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Home > Category Index for Science Quotations > Category Index I > Category: Incomprehensible

Incomprehensible Quotes (29 quotes)

A man must cling to the belief that the incomprehensible is comprehensible; otherwise he would not try to fathom it.
In The Maxims and Reflections of Goethe (1906), 194.
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All power, all subordination rests on the executioner: he is the horror and the bond of human association. Remove this incomprehensible agent from the world, and the very moment order gives way to chaos, thrones topple, and society disappears
In Joseph de Maistre and Richard A. Lebrun (trans.), The St. Petersburg Dialogues (1993), 20.
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As children we all possess a natural, uninhibited curiosity, a hunger for explanation, which seems to die slowly as we age—suppressed, I suppose, by the high value we place on conformity and by the need not to appear ignorant.
It betokens a conviction that somehow science is innately incomprehensible. It precludes reaching deeper, thereby denying the profound truth that understanding enriches experience, that explanation vastly enhances the beauty of the natural world in the eye of the beholder.
In Toward the Habit of Truth (1990).
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Büchsel in his reminiscences from the life of a country parson relates that he sought his recreation in Lacroix’s Differential Calculus and thus found intellectual refreshment for his calling. Instances like this make manifest the great advantage which occupation with mathematics affords to one who lives remote from the city and is compelled to forego the pleasures of art. The entrancing charm of mathematics, which captivates every one who devotes himself to it, and which is comparable to the fine frenzy under whose ban the poet completes his work, has ever been incomprehensible to the spectator and has often caused the enthusiastic mathematician to be held in derision. A classic illustration is the example of Archimedes….
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 22. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 186. From the original German, “Wenn Büchsel in seinen Erinnerungen aus dem Leben eines Landgeistlichen erzählt, dass er in der Differentialrechnung von Lacroix Erholung gesucht und geistige Erfrischung ftir seinen Beruf gefunden habe, so erkennen wir darin den grossen Vorzug, den die Beschaftigung mit der Mathematik für jemanden hat, der fern von einer Stadt lebt und auf ihre Kunstgenüsse verzichten muss. Der berückende Zauber der Mathematik, dem jeder unterliegt, der sich ihr ergiebt, und der dem holden Wahnsinn vergleichbar ist, unter dessen Bann der Dichter sein Work vollendet, ist dem betrachtenden Mitmenschen immer unbegreiflich gewesen und hat den begeisterten Mathematiker oft zum Gespött werden lassen. Als klassisches Beispiel wird jedem Schüler Archimedes…”
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Explanation separates us from astonishment, which is the only gateway to the incomprehensible.
…...
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For the little that one has reflected on the origin of our knowledge, it is easy to perceive that we can acquire it only by means of comparison. That which is absolutely incomparable is wholly incomprehensible. God is the only example that we could give here. He cannot be comprehended, because he cannot be compared. But all which is susceptible of comparison, everything that we can perceive by different aspects, all that we can consider relatively, can always be judged according to our knowledge.
'Histoire naturelle de l'Homme', Histoire Naturelle, Générale et Particulière, Avec la Description du Cabinet du Roi (1749), Vol. 2, 431. Trans. Phillip R. Sloan.
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I think the name atomic theory was an unfortunate one. We talk fluently about atoms as the smallest particles that exist, and chemists regard them as indivisible … To my mind the infinitely small is as incomprehensible as the infinitely great. … we cannot comprehend it, we cannot take it in. And so with the atom. Therefore I think that it would have been better to have taken a different word—say minim—which would have been a safer term than atom.
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493.
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If it’s green or wriggles, it’s biology. If it stinks, it’s chemistry. If it doesn’t work, it’s physics or engineering. If it’s green and wiggles and stinks and still doesn’t work, it’s psychology. If it’s incomprehensible, it’s mathematics. If it puts you to sleep, it’s statistics.
Anonymous
In Journal of the South African Institute of Mining and Metallurgy (1978), 79, 97, and additional lines from other sources.
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If we make a couple of discoveries here and there we need not believe things will go like this for ever. An acrobat can leap higher than a farm-hand, and one acrobat higher than another, yet the height no man can overleap is still very low. Just as we hit water when we dig in the earth, so we discover the incomprehensible sooner or later.
Aphorisms, trans. R. J. Hollingdale (1990), 92.
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If we reflect that a small creature such as this is provided, not only with external members, but also with intestines and other organs, we have no reason to doubt that a like creature, even if a thousand million times smaller, may already be provided with all its external and internal organs... though they may be hidden from our eyes. For, if we consider the external and internal organs of animalcules which are so small that a thousand million of them together would amount to the size of a coarse grain of sand, it may well be, however incomprehensible and unsearchable it may seem to us, that an animalcule from the male seed of whatever members of the animal kingdom, contains within itself... all the limbs and organs which an animal has when it is born.
Letter to the Gentlemen of the Royal Society, 30 Mar 1685. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 5, 185.
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It is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.
In Reflections on the Human Condition (1973), 97.
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It is true that mathematics, owing to the fact that its whole content is built up by means of purely logical deduction from a small number of universally comprehended principles, has not unfittingly been designated as the science of the self-evident [Selbstverständlichen]. Experience however, shows that for the majority of the cultured, even of scientists, mathematics remains the science of the incomprehensible [Unverständlichen].
