Mathematicians From Poland

"Do not lose your faith. A mighty fortress is our mathematics. Mathematics will rise to the challenge, as it always has."

"Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years old, reading Jules Verne or H. G. Wells, and have fallen asleep."

"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."

"Whatever is worth saying, can be stated in fifty words or less."

"I'm an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate..."

"For many years I was the youngest among my mathematical friends. It makes me melancholy to realize that I now have become the oldest in most groups of scientists."

"The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down."

"In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug."

"With sixty professors there are roughly eighteen hundred pairs of professors. Out of that many pairs it was not surprising that there were some whose members did not like one another."

"Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?"

"I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish."

"[I]t was seeing the gist, the inner core of a problem, that enabled him to open so many new roads—roads that often led to new branches of mathematics. ...Cellular automata theory, which he proposed to von Neumann; the of solving intractable problems, not only in probability theory but in areas such as number theory where the method would not have been thought applicable; and his work on nonlinear processes that anticipated today's interest in solitons and "chaos." We still do not know—it remains a government secret—what jumped into Ulam's head that made it possible for Edward Teller to build the H-bomb."

"The mathematicians know a great deal about very little and the physicists very little about a great deal."

"It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs."

"I was still very hopeful that much work lay ahead of me. Perhaps because much of what I had worked on or thought about had not yet been put into writing, I felt I still had things in reserve. Given this optimistic nature, I feel this way even now when I am past sixty."

"Thanks to my memory, which enabled me to quote Latin and to discuss Greek and Roman civilization, it became obvious to some of my colleagues in other fields that I was interested in things outside mathematics. This lead quickly to very pleasant relationships."

"I thought that the description of Don Quixote's fight with the windmills the funniest thing imaginable."

"Ada came from Lwów. She was a very good looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her."

"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."

"The word is not the thing."

"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."

""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."

"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..."

"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."

"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?""

"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!"

"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."

"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."

"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.""

"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."

""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."

"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."

"Nature does not provide identical objects; on the contrary, these are always human creations. What nature provides is a tree full of apples which are all recognisably alike and yet are not identical, small apples and large ones, red ones and pale ones, apples with maggots and apples without. To make a statement about all these apples together, and about crab-apples, Orange Pippins, and Beauties of Bath, is the whole basis of reasoning."

"The whole structure of thought in the Middle Ages is one which we find hard to grasp today. It was an orderly structure, but the principles by which it was ordered seem to us now outlandish and meaningless."

"We are all afraid - for our confidence, for the future, for the world. That is the nature of the human imagination. Yet every man, every civilization, has gone forward because of its engagement with what it has set itself to do. The personal commitment of a man to his skill, the intellectual commitment and the emotional commitment working together as one, has made the Ascent of Man."

"The great flood was the seventeenth century. That was the time of change, the hanging moment of instability in which men like Cromwell and Newton could remake the world."

"About 1660 therefore, Europe was in the course of a great revolution in thought. This was the Scientific Revolution, and it reached into all forms of culture. We sometimes speak as if science has step by step squeezed other interests out of our culture, and is slowly strangling the traditional ways of thinking. Nothing of the kind. The Scientific Revolution in the seventeenth century was a universal revolution. Indeed it could not have begun unless there had already been a deep change in the attitude to everything natural and super-natural among thoughtful men."

"The world can only be grasped by action, not by contemplation."

"Since the word "knowledge" occurs in my general title... I am going to be talking about epistemology, although I prefer to use the eighteenth-century, indeed, medieval phrase, "natural philosophy." ...that enterprise of the human mind which attempts to trace lawfulness to nature, dead and living, but which is not directed to specific inquiries into how this or that law works. Philosophy in the sense in which I practice it, natural philosophy, is concerned with lawfulness rather than with laws and the general nature of laws rather than with the specific structure of this or that law. Natural philosophy was one of the three topics (moral philosophy and metaphysical philosophy were the others) to which one graduated in medieval universities after having studied the seven liberal arts. I believe that we need to review the whole of our natural philosophy in the light of scientific knowledge that has arisen in the last fifty years."

"There has never been another moment in English history to equal the promise of that moment in the 1660’s when the Royal Society was formally founded. And though it was less dramatic elsewhere, it was a high moment throughout Europe."

"Newton was born during Cromwell’s revolution in the troubled 1640s; he was eighteen at the Restoration in 1660; and he published the Principia during the intrigues which ended by bringing William of Orange to England in the revolution of 1688. These are the moments when the powerful or the forceful character feels the ferment of the times, when his thoughts quicken and when he can inject into the uncertainties of others the creative ideas which will strengthen them with purpose. At such a moment the man who can direct others, in thought or in action, can remake the world."

"Fifty years from now, if an understanding of man's origins, his evolution, his history, his progress is not in the common place of the school books, we shall not exist."

"Unhappily, common sense has no recorded history."

"There are three creative ideas which, each in its turn, have been central to science. They are the idea of order, the idea of causes, and the idea of chance."

"It's said that science will dehumanize people and turn them into numbers. That's false, tragically false. Look for yourself. This is the concentration camp and crematorium at Auschwitz. This is where people were turned into numbers. Into this pond were flushed the ashes of some four million people. And that was not done by gas. It was done by arrogance, it was done by dogma, it was done by ignorance. When people believe that they have absolute knowledge, with no test in reality, this is how they behave. This is what men do when they aspire to the knowledge of gods.Science is a very human form of knowledge. We are always at the brink of the known; we always feel forward for what is to be hoped. Every judgment in science stands on the edge of error and is personal. Science is a tribute to what we can know although we are fallible. In the end, the words were said by Oliver Cromwell: "I beseech you in the bowels of Christ: Think it possible you may be mistaken."I owe it as a scientist to my friend Leo Szilard, I owe it as a human being to the many members of my family who died here, to stand here as a survivor and a witness. We have to cure ourselves of the itch for absolute knowledge and power. We have to close the distance between the push-button order and the human act. We have to touch people."

"And I am infinitely saddened to find myself suddenly surrounded in the west by a sense of terrible loss of nerve, a retreat from knowledge into—into what? Into Zen Buddhism; into falsely profound questions about, Are we not really just animals at bottom; into extra-sensory perception and mystery. They do not lie along the line of what we are able to know if we devote ourselves to it: an understanding of man himself. We are nature’s unique experiment to make the rational intelligence prove itself sounder than the reflex. Knowledge is our destiny. Self-knowledge, at last bringing together the experience of the arts and the explanations of science, waits ahead of us."

"What we really mean by free will... is the visualizing of alternatives and making a choice between them. ...the central problem of human consciousness depends on this ability to imagine."

"Science and the arts shared the same language at the Restoration. They no longer seem to do so today. But the reason is that they share the same silence: they lack the same language. And it is the business of each of us to make that one universal language which alone can unite art and science, and layman and scientist, in a common understanding."