Mathematicians from Poland

"If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash. For it is not unknown that Lactantius, the writer celebrated in other ways but very little in mathematics, spoke somewhat childishly of the shape of the earth when he derided those who declared the earth had the shape of a ball. So it ought not to surprise students if such should laugh at us also. Mathematics is written for mathematicians to whom these our labors, if I am not mistaken, will appear to contribute something even to the ecclesiastical state the headship of which your Holiness now occupies.(Author's preface to de revolutionibus)"

"Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if only we face the facts, as they say, "with both eyes open.""

"To know the mighty works of God, to comprehend His wisdom and majesty and power; to appreciate, in degree, the wonderful workings of His laws, surely all this must be a pleasing and acceptable mode of worship to the Most High, to whom ignorance cannot be more grateful than knowledge."

"Neque enim ita mihi mea placent, ut non perpendam, quid alii de illis iudicaturi sint. Et quamvis sciam, hominis philosophi cogitationes esse remotas à iudicio vulgi, propterea quòd illius studium sit veritatem omnibus in rebus, quatenus id à Deo rationi humanæ permissum est, inquirere, tamen alienas prorsus à rectitudine opiniones fugiendas censeo. Itaque cum mecum ipse cogitarem, quàm absurdum ἀκρόαμα existimaturi essent illi, qui multorum seculorum iudiciis hanc opinionem confirmatam norunt, quòd terra immobilis in medio cœli, tanquam centrum illius posita sit, si ego contra assererem terram moveri..."

"When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere. Wherefore I took upon myself the task of re-reading the books of all the philosophers which I could obtain, to seek out whether any one had ever conjectured that the motions of the spheres of the universe were other than they supposed who taught mathematics in the schools. And I found first, that, according to Cicero, Nicetas [assumed by modern editors to mean Hicetas] had thought the earth was moved. Then later I discovered, according to Plutarch, that certain others had held the same opinion. ... When from this, therefore, I had conceived its possibility, I myself also began to meditate upon the mobility of the earth. And although the opinion seemed absurd, yet because I knew the liberty had been accorded to others before me of imagining whatsoever circles they pleased to explain the phenomena of the stars, I thought I also might readily be allowed to experiment whether, by supposing the earth to have some motion, stronger demonstrations than those of the others could be found as to the revolution of the celestial sphere. Thus, supposing these motions which I attribute to the earth later on in this book, I found at length by much and long observation, that if the motions of the other planets were added to the rotation of the earth and calculated as for the revolution of that planet, not only the phenomena of the others followed from this, but also it so bound together both the order and magnitude of all the planets and the spheres and the heaven itself, that in no single part could one thing be altered without confusion among the other parts and in all the universe. Hence for this reason in the course of this work I have followed this system."

"Nor do I doubt that skilled and scholarly mathematicians will agree with me if, what philosophy requires from the beginning, they will examine and judge, not casually but deeply, what I have gathered together in this book to prove these things. ...Mathematics is written for mathematicians, to whom these my labours, if I am not mistaken, will appear to contribute something. ...What... I may have achieved in this, I leave to the decision of your Holiness especially, and to all other learned mathematicians. ...If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash."

"Those who devised the eccentrics seen thereby in large measure to have solved the problem of apparent motions with approximate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts. On the contrary, their experience was just like someone taking from various places hands, feet, a head, and other pieces, very well depicted it may be, but for the representation of a single person; since these fragments would not belong to one another at all, a monster rather than a man would be put together from them."

"What indeed is more beautiful than heaven, which of course contains all things of beauty."

"For when a ship is floating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In the same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating."

"We are taught all this [the motion of the earth on its axis and around the sun] by the order of succession, in which those phenomena (various planetary happenings) follow each other, and by the harmony of the world, if we will only, as the saying goes, look at the matter with both eyes."

"Hence I feel no shame in asserting that this whole region engirdled by the moon, and the center of the earth, traverse this grand circle amid the rest of the planets in an annual revolution around the sun. Near the sun is the center of the universe. Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth."

"At rest, however, in the middle of everything is the sun. For, in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. The Thrice Greatest labels it a visible god, and Sophocles' Electra, the all-seeing. Thus indeed, as though seated on a royal throne, the sun governs the family of planets revolving around it."

"We find then in this arrangement an admirable harmony of the world, and a dependable, harmonious interconnexion of the motion and the size of the paths, such as otherwise cannot be discovered. For here the penetrating observer can note why the forward and the retrograde movement of Jupiter appears greater than that of Saturn, and smaller than that of Mars, and again greater with Venus than with Mercury; and why such retrogression appears oftener with Saturn than with Jupiter, less often with Mars and Venus than with Mercury. Moreover, why Saturn, Jupiter, and Mars, when they rise in the evening, appear greater than when they disappear and reappear [with the sun] . . . And all this results from the same cause, namely the motion of the earth."

"The forward and backward arcs appear greater in Jupiter than in Saturn and smaller than in Mars, and on the other hand greater in Venus than in Mercury. This reversal in direction appears more frequently in Saturn than in Jupiter, and also more rarely in Mars and Venus than in Mercury. Moreover, when Saturn, Jupiter, and Mars rise at sunset, they are nearer to the earth than when they set in the evening or appear at a later hour. But Mars in particular, when it shines all night, seems to equal Jupiter in size, being distinguished only by its reddish color. Yet in the other configurations it is found barely among the stars of the second magnitude, being recognized by those who track it with assiduous observations. All these phenomena proceed from the same cause, which is the earth's motion. Yet none of these phenomena appears in the fixed stars. This proves their immense height, which makes even the sphere of the annual motion, or its reflection, vanish from before our eyes. For, every visible object has some measure of distance beyond which it is no longer seen, as is demonstrated in optics. From Saturn, the highest of the planets, to the sphere of the fixed stars there is an additional gap of the largest size. This is shown by the twinkling lights of the stars. By this token in particular they are distinguished from the planets, for there had to be a very great difference between what moves and what does not move. So vast, without any question, is the divine handiwork of the most excellent Almighty."

"To know that we know what we know, and that we do not know what we do not know, that is true knowledge."

"Therefore alongside the ancient hypotheses, which are no more probable, let us permit these new hypotheses also to become known, especially since they are admirable as well as simple and bring with them a huge treasure of very skillful observations. So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it."

"The nationality question has been a subject of various writings; an honoring controversy over the claim to the founder of our current world view is conducted between Poles and Germans, but as already mentioned nothing certain can be determined concerning the nationality of Copernicus' parents; the father seems to have been of Slavic birth, the mother German; he was born in a city whose municipal authorities and educated inhabitants were Germans, but which at the time of his birth was under Polish rule; he studied at the Polish capital, Krakau, then in Italy, and lived out his days as a canon in Frauenburg; he wrote Latin and German. In science, he is a man who belongs to no single nation, whose labors and strivings belong to the whole world, and in C. we do not honor the Pole nor the German, but the man of free spirit, the great astronomer, the father of the new astronomy, the originator of the true Weltanschauung (world view)."

