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Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index T > Category: Truly

Truly Quotes (33 quotes)

Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Former arbiters of taste must have felt (as so many apostles of ‘traditional values’ and other highminded tags for restriction and conformity do today) that maintaining the social order required a concept of unalloyed heroism. Human beings so designated as role models had to embody all virtues of the paragon–which meant, of course, that they could not be described in their truly human and ineluctably faulted form.
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Genius itself has been analyzed by the shrewdest observers into a higher capacity of attention. “Genius,” says Helvetius … “is nothing but a continued attention,” (une attention suivie). “Genius,” says Buffon, “is only a protracted patience,” (une longue patience). “In the exact sciences, at least,” says Cuvier, “it is the patience of a sound intellect, when invincible, which truly constitutes genius.” And Chesterfield has also observed, that “the power of applying an attention, steady and undissipated, to a single object, is the sure mark of a superior genius.”
In Lectures on Metaphysics and Logic (1860), Vol. 1, 179.
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Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
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I am truly a ‘lone traveler’ and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart; in the face of all these ties, I have never lost a sense of distance and a need for solitude.
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If a project is truly innovative, you cannot possibly know its exact cost and exact schedule at the beginning. And if you do know the exact cost and the exact schedule, chances are that the technology is obsolete.
From interview with Technology Review, quoted in Douglas Martin, 'Joseph Gavin, Who Helped Put First Man on Moon, Dies at 90', New York Times (4 Nov 2010)
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If there is real love, it is not difficult to exercise tolerance, for tolerance is the daughter of love—it is the truly Christian trait, which, of course, Christians of today do not practice.
English translation of the original German, “Liebt man sich wirklich, so ist es ja nicht schwer, die Toleranz zu üben, denn die Toleranz ist die Tochter der Liebe—es ist die eigentlich christliche Eigenschaft, die freilich von der heutigen Christenwelt nicht geübt wird.” In a letter to his father (7 Apr 1851), published in Briefe an seite Eltern, 1839 bis 1864 (1907).
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If you wish to make an apple pie truly from scratch, you must first invent the universe.
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Mr. Cayley, of whom it may be so truly said, whether the matter he takes in hand be great or small, "nihil tetigit quod non ornavit," …
In Philosophic Transactions of the Royal Society (1864), 17, 605. [“Nihil tetigit quod non ornavit” translates as “He touched nothing without embellishing it”. —Webmaster]
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O you who believe!
Seek help in patience and prayer.
Truly! Allah is with the patient.
Quran
Surah al-Baqarah 2:153. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 178
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Proofs are the last thing looked for by a truly religious mind which feels the imaginative fitness of its faith.
Interpretations of Poetry and Religion (1900), 95.
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Scientists were rated as great heretics by the church, but they were truly religious men because of their faith in the orderliness of the universe.
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Take nature out of Shakespeare and it would be incalculably impoverished; without his bunch of radish or shotten herring Falstaff wouldn’t be truly Falstaff, nor would Ophelia’s lament be so poignant without her rosemary for remembrance and rue for you.
In 'Fifty Years On, the Silence of Rachel Carson’s Spring Consumes Us', The Guardian (25 Sep 2012).
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The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 39.
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The exciting about science and discovery, as much as how far we have come, is how far we still have to go. If we know what we do now, then the future truly is ours.
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The genuine spirit of Mathesis is devout. No intellectual pursuit more truly leads to profound impressions of the existence and attributes of a Creator, and to a deep sense of our filial relations to him, than the study of these abstract sciences. Who can understand so well how feeble are our conceptions of Almighty Power, as he who has calculated the attraction of the sun and the planets, and weighed in his balance the irresistible force of the lightning? Who can so well understand how confused is our estimate of the Eternal Wisdom, as he who has traced out the secret laws which guide the hosts of heaven, and combine the atoms on earth? Who can so well understand that man is made in the image of his Creator, as he who has sought to frame new laws and conditions to govern imaginary worlds, and found his own thoughts similar to those on which his Creator has acted?
In 'The Imagination in Mathematics', North American Review, 85, 226.
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The physician being, then, truly a blind man, armed with a club, who, as chance directs the weight of his blow, will be certain of annihilating nature or the disease.
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The sciences are said, and they are truly said, to have a mutual connection, that any one of them may be the better understood, for an insight into the rest.
