Mathematicians From The United States

"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."

"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."

"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."

"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."

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

"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."

"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."

"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."

"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."

"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."

"}|Information is information|"

"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."

"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."

"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."

"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."

"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."

"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."

"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."

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

"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."

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

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

"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. ..."

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

"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."

"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."

"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."

"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."

"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.'"

"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."

"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."

"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."

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

"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 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."

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

""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 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."

"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."

"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!"

"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."

"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.""

"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."

"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."

"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?""

""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 word is not the thing."

"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!"