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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Otherwise Quotes (24 quotes)

A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.
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Above, far above the prejudices and passions of men soar the laws of nature. Eternal and immutable, they are the expression of the creative power they represent what is, what must be, what otherwise could not be. Man can come to understand the: he is incapable of changing them.
In Cours d’economie Politique (1896-97)
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Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries—not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
From A Logical Point of View (1953), 44. [Note: “qua” means “in the character or role of,” thus “qua lay physicist” means “in the role of lay physicist,” or perhaps even (?) “putting on my lay physicist hat.” —Webmaster]
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Belief is a luxury—only those who have real knowledge have a right to believe; otherwise belief is merely plausible opinion.
In On Love & Psychological Exercises: With Some Aphorisms & Other Essays (1998), 55.
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I cannot conceive of a God who rewards and punishes his creatures, or has a will of the type of which we are conscious in ourselves. An individual who should survive his physical death is also beyond my comprehension, nor do I wish it otherwise; such notions are for the fears or absurd egoism of feeble souls.
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I would think I knew nothing in physics if I could say only how things could be but, without demonstrating that they can’t be otherwise.
From the original French, “Pour la Physique, ie croyrois n’y rien sçauoir, si ie ne sçauois que dire comment les choses peuuent estre, sans demonstrer qu’elles ne peuuent estre autrement,” in letter (11 Mar 1640) to Père Marin Mersenne, collected in Lettres de Mr Descartes (1659), Vol. 2, 213. As translated by John Cottingham, et al., (trans.), in The Philosophical Writings of Descartes: Volume 3, The Correspondence (1991), 145.
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If the study of all these sciences which we have enumerated, should ever bring us to their mutual association and relationship, and teach us the nature of the ties which bind them together, I believe that the diligent treatment of them will forward the objects which we have in view, and that the labor, which otherwise would be fruitless, will be well bestowed.
Plato
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In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
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In light of new knowledge ... an eventual world state is not just desirable in the name of brotherhood, it is necessary for survival ... Today we must abandon competition and secure cooperation. This must be the central fact in all our considerations of international affairs; otherwise we face certain disaster. Past thinking and methods did not prevent world wars. Future thinking must prevent wars.
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In the center of everything rules the sun; for who in this most beautiful temple could place this luminary at another better place whence it can light up the whole at once? ... In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise.
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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It is not enough to teach man a specialty. Through it he may become a kind of useful machine, but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he—with his specialized knowledge—more closely resembles a well-trained dog than a harmoniously developed person.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
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Newton advanced, with one gigantic stride, from the regions of twilight into the noon day of science. A Boyle and a Hooke, who would otherwise have been deservedly the boast of their century, served but as obscure forerunners of Newton's glories.
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1845), 5.
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One summer night, out on a flat headland, all but surrounded by the waters of the bay, the horizons were remote and distant rims on the edge of space. Millions of stars blazed in darkness, and on the far shore a few lights burned in cottages. Otherwise there was no reminder of human life. My companion and I were alone with the stars: the misty river of the Milky Way flowing across the sky, the patterns of the constellations standing out bright and clear, a blazing planet low on the horizon. It occurred to me that if this were a sight that could be seen only once in a century, this little headland would be thronged with spectators. But it can be seen many scores of nights in any year, and so the lights burned in the cottages and the inhabitants probably gave not a thought to the beauty overhead; and because they could see it almost any night, perhaps they never will.
In The Sense of Wonder (1956), as condensed in Reader’s Digest (1986), 129, 174.
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Scientists are supposed to live in ivory towers. Their darkrooms and their vibration-proof benches are supposed to isolate their activities from the disturbances of common life. What they tell us is supposed to be for the ages, not for the next election. But the reality may be otherwise.
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The average gambler will say “The player who stakes his whole fortune on a single play is a fool, and the science of mathematics can not prove him to be otherwise.” The reply is obvious: “The science of mathematics never attempts the impossible, it merely shows that other players are greater fools.”
Concluding remarks to his mathematical proof, with certain assumptions, that the best betting strategy for “Gambler’s Ruin” would be to always make his largest stake on his first play. In 'Gambler’s Ruin', Annals of Mathematics (Jul 1909), 2nd Series, 10, No. 4, 189. This is also seen, without primary source, quoted as “It is true that a man who does this is a fool. I have only proved that a man who does anything else is an even bigger fool,” in Harold Eves, Return to Mathematical Circles (1988), 39.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
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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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There’s no question in my mind that the capability of [the space shuttle] to put 65,000 pounds in low earth orbit—to put payloads up there cheaper than we’ve been able to do it before, not having to throw away the booster—will absolutely revolutionize the way we do business here on earth in ways that we just can’t imagine. It will help develop science and technology. With the space shuttle—when we get it operational—we’ll be able to do in 5 or 10 years what it would take us 20 to 30 years to do otherwise in science and technology development.
Interview for U.S. News & World Report (13 Apr 1981), 56.
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To preach conservation at such a time, when all our resources, national and otherwise are being sacrificed in unprecedented measure, might seem to some anomalous, even ironical. ... But we firmly believe, and now are more acutely aware than ever, that conservation is basically related to the peace of the world and the future of the race.
Breaking New Ground
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We debase the richness of both nature and our own minds if we view the great pageant of our intellectual history as a compendium of new in formation leading from primal superstition to final exactitude. We know that the sun is hub of our little corner of the universe, and that ties of genealogy connect all living things on our planet, because these theories assemble and explain so much otherwise disparate and unrelated information–not because Galileo trained his telescope on the moons of Jupiter or because Darwin took a ride on a Galápagos tortoise.
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Would it (the world) otherwise (without consciousness) have remained a play before empty benches, not existing for anybody, thus quite properly not existing?
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Young writers find out what kinds of writers they are by experiment. If they choose from the outset to practice exclusively a form of writing because it is praised in the classroom or otherwise carries appealing prestige, they are vastly increasing the risk inherent in taking up writing in the first place.
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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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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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