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Who said: “The conservation of natural resources is the fundamental problem. Unless we solve that problem it will avail us little to solve all others.”
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Discover Quotes (196 quotes)
Discovered Quotes, Discovering Quotes, Discoverable Quotes, Discoverd Quotes

Le premier regard de l’homme jeté sur l’univers n’y découvre que variété, diversité, multiplicité des phénomènes. Que ce regard soit illuminé par la science,—par la science qui rapproche l’homme de Dieu,—et la simplicité et l’unité brillent de toutes parts.
Man’s first glance at the universe discovers only variety, diversity, multiplicity of phenomena. Let that glance be illuminated by science—by the science which brings man closer to God,—and simplicity and unity shine on all sides.
Original French quoted in René Vallery-Radot, La Vie de Pasteur (1901), 209. Translation by Google translate, tweaked by Webmaster. The English version of the book, omits this passage, except for “Science, which brings man nearer to God.” In The Life of Pasteur (1902), Vol. 1, 194.
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Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l’on peut découvrir par l’observation, et dont l’étude est l’objet de la philosophie naturelle.
Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Opening statement from 'Discours Préliminaire' to Théorie Analytique de la Chaleur (1822), i, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 1.
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Primo enim paranda est Historia Naturalis et Experimentalis, suffidens et bona; quod fundamentum rei est: neque enim fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat.
For first of all we must prepare a Natural and Experimental History, sufficient and good; and this is the foundation of all; for we are not to imagine or suppose, but to discover, what nature does or may be made to do.
In Novum Organum, Book 2, Aphorism 10. As translated in Francis Bacon and James Spedding with ‎Robert Leslie Ellis (eds.), 'The New Organon', The Works of Francis Bacon: Translations of the Philosophical Works (1858), Vol. 4, 127. Also seen in epigraphs as a shorter quote, “Non fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat,” which can also be translated as “We have not to imagine or to think out, but to find out what Nature does or produces.”
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Salviati: …Now you see how easy it is to understand.
Sagredo: So are all truths, once they are discovered; the point is in being able to discover them.
[Commonly seen merged in a paraphrase as: All truths are easy to understand once they are discovered; the point is to discover them.]
Lines of two characters in Dialogue Concerning the Two Chief World Systems (1632), as translated by S. Drake (1967). As quoted and cited in Barnaby Sheppard, The Logic of Infinity (2014), 398 & 440 footnote. Galileo’s work is written as a series of dialogues over four days between Salviati (supporting the Copernican system), Sagredo (a neutral layman) and Simplicio (supporting the Ptolemaic system).
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A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
In Budget of Paradoxes (1872), 172.
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A mathematical truth is timeless, it does not come into being when we discover it. Yet its discovery is a very real event, it may be an emotion like a great gift from a fairy.
…...
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A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
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Adventure isn’t hanging on a rope off the side of a mountain. Adventure is an attitude that we must apply to the day to day obstacles of life - facing new challenges, seizing new opportunities, testing our resources against the unknown and in the process, discovering our own unique potential.
…...
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Alike in the external and the internal worlds, the man of science sees himself in the midst of perpetual changes of which he can discover neither the beginning nor the end.
In First Principles (1864, 1898), 68.
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All fresh meat is eaten in a state of decay. The process may not have proceeded so far that the dull human nose can discover it, but a carrion bird or a carrion fly can smell it from afar.
In New Dietetics: What to Eat and How (1921), 384.
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All great theorems were discovered after midnight.
In Howard W. Eves Return to Mathematical Circles, (1988), 157.
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All Nature bristles with the marks of interrogation—among the grass and the petals of flowers, amidst the feathers of birds and the hairs of mammals, on mountain and moorland, in sea and sky-everywhere. It is one of the joys of life to discover those marks of interrogation, these unsolved and half-solved problems and try to answer their questions.
In Riddles of Science (1932), 5.
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Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.
…...
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An archaeologist is a scientist who seeks to discover past civilizations while the present one is still around.
Anonymous
In Evan Esar, 20,000 Quips & Quotes (1968, 1995), 40.
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Archimedes, who combined a genius for mathematics with a physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics. … The day (when having discovered his famous principle of hydrostatics he ran through the streets shouting Eureka! Eureka!) ought to be celebrated as the birthday of mathematical physics; the science came of age when Newton sat in his orchard.
In An Introduction to Mathematics (1911), 37.
