts deep wounds on the history of peoples, which take generations to heal. No armed victory can compensate for the pain of mothers, the fear of children, or stolen futures. May diplomacy silence the weapons! May nations chart their futures with works of peace, not with violence and bloodstained conflicts!"

"Please join me in thanking Our Lord for the election of Pope Leo XIV, Successor of St. Peter, as Shepherd of the Church throughout the world.The Shrine of Our Lady of Guadalupe in La Crosse has a particularly strong bond with the Roman Pontiff, especially through its affiliation with the Papal Basilica of St. Mary Major. I urge all pilgrims and friends of the Shrine to pray fervently for Pope Leo XIV that Our Lord, through the intercession of Our Lady of Guadalupe, St. Peter the Apostle and Pope St. Leo the Great, may grant him abundant wisdom, strength and courage to do all that Our Lord asks of him in these tumultuous times. May God bless Pope Leo and grant him many years."

"I don't think I'm revealing any secrets when I write that a long and warm round of applause followed that ‘I accept,’ which made him the 267th Pope of the Catholic Church. [...] I met Cardinal Prevost years ago, in connection with a thorny issue involving the Church in Peru. Even then, I saw in him a sense of balance, calmness, love for people and attention to detail. [...] Pope Leo XIV, he continues, is well aware of the world's problems, as he demonstrated from his very first words from the Loggia, evoking a ‘disarmed and disarming’ peace. [...] I am certain that he will find strength in the grace of the Lord, in his experience as a religious and in the example of the great Father Augustine, whom he mentioned in his first speech. We are close to him with our affection, our obedience and our prayers."

"I met Leo XIV in Peru, and I was struck by his serenity. He is the right man to lead the Church."

"This morning's meeting went very well. We also discussed the need to make the Church more collegial. He is an excellent Pope and received well over 100 votes."

"It’s shocking, mind-numbing, mind-blowing. How do you describe that? I don’t know. I still haven’t figured out how to tell anybody what I feel, other than out of my head, crazy with happiness, pride, joy, love for my brother.When he made his appearance, then it became real. It’s one thing to hear the name, but when Rob came out onto the balcony and we saw him, it just brought tears to my eyes. You know that’s my little brother. He’s now pope. I don’t know how to describe it spiritually. He was special. When we were kids and went to play games, he wanted to play priest. How many little kids want to play priest, you know? As soon as he got out of eighth grade, he went directly into the seminary. It was like he knew what he wanted to do, and more power to him, and he’s been quite successful at it, right?"

"Two events related to clergy sexual abuse have touched the figure of Prevost. The first dates back to the early 2000s, when, as Augustinian provincial in Chicago, he was involved in a case of hospitality to a priest already convicted of paedophilia. The second, more recent, concerns his episcopate in Peru: he allegedly handled an investigation into two priests accused of molestation with little transparency."

"Sinner: The ball, there it is. If you want to play a little. Pope Leo XIV: But we'll break something here! We'd better not."

"It will be a pontificate in continuity with the magisterium of Pope Francis. I am very happy about that. This is what the majority of the cardinals wanted ... but with a style of their own. [...] Pope Leo XIV, in his first message, spoke of a “synodal Church.” Having participated in the work of the Synod, we have a Pope who knows synodality, who understands it, who dares to be synodal. There will not be a revolution, but an evolution."

"When a student picks a research topic, the decision is influenced by the research interests of the advisor, the state of the field in which the problem lives, the personality of the advisor, the chemistry between them ... who else in working on whichever problem. It's immensely complicated. And asking for a sort of simple prescription for how to assign research problems — it reminds a little of the question of how to decide who should marry whom."

"First of all, there are problems that no one knows how to solve. There are problems that have been studied but untouched, or problems on which there is partial progress. There are problems that sound compelling when formulated, but which no one has thought of yet. There are concepts which are very useful in solving problems .. or which perhaps ... sound very natural and compelling when formulated, but have not been formulated yet. And all of these things interact. So, by solving problems, one is led to concepts — and, by thinking about concepts, one is led to problems."

"Charles Fefferman (Charlie) is a mathematician of the first rank whose outstanding findings, both classical and revolutionary, have inspired further research by many others. He is one of the most accomplished and versatile mathematicians of all time, having so far contributed with fundamental results to harmonic analysis, s, , , quantum mechanics, fluid mechanics, and , together with more sporadic incursions into other subjects such as neural networks, financial mathematics, and crystallography."

"That geometric considerations enter in a decisive way in many questions of harmonic analysis is by now a well-known fact. In explicit form such ideas arose first in the estimation of the of surface-carried measure; they have since played a key role in averages over lower-dimensional varieties, restriction theorems, in connection with the study of s and Fourier integral operators, and in application to linear and non-linear s."

"(edited by Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, and Vital D. Milman; quote from p. 434)"

"What I like about mathematics is the interplay with other people. And that generates extra energy — because it really helps you think."

"Working with Eli Stein is amazing. There are good teachers and there are great teachers — and then there is Eli. He was simply the best teacher, I believe, of advanced math, I believe, in the whole world, by far. ... he conveyed a spirit of optimism. ... He has a wonderful style of explaining math — in which almost all of the effort of explanation goes into finding the right point of view and getting the essence of the problem."

"This booklet had first an elementary explanation of the geometry of Zonohedra, then a more difficult account of the growths of the thirty-one zone star. This system, based on the 31 lines that pass through the center of an and either a vertex, edge midpoint of face midpoint is new and unusual."

"I have applied for a patent on this structural system. The patent is assigned to Zomeworks Corporation. The predecessors of this system are the octet truss and the MERO space grid system. The relative potentials of these systems are discussed briefly by a comparison of their geometric possibilities."

"The forms possible using this system are limitless; there is no attempt here to explore these possibilities—the examples shown are small probings. The booklet describes the mathematics of the process that creates these limitless forms."

"Zomes can cluster together like soap bubbles. Their zones can be stretched, shrunk, or omitted completely to make the various zomes' different shapes and sizes. The zomes can also pack several layers deep."

"The , because of its shape and the arrangement of its structural members is extremely strong, but its uses are limited because of the inflexibility of its shape. It is always part of a sphere... any variation would destroy the structural properties... It is complicated in structure and simple in shape. Zomes are simple in structure and complicated in shape."

"The regular polyhedra are like seeds from which growths may appear. They are the connecting joints for the zonohedra."

"Zonohedra have bands of parallel edges. Any such band... can be stretched to alter the shape of the zonohedron. Stretching the band... does not alter any angles."

"Stretching zones allows... buildings of different shapes using the same kinds of components."

"The and the are duals of each other—the vertices of one match the face midpoints of the other and vice versa."

"The icosahedron and the dodecahedron have five fold symmetry. They cannot occur as crystals."