"The division of the seamless garment of Christendom into separate nations or sovereign states, which today we accept as a matter of course, was then only beginning. And the idea that people belong to all sorts of different races, with boasts of racial "purity" or "superiority", is something that has come up practically within the memories of people still alive. Hence if the astronomer had been asked concerning his race and nation, he might have replied that he was a loyal son of the Churchbut otherwise would scarcely have understood the questions. Even for us today it is not an easy question to answer. Torun was founded by Germans; its leading citizens, like those of Cracow, were mostly Germans. Hence the astronomer may well have been of German extraction.[http://books.google.com/books?as_brr=0&id=plI3AAAAIAAJ&dq=author%3A%22Angus+Armitage%22&q=of+German+extraction&pgis=1#search The possible connection of the family on both sides with Silesia does not prove much either way for its population was a mixed one. On the other hand, the ancestors, especially on the father's side, must have lived for so many generations under allegiance to the King of Poland as to be, for all practical purposes, Poles. And Copernicus followed the family tradition in siding with the Poles against the Germans in times of crisis. In any case, it was Poland, and Cracow above all, that first nourished the youthful genius of Copernicus. And since his death it is chiefly the Poles who have gloried in their share in him, and have cherished the renown his achievements have brought to their heroic and ill-starred nation."

"In our time Nicholas Copernicus may not undeservedly be called a second Ptolemy. Through observations made by himself he discovered certain gaps in Ptolemy, and he concluded that the hypotheses formulated by Ptolemy admit something unsuitable in violation of the axioms of mathematics. Moreover, he found the Alfonsine computations in disagreement with the motions of the heavens. Therefore, with wonderful intellectual acumen he formulated different hypotheses. He restored the science of the heavenly motions in such a way that nobody before him reasoned more accurately about the movements of the heavenly bodies."

"He was a man of grave and cultivated mind, of rapid and mature intelligence; inferior to no preceding astronomer, unless in order of succession and time ; a man, who in natural ability was far superior to Ptolemy, Hipparchus, Eudoxus, and all those others who followed in their footsteps. What he was, he became through having liberated himself from certain false axioms of the common and vulgar philosophy — I will not say blindness. Nevertheless, he did not depart far from them ; because, studying mathematics rather than Nature, he failed to penetrate and dig deep enough altogether to cut away the roots of incongruous and vain principles, and thus, removing perfectly all opposing difficulties, free himself and others from so many empty investigations into things obvious and unchangeable. In spite of all this, who can sufficiently praise the magnanimity of this Pole, who, having little regard to the foolish multitude, stood firm against the torrent of contrary opinion, and, although well-nigh unarmed with living arguments, resuming those rusty and neglected fragments which antiquity had transmitted to him, polished, repaired, and put them together with reasonings more mathematical than philosophical ; and so rendered that cause formerly contemned and contemptible, honourable, estimable, more probable than its rival, and certainly convenient and expeditious for purposes of theory and calculation ? Thus this Teuton, although with means insufficient to vanquish, overthrow, and suppress falsehood, as well as resist it, nevertheless resolutely determined in his own mind, and openly confessed this final and necessary conclusion : that it is more possible that this globe should move with regard to the universe, than that the innumerable multitude of bodies, many of which are known to be greater and more magnificent than our earth, should be compelled, in spite of Nature and reason, which, by means of motions evident to the senses, proclaim the contrary, to acknowledge this globe as the centre and base of their revolutions and influences. Who then will be so churlish and discourteous towards the efforts of this man, as to cover with oblivion all he has done, by being ordained of the Gods as an Aurora - which was to precede the rising of this Sun of the true, ancient philosophy, buried during so many centuries in the tenebrous caverns of blind, malignant, froward, envious ignorance ; and, taking note only of what he failed to accomplish, rank him amongst the number of the herded multitude, which discourses, guides itself, precipitates to destruction, according to the oral sense of a brutal and ignoble belief, rather than amongst those who, by the use of right reason, have been able to rise up, and resume the true course under the faithful guidance of the eye of divine intelligence."

"To follow Ptolemy in ancient times meant merely to reject the cumbrous crystalline spheres. To follow Copernicus was a far more radical step, it meant to reject the whole prevailing conception of the universe."

"He had himself become convinced that the whole universe was made of numbers, hence whatever was mathematically true was really or astronomically true. Our earth was no exception it, too, was essentially geometrical in nature therefore the principle of relativity of mathematical values applied to man's domain just as to any other part of the astronomical realm. The transformation to the new world-view, for him, was nothing but a mathematical reduction... of a complex geometrical labyrinth into a beautifully simple and harmonious system."

"Copernicus had formed a rudimentary conception of scientific hypothesis, accommodated to his new astronomical method. A true hypothesis is one which binds together rationally... things which had before been held distinct; it reveals the reason, in terms of that which unites them, why they are as they are."

"The Copernican theory contains many absurd or erroneous assertions."

"Copernicus entered the University of Bologna, as a student of canon law, at the opening of the winter term of 1496-7. The occurrence of his name in the annals of the 'Natio Germanorum' must be regarded as a strong point in favour of the upholders of his Teutonic origin. Indeed, taken in connexion with his unquestioned use of German as his mother-tongue, it might — at least by impartial outsiders possessing intelligence of the ordinary blunt, though serviceable type — be fairly held to terminate the controversy. This, however, seems beyond hope. Controversies rarely die save of inanition. For adverse facts they not unfrequently prove to have the digestion of ostriches. And in the present instance, where common sense and technical argument might be said to be arrayed one against the other, it is plain that the view taken depends, in great measure, upon the natural bias of the mind."

"He is the supreme example of a man who revolutionized science by looking at the old facts in a new way."

"What Luther's burning of the Papal Bull was in the religious field, in the field of natural science was the great work of Copernicus, in which he, although timidly... threw down a challenge to ecclesiastical superstition. From then on natural science was in essence emancipated from religion, although the complete settlement of accounts in all details has gone on to the present day and in many minds is still far from being complete. But from then on the development of science went forward with giant strides, increasing, so to speak, proportionately to the square of the distance in time from its point of departure, as if it wanted to show the world that for the motion of the highest product of organic matter, the human mind, the law that holds good is the reverse of that for the motion of inorganic matter."

"[Copernicus] did not ignore the Bible, but he knew very well that if his doctrine were proved, then it could not contradict the Scriptures when they were rightly understood."