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As one penetrates from seam to seam, from stratum to stratum and discovers, under the quarries of Montmartre or in the schists of the Urals, those animals whose fossilized remains belong to antediluvian civilizations, the mind is startled to catch a vista of the milliards of years and the millions of peoples which the feeble memory of man and an indestructible divine tradition have forgotten and whose ashes heaped on the surface of our globe, form the two feet of earth which furnish us with bread and flowers.
From 'La Peau de Chagrin' (1831). As translated as The Wild Ass’s Skin (1906) trans. Herbert J. Hunt, The Wild Ass's Skin (1977), 40-1.
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As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics, acoustics, kinetics and statistical mechanics ... all had fallen into order before the. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.
A Short History of Nearly Everything. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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As they discover, from strata to strata and from layer to layer, deep in the quarries of Montmartre or the schists of the Urals, these creatures whose fossilized remains belong to antediluvian civilizations, it will strike terror into your soul to see many millions of years, many thousands of races forgotten by the feeble memory of mankind and by the indestructible divine tradition, and whose piles of ashes on the surface of our globe form the two feet of soil which gives us our bread and our flowers.
From 'La Peau de Chagrin' (1831). As translated as by Helen Constantine The Wild Ass’s Skin (2012), 19.
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As we push ever more deeply into the universe, probing its secrets, discovering its way, we must also constantly try to learn to cooperate across the frontiers that really divide earth’s surface.
In 'The President’s News Conference at the LBJ Ranch' (29 Aug 1965). Collected in Public Papers of the Presidents of the United States: Lyndon B. Johnson: 1965 (1966), 945.
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At this very minute, with almost absolute certainty, radio waves sent forth by other intelligent civilizations are falling on the earth. A telescope can be built that, pointed in the right place, and tuned to the right frequency, could discover these waves. Someday, from somewhere out among the stars, will come the answers to many of the oldest, most important, and most exciting questions mankind has asked.
In Intelligent Life in Space (1962), 111.
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Blessings on Science! When the earth seem’d old,
When Faith grew doting, and the Reason cold,
Twas she discover’d that the world was young,
And taught a language to its lisping tongue:
’Twas she disclosed a future to its view,
And made old knowledge pale before the new.
From poem, 'Railways' (1846), collected in The Poetical Works of Charles Mackay: Now for the First Time Collected Complete in One Volume (1876), 214.
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But as a philosopher said, one day after mastering the winds, the waves, the tides and gravity, after all the scientific and technological achievements, we shall harness for God the energies of love. And then, for the second time in the history of the world, man will have discovered fire.
Speech accepting nomination as candidate for vice president, Democratic National Committee, Washington, D.C. (8 Aug 1972) as reported in New York Times (9 Aug 1972), 18. Shriver slightly paraphrased the similar sentiment written in 1934 by Pierre Teilhard de Chardin, translated by René Hague in 'The Evolution of Chastity', Toward the Future (1975), 86-87.
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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But that which will excite the greatest astonishment by far, and which indeed especially moved me to call the attention of all astronomers and philosophers, is this: namely, that I have observed four planets, neither known nor observed by any one of the astronomers before my time, which have their orbits round a certain bright star [Jupiter], one of those previously known, like Venus or Mercury round the sun, and are sometimes in front of it, sometimes behind it, though they never depart from it beyond certain limits. All of which facts were discovered and observed a few days ago by the help of a telescope devised by me, through God’s grace first enlightening my mind.
In pamphlet, The Sidereal Messenger (1610), reprinted in The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (1880), 9.
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Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.
In 'Recent Work on the Principles of Mathematics The International Monthly (Jul 1901), 4, No. 1, 90.
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Chemistry is the science or study of those effects and qualities of matter which are discovered by mixing bodies variously together, or applying them to one another with a view to mixture, and by exposing them to different degrees of heat, alone, or in mixture with one another, in order to enlarge our knowledge of nature, and to promote the useful arts.
From the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 11.
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Chemistry is the study of the effects of heat and mixture, with a view of discovering their general and subordinate laws, and of improving the useful arts.
This is an editor’s shorter restatement of the definition given by Black in the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 11, footnote. For the definitions as given by Black, see elsewhere on this web page.
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Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.
In How to Tell the Liars from the Statisticians (1983), 127.
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Chymistry. … An art whereby sensible bodies contained in vessels … are so changed, by means of certain instruments, and principally fire, that their several powers and virtues are thereby discovered, with a view to philosophy or medicine.
