Mathematicians From The United States

"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 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."

"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 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."

"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."

"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."

"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.""

"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."

"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."

"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."

"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."

"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."

"[The Many-worlds interpretation is the] only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world."

"The physical "reality" is assumed to be the wave function of the whole universe itself."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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?"

"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."

"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."

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

"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"

"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."

"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."

"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.""

"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."

"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."

"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."

"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."

"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."

"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"."

"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."

"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 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."

"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."

"[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."

"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."

"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 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."

"A significant idea of organization cannot be obtained in a world in which everything is necessary and nothing is contingent'"

"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"."

"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."

"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."

"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."

"Any labor which competes with slave labor must accept the economic conditions of slave labor."