"Five fold symmetry does appear among other symmetries in nature."

"[[w:Recursion|[R]ecursive]] growth... In the case of... five fold symmetry there isn't uniformity. ...Instead of reproducing itself... it becomes steadily more intricate."

"The more you examine properties of objects and phenomena the more you find yourself presented with a few terms, usually simple, from a long series of terms. Often you cannot touch the terms which are further or lower in the series, but you can define the properties which they have. One gets the feeling of living in a container—one of an infinite number—to which are shunted objects and phenomena which have passed through one filter but can't pass through another; a great process like that which takes place in a gravel yard, only we are unable to see gravel other than that of our own size but sense that it exists in endless different piles beyond—everything from sand to planet sized boulders."

"The coherence proof demonstrates that if one builds a structure using the A and B lines of the 31 zone star (...C lines ...used only within ...forms defined by ...A and B lines) and always follow the rule... no matter how far or intricately one builds, two extensions of two entirely different limbs of the same structure can always be locked back together in a perfect fit with a combination of our simple parts."

"We have associated the thirty-one zone star throughout with the icosahedron and... dodecahedron. It also fits perfectly with the three smaller regular polyhedra. The , the and the fit inside the icosahedron and... dodecahedron. Their vertices touch a vertex, an edge midpoint or a face midpoint of the larger figure. This regular match... positions the smaller figure so that regular patterns on the large figure project inwards as regular patterns on the small figure. In each case either five or ten small figures fit at once within the larger..."

"Each of the regular polyhedra is thus a convenient core from which to define the regular thirty-one zone star. The geometric regularities insure simplicity in the connections. Any one of the regular polyhedra can be used with the same pattern of flanges or holes on each of its faces as a connector for the thirty-one zone structural system."

"The joint must... be strong and inexpensive. If the joint is a ball and the A, B and C connections are... holes which the members screw into... holes of the same type... and the ends of all structural members are identical. ...[Y]ou can't make mistakes..."

"There is a mistake-proof flange joint for both A and C connections if one hierarchy is introduced. You must always orient the joint to suit A lines."

"I went to in Massachusetts for a couple of years and I went to UCLA for a year or two and then I went back to Amherst... I never quite fit... that... college thing. ...I joined the Army in 1960 and got married and Holly and I went to Germany... after I got out of the Army, I went to school in ."

"Holly had... toys made from polyhedra and she built one of these things and... it... blew my mind... I... found some mathematics books that described the geometry of polyhedra and convex figures. This wasn't too difficult since I had always been fascinated by math. It was the subject I had spent the most time on in school and... was studying at the time."

"[W]e left and... moved to Albuquerque where I worked as a surveyor and... welding trailer frames for Fruehof and Holly had a job and we didn’t spend much... I began to experiment more and more with structures."

"I found out that the people at were building domes and I went up there and helped... Then they came down and helped me. ...We built the first structures from car tops. We chopped the tops out of over a thousand cars... ...[W]e paid 25 cents apiece for them. ...They’re a good building material ...except that getting stuff from junkyards ...is ...bad for your ...mentality. You... become a parasite on something you criticize... You’re feeding on something you hate."

"We built and did solar heating experiments... solar heated a dome in 1967 with a big chimney—a rock storage bin—down the side of a hill. Many of those first things didn’t... work... well. I didn’t know what I was doing."

"I read this book of ’, Direct Use of the Sun’s Energy, and it just lit up my brain."

"When you start experimenting with, say, solar heating by covering collectors with glass or plastic and feeling the warm air blow out of them... well, it’s so exciting that you just get hooked and can’t stop."

"[W]e started Zomeworks. Barry Hickman and Ed Heinz and I issued stock like a corporation and got a lawyer... [I]t was quite an abrupt change from just casually working together on a project the way we had before."

"We started making playground climbers–using the 31–zone truss which is... explained in the Zome Primer –and... we were working on solar heating experiments."

"Right after we started Zomeworks, Day Chahroudi came out from California. He’d read the Dome Cookbook and he came walking up the road one afternoon with a rucksack on his back. ...[W]hen he started telling me his ideas about how things worked—physics ...I was so impressed by his ...approach to engineering problems that I persuaded him to stay ...He did and ...soon he developed a solar tracker... very simple and easy to build."

"So many... good ideas... worked... but they couldn’t keep working. Some of the first buildings we put up weren’t good buildings because they leaked. Many of those first solar heaters weren’t... very good..."

"Some of our hardware is getting pretty good, but it... doesn’t make economic sense for most people. ...[O]ur zomes and heaters and so forth do not yet compete on a dollar basis with... conventional counterparts. It’s very exciting intellectually to work with these ideas but their validity will not really be proven until they start to replace... things they’re meant to replace."

"[W]e haven’t had the money... to tool up to manufacture the parts for the playground climbers on a competitive basis. The people... simply can’t afford to buy them. ...[T]hey just can’t hold their own in the market and so we’re not building them anymore."

"The Skylid has no switches or wires or motors... Instead, the unit contains a series of louvers. Each... is supported and balanced so that it hinges easily around its center and... the louvers are connected with a tie rod so they’ll open and close simultaneously. ...[M]ounted on one of the panels are two canisters—one on the outside and one inside ...connected by ...tubing. ... ...with a very low ...can expand ...in one canister and ...condense in the other with a temperature difference of... 1 degree Fahrenheit. This shifting of the Freon’s weight will open and close the... louvers... and the... sun—even the shade of a cloud—produces... enough temperature variation to boil the Freon from one container to the other. ...[A] locking chain... secure[s] the panels anywhere from full open to full close... to override the automatic mechanism."

"I want to build buildings and design systems that are beautiful and simple and that really work. ...It’s not ...exotic or earthshaking to fill 55-gallon drums with water, paint them black and place them in the walls of a home for use as solar collectors ...but it works."

"[T]he philosophical tactics and... approach taken by the giant corporations and... power groups miss the point... A pencil can break on you and you can sharpen it with your thumbnail and go right on... but if a circuit board or a resistor or condenser quits somewhere inside this recorder, we’re stopped and there’s probably not a lot we can do about it. ...[Y]et we increasingly use tape recorders instead of pencils."

"At one time an individual could fix everything in his life with his thumb nail or his teeth. ...I believe the ground rules can be transformed so that technology simplifies life instead of continually complicating it."

"I don't think that building everything out of stones and living in animal skins is necessarily... healthier... I'm saying... life can be much more satisfying for an individual if he feels that he is in control of his destiny... Society and the tools of society, should be organized to give each one of us that feeling."

"[W]hen I was... 18 I... read... Lewis Mumford and... [saw] that... we could have a science and technology... understood and controlled by the individual instead of the other way around. ...I've been trying to crack the crap in science for 15 or 16 years now."