An antiquated definition, as quoted in Samuel Johnson, entry for 'Chymistry' in Dictionary of the English Language (1785). Also in The Quarterly Journal of Science, Literature, and the Arts (1821), 284, wherein a letter writer (only identified as “C”) points out that this definition still appeared in the, then, latest Rev. Mr. Todd’s Edition of Johnson’s Dictionary, and that it showed “very little improvement of scientific words.” The letter included examples of better definitions by Black and by Davy. (See their pages on this website.)
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Contrary to popular parlance, Darwin didn't discover evolution. He uncovered one (most would say the) essential mechanism by which it operates: natural selection. Even then, his brainstorm was incomplete until the Modern Synthesis of the early/mid-20th century when (among other things) the complementary role of genetic heredity was fully realized. Thousands upon thousands of studies have followed, providing millions of data points that support this understanding of how life on Earth has come to be as it is.
In online article, 'The Day That Botany Took on Bobby Jindal by Just Being Itself', Huffington Post (5 Aug 2013).
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Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.
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Darwin grasped the philosophical bleakness with his characteristic courage. He argued that hope and morality cannot, and should not, be passively read in the construction of nature. Aesthetic and moral truths, as human concepts, must be shaped in human terms, not ‘discovered’ in nature. We must formulate these answers for ourselves and then approach nature as a partner who can answer other kinds of questions for us–questions about the factual state of the universe, not about the meaning of human life. If we grant nature the independence of her own domain–her answers unframed in human terms–then we can grasp her exquisite beauty in a free and humble way. For then we become liberated to approach nature without the burden of an inappropriate and impossible quest for moral messages to assuage our hopes and fears. We can pay our proper respect to nature’s independence and read her own ways as beauty or inspiration in our different terms.
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Data is not necessarily information. Information does not necessarily lead to knowledge. And knowledge is not always sufficient to discover truth and breed wisdom.
From post 're:The Pursuit of Knowledge, from Genesis to Google' to the 'Interesting People' List (6 Jan 2005), now archived at interesting-people.org website
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Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.
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Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.
In McGraw Hill, Science and Technology Encyclopedia
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Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.
Vitruvius
In De Architectura, Book 1, Chap 6, Sec. 9. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 27-28.
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Everybody now wants to discover universal laws which will explain the structure and behavior of the nucleus of the atom. But actually our knowledge of the elementary particles that make up the nucleus is tiny. The situation calls for more modesty. We should first try to discover more about these elementary particles and about their laws. Then it will be the time for the major synthesis of what we really know, and the formulation of the universal law.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium—the extreme rarity of which renders it commercially unimportant—as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 20.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
In Letter to Johannes Kepler. As quoted in The Portable Renaissance Reader (1968), 597.

For me, the first challenge for computing science is to discover how to maintain order in a finite, but very large, discrete universe that is intricately intertwined. And a second, but not less important challenge is how to mould what you have achieved in solving the first problem, into a teachable discipline: it does not suffice to hone your own intellect (that will join you in your grave), you must teach others how to hone theirs. The more you concentrate on these two challenges, the clearer you will see that they are only two sides of the same coin: teaching yourself is discovering what is teachable.
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For several years this great man [Isaac Newton] was intensely occupied in endeavoring to discover a way of changing the base metals into gold. … There were periods when his furnace fires were not allowed to go out for six weeks; he and his secretary sitting up alternate nights to replenish them.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 256.
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From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
In Cours d’Economie Politique (1896-97).
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Genetics has always turned out to be much more complicated than it seemed reasonable to imagine. Biology is not like physics. The more we know, the less it seems that there is one final explanation waiting to be discovered.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 275.
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Having discovered … by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,—that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.
In Lecture VI of his Biennial Course, by William Hamilton and Henry L. Mansel (ed.) and John Veitch (ed.), Metaphysics (1860), Vol. 1, 101.
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He who studies it [Nature] has continually the exquisite pleasure of discerning or half discerning and divining laws; regularities glimmer through an appearance of confusion, analogies between phenomena of a different order suggest themselves and set the imagination in motion; the mind is haunted with the sense of a vast unity not yet discoverable or nameable. There is food for contemplation which never runs short; you are gazing at an object which is always growing clearer, and yet always, in the very act of growing clearer, presenting new mysteries.
From 'Natural History', Macmillan's Magazine (1875), 31, 366.