"It was Copernicus who by his work showed us how fragile time-honored scientific conceptions can be."

"Of all discoveries and opinions, none may have exerted a greater effect on the human spirit than the doctrine of Copernicus. The world had scarcely become known as round and complete in itself when it was asked to waive the tremendous privilege of being the center of the universe. Never, perhaps, was a greater demand made on mankind — for by this admission so many things vanished in mist and smoke! What became of our Eden, our world of innocence, piety and poetry; the testimony of the senses; the conviction of a poetic — religious faith? No wonder his contemporaries did not wish to let all this go and offered every possible resistance to a doctrine which in its converts authorized and demanded a freedom of view and greatness of thought so far unknown, indeed not even dreamed of."

"I thought that this auction with other nations for geniuses and heroes, for merits and cultural achievement, was really quite awkward from the point of view of propaganda tactics because with our half-French Chopin and not quite native Copernicus, we cannot compete with the Italians, French, Germans, English, or Russians. Therefore, it is exactly this approach that condemns us to inferiority."

"The beginning of astronomy, except observations, I think is not to be derived from farther time than from Nicolaus Copernicus; who in the age next preceding the present revived the opinion of Pythagoras, Aristarchus, and Philolaus."

"To reassert the reign of beauty, Copernicus goes back to what he had once called "the first principles of uniform motion." He rejects non-uniformities and inconsistancies of motion - his "mind shudders" at the very consideration of them - and even at the cost of setting the earth in motion, he arrives at a system that has all the earmarks of divine handicraft; the s are gone, the phenomena are saved; the whole system has symmetry, parsimony, necessity. ... The device of uniform motion in a circle was not forced by the data; and as Kepler's ellipses showed later, it was not even the most functional device from the mathematical point of view. Yet the metaphor of uniform circular motion as the divine key... - even as in antiquity - had infected the thinking from which the scientific revolution of the seventeenth century came. ...the function of a metaphor ..."can be a restructuring of the world," in the words of Sir Ernst Gombrich."

"Copernicus, Kepler and Galileo were ‘revisionists’ in rejecting the geocentric system of Ptolemy (which held sway for some 1500 years) and, against an oppressive and repressive mainstream opinion (and officialdom), reinstated—with improvements—the heliocentric system of Aristarchos of Samos (3rd cent BCE)."

"When printed, the book was accepted by the holy Church and it has been read and studied by everyone without the faintest hint of any objection ever being conceived against its doctrines. Yet now that manifest experiences and necessary proofs have shown them to be well grounded, persons exist who would strip the author of his reward without so much as looking at his book."

"The fool will upset the whole science of astronomy."

"Certain people believe it is a marvelous achievement to extol so crazy a thing, like that Polish astronomer who makes the earth move and the sun stand still. Really, wise governments ought to repress impudence of mind."

"If Tellus winged be, The earth a motion round; Then much deceived are they Who nere before it found. Solomon was the wisest, His wit nere this attained; Cease, then, Copernicus, Thy hypothesis is vain."

"It gave me pleasure to contemplate the right of the Polish nobleman to upset with his simple veto the determinations of a [parliamentary] session; and the Pole Copernicus seemed to have made of this right against the determinations and presentations of other people, the greatest and worthiest use."

"On the five-hundred-thirtieth anniversary of the birth, and the four-hundred-sixtieth anniversary of the death, of Mikołaj Kopernik, the Senate of the Polish Republic expresses its highest esteem and praise for this exceptional Pole, one of the greatest scientists in world history. Mikołaj Kopernik, world-famous astronomer and author of the landmark work, De revolutionibus orbium coelestium, "stopped the Sun and moved the Earth." He distinguished himself for Poland as an exceptional mathematician, economist, lawyer, physician and priest, as well as defender of Olsztyn Castle during the Polish-Teutonic war. May the memory of his achievements endure and be a source of inspiration to future generations."

"Poles and Germans have a common history of great scientists: Today we no longer perceive Copernicus, Hevelius, Schopenhauer and Fahrenheit as the property of one nation but as representatives of one transnational culture."

"It was not only... with classical antiquity that Copernicus showed himself a man of the Renaissance. He also strove to achieve the many-sided accomplishments of that humanistic ideal, the universal man. He was competent in canon law; he practiced medicine; he wrote a tract on coinage; he served his cathedral chapter as an administrator and diplomatic representative; he painted his own portrait; he made many of his own astronomical instruments; and he established the heliocentric system on a firm basis."

"Germans and Poles have bitterly disputed the question of Copernicus's ethnic origin, each national group claiming the distinguished astronomer for its own. Where does the truth lie in this controversy? Politically, Copernicus was a subject of the king of Poland; he remained loyal to the Roman Catholic church ; and he wrote chiefly in Latin, but a few of his private letters were composed in German."

"Copernicus made his revolutionary suggestion on purely theoretical grounds. The invention of the telescope came after and not before, the publication of his great work. This is a fact upon which we may well ponder, for it shows that the insight into natural phenomena has come as much from the genius of the theoretical as from that of the experimental and observational investigator."

"These are the moments when the powerful mind 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."

"The air in a man's lungs contains 10,000,000,000,000,000,000,000 atoms, so that sooner or later every one of us breathes an atom that has been breathed before by anyone you can think of who has ever lived — Michelangelo or George Washington or Moses."

"I grew up to be indifferent to the distinction between literature and science, which in my teens were simply two languages for experience that I learned together."

"The most modest research worker at his bench, pushing a probe into a neuron to measure the electric response when a light is flashed, is enmeshed in a huge and intertwined network of theories that he carries into his work from the whole field of science, all the way from Ohm’s law to Avogadro's number. He is not alone; he is sustained and held and in some sense imprisoned by the state of scientific theory in every branch. And what he finds is not a single fact either: it adds a thread to the network, ties a knot here and another there, and by these connections at once binds and enlarges the whole system."

"The progress of science is the discovery at each step of a new order which gives unity to what had long seemed unlike. Faraday did this when he closed the link between electricity and magnetism. Clerk Maxwell did it when he linked both with light. Einstein linked time with space, mass with energy, and the path of light past the sun with the flight of a bullet; and spent his dying years in trying to add to these likenesses another, which would find a single imaginative order between the equations between Clerk Maxwell and his own geometry of gravitation When Coleridge tried to define beauty, he returned always to one deep thought: beauty he said, is "unity in variety." Science is nothing else than the search to discover unity in the wild variety of nature — or more exactly, in the variety of our experience."

"It has been one of the most destructive modern prejudices that art and science are different and somehow incompatible interests. We have fallen into the habit of opposing the artistic to the scientific tempers; we even identify them with a creative and a critical approach."