"Peter Van Dresser... built a solar heater here in New Mexico in 1956 or '58. We published his book, Landscape for Humans. One of the greatest forces... has been Harold Hay from California. ...I ...heard him in ’68 at the Solar Energy Conference. I had... a design and... modest success... Harold showed everyone... dead simple methods of doing the same job. He... completely changed my head around on how to attack these problems. ...[W]e’ve worked together a lot since then trying to bring some reforms into the Solar Society."

"[W]hen you're experimenting, about 80% of the ideas you try are failures... But we put all these concepts together and they performed the first time. ...[W]e had pretested most of the ideas we incorporated into this [our] home. We'd never used aluminum-skinned, honeycomb-cored structural sandwiches and... no one had... fabricated a complete building from the material... but every architectural and engineering book mentions the possibility... The 55-gallon, water-filled drums... [W]e... knew the amounts of energy... such... could pick up."

"[T]here's Dave Harrison's bead wall. I teach... classes at the University of New Mexico and Dave... one of my students... said. "...I've got this idea of building a wall out of two panes of glass... and you can blow Styrofoam beads between the panes at night to insulate the wall." ...Here's a problem ...nobody has thought of a way to solve. I've tried... and... Harold Hay has... and... a lot of others... Dave Harrison has the answer! ...[A] ...low-tech ...answer ...simple ...easy to understand, that a heating and ventilating man in any town can fix... [W]e’ve made a deal with Dave so that he’ll get a big part of any royalties we realize..."

"[T]he beadwall insulated window panels... this wonderful invention of David C. Harrison’s... a kind of super curtain that... transform[s] a clear dual-panel of glass into an opaque, well-insulated wall and back again."

"We’ve built two greenhouses utilizing the beadwall, and our test results show... it will do much of the heating and cooling required by an average office building or home."

"[W]ith its unique construction—there are never any air leaks."

"[I]f folks don’t like the idea once they’ve given it the once-over, we’ll be glad to buy the plans back at the full $15.00 purchase price."

"A few years ago Peter Van Dresser mentioned the Clothesline Paradox."

"Solar energy advocates are continuously humiliated by being shown "energy pies." Slices are assigned to coal, gas, oil, hydroelectric and even nuclear. but is evidently too small to appear."

"If you... remove the electric clothes dryer and install a clothesline the consumption of electricity drops slightly, but there is no credit given anywhere on the charts and graphs to solar energy which is now drying clothes."

"[C]oal, oil and natural gas are all solar energy products... and hydroelectric power is solar energy..."

"The graphs which demonstrate a huge dependence on fossil fuels are fine in one respect. They are alarming. But they are... [m]isleading... [in] that they blind people to obvious answers and prime them to a frenzy of effort in poor directions. Attention... to such... trains people to attempt to deliver what is shown in these accounting systems rather than what is needed."

"If you... ride and graze a horse... the horse's energy... does not appear on anyone's energy accounting."

"If you install interior greenhouse lights the electricity... is faithfully recorded. If you grow the plants outside no attempt is made at an accounting."

"If you drive to... buy a newspaper the gasoline consumption appears. If you walk—using food energy—the event has disappeared from sight..."

"The 's energy study shows the U.S.'s energy consumption in 1968 at... 62 quadrillion BTU ...[T]he average daily caloric intake is... 10,000 BTU/day/person—about 1.2% of the total consumption listed by the Bureau of Mines. But this... doesn't appear... on the graphs. Nuclear energy with 1% does... The food is solar energy. Why is it not included?"

"If we use the figure of 0.5% efficiency (Ayres and Scarlott)... we have consumed... 2,000,000 BTU/person/day of sunlight in producing the 10,000 BTU/person consumed. Solar energy then fills over 2/3 of the new energy pie."

"Why wouldn't it be fair to expand the slice—4% (1973—Bureau of Mines) given to hydroelectric power by a similar factor of efficiency—for the solar energy consumed in raising the water to its working head?"

"Every time the sun shines on the surface of a house and especially when it shines through a window there is "solar heating"...According to the NSF/NASA Energy Panel of 1972 the percentage of thermal energy for buildings supplied by the sun was too small to be measurable. ...Shouldn't we recalculate the energy consumption of every building assuming it were kept in the shade all day and... attribute the difference to solar energy? ...I would guess the average shaded fuel consumption to be 15% higher..."

"[O]ur next concern in heating the building is what keeps the earth warm..? What supplies the United States with the energy to maintain an average temperature of 60 degrees Fahrenheit as it spins in empty space at absolute zero? This is a heating contract that no oil company would be quick to try and fill."

"[I]t is very important to examine what the limits of an accounting system are—to know what the numbers and quantities... really mean."

"The design of houses can be stilted by such graphs."

"Now that the experts have started this infantile accounting system, which evidently finds us... independent of the sun, solar energy will be admitted only so long as it has been properly collected, stored and transferred."

"Legislation aimed at encouraging the use of solar energy equipment by subsidizing... certain hardware must end by being pathetic and blundering."

"It would take an enormous crew of experts to determine the efficiency of different orientations of windows, different arrangements of shade trees, etc... To ignore these efforts and only to reward the purchase of "off the shelf hardware" is to further the disease of narrow minded quantification."

"If you purchase certain kinds of hardware to exploit solar energy it will be accounted for and credit will be given to the sun. If you depend on more customary old-fashioned uses of solar energy, growing food, drying clothes, sun bathing, warming a house with south windows, the sun credit is totally ignored."

"Our present accounting system... can only discourage good house design. If the natural solar contribution to house heating from windows is ignored, then the designer knows this... No tax incentives—no credit to the sun in ERDA's graphs."

"[W]e would be much better informed if alongside every graph showing our use of oil, coal and uranium there were also an indication or the total energy received from the sun. Since we can't do without it, let's not omit it from our accounts."

"In the case of the United States a conservative estimate of the solar energy received in one year might be... Twenty nine thousand three hundred quadrillion Btu as opposed to the 62 quadrillion shown as used during 1968 by the U.S. Bureau of Mines."

"When small children first start paying attention to... their allowances they briefly commit their... minds to their few coins and... chores... without... considering the budget of the family's household. We can't allow our entire civilization to be similarly ignorant for long. We must ask who's keeping score and why they have such peculiar methods."

"The great problem with movable insulation is cracks. A door, shutter, or curtain is placed... The optimist notes the R value... but does not achieve it."

"The effect of clothes and blankets on heat loss is naturally investigated by everyone."

"A sniper scope or camera... that shows... temperatures as... colors would be an enormous help to the investigator. 30 minutes with such... could be as valuable as a week's work... without it. ...[N]ature ...treats you to such a view of the window or skylight with a pattern of frost. ...[S]eals ...[are] the entire problem."