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The Sun truly “comes up like thunder,” and it sets just as fast. Each sunrise and sunset lasts only a few seconds. But in that time you see at least eight different bands of color come and go, from a brilliant red to the brightest and deepest blue. And you see sixteen sunrises and sixteen sunsets every day you’re in space. No sunrise or sunset is ever the same.
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The theory of punctuated equilibrium, proposed by Niles Eldredge and myself, is not, as so often misunderstood, a radical claim for truly sudden change, but a recognition that ordinary processes of speciation, properly conceived as glacially slow by the standard of our own life-span, do not resolve into geological time as long sequences of insensibly graded intermediates (the traditional, or gradualistic, view), but as geologically ‘sudden’ origins at single bedding planes.
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The truly awesome intellectuals in our history have not merely made discoveries; they have woven variegated, but firm, tapestries of comprehensive coverage. The tapestries have various fates: Most burn or unravel in the foot steps of time and the fires of later discovery. But their glory lies in their integrity as unified structures of great complexity and broad implication.
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The truly wise ask what the thing is in itself and in relation to other things, and do not trouble themselves about the use of it,—in other words, about the way in which it may be applied to the necessities of existence and what is already known. This will soon be discovered by minds of a very different order—minds that feel the joy of living, and are keen, adroit, and practical.
In The Maxims and Reflections of Goethe (1906), 190.
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There is a theory that creativity arises when individuals are out of sync with their environment. To put it simply, people who fit in with their communities have insufficient motivation to risk their psyches in creating something truly new, while those who are out of sync are driven by the constant need to prove their worth.
In 'Beyond the Soapsuds Universe', Discover Magazine (1997). The author explains (in a blog found online) that this “idea comes from a theory by Mihaly Csikszentmihalyi, who wrote a book called Flow: the Psychology of Optimal Experience. You do need someone to come in from outside. One of the theories about why mathematicians do their best work when they’re young is because they’re not yet educated enough to know what seems obviously wrong. So they try new things.”
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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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There’s pretty good evidence that we generally don’t truly want good information—but rather information that confirms our prejudices. We may believe intellectually in the clash of opinions, but in practice we like to embed ourselves in the reassuring womb of an echo chamber.
In New York Times (18 Mar 2009).
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This theme of mutually invisible life at widely differing scales bears an important implication for the ‘culture wars’ that supposedly now envelop our universities and our intellectual discourse in general ... One side of this false dichotomy features the postmodern relativists who argue that all culturally bound modes of perception must be equally valid, and that no factual truth therefore exists. The other side includes the benighted, old-fashioned realists who insist that flies truly have two wings, and that Shakespeare really did mean what he thought he was saying. The principle of scaling provides a resolution for the false parts of this silly dichotomy. Facts are facts and cannot be denied by any rational being. (Often, facts are also not at all easy to determine or specify–but this question raises different issues for another time.) Facts, however, may also be highly scale dependent–and the perceptions of one world may have no validity or expression in the domain of another. The one-page map of Maine cannot recognize the separate boulders of Acadia, but both provide equally valid representations of a factual coastline.
The World as I See It (1999)
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Truly, we do live on a “water planet.” For us, water is that critical issue that we need. It’s the most precious substance on the planet, and it links us to pretty much every environmental issue, including climate change, that we’re facing.
From interview by Kathleen Walter, Newsmax (28 Sep 2009).
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We are not to think that Jupiter has four satellites given him by nature, in order, by revolving round him, to immortalize the name of the Medici, who first had notice of the observation. These are the dreams of idle men, who love ludicrous ideas better than our laborious and industrious correction of the heavens.—Nature abhors so horrible a chaos, and to the truly wise, such vanity is detestable.
From Nodus Gordius, Appendix, as cited in John Elliot Drinkwater Bethune, Life of Galileo Galilei: With Illustrations of the Advancement of Experimental Philosophy (1832), 93.
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When we are motivated by goals that have deep meaning, by dreams that need completion, by pure love that needs expressing, then we truly live life.
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Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but the seeds of it, and we are carried no farther than industry and application have carried us.
In Conduct of the Understanding, Sect. 6.
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[Comte] may truly be said to have created the philosophy of higher mathematics.
In System of Logic (1846), 369.
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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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- 80 -
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- 70 -
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- 60 -
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- 40 -
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