"The sneer that science is only critical came from others. It was made by the timid and laboured artists of the nineties in order that they might by comparison appear to be creative and intuitive. Yet this finesse could not hide their own knowledge that the best minds were already being drawn to the more adventurous practice of the new sciences."

"Science is not a special sense. It is as wide as the literal meaning of its name: knowledge."

"Many people affect to believe that science has progressively strangled the arts, or distorted them into some unpleasant “modern” form; and therefore that the arts can be revived only by throwing over science. Often of course this is merely an elderly sentiment in favour of the art of our younger days, and the real scapegoat is not science but change."

"Science changes our values in two ways. It injects new ideas into the familiar culture. And it subjects it to the pressure of technical change, in the way I have just been describing, until the whole basis of our culture has imperceptibly been remade."

"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."

"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."

"Unhappily, common sense has no recorded history."

"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."

"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."

"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 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."

"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."

"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."

"This ability to order things into likes and unlikes is, I think, the foundation of human thought."

"On the one hand, all science, and indeed all thinking starts from and rests upon notions of order; what marks the Middle Ages is that their order was always a hierarchy. And on the other hand what marks the scientific view is not that it turned to the mechanism of causes, but that it saw the world as a mechanism at all—a machine of events."

"The Scientific Revolution revolution was a change from a world of things ordered according to their ideal nature, to a world of events running in a steady mechanism of before and after."

"Of these massive achievements I shall single out two. One is Newton’s working out of the concept of the cause, by making it over from its scholastic form in, say, St. Thomas Aquinas, to the modern form which now seems so obvious to us. This is one theme in this chapter. But I shall go to it by way of a related achievement, and to my mind one which is as remarkable: the marriage of the logical with the empirical method."

"In order to act in a scientific manner, in order to act in a human manner at all, two things are necessary: fact and thought. Science does not consist only a finding the facts; nor is it enough only to think, however rationally. The processes of science are characteristic of human action in that they move by the union of empirical fact and rational thought, in a way which cannot be disentangled."

"In Whitehead’s view, the Middle Ages were quite as logical in their speculations about nature as we are. It is not as rationalists that we have the advantage of them; our material successes stem from joining to their logic a ruthless appeal, at each bold deductive step, back to the hard empirical facts."

"The outlook before the Scientific Revolution was content with scholastic logic applied to a nature of hierarchies. The Scientific Revolution ended that: it linked the rational and the empirical, thought and fact, theory and practical experiment. And this has remained the content of science ever since."

"The [eighteenth] century settled down in two camps of Philistines: the literary Philistines and, largely to spite them, the scientific Philistines. It was the beginning of the mistaken opposition between them from which we still suffer."

"Order is the selection of one set of appearances rather than another because it gives a better sense of the reality behind the appearances."

"We cannot change our character, we can only enlarge it. If we are wise, then we go on learning all through life, and go on fitting what is new to what we have learnt before, piece by piece."

"The purpose of science is to describe the world in an orderly scheme or language which will help us to look ahead. We want to forecast what we can of the future behaviour of the world; particularly we want to forecast how it would behave under several alternative actions of our own between which we are usually trying to choose."

"Science is a way of describing reality; it is therefore limited by the limits of observation; and it asserts nothing which is outside observation. Anything else is not science; it is scholastics."

"Of course, everyone is free to prefer his favourite article of faith to the scientific, that is the empirical method. But do not let us imagine that his faith is then anything except a piece of comfortable and customary superstition. To try to make a nice distinction between what science can predict and what is somehow supernaturally determined is a piece of elegant but really quite shameless self-deception. Science is a practical study of what can be observed, and the prediction from that of what will be observed. To say that causes are somehow getting under this observable world, when anything under it is essentially unobservable, is neither helpful nor meaningful; it is just a piece of faithful comfort. We might as well say that the electrons are really pushed about by blue fairies with red noses who know exactly what they are doing, only it happens that every time we look in their direction these fairies instantly hide. If they are essentially unobservable, beyond all hope of future unravelling, then it simply does not make sense to bring them into any system, logical, metaphysical, or even religious."

"Life is not an examination; we do not get marks for the steps; what matters is getting the right answer. So it is perfectly possible to base a system of prediction on no principle except trying to get the right answer. This is exactly what all plants and animals do. The bat avoids obstacles by shouting at them that shrill cry just beyond my hearing, and then listens for the echo. Whatever system it has for translating the echo into a prediction it has found by evolution, and evolution has found it by trial and error."

"The laws of science have two functions, to be true and to be helpful; probably each of these functions includes the other. If the statistical law does both, that is all that can be asked of it. We may persuade ourselves that it is intellectually less satisfying than a causal law, and fails somehow to give us the same feeling of understanding the process of nature. But this is an illusion of habit."

"Science as we know it is indeed a creation of the last three hundred years. It has been made in and by the world that took its settled shape about 1660, when Europe at last shook off the long nightmare of religious wars and settled into a life of inquisitive trade and industry. Science is embodied in those new societies; it has been made by them and has helped to make them."

"The mastery and the greatness of science rests in the end on this, that here the rational and the empirical are knotted together. Science is fact and thought giving strength to one another."

"We do not construct the world from our experiences; we are aware of the world in our experiences."

"We are troubled by a two-sidedness in our own behaviour, where one side is what we have long been taught to value, and the other is worldly success. We are faced every day with actions of which our own code of conduct makes us ashamed, but which we find compelling if we are to battle with the hard facts of society. We do not consciously blame science for this rift until it throws out some unavoidable challenge, such as in our time has been set by the atomic bomb. But that sharp issue is merely a symbol. Beyond all our actions stands the larger shadow: how are we to choose between that which we have been taught to think right and something else which manifestly succeeds?"

"There has never been a great book or a powerful work of art which has not been thought immoral by those with an older tradition."

"There is indeed no system of morality which does not set a high value on truth and on knowledge, above all on a conscious knowledge of oneself. It is therefore at least odd that science should be called amoral, and this by people who in their own lives set a high value on being truthful. For whatever else may be held against science, this cannot be denied, that it takes for ultimate judgment one criterion alone, that it shall be truthful."

"At bottom, we have remain individually too greedy to distribute our surplus, and collectively too stupid to pile it up in any more useful form than the traditional mountains of arms."

"If any ideas have a claim to be called creative, because they have created something, then certainly it is the ideas of science."

"A good prediction is one which defines its area of uncertainty; a bad prediction ignores it."

"Science is a great many things, and I have called them a great many names; but in the end they all return to this: science is the acceptance of what works and the rejection of what does not. That needs more courage than we might think."

"Here is the ultimate hope of saving ourselves from extinction. We must learn to understand that the contents of all knowledge is empirical; that its test is whether it works; and we must learn to act on that understanding in the world as well as in the laboratory."