"A crack... of 2 in2/ft2... can conduct 1/3 Btu/ft2hr°F."

"If you... have cracks... torture the air... by pressing the insulation panel... against the glass... air... must then spread in a thin film... Experimenting with smoke... once this layer is less than 1/16"... it is slowed... and acts almost like a syrup."

"Treat a glass area like a ship—break it into separate compartments so that a leak in one place won't be fatal."

"A [1974] test on conventional window shades showed... 1) A roller shade inside a with 1/4" gaps at the sides of the shade reduced heat loss through a single glazed window by about 28%. 2) A drape drawn in front of the... window reduced heat loss by about 6%. 3) A venetian blind reduced heat loss by 7%.During the summer the shading devices reduced heat gain by the following... 1) white, opaque roller shade 50% 2) venetian blinds (slats at 45%) 18% 3) venetian blinds (slats closed) 29%"

"Tests done at Zomeworks on 45° sloped skylights with our insulating Skylids installed beneath a single pain of glass show a reduction of heat loss of about 75%... The louvers average 3" thick, have aluminum skins and are filled with figerglass—most of the heat loss occurs through air leaks..."

"The Beadwall seems to be the perfect answer for superior insulation against heat loss."

"Tests done by thermal decay of a glass aquarium show a U factor of the naked glass of about 1 1/3 and of the glass covered with Nightwall, of about 1/3."

"Movable insulation can... be used to prevent heat gain. ...[T]he best position ...is outside the glass rather than inside."

"A particularly attractive use of insulating panels is to have them double as reflectors—during the day they bounce additional energy through the same window they will insulate at night. Often it is most cost-effective to have a movable reflector outside a south window or skylight that is changed seasonally... not daily."

"SUMMARY 1) It is best to have a way to prevent both heat gain and heat loss. 2) Be skeptical of mechanical seals. 3) Do not use single glazing unless it is a mild climate or the movable insulation is controlled by a reliable automatic means. 4) Do not install anything you cannot fix. 5) Look for two uses for one material. 6) Break the area to be insulated into pieces so that an air leak in one area will be isolated. 7) Always use strong, durable materials outside."

"[I]t's more satisfying to develop and manufacture less expensive items which pay for themselves. It makes me sleep better at night."

"The tendency is not to care about spending somebody else's money—so even at this time when we're supposed to be conserving energy we're instituting policies that make people conserve less."

"ZW is a privately owned corporation. We are not supported by federal grants. We depend on your business for support."

"You don't need to have a [government energy] policy... there already is a policy—it's each individual's policy. We need the government for some things like the armed forces, but not in the marketplace."

"We don't have a shortage of fuel... gas is still cheap and we have an abundance of coal and uranium. The goals might encourage energy conservation—but it would aid in energy conservation if we all dropped dead, too. Energy conservation is not an end in itself—no one really gives a damn about energy conservation—it's happiness that people are concerned with."

"We've gone too far in letting the government into our affairs..."

"I care about the spirit of innovation... I'm an inventor, but it's a bad time for people to do that. Many of us who developed the ideas behind direct gain heating—and have been successful—our ideas have been co-opted by the government, and it's disappointing that the government does not now turn to us for new ideas. ...They're stacking the decks against the little guy ..."

"Drop City, Colorado, a rural vacant lot full of elegant funky domes and ditto people, has been well photographed and poorly reported in national magazines. Visitors and readers... assumed that the domes were geodesic Fuller domes, which some... are. But most... were designed by another guy who designed by another geometry: Steve Baer."

"This tabloid contains the crystallographic theory and junkyard practice behind Baer's domes: from how to distort a polyhedron without affecting connector angles to how to chop out a car without losing your foot. ...Baer's theory is unique in architecture. So is his practice; instead of dying of dissertation dry rot, his notions stand around in the world bugging the citizens."

"The Dome Cookbook is published by Lama Foundation, an intentional community in New Mexico, built largely of Baer domes."

"High above the roofs of... Martineztown, one of Albuquerque's oldest s... a growing army of... structures...point south to capture sunlight... [for] two large buildings... Zomeworks Corporation, one of the nation's earliest companies."

"Founded in 1969... some of the buildings were called "zomes"—or "dodecahedral structures"... Others were heated in a simple way with... "passive" solar heating."

"Ten years later Zomeworks has moved to a newly renovated showroom (once the home of Martineztown dance hall)... [P]anels insulate many of the windows at night... attached by small magnetic clips... only one of the passive solar devices developed by Zomeworks..."

"Many other Zomeworks ideas... as... black 55 gallon drums behind glass... (the "drumwall") have... become classics..."

"[T]he devices are cheap. A thermosyphoning solar water heater... costs less than half as much as most solar water heaters. A solar preheater... is even less."

"The company... manufactures... "skylids" (insulated shutters for skylights that open and close with the sun) and "beadwalls" (double pain windows that fill and drain with beads to let the sun in or keep the cold out)."

"[T]he company's newest product, "Big Fin" water heaters... can be placed inside a greenhouse or other glass enclosed area. After its copper pipes have been heated by the sun, the water... flows to an elevated heating tank by... natural convection and the cool water at the bottom of the tank flows back... There's no electric pump. The cost... $850."

"According to Baer... the best solar ideas come from people who are taking a chance—"and not just drawing a salary.""

"Baer says that solar energy is already supplying a large proportion of our needs through daylight, which makes the use of electric lights during the day unnecessary, and in agriculture, where it enables the production of food. Yet this... "unreclaimed" solar energy is not... counted in the statistics."

"New challenges driven by evolving global technology inspire fresh trends and approaches in teaching statistics in business schools of the 21st century."

"One should mention right at the start that one still does not understand whether quantum mechanics and special relativity are compatible at a fundamental level in our Minkowski four-space world. One generally assumes that this means finding a complete Yang-Mills gauge theory or the interaction of gauge fields with fermionic matter fields, the simplest form being quantum chromodynamics (QCD). Associated with this picture is the belief that the fundamental vector meson excitations are massive (as opposed to photons, which arise in the limiting case of an abelian gauge symmetry. The proof of the existence of a “mass gap” appears a necessary integral part of solving the entire puzzle. This question remains one of the deepest open issues in theoretical physics, as well as in mathematics. Basically the question remains: can one give a mathematical foundation to the theory of fields in four-dimensions? In other words, can do quantum mechanics and special relativity lie on the same footing as the classical physics of Newton, Maxwell, Einstein, or Schrödinger—all of which fits into a mathematical framework that we describe as the language of physics. This glaring gap in our fundamental knowledge even dwarfs questions of whether there are other more complicated and sophisticated approaches to physics—those that incorporate gravity, strings, or branes—for understanding their fundamental significance lies far in the future. In fact, one believes that stringy proposals, if they can be fully implemented, have limiting cases that appear as relativistic quantum fields, just as relativistic quantum fields describe non-relativistic quantum theory and classical physics in various limiting cases."