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He who wonders discovers that this in itself is wonder.
In M.C. Escher: The Graphic Work (1978), 8.
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Humanity, in the course of time, had to endure from the hands of science two great outrages against its naive self-love. The first was when humanity discovered that our earth was not the center of the universe…. The second occurred when biological research robbed man of his apparent superiority under special creation, and rebuked him with his descent from the animal kingdom, and his ineradicable animal nature.
From a series of 28 lectures for laymen, Part Three, 'General Theory of the Neurons', Lecture 18, 'Traumatic Fixation—the Unconscious' collected in Sigmund Freud and G. Stanley Hall (trans.), A General Introduction to Psychoanalysis (1920), 246-247.
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I am awaiting the day when people remember the fact that discovery does not work by deciding what you want and then discovering it.
In 'How Not to Create Tigers', Physics Today (Aug 1999), 52, No. 8, 12. Collected in Why Quark Rhymes with Pork: And Other Scientific Diversions (2012), 150.
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I believe television is going to be the test of the modern world, and that in this new opportunity to see beyond the range of our vision we shall discover either a new and unbearable disturbance of the general peace or a saving radiance in the sky. We shall stand or fall by television—of that I am quite sure
In 'Removal' (Jul 1938), collected in One Man's Meat (1942), 3.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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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 grew up in Leicestershire, in Leicester, which is on the Jurassic, and it’s full of lovely fossils. Ammonites, belemnites, brachiopods—very beautiful. How did they get there, in the middle of the rocks, in the middle of England, and so on? And I had the collecting bug, which I still have, actually, which is the basis of so much of natural history, really, and so much of science. And so collecting all these things, and discovering what they were, and how they lived, and when they had lived, and all that, was abiding fascination to me from the age of I suppose about eight. And I still feel that way, actually.
Speaking about fossils that first inspired his love of natural history. In video by Royal Society of Biology, 'Sir David Attenborough, Biology: Changing the World Interview,' published on YouTube (13 Feb 2015).
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I have no patience with the doctrine of “pure science,”—that science is science only as it is uncontaminated by application in the arts of life: and I have no patience with the spirit that considers a piece of work to be legitimate only as it has direct bearing on the arts and affairs of men. We must discover all things that are discoverable and make a record of it: the application will take care of itself.
In 'The Survey Idea in Country Life', collected in John Phelan, Readings in Rural Sociology (1920), 480.
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I have presented the periodic table as a kind of travel guide to an imaginary country, of which the elements are the various regions. This kingdom has a geography: the elements lie in particular juxtaposition to one another, and they are used to produce goods, much as a prairie produces wheat and a lake produces fish. It also has a history. Indeed, it has three kinds of history: the elements were discovered much as the lands of the world were discovered; the kingdom was mapped, just as the world was mapped, and the relative positions of the elements came to take on a great significance; and the elements have their own cosmic history, which can be traced back to the stars.
In The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), Preface, viii.
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I read … that the celebrated Amontons, using a thermometer of his own invention, had discovered that water boils at a fixed degree of heat. I was at once inflamed with a great desire to make for myself a thermometer of the same sort, so that I might with my own eyes perceive this beautiful phenomenon of nature.
From 'Experimenta circa gradum caloris liquorum nonnullorum ebullientium instituta', Philosophical Transactions (1724), 33, 1, as translated in William Francis Magie, A Source Book in Physics (1935), 131.
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I write to discover what I think. After all, the bars aren’t open that early.
On his habit of writing in the early morning hours. As quoted in Wall Street Journal (31 Dec 1985).
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If I had been taught from my youth all the truths of which I have since sought out demonstrations, and had thus learned them without labour, I should never, perhaps, have known any beyond these; at least, I should never have acquired the habit and the facility which I think I possess in always discovering new truths in proportion as I give myself to the search.
In Discours de la Méthode (1637). In English from John Veitch (trans.), A Discourse on Method (1912), 57.
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If I have succeeded in discovering any truths in the sciences…, I can declare that they are but the consequences and results of five or six principal difficulties which I have surmounted, and my encounters with which I reckoned as battles in which victory declared for me.
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 53. Also seen translated as, “If I found any new truths in the sciences…, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.”
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If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.
Quoted in D MacHale, Comic Sections (1993)
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If you do not know how to ask the right question, you discover nothing.
Widely quoted without citation. If you know a primary source, please contact Webmaster.