"I have seen in my lifetime an abyss open in the human mind: a gulf between the endeavour to be man, and the relish in being brute. The scientist has indeed had a hand in this, and every other specialist too, with his prim detachment and his oracular airs. But of course, the large strain which has opened this fault is social. We have made men live in two halves, a Sunday half and a workday one. We have ordered them to love their neighbor and to turn the other cheek, in a society which has constantly compelled them to shoulder their neighbor aside and to turn their backs. So we have created a savage sense of failure which, as we now know to our cost, can be tapped with an ease which is frightening; and which can thrust up, with explosive force, a symbol to repeat to an unhappy people its most degrading dream."

"Can science heal that neurotic flaw in us? If science cannot, then nothing can. Let us stop pretending. There is no cure in high moral precepts. We have preached them too long to men who are forced to live how they can: that makes the strain which they have not been able to bear. We need an ethic which is moral and which works. It is often said that science has destroyed our values and put nothing in their place. What has really happened of course is that science has shown in harsh relief the division between our values and our world. We have not begun to let science get into our heads; where then was it supposed to create these values?"

"The discoveries of science, the works of art are explorations — more, are explosions, of a hidden likeness. The discoverer or the artist presents in them two aspects of nature and fuses them into one. This is the act of creation, in which an original thought is born, and it is the same act in original science and original art."

"Science, like art, is not a copy of nature but a re-creation of her."

"We re-make nature by the act of discovery, in the poem or in the theorem. And the great poem and the deep theorem are new to every reader, and yet are his own experience, because he himself re-creates them."

"Mass, time, magnetic moment, the unconscious: we have grown up with these symbolic concepts, so that we are startled to be told that man had once to create them for himself. He had indeed, and he has: for mass is not an intuition in the muscle, and time is not bought ready-made at the watchmaker's."

"The symbol and the metaphor are as necessary to science as to poetry."

"In effect what Luther said in 1517 was that we may appeal to a demonstrable work of God, the Bible, to override any established authority. The Scientific Revolution begins when Nicolaus Copernicus implied the bolder proposition that there is another work of God to which we may appeal even beyond this: the great work of nature. No absolute statement is allowed to be out of reach of the test, that its consequence must conform to the facts of nature. The habit of testing and correcting the concept by its consequences in experience has been the spring within the movement of our civilization ever since. In science and in art and in self-knowledge we explore and move constantly by turning to the world of sense to ask, Is this so? This is the habit of truth, always minute yet always urgent, which for four hundred years has entered every action of ours; and has made our society and the value it sets on man."

"No fact in the world is instant, infinitesimal and ultimate, a single mark. There are, I hold, no atomic facts. In the language of science, every fact is a field — a crisscross of implications, those that lead to it and those that lead from it. … We condense the laws around concepts. Science takes its coherence, its intellectual and imaginative strength together, from the concepts at which its laws cross, like knots in a mesh."

"Positivists and analysts alike believe that the words is and ought belong to different worlds, so that sentences which are constructed with is usually have verifiable meaning, but sentences constructed with ought never have. This is because Ludwig Wittgenstein's unit, and Bertrand Russell's unit, is one man; all British empiricist philosophy is individualist. And it is of course clear that if the only criterion of true and false which a man accepts is that man's, then he has no base for social agreement. The question of how man ought to behave is a social question, which always involves several people; and if he accepts no evidence and no judgment except his own, he has no tools with which to frame an answer."

"There is a social injunction implied in the positivist and analyst methods. This social axiom is that We OUGHT to act in such a way that what IS true can be verified to be so."

"Has there ever been a society which has died of dissent? Several have died of conformity in our lifetime."

"Tolerance among scientists cannot be based on indifference, it must be based on respect. Respect as a personal value implies, in any society, the public acknowledgements of justice and of due honor. These are values which to the layman seem most remote from any abstract study. Justice, honor, the respect of man for man: What, he asks, have these human values to do with science? [...] Those who think that science is ethically neutral confuse the findings of science, which are, with the activity of science, which is not."

"Nature is more subtle, more deeply intertwined and more strangely integrated than any of our pictures of her — than any of our errors. It is not merely that our pictures are not full enough; each of our pictures in the end turns out to be so basically mistaken that the marvel is that it worked at all."

"The painter's portrait and the physicist's explanation are both rooted in reality, but they have been changed by the painter or the physicist into something more subtly imagined than the photographic appearance of things."

"The force that makes the winter grow Its feathered hexagons of snow, and drives the bee to match at home Their calculated honeycomb, Is abacus and rose combined.An icy sweetness fills my mind, A sense that under thing and wing Lies, taut yet living, coiled, the spring."

"Dissent is the mark of freedom."

"There is today almost no scientific theory which was held when, say, the Industrial Revolution began about 1760. Most often today's theories flatly contradict those of 1760; many contradict those of 1900. In cosmology, in quantum mechanics, in genetics, in the social sciences, who now holds the beliefs that seemed firm sixty years ago? Yet the society of scientists has survived these changes without a revolution, and honors the men whose beliefs it no longer shares. No one has recanted abjectly at a trial before his colleagues. The whole structure of science has been changed and no one has been either disgraced or deposed. Through all the changes of science, the society of scientists is flexible and single-minded together, and evolves and rights itself. In the language of science, it is a stable society."

"The most remarkable discovery made by scientists is science itself. The discovery must be compared in importance with the invention of cave-painting and of writing. Like these earlier human creations, science is an attempt to control our surroundings by entering into them and understanding them from inside. And like them, science has surely made a critical step in human development which cannot be reversed. We cannot conceive a future society without science. I have used three words to describe these far - reaching changes : discovery, invention and creation. There are contexts in which one of these words is more appropriate than the others."

"Christopher Columbus discovered the West Indies, and Alexander Graham Bell invented the telephone. We do not call their achievements creations because they are not personal enough. The West Indies were there all the time; and as for the telephone, we feel that Bell's ingenious thought was somehow not fundamental. The groundwork was there, and if not Bell then someone else would have stumbled on the telephone almost as accidently as on the West Indies."

"A fact is discovered, a theory is invented; is any theory ever deep enough for it to be truly called a creation? Most scientists would answer: no! Science, they would say, engages only part of the mind - the rational intellect - but creation must engage the whole mind. Science demands none of that ground swell of emotion, none of the rich bottom of personality, which fills out the work of art..."

"To imagine is the characteristic act, not of the poet's mind, or the painter's, or the scientist's, but of the mind of man."

"To imagine means to make images and to move them about inside one's head in new arrangements."

"With the... symbolic memory we spell out the future—not one but many futures, which we weigh one against another."