"Cook’s theory has a special meaning to mathematical logic since Cook’s theory can be viewed as a branch of recursion theory. Freeman Dyson wrote a fantastic article in the 1980s, which recorded the story of how Gödel insisted on his “Unfashionable pursuits” in logic. In fact, when (computer science) people were talking about the unfairness of the late appointment of professorship to Gödel in the Institute for Advanced Study at Princeton, Stephen Cook reinstated the dignity of mathematical logic."

"English Quotation"

"In the cafeteria, we just ignored the sign [for segregated seating]. But at some point, we started eating at our desks. When we left work, our lives were definitely separate — separate communities, separate schools for our children, separate grocery stores and churches."

"But then we’d be back with our colleagues on the job. People are people. My father’s advice helped. He said, “You’re no better than anybody else, but nobody is better than you.”"

"I was always interested in math. I counted everything as a child — the number of steps up the stairs, the dishes, the steps to church. Those thoughts just came naturally. While I skipped grades in school, my parents made sure I stayed grounded."

"It’s just there. You can’t do anything without it. It’s in everything. I like to work problems. If you do your best, nobody can ask you to do it over again. I never had to repeat what I did."

"I believed I was where I was supposed to be. When I was a student, my mentor told me I’d make a good research mathematician. I said, “What is that?” and he told me I’d have to find out for myself. At NASA, I happened to be at the right place at the right time. When you put bright people in a room and they had something to do, they worked on it until they got it done. But honestly, it was never work to me."

"We put in some long hours at times, and I had three children at home. But they were very responsible, and I had family and friends who helped look after them."

"I’ve spent a lot of time tutoring kids in math as a volunteer. I’ve always enjoyed helping people understand what they can find in math. There’s no judgment there."

"I grew up in 1960’s in Winston Salem, NC. in a low-income, single parent household. At the time, the schools in Winston-Salem were segregated but, due primarily to the dedication of my teachers and my own motivation"

"I received a very strong public school education. For as long as I can remember, even before I started school, I had a love for mathematics. I think there was something about both the logic of math and the fact that in math there was a “right answer” that appealed to me (clearly before I knew about stochastic mathematics)."

"For a long time, I wanted to be a math teacher, but in high school I started to think about working in jobs where I could “apply” mathematics (though I only had a vague idea of what that meant)."

"In 1980 I joined AT&T Bell Laboratories in Holmdel, NJ. Eventually I had a 25- year career at Bell Laboratories and, after the breakup of the Bell System, AT&T Laboratories."

"During my time at AT&T I learned the importance of mentoring. I have mentored hundreds of people over my career, first at AT&T and, more recently, at the Johns Hopkins University Applied Physics Laboratory (JHUAPL), where I continued my career after leaving AT&T. I am very proud of the impact I have had on the careers of so many people."

"I didn't know they lay of the land," quips Bozeman. They wanted her to go back to school to finish her Ph.D. She just looked at them thinking, I have a husband and two small children, how am I going to go back to Vanderbilt four hours away?"

"My mother only finished the 12th grade but she was always excited about math."

"My math teacher, Mr. Frank Holly, would not let me stop doing math."

"That was the one course that didn't come easily, let's put it that way."

"I don't know how much I helped but he gave me credit on the paper. That was a boost to my ego and really got me going in math."

"Male faculty tend to be less sensitive to the ways in which women treat their studies."

"Women make a B on an exam and they are crushed, they think it's terrible. Men make a B and they think it's great."

"I grew up on a small farm in Camp Hill, Alabama, with my four siblings. My elementary school education took place in a one-room school house in my community. Although my love of mathematics was passed down from my mother, both of my parents instilled in me a love of learning and a concern for the education of others."

"I am very proud of all the students that I have taught, supervised in research or summer programs, or mentored over my 35-plus years as a faculty member at Spelman College, a place that supported me through enough different roles and opportunities that I enjoyed going to work every day."

"Until a few years ago, I was a “wayward” mathematician. I thought all I could do was teach and I wanted out. While teaching is noble and one of the highest callings, I wanted to do something other than my tenure-track position."

"Now don’t get me wrong, I knew mathematicians did more than teach. But personally, I had not done a lot of applied mathematical work. Nothing wrong with it, I just hadn’t. (My area of research was a branch of Combinatorics called Matroid Theory.) However, when I started looking I found all kinds of employment opportunities."

"When I finished my PhD, there didn’t seem to be a shortage of academic jobs. You might not get a position at Research I institution, but you could find a tenure-track position at a pretty decent institution and be happy."

"I still see colleges and universities hiring for these positions, but when comparing the number of open positions to the number of Ph.D. graduates annually…there are not enough academic jobs. So what to do? I recommend considering jobs outside academia."

"All too often in the MATH community, because of its traditions, a common sentiment is one that unless you are tenure-track faculty, you’re not a good mathematician. It took time…but I got over that nonsense. I wanted to do something different with my mathematics. I went BIG."

"It has history to discover, outlets for shopping, good food and a quiet atmosphere."

"I aspired to do something outside of farm work and I knew that having a good education would be the key."

"That motivated me to do well in school so that I could get a scholarship and go to college. I had a great support system and many mentors along the way who kept me motivated."

"It’s always refreshing to hear how my work is now being used outside of the government and I am still amazed by the technological advancements navigation has made since the GPS Project began in 1973."

"It never gets too old. I am just so pleased that I was able to make a contribution. When I was working, I never imagined that the GPS would be used in the civilian world. I love seeing all the ways that it can be used and I probably have no idea how vastly used it is."

"I’ve always loved math, but I don’t think it always loved me back"

"My journey is weird because I feel like I operated in the complete absence of a mathematical community."

"I was always drawn to puzzles and captivated by mathematical thinking and trying to understand how things work. When I was little there were Magic School Bus books with information bubbles."

"I never thought of myself as a mathematician. I went to a performing arts school from the fourth to the eighth grade. Most of my formative years were spent in classes where there was creative dance, piano and art."

"I was a creative writing major at that school. There was math happening but this was in no way an environment of STEM that I’ve experienced today."

"In high school, I got accepted into a magnet program. I switched to a different school because I had heard this program was like my art school but just for math and science, I thought it would be interesting to see how that would turn out and it didn’t go so great."

"I was dismissed after the first year because I didn’t get high enough grades in geometry and statistics, and this was a program where you couldn’t get C’s and I got C’s in those courses."

"ou don’t need to have a special brain or be a certain kind of person to take on math"

"I find it very rewarding,” said Eubanks-Turner. “Most teachers join the program because they love learning mathematics. Even teachers who have been in the classroom 20 or 30 years learn something they never knew or see an aspect of math in a new way."

