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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index S > Category: Subtle

Subtle Quotes (37 quotes)


A good notation has a subtlety and suggestiveness which at times make it almost seem like a live teacher. … a perfect notation would be a substitute for thought.
In 'Introduction' by Bertrand Russell written for Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1922), 17-18.
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Academies have been instituted to guard the avenues of their languages, to retain fugitives, and repulse intruders; but their vigilance and activity have hitherto been vain; sounds are too volatile and subtile for legal restraints; to enchain syllables, and to lash the wind, are equally the undertakings of pride, unwilling to measure its desires by its strength.
From Dictionary of the English Language (1818), Vol. 1, Preface, xxiii. Note: Subtile means subtle.
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Alcoholism, the opium habit and tobaccoism are a trio of poison habits which have been weighty handicaps to human progress during the last three centuries. In the United States, the subtle spell of opium has been broken by restrictive legislation; the grip of the rum demon has been loosened by the Prohibition Amendment to the Constitution, but the tobacco habit still maintains its strangle-hold and more than one hundred million victims of tobaccoism daily burn incense to the smoke god.
In Tobaccoism: or, How Tobacco Kills (1922), Preface, 7.
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As for those wingy mysteries in divinity, and airy subtleties in religion, which have unhinged the brains of better heads, they never stretched the pia mater of mine: methinks there be not impossibilities enough in Religion for an active faith.
In T. Chapman (ed.), Religio Medici (1643, 1831), part 1, sect. 9, 17.
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As usual, nature’s imagination far surpasses our own, as we have seen from the other theories which are subtle and deep.
In The Character of Physical Law (1965, 2001), 162.
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Do you remember what Darwin says about music? He claims that the power of producing and appreciating it existed among the human race long before the power of speech was arrived at. Perhaps that is why we are so subtly influenced by it. There are vague memories in our souls of those misty centuries when the world was in its childhood.
Spoken by character, Sherlock Holmes, in A Study in Scarlet (1887), Chap. 5. Collected in Works of Arthur Conan Doyle (1902), Vol. 11, 68-69.
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Every appearance in nature corresponds to some state of the mind, and that state of the mind can only be described by presenting that natural appearance as its picture. An enraged man is a lion, a cunning man is a fox, a firm man is a rock, a learned man is a torch. A lamb is innocence; a snake is subtle spite; flowers express to us the delicate affections. Light and darkness are our familiar expressions for knowledge and ignorance ; and heat for love. Visible distance behind and before us, is respectively our image of memory and hope.
In essay, 'Language', collected in Nature: An Essay ; And, Lectures on the Times (1844), 23-24.
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Every so often, you have to unlearn what you thought you already knew, and replace it by something more subtle.
With co-author Jack Cohen. In Terry Pratchett, Ian Stewart and Jack Cohen, Chap. 4, 'Science and Magic', The Science of Discworld (Rev. Ed. 2002), 14. Pratchett wrote the fantasy story told in the odd-numbered chapters. Following each, relevant real science is provided by his co-authors, Stewart and Cohen, in the even-numbered chapters (such as Chap. 4), but which of the two wrote which lines, is not designated.
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Great thinkers build their edifices with subtle consistency. We do our intellectual forebears an enormous disservice when we dismember their visions and scan their systems in order to extract a few disembodied ‘gems’–thoughts or claims still accepted as true. These disarticulated pieces then become the entire legacy of our ancestors, and we lose the beauty and coherence of older systems that might enlighten us by their unfamiliarity–and their consequent challenge in our fallible (and complacent) modern world.
…...
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He who has mastered the Darwinian theory, he who recognizes the slow and subtle process of evolution as the way in which God makes things come to pass, … sees that in the deadly struggle for existence that has raged throughout countless aeons of time, the whole creation has been groaning and travailing together in order to bring forth that last consummate specimen of God’s handiwork, the Human Soul
In The Destiny of Man Viewed in the Light of his Origin (1884), 32. Collected in Studies in Religion (1902), 19–20.
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I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are permutations and aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then from the top down, the result is always different. Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.
Letter to Mrs Arthur Severn (Jul 1878), collected in The Letters of a Noble Woman (Mrs. La Touche of Harristown) (1908), 50. Also in 'Gleanings Far and Near', Mathematical Gazette (May 1924), 12, 95.
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I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.
From 'Fundamental Conceptions and Methods in Mathematics', Bulletin American Mathematical Society (1904), 9, 133. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 182.
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it’s combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.
In The Phenomenon of Man (1975), pp 218, 220, 223, 227, 228, 277.
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It is not therefore the business of philosophy, in our present situation in the universe, to attempt to take in at once, in one view, the whole scheme of nature; but to extend, with great care and circumspection, our knowledge, by just steps, from sensible things, as far as our observations or reasonings from them will carry us, in our enquiries concerning either the greater motions and operations of nature, or her more subtile and hidden works. In this way Sir Isaac Newton proceeded in his discoveries.
An Account of Sir Isaac Newton's Philosophical Discoveries, in Four Books (1748), 19.
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It is possible for a mathematician to be “too strong” for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)
In A Mathematician's Miscellany (1953). Reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 144.
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It pays to be obvious, especially if you have a reputation for subtlety.
In Foundation (1951), 88.
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Now the serpent was more subtle than any beast of the field.
Bible
(circa 725 B.C.)