"I am using the word image in a wide meaning, which does not restrict it to the mind's eye as a visual organ. An image in my usage is what Charles Pierce called a sign..."

"[T]he most important images for human beings are simply words, which are abstract symbols. ...[E]volution has greatly enlarged the front lobes of the human brain, which govern the sense of the past and the future; and... they are probably the seat of our other images."

"The images play out for us events which are not present in our senses, and... create the future—a future that... may never come to exist in that form."

"Almost everything that we do that is worth doing is done in the first place in the mind's eye."

"The richness of human life is that we have many lives, we live the events that do not happen (and some that cannot) as vividly as those that do, and if thereby we die a thousand deaths, that is the price we pay..."

"Imagination is the manipulation of images in one's head... the rational manipulation... as well as the literary and artistic manipulation."

"When a child begins to play games... he enters the gateway to reason and imagination together."

"[T]he human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight... induction, which—like other forms of imagination—cannot be formalized."

"The strength of the imagination, its enriching power and excitement, lies in its interplay with reality—physical and emotional."

"All great scientists have used their imaginations freely, and let it ride them to outrageous conclusions without crying "Halt!""

"The symbol is the tool which gives man his power, and it is the same tool whether the symbols are images or words, mathematical signs or s."

"[S]ymbols have a reach and a roundness that goes beyond their literal and practical meaning. They are the rich concepts under which the mind gathers many particulars into one name, and many instances into one general induction."

"When a man counts one, two, three, he is not only doing mathematics, he is on the path to the mysticism of numbers in Pythagoras and Vitruvius and Kepler, to the Trinity and the signs of the Zodiac."

"[I]magination... is the faculty... the common root from which science and literature... spring and grow and flourish together. ...the great ages of science are the great ages of all the arts... [P]owerful minds have taken fire from one another... without asking... to tie their imagination to falling balls or a haunted island. ...When Galileo was looking through his telescope at the moon, Shakespeare was writing The Tempest and all Europe was in ferment, from Johannes Kepler to Peter Paul Rubens, and from the first table of logarithms by John Napier to the Authorized version of the Bible."

"Let me end with... man's ageless fantasy, to fly to the moon. ...Plutarch and Lucian, Ariosto and Ben Jonson wrote about it, before the days of Jules Verne and H. G. Wells and science fiction. The seventeenth century was heady with... fables about voyages to the moon. Kepler wrote one full of deep scientific ideas... wrote... '... wrote... The Discovery of a New World. They did not draw a line between science and fancy... they all tried to guess where... earth's gravity would stop. Only Kepler understood that gravity has no boundary, and put a law to it—... the wrong law. All this was a few years before Isaac Newton was born, and it was all in his head that day in 1666, when he... came to conceive... that the moon is like a ball... thrown so hard that it falls exactly as fast as the horizon... he went on to calculate how long... the distant moon would take to round the earth... [T]he imagination that day chimed with nature, and made a harmony."

"In every age there is a turning point, a new way of seeing and asserting the coherence of the world. It is frozen in the statues of Easter Island that put a stop to time—and in the medieval clocks of Europe that once also seemed to say the last word about the heavens for ever. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or of man. But in retrospect, what commands our attention as much are the continuities—the thoughts that run or recur from one civilization to another."

"Man is not the most majestic of the creatures; long before the mammals even, the dinosaurs were far more splendid. But he has what no other animal possesses: a jigsaw of faculties, which alone, over three thousand million years of life, made him creative. Every animal leaves traces of what he was. Man alone leaves traces of what he created."

"In a parched African landscape like this at Omo, man first put his foot to the ground. That seems a pedestrian way to begin the ascent of man."

"Of course it's tempting to close one's eyes to history, and instead speculate about the roots of war in some possible animal instinct: as if, like the tiger, we still had to kill to live, or, like the robin redbreast, to defend a nesting territory. But war, organized war, is not a human instinct. It is a highly planned and cooperative form of theft. And that form of theft began 10,000 years ago when the harvesters of wheat accumulated a surplus and the nomads rose out of the desert to rob them of what they themselves could not provide. The evidence for that, we saw, in the walled city of Jericho and its prehistoric tower... That is the beginning of war."

"One aim of the physical sciences has been to give an exact picture of the material world. One achievement of physics in the twentieth century has been to prove that that aim is unattainable. There is no absolute knowledge and those who claim it, whether they are scientist or dogmatist, open the door to tragedy. All knowledge, all information is imperfect. We have to treat it with humility."

"The symbol of the University is the iron statue outside the Rathskeller of a barefoot goose girl that every student kisses at graduation. The University is a Mecca to which students come with something less than perfect faith. It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known but to question it."

"The Principle of Uncertainty is a bad name. In science, or outside of it, we are not uncertain; our knowledge is merely confined, within a certain tolerance. We should call it the Principle of Tolerance. And I propose that name in two senses. First, in the engineering sense: Science has progressed, step by step, the most successful enterprise in the ascent of man, because it has understood that the exchange of information between man and nature, and man and man, can only take place with a certain tolerance. But second, I also use the word, passionately, about the real world. All knowledge – all information between human beings – can only be exchanged within a play of tolerance. And that is true whether the exchange is in science, or in literature, or in religion, or in politics, or in any form of thought that aspires to dogma. It's a major tragedy of my lifetime and yours that scientists were refining, to the most exquisite precision, the Principle of Tolerance – and turning their backs on the fact that all around them, tolerance was crashing to the ground beyond repair. The Principle of Uncertainty or, in my phrase, the Principle of Tolerance, fixed once for all the realization that all knowledge is limited. It is an irony of history that at the very time when this was being worked out, there should rise, under Hitler in Germany and other tyrants elsewhere, a counter-conception: a principle of monstrous certainty. When the future looks back on the 1930's, it will think of them as a crucial confrontation of culture as I have been expounding it – the ascent of man against the throwback to the despots' belief that they have absolute certainty."

"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."

"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."

"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."

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

"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."

"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."

"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."

"I believe that the world is totally connected: that is to say, that there are no events anywhere in the universe which are not tied to every other event in the universe. ...It is... an essential part of the methodology of science to divide the world for any experiment into... relevant and... irrelevant. We make a cut. We put the experiment... into a box. ...the moment we do that, we do violence to the connections ...I get a set of answers which I try to decode in this context. ...I am certainly not going to get the world right, because the basic assumption that I have made about the world is a lie. ...it is bound to give me only an approximation to what goes inside the fence. Therefore, when we practice science (and this is true of all our experience) we are always decoding a part of nature which is not complete. We simply cannot get out of our own finiteness."