In Ueber Wert und angeblichen Unwert der Mathematik, Jahresbericht der Deutschen Maihemaliker Vereinigung (1904), 357.
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It reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypotheses. To refute the latter I collected many proofs, but I do not publish them ... I would dare to publish my speculations if there were people men like you.
[Declaring his belief in the heliocentric theory of Copernicus.]
Letter to Kepler (1596). Quoted in Will Durant, Ariel Duran, The Age of Reason Begins (1961), 603. From Hermann Kesten, Copernicus and His World, translated by E.B. Ashton (pseud.) and Norbert Guterman (1945), 348-349.
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Mathematics is often considered a difficult and mysterious science, because of the numerous symbols which it employs. Of course, nothing is more incomprehensible than a symbolism which we do not understand. … But this is not because they are difficult in themselves. On the contrary they have invariably been introduced to make things easy. … [T]he symbolism is invariably an immense simplification. It … represents an analysis of the ideas of the subject and an almost pictorial representation of their relations to each other.
In Introduction to Mathematics (1911), 59-60.
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May the conscience and the common sense of the peoples be awakened, so that we may reach a new stage in the life of nations, where people will look back on war as an incomprehensible aberration of their forefathers!
…...
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My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble minds. That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God.
As quoted in obituary, 'Einstein Noted as an Iconoclast In Research, Politics and Religion', The New York Times (19 Apr 1955), 25.
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Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ’d, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 15, 113.
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No other part of science has contributed as much to the liberation of the human spirit as the Second Law of Thermodynamics. Yet, at the same time, few other parts of science are held to be so recondite. Mention of the Second Law raises visions of lumbering steam engines, intricate mathematics, and infinitely incomprehensible entropy. Not many would pass C.P. Snow’s test of general literacy, in which not knowing the Second Law is equivalent to not having read a work of Shakespeare.
In The Second Law (1984), Preface, vii.
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Relativity was a highly technical new theory that gave new meanings to familiar concepts and even to the nature of the theory itself. The general public looked upon relativity as indicative of the seemingly incomprehensible modern era, educated scientists despaired of ever understanding what Einstein had done, and political ideologues used the new theory to exploit public fears and anxieties—all of which opened a rift between science and the broader culture that continues to expand today.
'The Cultural Legacy of Relativity Theory' in Albert Einstein, Robert W. Lawson, Robert Geroch, Roger Penrose and David C. Cassidy, Relativity (2005), 226.
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Religion has been compelled by science to give up one after another of its dogmas—of those assumed cognitions which it could not substantiate. In the mean time, Science substituted for the personalities to which Religion ascribed phenomena certain metaphysical entities; and in doing this it trespassed on the province of religion; since it classed among the things which it comprehended certain forms of the incomprehensible.
In First Principles (1864), 109.
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Rules of Thumb
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Anonymous
In Arthur Bloch, The Complete Murphy's Law: A Definitive Collection (1991), 126.
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Some people say they cannot understand a million million. Those people cannot understand that twice two makes four. That is the way I put it to people who talk to me about the incomprehensibility of such large numbers. I say finitude is incomprehensible, the infinite in the universe is comprehensible. Now apply a little logic to this. Is the negation of infinitude incomprehensible? What would you think of a universe in which you could travel one, ten, or a thousand miles, or even to California, and then find it comes to an end? Can you suppose an end of matter or an end of space? The idea is incomprehensible. Even if you were to go millions and millions of miles the idea of coming to an end is incomprehensible. You can understand one thousand per second as easily as you can understand one per second. You can go from one to ten, and then times ten and then to a thousand without taxing your understanding, and then you can go on to a thousand million and a million million. You can all understand it.
In 'The Wave Theory of Light' (1884), Popular Lectures and Addresses (1891), Vol. 1, 322.
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That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God.
…...
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The Bohr atom was introduced to us by Bohr himself. I still have the notes I took during his lectures … His discourse was rendered almost incomprehensible by his accent; there were endless references to what I recorded as “soup groups”, only later emended to “sub-groups”.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 116-117.
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The most incomprehensible thing about the world is that it is comprehensible.
In Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972, 1973), 18.
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The way we have to describe Nature is generally incomprehensible to us.
In 'Electrons and Their Interactions', QED: The Strange Theory of Light and Matter (1985), Chap. 3, 77.
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They had neither compass, nor astronomical instruments, nor any of the appliances of our time for finding their position at sea; they could only sail by the sun, moon, and stars, and it seems incomprehensible how for days and weeks, when these were invisible, they were able to find their course through fog and bad weather; but they found it, and in the open craft of the Norwegian Vikings, with their square sails, fared north and west over the whole ocean, from Novaya Zemlya and Spitsbergen to Greenland, Baffin Bay, Newfoundland, and North America.
In northern mists: Arctic exploration in early times - Volume 1 - Page 248 https://books.google.com/books?id=I1ugAAAAMAAJ Fridtjof Nansen - 1911
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We have several stones whose generation is incomprehensible unless it is supposed that they come from some kind of seed, if I may be permitted to use this term; that is to say, from a germ in which the organic particles of these stones are enclosed ‘en petit’, just as those of the largest plants are enclosed in the germs of their grains.
In Histoire de l' Académie Royale des Sciences Annee: Avec les Memoires de Mathematique et de Physique (1702), 230.
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What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?
Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.
Opening paragraphs of 'Preface', From Here to Infinity (1996), vii.
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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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