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In a Dublin hospital, many years ago, it was noticed that the death-rate was markedly higher in the ground-floor wards than it was in the wards upstairs. This fact was commented on in an official report, and marked down as requiring investigation. Then it was discovered that, when new patients came in, the porter of the hospital was in the habit of putting them upstairs if they could walk by themselves, and downstairs if they could not.
From 'Figures Can Lie', Science Digest (Sep 1951), 30, No. 3, 53. (As condensed from The Listener). Excerpted in Meta Riley Emberger and Marian Ross Hall, Scientific Writing (1955), 407.
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In the 1860s, Pasteur not only applied his germ theory to create “Pasteurization,” rescuing France’s wine and vinegar industries, but also found both the cause and cure of silkworm disease, saving growers millions of dollars. When Napoleon asked the scientist why he had not legitimately profited by his findings, Pasteur replied: “In France scientists would consider they lowered themselves by doing so.”
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 190.
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Induction may be defined, the operation of discovering and proving general propositions.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 347.
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Is not Cuvier the great poet of our era? Byron has given admirable expression to certain moral conflicts, but our immortal naturalist has reconstructed past worlds from a few bleached bones; has rebuilt cities, like Cadmus, with monsters’ teeth; has animated forests with all the secrets of zoology gleaned from a piece of coal; has discovered a giant population from the footprints of a mammoth.
From 'La Peau de Chagrin' (1831). As translated by Ellen Marriage in The Wild Ass’s Skin (1906), 21-22.
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Is not Cuvier the greatest poet of our age? Of course Lord Byron has set down in fine words certain of our souls’ longings; but our immortal naturalist has reconstructed whole worlds out of bleached bones. Like Cadmus, he has rebuilt great cities from teeth, repopulated thousands of forests with all the mysteries of zoology from a few pieces of coal, discovered races of giants in the foot of a mammoth.
From 'La Peau de Chagrin' (1831). As translated as by Helen Constantine The Wild Ass’s Skin (2012), 19.
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It is clear that all the valuable things, material, spiritual, and moral, which we receive from society can be traced back through countless generations to certain creative individuals. The use of fire, the cultivation of edible plants, the steam engine–each was discovered by one man.
…...
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It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others.
In An Essay on the Psychology of Invention in the Mathematical Field (1954), 54.
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It is not merely as an investigator and discoverer, but as a high-principled and unassuming man, that Scheele merits our warmest admiration. His aim and object was the discovery of truth. The letters of the man reveal to us in the most pleasant way his high scientific ideal, his genuinely philosophic temper, and his simple mode of thought. “It is the truth alone that we desire to know, and what joy there is in discovering it!” With these words he himself characterizes his own efforts.
From History of Chemistry (1899). As quoted in Victor Robinson, Pathfinders in Medicine (1912), 121.
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It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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It is through science that we prove, but through intuition that we discover.
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It is very different to make a practical system and to introduce it. A few experiments in the laboratory would prove the practicability of system long before it could be brought into general use. You can take a pipe and put a little coal in it, close it up, heat it and light the gas that comes out of the stem, but that is not introducing gas lighting. I'll bet that if it were discovered to-morrow in New York that gas could be made out of coal it would be at least five years before the system would be in general use.
From the New York Herald (30 Jan 1879), as cited in Leslie Tomory, 'Building the First Gas Network, 1812-1820', Technology and Culture (Jan 2011), 52, No. 1, 75-102.
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It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
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It was one thing to declare that we had not yet discovered the traces of a beginning, and another to deny that the earth ever had a beginning.
As quoted in Charles Lyell, Principles of Geology: Being an Attempt to Explain the Former Changes of the Earth’s Surface (1833), Vol. 3, 383. The quote is Playfair’s comment on Hutton’s conclusion: “The result, therefore of our present inquiry is, that we find no vestige of a beginning, no prospect of an end.” In defence of Hutton, Playfair was pointing out that the doctrine of Hutton was not opposed to the belief of a creation. Hutton’s conclusion is in Dissertation on the Theory of the Earth (1795)
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It was one thing to declare that we had not yet discovered the trace of a beginning, and another to deny that the earth ever had a beginning.
Epigraph in Charles Clay, 'Observations on the Theory of the Earth’s Original Formation', Geological Sketches and Observations on Vegetable Fossil Remains (1839), 69.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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It’s not for glory that Soviet cosmonauts are in this assault on the cosmos; they are motivated by a limitless love for and devotion to their country, the Party and the people, and by a desire to help Soviet scientists to discover the secrets of the universe.