"Let me close by reminding you of what Newton actually did on the day that he conceived G = k \frac{mm'}{r^2}. ...Newton did not have any subsidies, grants, funds, Secret Service money. But he had the moon. He said, "... I cannot throw a ball round the world, but let me picture the moon as if it were a ball which has been flung around the world... How long will it take to go round the world?" ...He knew the value of gravity at the earth's surface ...but he did not know the value of the earth's gravity for the moon. He said, "Let us suppose that it is given by an inverse square law. Now, how long will it take the moon to go around?" It comes out at twenty-eight days. As Newton said, "They agreed pretty nearly.""

"Progress is the exploration of our own error. Evolution is a consolidation of what have always begun as errors. And errors are of two kinds: errors that turn out to be true and errors that turn out to be false (which are most of them). But they both have the same character of being an imaginative speculation. ...it seems to me terribly important to say this in an age in which most nonscientists are feeling a kind of loss of nerve. ...by the time science becomes a closed—that is, computerizable—project, it is not science anymore. It is not in the area of the exploration of errors."

"[A]ll our symbols have the same purpose; words are merely the symbols we use most commonly. The function of words in human thought is to stand for things which are not present to the senses, and allow the mind to manipulate them—things, concepts, ideas, everything that does not have a physical reality in front of us now."

"The language of ideas creates a different universe: a universe which has multiplied the monkey's vocabulary of forty words to the million words in the English dictionary."

"Human beings can imagine situations which are different from those in front of their eyes... because they make and hold in their minds images for absent things."

"When a child... discovers his own imagination, he suddenly walks into a new life. ...seeing situations that do not exist. ...in part as fantasy, and in part as a quite rational exploration of future experiences. ...play ...frolics in the fantasy world, and it experiments in the rational world... They project themselves into all worlds, possible and impossible, and discover for themselves the knife-edge boundary between them."

"The ability... to experiment with imaginary situations, gives man a freedom... the pleasure in trying out and exploring imaginary situations. A child's play is concerned with this pleasure; and so is much of art, and much of science... [P]ure science... is a form of play, in this sense."

"He first became familiar to the British public through appearances on the BBC television version of The Brains Trust in the late 1950s, but is better known for his... series The Ascent of Man (1973). This was an inspiration for Carl Sagan to make Cosmos in 1980. During the making of The Ascent of Man he was interviewed by Michael Parkinson, and Bronowski's description of a visit to Auschwitz—he had lost many family members during the Nazi era—was described by Parkinson as one of his most memorable interviews. ...Bronowski died of a heart attack in East Hampton, New York a year after The Ascent of Man was completed, and was buried in the western side of London's ..."

"[[Richard von Mises|[V]on Mises]] and raised the objection that in Reichenbach's theory a theory was said to be "valid with a probability of 70%," if 70 per cent of the conclusions of the theory were confirmed by experiment. However, we know... a theory which is in disagreement with experience in 30% of... experiments is called "false" or "wrong." We come to the same conclusion if we apply Carnap's "." An attempt to avoid these difficulties and to advance a radically different approach... was made by Jacob Bronowski. His purpose was to formalize the criterion for the validity of a theory that was advocated by men like John Frederick Herschel and William Whewell. ...these scientists and philosophers saw the main achievement of a theory in its unifying and simplifying power. The simpler the theory... the more probable the theory. If the theory consists in a complete enumeration of all observable facts, the "theory" would have a very high probability... However, von Mises and Bronowski rejected this... If we have two theories which yield the same observable facts, the scientist prefers the... more economical or just simpler. Bronowski compares the scientific theory with a code... We prefer the code which is more practical, more efficient. ...to improve the code, we try systematically... "to break down the code into its constituent symbols and their laws of arrangement." ...If we break down [chemical] elements into... elementary particles (protons, neutrons, and electrons) and the forces acting between them, we have a code which describes... the interaction between hydrogen and oxygen... from which can be derived much more information than from any theory in which "oxygen" and "hydrogen"...occur as primitive symbols. ...Bronowski calls a theory the more probable, the more the code... is broken down into constituent symbols and laws of arrangement."

"Every acceptance of a debatable theory is due to a compromise between Reichenbach's and Bronowski's criteria: agreement with facts and efficiency as a code."

"The criteria of Reichenbach and Carnap, which are based, like John Stuart Mill's inductive logic, upon agreement with observations, have to be complemented by the criterion of economy and simplicity which was advanced in the history of science by men like William Ockham, Isaac Newton, and Ernst Mach. In out twentieth century, the importance of criteria other than mere agreement with observation was stressed by von Mises and Bronowski."

"The ashes of millions of people were flushed into the pond at Auschwitz, but on that sunny day... I stood at its edge... twenty-four years earlier I sat in front of our television set and watched... Bronowski... as a scientist, a human being, a survivor and a witness at the edge of this pond. Many members of his family had died at Auschwitz. He reminded us that it is said that science will turn people into numbers and told... passionately that this is '...tragically false', and that it was here... that people were turned into numbers and murdered not by the gas... but by the arrogance, the dogma and ignorance... and by the murderers'... belief that they possessed absolute knowledge... never—unlike scientists—tested... against objective reality. ...Bronowski ...reminded us that science is a very human form of knowledge in which every judgement stands on the edge of error and is personal. Quoting the words of Oliver Cromwell—'I beseech you, in the bowels of Christ, think it possible you may be mistaken'—he reached into the water... telling us that we must close the distance between the push-button order and the human act... ending with the words: 'We have to touch people.' ...Bronowski's active defiance of failings such as despair, failing of nerve, fashionable pessimism and irresponsibility had made a permanent and indelible impression on me..."

"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."

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

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

"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."

"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..."

"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."

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

"Thinking very hard about the same problem for several hours can produce a severe fatigue, close to a breakdown. I never really experienced a breakdown, but have felt "strange inside" two or three times during my life."

"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."

"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."

"It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me."

"It is most important in creative science not to give up. If you are an optimist you will be willing to "try" more than if you are a pessimist."

"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."

"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."

"In mathematics, as in physics, so much depends on chance, on a propitious moment."

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

"There may be such a thing as habitual luck. People who are said to be lucky at cards probably have certain hidden talents for those games in which skill plays a role. It is like hidden parameters in physics, this ability that does not surface and that I like to call "habitual luck"."

"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."

"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."

"Very soon I discovered that if one gets a feeling for no more than a dozen other radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships."

"The story that Dick Feynman could open safes whose combinations had been forgotten by their owners is true."

"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."

"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?"

"According to recent studies, at least one star out of three is multiple."

"By an incredible coincidence, Gamow and Edward Condon, who had discovered simultaneously and independently the explanation of radioactivity (one in Russia, the other in this country), came to spend the last ten years of their lives within a hundred yards of each other in Boulder."

