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Who said: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
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Immediately Quotes (21 quotes)

A wise man in China asked his gardener to plant a shrub. The gardener objected that it only flowered once in a hundred years. “In that case,” said the wise man, “plant it immediately.” [On the importance of fundamental research.]
'A Scientist and the World He Lives In', Speech to the Empire Club of Canada (27 Nov 1986) in C. Frank Turner and Tim Dickson (eds.), The Empire Club of Canada Speeches 1986-1987 (1987), 149-161.
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Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
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Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
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He [Sylvester] had one remarkable peculiarity. He seldom remembered theorems, propositions, etc., but had always to deduce them when he wished to use them. In this he was the very antithesis of Cayley, who was thoroughly conversant with everything that had been done in every branch of mathematics.
I remember once submitting to Sylvester some investigations that I had been engaged on, and he immediately denied my first statement, saying that such a proposition had never been heard of, let alone proved. To his astonishment, I showed him a paper of his own in which he had proved the proposition; in fact, I believe the object of his paper had been the very proof which was so strange to him.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 268.
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In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Not every one of our desires can be immediately gratified. We’ve got to learn to wait patiently for our dreams to come true, especially on the path we’ve chosen. But while we wait, we need to prepare symbolically a place for our hopes and dreams.
…...
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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Our first endeavors are purely instinctive prompting of an imagination vivid and undisciplined. As we grow older reason asserts itself and we become more and more systematic and designing. But those early impulses, though not immediately productive, are o
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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So-called extraordinary events always split into two extremes naturalists who have not witnessed them: those who believe blindly and those who do not believe at all. The latter have always in mind the story of the golden goose; if the facts lie slightly beyond the limits of their knowledge, they relegate them immediately to fables. The former have a secret taste for marvels because they seem to expand Nature; they use their imagination with pleasure to find explanations. To remain doubtful is given to naturalists who keep a middle path between the two extremes. They calmly examine facts; they refer to logic for help; they discuss probabilities; they do not scoff at anything, not even errors, because they serve at least the history of the human mind; finally, they report rather than judge; they rarely decide unless they have good evidence.
Quoted in Albert V. Carozzi, Histoire des sciences de la terre entre 1790 et 1815 vue à travers les documents inédités de la Societé de Physique et d'Histoire Naturelle de Genève, trans. Albert V. and Marguerite Carozzi. (1990), 175.
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Standing now in diffused light, with the wind at my back, I experience suddenly a feeling of completeness–not a feeling of having achieved something or of being stronger than everyone who was ever here before, not a feeling of having arrived at the ultimate point, not a feeling of supremacy. Just a breath of happiness deep inside my mind and my breast. The summit seemed suddenly to me to be a refuge, and I had not expected to find any refuge up here. Looking at the steep, sharp ridges below us, I have the impression that to have come later would have been too late. Everything we now say to one another, we only say out of embarrassment. I don’t think anymore. As I pull the tape recorder, trancelike, from my rucksack, and switch it on wanting to record a few appropriate phrases, tears again well into my eyes. “Now we are on the summit of Everest,” I begin, “it is so cold that we cannot take photographs…” I cannot go on, I am immediately shaken with sobs. I can neither talk nor think, feeling only how this momentous experience changes everything. To reach only a few meters below the summit would have required the same amount of effort, the same anxiety and burden of sorrow, but a feeling like this, an eruption of feeling, is only possible on the summit itself.
In Everest: Expedition to the Ultimate (1979), 180.
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The more a science advances, the more will it be possible to understand immediately results which formerly could be demonstrated only by means of lengthy intermediate considerations: a mathematical subject cannot be considered as finally completed until this end has been attained.
In Formensystem binärer Formen (1875), 2.
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There are no physicists in the hottest parts of hell, because the existence of a ‘‘hottest part’’ implies a temperature difference, and any marginally competent physicist would immediately use this to run a heat engine and make some other part of hell comfortably cool. This is obviously impossible.
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To find the cause of our ills in something outside ourselves, something specific that can be spotted and eliminated, is a diagnosis that cannot fail to appeal. To say that the cause of our troubles is not in us but in the Jews, and pass immediately to the extermination of the Jews, is a prescription likely to find a wide acceptance.
In The Passionate State of Mind (1955), 79.
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To solve a problem is to create new problems, new knowledge immediately reveals new areas of ignorance, and the need for new experiments. At least, in the field of fast reactions, the experiments do not take very long to perform.
From Nobel Lecture (11 Dec 1967), 'Flash Photolysis and Some of its Applications.' In Nobel Lectures: Chemistry 1963-1970 (1972), 261.
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True wisdom consists not in seeing what is immediately before our eyes, but in foreseeing what is to come.
Terence
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We see, then, that the disappearance of the conscious personality, the predominance of the unconscious personality, the turning by means of suggestion and contagion of feelings and ideas in an identical direction, the tendency to immediately transform the suggested ideas into acts; these, we see, are the principal characteristics of the individual forming part of a crowd. He is no longer himself, but has become an automaton who has ceased to be guided by his will.
From Psychologie des Foules (1895), 20. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 12. Original French text: “Donc, évanouissement de la personnalité consciente, prédominance de la personnalité inconsciente, orientation par voie de suggestion et de contagion des sentiments et des idées dans un même sens, tendance a transformer immédiatement en actes les idée suggérées, tels sont les principaux caractères de l’individu en foule. II n’est plus lui-même, il est devenu un automate que sa volonté ne guide plus.”
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You can recognize truth by its beauty and simplicity. When you get it right, it is obvious that it is right—at least if you have any experience—because usually what happens is that more comes out than goes in. … The inexperienced, the crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated, and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought.
In The Character of Physical Law (1965), 171.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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