": I knew I wanted to be a mathematician later when I was in college.2I originally majored in computer science, but I really disliked computer programming. I loved the logical thinking involved in creating computer algorithms, which I realized was just mathematical thinking, but I found the actual coding and"

"There’s a thinking that lends well to doing mathematics. Mathematicians have to be precise in their thinking and they have to be good at analyzing definitions and proofs. In fact, even when mathematicians"

"Although I did not realize it, I did many things to build my mathematical abilities."

"I was awarded a National Physical Science Consortium fellowship to pursue graduate studies in mathematics and earned my M.S. and Ph.D. in Applied Mathematics from North Carolina State University in Raleigh, North Carolina. After graduate school, I completed a postdoctoral fellowship at the Environmental Protection Agency in the National Health and Environmental Effects Research Laboratory in Research Triangle Park, North Carolina."

"I always had an affinity for mathematics. As a child I was always interested in studying patterns, working on puzzles, and solving logic problems; and I was very intrigued by the various ways in which mathematics showed up in everyday life. While in junior high school"

"I am most proud of being a mentor. Throughout my career, I have spent a great deal of time working with students who need additional supports outside of the classroom. I work with them to master good study habits; set goals and create action plans; manage time, stress, and life circumstances; and prepare for their future careers. It gives me great joy to know that I have mentees who have become successful teachers, doctors, and researchers; but more importantly have gone on to mentor others in need of support."

"Personally, I am most proud of taking a leap of faith, leaving a tenured faculty position, to relocate to the DC-area to be near and help care for my aging parents. It has been the best decision of my life."

"My thesis is this thing that was initially going to be a grenade launched at my ex-prison, for better or for worse, and instead turned into some kind of positive seed bomb where flowers have sprouted beside the foundations I thought I wanted to crumble."

"My thesis is that thing I got sick of just when I should have been fine-tuning its organization. It’s where I find typos that have already gone to print. I am a writer; don’t ask me about my writing."

"For 7 years I called myself an escaped graduate student. I laughed and made light, but each passing month increased my shame burden. Having kids made it easier to throw my hands up like I was okay with things and not at all failing, but I was never okay. I’m still not okay. After my defense"

"I had to fill out an exit survey. They asked how many years spent on coursework (3), how many years spent on dissertation (10). TEN YEARS?! WHAT KIND OF PERSON SPENDS TEN YEARS ON ONE DOCUMENT AND STILL HAS TO BUILD UP COURAGE TO DISCUSS IT OPENLY?"

"When I entered graduate school, I was a sponge for external pressures. Please tell me the rules I must abide by in order to make no waves! Which jokes should I not find offensive? Oh, am I here because of Affirmative Action?"

"In my second year, my body temporarily lost the ability to properly deal with sugar. I don’t know if this is a thing. My doctor never really figured it out even after she got “really scientific about it.” Whatever it was, I realized stress had sent me to the hospital and I was thoroughly against that on principle, so I gave up stress."

"After completing the my undergraduate studies at Xavier University of Louisiana, I went to the University of Nebraska-Lincoln (UNL) to earn my doctorate. In 2008, I was one of the first two African-American women to earn a doctoral degree in Mathematics from UNL."

"My current research focuses on oscillation criteria for certain linear and nonlinear second order dynamic equations. While I am also interested in applications of time scales to biology, economics, and statistics, I have a keen interest in increasing the number women, especially those underrepresented, in STEM and improving the undergraduate preparation of mathematics majors."

"While I was in middle school, I went to Algebra with an adequate math foundation and without Pre-Algebra although I barely passed the entrance exam. Within a few weeks, I began to struggle. While I was trying to understand just how letters belonged in mathematics, my Algebra teacher Mrs. Gwendolyn Scott found a way to “motivate” me."

"She moved my seat, gave me extra work, and required a parental signature on all graded assessments. Since Cs were not acceptable grades and guaranteed at least 6 weeks of punishment, I was going to spend my entire eighth grade year punished because I was making Ds and Fs. Mrs. Scott’s “motivation” helped me discover my interest in math."

"My initial intellectual interest was not in mathematics but in science. My mother (for some reason) decided to give me a Gilbert chemistry set for Christmas when I was 9."

"My interest in mathematics was sparked and sustained in high school not by courses per se but by a number of well written, engaging books aimed at readers with a high school mathematics background."

"I suppose many would say I should be proud of these educational attainments and indeed I take a lot of satisfaction in them as I come from a very modest social background—my parents had steady jobs, thank goodness but we lived in a housing project until I was 16. After Mr. Wilson, I did not meet another African American scientist let alone a mathematician until I was nearly done with graduate school."

"But whatever success I had or will have is bound up in the swirl of social and political forces that pushed mid-century America forward and these were largely beyond my control. I was born when the momentum of the New Deal, World War II and then Sputnik created sustained support for fostering STEM excellence in education."

"Although I was never in the American South and was a little too young to participate in civil rights demonstrations very much, I benefited quite directly from the Birmingham children’s march. The appalling assassination of Martin Luther King also had a profound impact on me. The shock wave of this movement percolated to the smallest scales of society so that it affected even the person to person interactions in mathematical culture that are so critical to career success or failure. I have also benefited from the support and friendship of the many African-American women mathematicians who preceded me and who have come onto the scene since. Collectively, our actions make it easier for all of us."

"What I’ve seen is an increased focus and acknowledgment of supporting our various institutions,"

"We invited faculty from the region, from HBCUs in the region, to come and participate in our technical assistance workshop,” Inniss said. “We actually invited program officers to come to campus to present on the different programs in DRL, and then we had a coaching component."

"Now, I have the knowledge and the understanding of what helped me to be productive in my own individual career that I’m able to kind of share that knowledge with my junior faculty, colleagues,"

"I’m helping people to understand your notice of award and all [the] award conditions, and what does this mean? [I’m] also helping people to understand how to effectively manage their awards, and what certain things mean. What does participant support cost? When do you have your budget, and how do you expand your budget, and just providing all that different context and information to help people to be effective with their grants."

"I know at NSF there was always a concerted effort to avoid implicit biases, and so I applaud them for that, and they continue to do that—to have an understanding that diversity breeds innovation, and I think that a lot of federal agencies understand that,” Innis said. “But also having opportunities for HBCUs and MSIs to lead on different programs—I think that is really helpful, and has helped us as well."

"When I was in high school, I was able to go to a college campus to take undergraduate math classes, which was a great experience. To pass this on to the next generation, each year for the last ~20 years, I've run an intensive 2-week math and biology course for high school students."

"Another outreach program that I am involved in is aimed at 1st and 2nd year college students. This project is driven by the fact that we really need more diverse students to become leaders in science, technology, engineering, and mathematics (STEM)."