"What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else."

"In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents."

"It is not so much whether a theorem is useful that matters, but how elegant it is."

"As one sharpens a knife on a whetstone, the brain can be sharpened on dull objects of thought. Every form of assiduous thinking has its value."

"Thoughts are steered in different ways."

"I am turned off when I see only formulas and symbols, and little text."

"Mathematics may be a way of developing physically, that is anatomically, new connections in the brain."

"[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."

"Teller’s calculations were faulty; his prototype would have been a dud. This was first noticed by Stanislaw Ulam... Having shown that the Teller scheme was a nonstarter, Ulam produced, in his typically absent-minded fashion, a workable alternative. “I found him at home at noon staring intensely out of a window with a very strange expression on his face,” Ulam’s wife recalled. “I can never forget his faraway look as peering unseeing in the garden, he said in a thin voice—I can still hear it—‘I found a way to make it work.’”"

"I contributed; Ulam did not. I'm sorry I had to answer it in this abrupt way. Ulam was rightly dissatisfied with an old approach. He came to me with a part of an idea which I already had worked out and difficulty getting people to listen to. He was willing to sign a paper. When it then came to defending that paper and really putting work into it, he refused. He said, "I don't believe in it.""

"With his unusual looks and magnetic green eyes, he always seemed to stand out in a crowd. I remember a party years later when Georgia O'Keefe pointed an imperious finger in his direction and exclaimed "Who is that man?""

"Engraved on my memory is the day when I found him at noon staring intensely out of a window in our living room with a strange expression on his face. Peering unseeing into the garden, he said "I found a way to make it work." "What work?" I asked. "The Super" he replied. "It is a totally different scheme, and it will change the course of history.""

"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."

"Stalin invented Slonimsky! Then he must have also invented the genetic content of one-quarter of me, for Z. Y. Slonimsky, known to the world of Jewish scholarship as Chaim Selig Slonimsky, was my paternal grandfather. A swarm of childhood memories invaded my brain. Ever since I could remember, my mother used to tell me amazing tales about my grandfather, who was a genius, but an impractical one. "Don’t follow in his footsteps," she cautioned me."

"A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."

"Suppose it is desired to test the efficiency of several treatments intended to destroy certain larvae on a field. The experiments are arranged in the usual way. The treatments compared are applied to particular plots with several replications and then the plots (or smaller parts of them) are inspected and all the surviving larvae are counted. Thus the observations represent the numbers of surviving larvae in several equal areas. It happens frequently that, while there is room for doubt as to whether there is any significant difference between the average number of survivors corresponding to particular treatments, there is no doubt whatever that the variablitity of the observations differs from treatment to treatment."

"The words "routine analyses" are used to denote the analyses performed by laboratories, frequently attached to industrial plants, and distinguished by the following characteristics: (1) All the analyses or measurements of the same kind, for example, are designed to measure the sugar content in beets or to determine the coordinates of a star. (2) The analyses are carried out day after day using the same methods and the same instruments. (3) While all the analyses are of the same kind, the quantity n varies from time to time, where n represents some small number, 2, 3, 4, 5."

"The future mathematical statistician needs early contacts with experimental sciences. He needs them because, at this stage of the development of statistics, the expeimental sciences are sources of theoretical problems. Also, he needs them because in almost any imaginable job which he may get after graduation, he will be called upon to apply his theory to experimental or observational problems."

"The development of modern science is marked by a pronounced tendency toward indeterminism. A somewhat brutal description of this tendency may be states as follows. In relation to some phenomena, instead of trying to establish a (deterministic) functional relationship between a variable y, and some other variables x1, x2, ... , xn, we try to build a (stochastic or probabilistic) model of these phenomena, predicting frequencies with which, in specified conditions, the same variable y will assume all of its possible values."

"A man who crosses the street must be careful not to be hit by a car, even if the car is an automatic vehicle without a driver, because the car is stronger than a man. We should be afraid of devices that function in a dangerous way for us. The robot will become such a device if we manage to equip it not so much in intelligence as in mechanisms imitating the effects of a certain human functionality. I mean equipping robots with mechanisms that function in a similar way to consciousness of existence and the instinct of self-preservation of a human being. I do not mean to say that the device will be conscious, but that its behavior will be similar to the behavior of a rational unit, such as a man aware of his existence. The machine will not receive consciousness, but it will behave as if it did."

"The fact that a computer player wins a game of chess or bridge with a human does not necessarily mean that the device is intelligent. The victory results from the fact that in the final analysis the device has been applied appropriate algorithms developed by man, e.g. using the properties of artificial neural networks. It is not the device that wins with a man, e.g. a chess player, but a man – the designer of the device. It is simply the rivalry of one intellect with another through the medium of computer science."

"How does artificial intelligence refer to social relationships – for example, the functioning of one or another political system? Well, the evolution of the world is not a closed and completed process. For sure, we are awaiting a change in social relations due to moving of the labor market, especially as a result of transferring the burden of performing various activities on the devices. The invention of machines during the English Industrial Revolution of the eighteenth and early nineteenth centuries resulted in mass strikes and revolts, because many workers were afraid that they would be replaced by the machines. The societies has somehow coped with it. Will they defend themselves in the situation of the next step towards the automation of everything? It's an open matter."

"Various threats come along with the development of information technologies. Connecting people with machines, such a cyborgization of societies, creates a new type of threats – such threats that bring us back a little bit to the Orwellian universe of Nineteen Eighty-Four, in which someone gets very strong tools to control everything. If every human being will be appropriately chipped and our nervous systems, or even our minds, will be incorporated into a global network – one can imagine that sooner or later someone would like to take these technological possibilities in order to get some unprecedented concentration of power and domination. The possibilities of direct physical control may be created, especially if we are connected to a network in a way that interferes with the structure of our nervous system – then we can imagine different possibilities of exerting direct influence. For now, this is the field of speculation."

"In some individual actions a very high level of simulation was achieved, e.g. in chess or Go. However, we are still very far from being able to model all human behaviors, even very primitive ones. The number of decisions made every day turns out to be so huge that it will take a long time until a device capable of dealing with all the problems, a device of which actions would be indistinguishable from human ones, will be created. We cannot predict if and when this will happen, because from previous experience it appears that no forecast in this area managed to meet the reality."

"My cousin Zygmunt found a distant relative in Italy, Professor Vettolani, who works as an astrophysicist in Bologna. When we contacted him, it turned out that our family traditions are quite compatible. So I think we are really connected by Etruscan blood. Although Zygmunt, who is a tireless researcher of family history, has several other theories about our origins. It turns out that in Italy there were two, no longer existing, settlements called Vetulani: one in Lazio, and the other in Tuscany, near Pisa."