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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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A people that were to honor falsehood, defamation, fraud, and murder would be unable, indeed, to subsist for very long.
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According to the theory of aerodynamics, as may be readily demonstrated through wind tunnel experiments, the bumblebee is unable to fly. This is because the size, weight and shape of his body in relation to the total wingspread make flying impossible. But the bumblebee, being ignorant of these scientific truths, goes ahead and flies anyway—and makes a little honey every day.
Anonymous
Sign in a General Motors Corporation factory. As quoted in Ralph L. Woods, The Businessman's Book of Quotations (1951), 249-50. Cited in Suzy Platt (ed)., Respectfully Quoted: A Dictionary of Quotations (1989), 118.
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Consciousness is never experienced in the plural, only in the singular. Not only has none of us ever experienced more than one consciousness, but there is also no trace of circumstantial evidence of this ever happening anywhere in the world. If I say that there cannot be more than one consciousness in the same mind, this seems a blunt tautology–we are quite unable to imagine the contrary.
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Engineers think that equations approximate the real world.
Physicists think that the real world approximates equations.
Mathematicians are unable to make the connection.
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 41.
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Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously… this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work….
In The Apprenticeship of a Mathematician (1992), 91.
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Here I am at the limit which God and nature has assigned to my individuality. I am compelled to depend upon word, language and image in the most precise sense, and am wholly unable to operate in any manner whatever with symbols and numbers which are easily intelligible to the most highly gifted minds.
In Letter to Naumann (1826), in Vogel, Goethe's Selbstzeugnisse (1903), 56.
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If it is true as Whewell says, that the essence of the triumphs of Science and its progress consists in that it enables us to consider evident and necessary, views which our ancestors held to be unintelligible and were unable to comprehend, then the extension of the number concept to include the irrational, and we will at once add, the imaginary, is the greatest forward step which pure mathematics has ever taken.
In Theorie der Complexen Zahlensysteme (1867), 60. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 281. From the original German, “Wenn es wahr ist, dass, wie Whewell meint, das Wesen der Triumphe der Wissenschaft und ihres Fortschrittes darin besteht, dass wir veranlasst werden, Ansichten, welche unsere Vorfahren für unbegreiflich hielten und unfähig waren zu begreifen, für evident und nothwendig zu halten, so war die Erweiterung des Zahlenbegriffes auf das Irrationale, und wollen wir sogleich hinzufügen, das Imaginäre, der grösste Fortschritt, den die reine Mathematik jemals gemacht hat.”
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If one be bird-witted, that is easily distracted and unable to keep his attention as long as he should, mathematics provides a remedy; for in them if the mind be caught away but a moment, the demonstration has to be commenced anew.
In De Augmentis, Bk. 6; Advancement of Learning, Bk. 2.
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In our days everything seems pregnant with its contrary. Machinery, gifted with the wonderful power of shortening and fructifying human labor, we behold starving and overworking it… . At the same pace that mankind masters nature, man seems to become enslaved to other men or his own infamy. Even the pure light of science seems unable to shine but on the dark background of ignorance.
Karl Marx
In Speech (14 Apr 1856) on the 4th Anniversary of the People’s Paper, collected in David McLellan (ed.), Karl Marx: Selected Writings (2000), 368.
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In the case of a Christian clergyman, the tragic-comical is found in this: that the Christian religion demands love from the faithful, even love for the enemy. This demand, because it is indeed superhuman, he is unable to fulfill. Thus intolerance and hatred ring through the oily words of the clergyman. The love, which on the Christian side is the basis for the conciliatory attempt towards Judaism is the same as the love of a child for a cake. That means that it contains the hope that the object of the love will be eaten up.
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It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 37-38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112.
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It must be borne in mind that the tragedy of life doesn’t lie in not reaching your goal. The tragedy lies in having no goal to reach. It isn’t a calamity to die with dreams unfulfilled, but it is a calamity not to dream. It is not a disaster to be unable to capture your idea, but it is disaster to have no idea to capture. It is not a disgrace not to reach for the stars, but it is a disgrace to have no stars to reach for. Not failure, but low aim is a sin.
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Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy.
In Opus Majus, Part 4, Distinctia Prima, cap. 1.
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Nature offers us a thousand simple pleasures—plays of light and color, fragrance in the air, the sun’s warmth on skin and muscle, the audible rhythm of life’s stir and push—for the price of merely paying attention. What joy! But how unwilling or unable many of us are to pay this price in an age when manufactured sources of stimulation and pleasure are everywhere at hand. For me, enjoying nature’s pleasures takes conscious choice, a choice to slow down to seed time or rock time, to still the clamoring ego, to set aside plans and busyness, and to simply to be present in my body, to offer myself up.
In Sisters of the Earth: Women’s Prose and Poetry (1991), 43.
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Often referred to as osteoporosis of the ocean, [ocean acidification] prevents shell building creatures such as lobster, oyster, crab, shrimp, and coral from extracting the calcium carbonate from the water that they need to build their shells and are thus unable to survive.
In 'What do the Arctic, a Thermostat and COP15 Have in Common?', Huffington Post (18 Mar 2010).
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Penguins are an indicator of the health of our watery planet, and if they are unable to survive, we had better take notice or we might find our own survival threatened.
In Penguins (1998), 160.
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The moral attitudes of a people that is supported by religion need always aim at preserving and promoting the sanity and vitality of the community and its individuals, since otherwise this community is bound to perish. A people that were to honor falsehood, defamation, fraud, and murder would be unable, indeed, to subsist for very long.
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The weeping philosopher too often impairs his eyesight by his woe, and becomes unable from his tears to see the remedies for the evils which he deplores. Thus it will often be found that the man of no tears is the truest philanthropist, as he is the best physician who wears a cheerful face, even in the worst of cases.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 323.
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There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
In 'Imagination in Mathematics', North American Review, 86, 223.
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Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.
In Pensées (1670), Section 7, No. 33. As translated in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 351. Also translated as “Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance,” in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', No. 3, collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 9. From the original French, “Ceux qui sont accoutumés à juger par le sentiment ne comprennent rien aux choses de raisonnement, car ils veulent d’abord pénétrer d’une vue et ne sont point accoutumés à chercher les principes. Et les autres, au contraire, qui sont accoutumés à raisonner par principes, ne comprennent rien aux choses de sentiment, y cherchant des principes et ne pouvant voir d’une vue,” in Ernest Havet (ed.), Pensées de Pascal (1892), 224.
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We have become a people unable to comprehend the technology we invent.
Report, Integrity in the College Curriculum (Feb 1985).
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When I observe the luminous progress and expansion of natural science in modern times, I seem to myself like a traveller going eastwards at dawn, and gazing at the growing light with joy, but also with impatience; looking forward with longing to the advent of the full and final light, but, nevertheless, having to turn away his eyes when the sun appeared, unable to bear the splendour he had awaited with so much desire.
In The Maxims and Reflections of Goethe (1906), 197-198.
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[The National Academy of Sciences] would be unable to give a unanimous decision if asked whether the sun would rise tomorrow.
In David M. Rorvik, 'Ecology’s Angry Lobbyist: Dr. Paul Ehrlich Argues That the Chief Cause of Pollution Is Overpopulation', Look (21 Apr 1970). As quoted and cited in Columbia World of Quotations (1966).
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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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- 40 -
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