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Organisms are not billiard balls, propelled by simple and measurable external forces to predictable new positions on life’s pool table. Sufficiently complex systems have greater richness. Organisms have a history that constrains their future in myriad, subtle ways.
In The Panda’s Thumb: More Reflections in Natural History (1987, 2010), 16.
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Our world will yet grow so subtle that it will be as ludicrous to believe in a god as it is today to believe in ghosts.
Aphorism 57 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 52.
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Oxigen [oxygen], as you well know, is my hero as well as my foe, and being not only strong but inexhaustible in strategies and full of tricks, I was obliged to call up all my forces to lay hold of him, and make the subtle Being my prisoner.
Letter to Michael Faraday (11 Dec 1860), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 340.
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Science advances through tentative answers to a series of more and more subtle questions which reach deeper and deeper into the essence of natural phenomena.
…...
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Science and mathematics [are] much more compelling and exciting than the doctrines of pseudoscience, whose practitioners were condemned as early as the fifth century B.C. by the Ionian philosopher Heraclitus as “night walkers, magicians, priests of Bacchus, priestesses of the wine-vat, mystery-mongers.” But science is more intricate and subtle, reveals a much richer universe, and powerfully evokes our sense of wonder. And it has the additional and important virtue—to whatever extent the word has any meaning—of being true.
Broca's Brain: Reflections on the Romance of Science (1979, 1986), 76.
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Science proceeds by successive answers to questions more and more subtle, coming nearer and nearer to the very essence of phenomena.
From Études sur la bière, Chap 6, Sec. vi. As translated by René J. Dubos, quoted and cited in Maurice B. Strauss, Familiar Medical Quotations (1968), 526.
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Subtle as the mind is it can effect little without knowledge. It cannot construct a bridge, or a building, or make a canal, or work a problem in algebra, unless it is provided with information.
In Chap. 7, The Story of My Heart: My Autobiography (1883), 176.
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Subtle is the Lord, but malicious He is not.
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Subtlety is not a proof of wisdom. Fools and even madmen are at times extraordinarily subtle. One can add that subtlety rarely combines with genius, which is usually ingenuous, or with greatness of character, which is always frank.
(1827). In Aleksandr Sergeevich Pushkin, John Bayley (ed.), Pushkin on Literature (1986), 211.
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The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practised, is of the same general nature authority and tradition furnish the data, and the mental operations are deductive.
In 'Scientific Education: Notes of an After-Dinner Speech' (Delivered to Liverpool Philomathic Society, Apr 1869), published in Macmillan’s Magazine (Jun 1869), 20, No. 116, 177. Collected in Lay Sermons, Addresses, and Reviews (1871), Chap 4, 66.
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The mathematics involved in string theory … in subtlety and sophistication vastly exceeds previous uses of mathematics in physical theories. … String theory has led to a whole host of amazing results in mathematics in areas that seem far removed from physics. To many this indicates that string theory must be on the right track.
In Book Review 'Pulling the Strings,' of Lawrence Krauss's Hiding in the Mirror: The Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond in Nature (22 Dec 2005), 438, 1082.
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The soul seems to be a very tenuous substance … [and] seems to be made of a most subtle texture, extremely mobile or active corpuscles, not unlike those of flame or heat; indeed, whether they are spherical, as the authors of atoms propound, or pyramidical as Plato thought, or some other form, they seem from their own motion and penetration through bodies to create the heat which is in the animal.
As quoted in Margaret J. Osler and Paul Lawrence Farber (eds.), Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall (2002), 169.
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There are few enough people with sufficient independence to see the weaknesses and follies of their contemporaries and remain themselves untouched by them. And these isolated few usually soon lose their zeal for putting things to rights when they have come face to face with human obduracy. Only to a tiny minority is it given to fascinate their generation by subtle humour and grace and to hold the mirror up to it by the impersonal agency of art. To-day I salute with sincere emotion the supreme master of this method, who has delighted–and educated–us all.
…...
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There remains something subtle, intangible and inexplicable. Veneration for this force beyond anything that we can comprehend is my religion.
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To be at once a Scholar and a Wanderer is to indulge the least congruous desires, in the same hour to gratify the last refinement of intellectual curiosity and to obey a call from the first rude state of nature. For the “wandering fever” is in a sense a temptation of original sin, still heard across the ages, and the scholar finds a subtle joy in returning to the wilderness rather in spite than because of being a scholar.
In A Wandering Scholar in the Levant (1896), 1-2.
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To create a human through genetic engineering that is more complex, more refined, more subtle, farther from animals, than the ones we have today.
The Genes of Hope. In Marc J. Madou, Fundamentals of Microfabrication: the Science of Miniaturization (2nd ed., 2002), 467.
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Try and penetrate with our limited means the secrets of nature and you will find that, behind all the discernible concatenations, there remains something subtle, intangible and inexplicable. Veneration for this force beyond anything that we can comprehend is my religion. To that extent I am, in point of fact, religious.
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You have chosen the most fascinating and dynamic profession there is, a profession with the highest potential for greatness, since the physician’s daily work is wrapped up in the subtle web of history. Your labors are linked with those of your colleagues who preceded you in history, and those who are now working all over the world. It is this spiritual unity with our colleagues of all periods and all countries that has made medicine so universal and eternal. For this reason we must study and try to imitate the lives of the “Great Doctors” of history.
epilogue to A Prelude to Medical History
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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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- 90 -
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- 70 -
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- 50 -
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- 40 -
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