In First Man in Space: The Life and Achievement of Yuri Gagarin: a Collection (1984), 104. Cited as written as a foreword of a book at the request of the author.
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Keep discovering…
Emirates
…...
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Kepler’s suggestion of gravitation with the inverse distance, and Bouillaud’s proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I have discovered two anagrams on his name, which are quite conclusive: the notion of gravitation was not new; but Newton went on.
In Budget of Paradoxes (1872), 82.
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Learning begets humility because the more a man knows, the more he discovers his ignorance.
Anonymous
In Hialmer Day Gould, New Practical Spelling (1905), 27
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Let Nature do your bottling and your pickling and preserving. For all Nature is doing her best each moment to make us well. She exists for no other end. Do not resist her. With the least inclination to be well, we should not be sick. Men have discovered—or think they have discovered—the salutariness of a few wild things only, and not of all nature. Why, “nature” is but another name for health, and the seasons are but different states of health. Some men think that they are not well in spring, or summer, or autumn, or winter; it is only because they are not well in them.
(23 Aug 1853). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: V: March 5-November 30, 1853 (1906), 395.
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Let us keep the discoveries and indisputable measurements of physics. But ... A more complete study of the movements of the world will oblige us, little by little, to turn it upside down; in other words, to discover that if things hold and hold together, it is only by reason of complexity, from above.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 43. Originally published in French as Le Phénomene Humain (1955).
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Life is good for only two things: to do mathematics and to teach it.
From François Arago, 'Mort de Poisson', Œvres Complètes de François Arago (1854), Vol.2, 662, translated by Webmaster from the original French, “La vie n’est bonne qu’à deux choses: à faire des mathématiques et à les professer.” Quote introduced by Arago as “Poisson … avait l’habitude de dire” (“Poisson … used to say”). Also seen in a book of quotes, Alphonse Rebière (ed.), Mathématiques et Mathématiciens: Pensées et Curiosités (1893), 158, as “La vie n’est bonne qu'à étudier et à enseigner les mathématiques”, which Webmaster translates as “Life is good only to study and to teach mathematics”. Also currently found online as “La vie n’est bonne que pour deux choses: découvrir les mathématiques et enseigner les mathématiques”, translated as “Life is good for only two things, discovering mathematics and teaching mathematics”, in Howard Whitley Eves, Mathematical Circles Adieu: A Fourth Collection of Mathematical Stories and Anecdotes (1977), 22. Arago was a contemporary of Poisson, and Webmaster speculates from the context of the biography that perhaps Arago knew the quote firsthand from Poisson. Webmaster has not yet been able to trace either version to a primary source written by Poisson. (Can you help?)
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Long lives are not necessarily pleasurable…. We will be lucky if we can postpone the search for new technologies for a while, until we have discovered some satisfactory things to do with the extra time. Something will surely have to be found to take the place of sitting on the porch re-examining one’s watch.
In 'The Long Habit', The Lives of a Cell: Notes of a Biology Watcher (1974), 57.
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M. Waldman … concluded with a panegyric upon modern chemistry…:— “The ancient teachers of this science” said he, “Promised impossibilities and performed nothing. The modern masters promise very little; they know that metals cannot be transmuted and that the elixir of life is a chimera. But these philosophers seem only made to dabble in dirt, and their eyes to pore over the microscope or crucible, have indeed performed miracles. They penetrate into the recesses of nature and show how she works in her hiding-places. They ascend into the heavens; they have discovered how the blood circulates, and the nature of the air we breathe. They can command the thunders of heaven, mimic the earthquake, and even mock the invisible world with its own shadows.”
In Frankenstein: Or, The Modern Prometheus (1823), Vol. 1, 73-74. Webmaster note: In the novel, when the fictional characters meet, M. Waldman, professor of chemistry, sparks Victor Frankenstein’s interest in science. Shelley was age 20 when the first edition of the novel was published anonymously (1818).
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Magnetism, galvanism, electricity, are “one form of many names.” Without magnetism we should never have discovered America; to which we are indebted for nothing but evil; diseases in the worst forms that can afflict humanity, and slavery in the worst form in which slavery can exist. The Old World had the sugar-cane and the cotton-plant, though it did not so misuse them.