"A challenge is that more than half the students that enter college wanting to major in STEM don't end up getting that STEM degree."

"There's a high attrition rate and the biggest drop off happens to be students of color and students from underserved backgrounds. When I was researching and finding out all these facts, it really made me want to figure out ways to support students and address this retention in STEM problem."

"I think that medical oncology could really use a mathematical modeling toolbox that can leverage clinical measurements to optimize treatments for individual patients. Mathematical modeling can also help us make predictions to improve clinical care."

"For example, you might first want to predict which drug or combination of drugs will work best on particular patients, and then it becomes important to know the right dose and schedule for administering that drug. Mathematical modeling can help answer these types of questions."

"You know, it wasn't difficult. It seemed like my path was paved for me. It was in the Lord's hands, and he said, 'This is what's going to happen"

"You had a lot of people there – a lot of people from all different cultures – and we all worked together. And if I ever needed anything – I know that doesn't sound believable, but if I ever needed anything -- they were there to help out"

"I'm just in there working, just doing my thing, trying to do the best that I can do. And knowing that I was among the minority there that I had to do my best if I was going to stay there"

"I hope that if my students can believe it, they can achieve it,"

"Every workshop always sold out and was sitting room only"

"It’s because teachers want to engage students and know how much they like music."

"Part of it is respecting and learning about the contributions different cultures have made to math in addition to Pythagoras — the one name people know"

"It’s also about wanting students to develop a positive math identity and not just see it as a procedure, but to realize that a lot of what they’re doing is math."

"Wow, math is everywhere."

"What does a math task look at when it’s both culturally relevant and cognitively demanding?"

"It’s an awesome book I really enjoyed doing"

"because we keep hearing about the achievement gap, often between black and white children. But for this book we focused on black children not from a deficit — not from what they don’t know — but from what they do know."

"I wanted it to be a math activity book, so I wrote bios about the women and made up activities to go with their math — fun activities that don’t need a teacher to teach it to you first. It’s a book that students can just pick up and do without a teacher, maybe while riding in the car to grandma’s house."

"When I was a young child, I loved the show “Square One”. This was shown on PBS and focused on showcasing abstract mathematical concepts. It showed different vignettes including “Mathman” which was a Pacman-type game, and Mathnet, a detective show like Dragnet."

"Another experience that stands out to me was learning how to multiply by watching School House Rock videos! “Three is a magic number” is still a favorite of mine. You could say that public television and educational videos were my thing when I was a kid."

"A year ago this answer would be different, but this past year I have been recognized nationally and locally for my teaching, research, and service as a mathematician. I am very proud of all of the things I have been able to start or participate in. I am grateful to all the great people I do impactful things with. I appreciate that I am increasing the rate of change in this field, positive second derivative."

"Externally: Last year I bought a house on my own. I never thought I would be a homeowner and I am so proud of myself for not letting my doubts keep me from realizing this dream. I also co-founded a publishing company, 619 Wreath LLC, with my friend Miloš Savić… and we wrote a book titled “Radical Grace: Essays and Conversations on Teaching”. These are things that make me feel like such a grown-up!"

"Internally: A while back I decided that I am not in competition with anyone but who I was yesterday. I try to reflect on everything in order to grow. I am very proud of where I am now and excited for the future."

"I remember my love of mathematics emerging in first grade when I was excited by math facts and bored with coloring."

"By seventh grade I knew that I would major in mathematics as a college student. What I did not know was there were so many areas of mathematics to study. I am an applied mathematician who uses mathematics to solve equations that model physical phenomena in the medical field."

"In particular, I study mathematical predictions for aneurysm prevention and treatment. My specialties are ordinary and partial differential equations and numerical analysis. Oddly, I also love some areas of core mathematics. I love linear and abstract algebra and real and complex analysis."

"Since the age of 13, I have had to manage a chronic disease called Myasthenia Gravis (MG). MG is a chronic autoimmune neuromuscular disease that causes weakness in the skeletal muscles. It manifests in difficulty with breathing, droopy eyelids, double vision, trouble speaking and swallowing and weakness in the arms and legs. I had every symptom and the disease was so debilitating that I could not attend school in tenth grade."

"I developed a duodenal ulcer from the medication and I eventually became unable to walk without a walker. But God! I eventually regained most of my strength, returned to finish high school on time, and I started college on August 27, 1983 (my 18th birthday). Although I still have to manage the MG and now a new illness (Fibromyalgia), I have been able to achieve all of my goals to date."

"I’ve been fortunate to have many incredible experiences at Raytheon Technologies and Raytheon Intelligence & Space. One that stands out to me occurred through my work with the Army Research Laboratory (ARL), which gave me the opportunity to travel and participate in NATO workshops and conferences."

"There are many factors that make Raytheon Intelligence & Space a great place to work, and two things in particular stand out as an RI&S employee."

"As I touched on earlier, is RI&S’ global impact. We’re not just working to address national challenges, but also global issues. For example, we develop advanced sensors, cyber services and software solutions, and we deliver cutting-edge technology that enables our customers to succeed in any domain, against any challenge."

"Second is our environmental sustainability efforts. We are committed to protecting the environment and conserving natural resources. RI&S — and Raytheon Technologies as a whole — is working to reduce our environmental footprint through responsible resource management, implementing innovative solutions and collaborating with stakeholders."

"In fact, Raytheon Technologies recently appointed a chief sustainability officer to help ensure that our products, solutions and platforms are built with sustainability in mind, and that we’re positively impacting the Earth’s climate and biodiversity in the process. I love that sustainability is something we’re working toward as a company."

"When I was a younger student, I was that kid who was able to do school. I knew how to talk to the right people and figure out what classes and things that I needed. That’s not because I had a legacy family that all went to college."

"That was because I just had something in me where I learned how to network and interact with people very, very early. And I just began to observe how folks [who had] what I thought was more power, I just observed to see how they moved in the world and began to engage them."

"I enjoyed math because of its power to help me understand things. Not to just sit in the library and do a long problem; it wasn’t about that for me."

"It really is like, man, if you can be math literate — I don’t care if you’re an artist, if you’re a nurse, if you’re a janitor — math literacy is going to help you push forward in your life and just open up so many opportunities."

"So that’s one of the reasons why I think I really fell in love with math, and why I enjoyed it, and why I try to help my students and everybody else around me see its power."

"I’ve learned through some of my research that Black girls want to be able to have more of a family, relaxed environment — to be able to laugh and be social — while at the same time doing their math work."

"In the various Branches of Mathematics being pretty well informed, ... I applyed myself to practise Land Surveying with Success, but my natural bent for Science encreasing, I thought my native country too unfavourable a Spot for prosecuting my enquiries with any advantage or encouragement, and accordingly resolved to adopt the well Known Maxim "Where Liberty dwells, there is my country." Here every man who acknowledges the rights of a rational being, ought to bring his mite of Knowledge or experience, to encrease the rising Glory of this happy People."