Written for fictional character, the Rev. Dr. Opimian, in Gryll Grange (1861), collected in Sir Henry Cole (ed.) The Works of Thomas Love Peacock(1875), Vol. 2, 382. [Hans Øersted discovered electromagnetism in 1820. Presumably the next reference to magnetism refers to a compass needle for navigation. —Webmaster]
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Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
As quoted in G. Simmons Calculus Gems (1992).
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Medical researchers have discovered a new disease that has no symptoms. It is impossible to detect, and there is no known cure. Fortunately, no cases have been reported thus far.
In Napalm and Silly Putty (2002), 104.
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My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.
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Newton has shown us that a law is only a necessary relation between the present state of the world and its immediately subsequent state. All the other laws since discovered are nothing else; they are in sum, differential equations.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 87.
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No pessimist ever discovered the secret of the stars or sailed an uncharted land, or opened a new doorway for the human spirit.
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No video, no photographs, no verbal descriptions, no lectures can provide the enchantment that a few minutes out-of-doors can: watch a spider construct a web; observe a caterpillar systematically ravaging the edge of a leaf; close your eyes, cup your hands behind your ears, and listen to aspen leaves rustle or a stream muse about its pools and eddies. Nothing can replace plucking a cluster of pine needles and rolling them in your fingers to feel how they’re put together, or discovering that “sedges have edges and grasses are round,” The firsthand, right-and-left-brain experience of being in the out-of-doors involves all the senses including some we’ve forgotten about, like smelling water a mile away. No teacher, no student, can help but sense and absorb the larger ecological rhythms at work here, and the intertwining of intricate, varied and complex strands that characterize a rich, healthy natural world.
Into the Field: A Guide to Locally Focused Teaching
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Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming.
In Conflict of Studies (1873), 13.
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Nothing is more humbling than to look with a strong magnifying glass at an insect so tiny that the naked eye sees only the barest speck and to discover that nevertheless it is sculpted and articulated and striped with the same care and imagination as a zebra. Apparently it does not occur to nature whether or not a creature is within our range of vision, and the suspicion arises that even the zebra was not designed for our benefit.
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Notwithstanding all that has been discovered since Newton’s time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 47.
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Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.
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Nowadays most people die of a sort of creeping common sense, and discover when it is too late that the only things one never regrets are one’s mistakes.
In The Picture of Dorian Gray (1891), Ch. 3, 61.
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Nuclear energy and foreign policy cannot coexist on the planet. The more deep the secret, the greater the determination of every nation to discover and exploit it. Nuclear energy insists on global government, on law, on order, and on the willingness of the community to take the responsibility for the acts of the individual. And to what end? Why, for liberty, first of blessings. Soldier, we await you, and if the
In 'The Talk of the Town', The New Yorker (18 Aug 1945), 13.
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Of all the offspring of Time, Error is the most ancient, and is so old and familiar an acquaintance, that Truth, when discovered, comes upon most of us like an intruder, and meets the intruder’s welcome.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 314.
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One doesn’t discover new lands without consenting to lose sight of the shore for a very long time.
In The Counterfeiters: A Novel (1951, 2012), 353. As translated by Dorothy Bussy from the original French, “On ne découvre pas de terre nouvelle sans consentir à perdre de vue, d'abord et longtemps, tout rivage”, in Les Faux Monnayeurs (1925).
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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One has to do something new in order to see something new.
Aphorism from Notebook J (1789).
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One of the most impressive discoveries was the origin of the energy of the stars, that makes them continue to burn. One of the men who discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine.
She said “Look at how pretty the stars shine!”
He said, “Yes, and right now I am the only man in the world who knows why they shine.”
She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.
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One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
In Albert Einstein, translated by G.B. Jeffery and W. Perrett, 'Geometry and Experience',Sidelights on Relativity (1922), 27.
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Our papers have been making a great deal of American “know-how” ever since we had the misfortune to discover the atomic bomb. There is one quality more important than know-how” and we cannot accuse the United States of any undue amount of it. This is “know-what,” by which we determine not only how to accomplish our purposes, but what our purposes are to be.
In The Human Use of Human Beings: Cybernetics and Society (1950), 210.
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People are usually surprised to discover that I hate the phrase “constitutional rights.” I hate the phrase because it is terribly misleading. Most of the people who say it or hear it have the impression that the Constitution “grants” them their rights. Nothing could be further from the truth. Strictly speaking it is the Bill of Rights that enumerates our rights, but none of our founding documents bestow anything on you at all [...] The government can burn the Constitution and shred the Bill of Rights, but those actions wouldn’t have the slightest effect on the rights you’ve always had.