"Can you imagine what it was like for a 19 year old Black female from Tupelo, Missippi who had been immersed in segregation for all her life to attend the University of Wisconsin? I underwent a major culture shock. ... I gravitated to students from Africa, a roomate from Thailand, and an office-mate from India, who was the only person to whom I could ask a mathematics question."

"I have devoted my entire life to increasing the number of highly qualified African Americans in mathematics and mathematics-related careers. High expectations, building self-confidence, and the creation of a nurturing environment have been essential components for the success of these students. They have fully justified my beliefs. Perhaps the most rewarding moments have come when younger faculty have undertaken the same goal and have surpassed my efforts reaching out to the broader community to help minorities and women achieve in mathematics"

"This award is especially gratifying to me in view of the success of my initiative on advancing the IEEE transnational frontier in Eastern Europe, particularly in Russia"

"And that’s only accelerating,It's great to be connected to a business that is committed to new ideas and innovation.”"

"I am the Global Head of Investment and Client Solutions and CIO of the Solutions and Multi Asset Group within the Investment Management division. Our business has a number of different businesses within it, but at the core, we are focused on solving problems for clients and not only developing investing strategies."

"In order to do that, you need a very good platform with a lot of resources. And you then need to put those resources together in flexible ways to deliver solutions. We do that in a number of contexts. Not everything is so customized—we do have products. But those products are inspired by client problems."

"I spend time on both the investment side and the client side, trying to think about ways to bridge them. I'm very involved with some of our largest clients, both institutional and high-net-worth individual clients. While we work on customized investment strategies, we also provide value to our clients beyond just the investments. It's not just managing a client’s assets, it's supporting them outside of investing, such as providing content, ideas and access to others within the firm."

"We are very cognizant of what is going on throughout the investment world. We're constantly looking at markets, looking at innovations in finance, scanning the latest research and connecting them to specific client situation."

"We want to provide a solution, but we first need new tools to help us better understand the problem. So we have to go and find or develop techniques to do that."

"Our clients’ problems can be complex, so we have to think critically and creatively about how we are going to solve them."

"Our team is made up of investors and analysts who have diverse background, and we use that to our advantage, gathering information from a variety of sources. Ideas can come out of academia like using data or analytics in new ways. Ideas may also come from our clients. For example, a client may come to us to find a way to generate income on a portfolio that integrates a particular liquidity and cashflow profile. We develop a solution for them and then may realize that it can be tailored to help us solve the needs of another client."

"I first worked as a management consultant after graduating from college. I was living in Australia at the time and enjoying it, but I knew I wanted to go back to school. I decided to pursue a doctorate in political science. While I was in graduate school, I also received a master's degree in economics."

"I entered academia on a tenure track at the University of California at Berkeley, while continuing to consult on projects. That led to consulting work for the asset management business of a major bank, which was trying to solve some investment problems for their own portfolios and for clients. I was coming at it from a slightly different angle, as a social scientist rather than just a pure finance guy. And we had some success. I think my different perspective helped me and my team develop ideas that had some traction. So I kept consulting while I was on the faculty at U.C. Berkeley. I had been consulting for Morgan Stanley for several years when the bank offered me the full-time position I have now."

"We work with clients to achieve their mission beyond just trying to maximize their wealth. For example, we have one client who had a significant liquidity event and she wants to donate her money eventually. But while she's in the process of doing that, she wants the investments to make money and have a particular social impact. The ability to help a client have a positive impact on the world is very fulfilling."

"We also work for large public pension funds. I relate to this as a former employee of the state of California. You realize in this role that you work for firemen and teachers and you have something beyond a fiduciary duty. These people are depending on your performance. Delivering that is rewarding."

"We need our team members to be flexible in their thinking and flexible about ideas and functions. The people who work on our teams are experts in certain fields but are able to engage very rigorously on the investment side, analyzing investments, understanding them, identifying new ideas. They also understand how to engage with our clients."

"Culturally, we look for people who are able to work in teams. It's not a one-man show. We have a number of different businesses, but all of them are characterized by delivering value by combining new ideas and high quality execution, so that, in the end, one plus one equals three."

"Every step in my career has served a purpose. Of course, each step provided me with a particular level of training. But the steps also bought me time to figure out what I like and what I don’t like professionally and personally. If I had to end with some advice, I would say: Take each of these steps seriously and not to rush ahead to the next one."

"When you don't feel valued, you feel like sh*t. When you feel like sh*t, you don't do good math."

"I grew up not having any clue what a Mathematician was… so I looked up and wrote to random Math Professors. It sounds silly, but this actually helped shape my career path. Doing math for a living is a sweet gig, and I am deeply grateful to be a part of the mathematics community."

"The spectacular results in the fluctuation theory of sums of independent random variables, obtained in the last 15 years by , , , , , , and others, have gradually led to the realization that the nature of the problem, as well as that of the methods of solution, is algebraic and combinatorial. After Baxter showed that the crux of the problem lay in simplifying a certain operator identity, several algebraic proofs (, , Wendel) followed. It is the present purpose to carry this algebraization to the limit: the result we present amounts to a solution of the for s. The solution is not presented as an algorithm, but by showing that every identity in a Baxter algebra is effectively equivalent to an identity of symmetric functions independent of the number of variables. Remarkably, the identities used so far in the combinatorics of fluctuation theory "translate" by the present method into classical identities of easy verification. The present method is nevertheless also useful for guessing and proving new combinatorial identities: by way of example, it will be shown in the second part of this note how it leads to a generalization of the Bohnenblust-Spitzer formula for the action of arbitrary ."

"It has been observed that whereas s and s are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance with those of artistic beauty. For example, courses in “art appreciation” are fairly common; it is however unthinkable to find any “mathematical beauty appreciation” courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term “beauty” as it is currently used by mathematicians."

"It cannot be a complete coincidence that several outstanding logicians of the twentieth century found shelter in s at some time in their lives: Cantor, , Gödel, Peano, and are some. was one of the saner among them, though in some ways his behavior must be classified as strange, even by mathematicians' standards. He looked like a cross between a and a large owl. He spoke softly in complete paragraphs which seemed to have been read out of a book, evenly and slowly enunciated, as by a . When interrupted, he would pause for an uncomfortably long period to recover the thread of the argument. He never made casual remarks: they did not belong in the baggage of ."

"The more experimental scientists and s are, the more common sense they have, and so on until you get to the mathematicians, who are totally devoid of common sense."

"The importance of the creation of the zero mark can never be exaggerated. This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol but helpful power, is the characteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power.’"