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People say to me, “Are you looking for the ultimate laws of physics?” No, I’m not; I’m just looking to find out more about the world and if it turns out there is a simple ultimate law which explains everything, so be it; that would be very nice to discover. If it turns out it’s like an onion with millions of layers, and we’re just sick and tired of looking at the layers, then that’s the way it is …
From Interview in BBC TV program Horizon (1981). As quoted in The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman 1983, (1999), 23.
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Physics tries to discover the pattern of events which controls the phenomena we observe. But we can never know what this pattern means or how it originates; and even if some superior intelligence were to tell us, we should find the explanation unintelligible.
In Physics And Philosophy: the Revolution In Modern Science (1942), 16.
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Reason is the slow and tortuous method by which those who do not know the truth discover it.
Anonymous
Webmaster presently believes this is an orphan quote, best attributed to Anonymous. It seem to be unsupported when attributed to Blaise Pascal, for example, as quoted, without citation, in Morris Kline, 'Ancients versus Moderns, A New Battle of the Books', The Mathematics Teacher (Oct 1958), 51, No. 6, 423. Also later published, without citation, in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972), 296. Webmaster has not yet found a primary source for this as a quote by Pascal - not in English, not in French, and not in any earlier books. This is suspicious. (Can you help?) Furthermore, this sentence is also often seen in more recent books and online quotes pages as a first sentence, followed by a second sentence, “The heart has its reasons, which reason does not know.” The second sentence is a known Pascal quote verified in original French texts. However, Webmaster has not yet found, in any original French text, any instance of these two sentences together. Thus, putting them together more definitely appears to be a misquote. Can you help? [It is included on the Blaise Pascal page to link it with this cautionary note. —Webmaster]
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Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns, there are things we know we know.
We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. ... And each year, we discover a few more of those unknown unknowns.
Answering a question concerning Iraq, on the facts about weapons of mass destruction, at a Press Conference, NATO Headquarters, Brussels, Belgium (6 June 2002). From transcript on U.S. Department of Defense website.
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Science is always discovering odd scraps of magical wisdom and making a tremendous fuss about its cleverness.
Referring to Freudian theories.
The Confessions of Aleister Crowley, ch. 14 (1929, rev 1970).
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Science will continue to surprise us with what it discovers and creates; then it will astound us by devising new methods to surprise us. At the core of science’s self-modification is technology. New tools enable new structures of knowledge and new ways of discovery. The achievement of science is to know new things; the evolution of science is to know them in new ways. What evolves is less the body of what we know and more the nature of our knowing.
'Speculations on the Future of Science'. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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Scientists often have a naive faith that if only they could discover enough facts about a problem, these facts would somehow arrange themselves in a compelling and true solution.
In Mankind Evolving: The Evolution of the Human Species, 128. As cited in Ted Woods & Alan Grant, Reason in Revolt - Dialectical Philosophy and Modern Science (2003), Vol. 2, 183.
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Simple as the law of gravity now appears, and beautifully in accordance with all the observations of past and of present times, consider what it has cost of intellectual study. Copernicus, Galileo, Kepler, Euler, Lagrange, Laplace, all the great names which have exalted the character of man, by carrying out trains of reasoning unparalleled in every other science; these, and a host of others, each of whom might have been the Newton of another field, have all labored to work out, the consequences which resulted from that single law which he discovered. All that the human mind has produced—the brightest in genius, the most persevering in application, has been lavished on the details of the law of gravity.
in The Ninth Bridgewater Treatise: A Fragment (1838), 57.
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Some of my youthful readers are developing wonderful imaginations. This pleases me. Imagination has brought mankind through the Dark Ages to its present state of civilization. Imagination led Columbus to discover America. Imagination led Franklin to discover electricity. Imagination has given us the steam engine, the telephone, the talking-machine and the automobile, for these things had to be dreamed of before they became realities. So I believe that dreams—day dreams, you know, with your eyes wide open and your brain-machinery whizzing—are likely to lead to the betterment of the world. The imaginative child will become the imaginative man or woman most apt to create, to invent, and therefore to foster civilization. A prominent educator tells me that fairy tales are of untold value in developing imagination in the young. I believe it.
Opening paragraph of preface, 'To My Readers', The Lost Princess of Oz (1917), 13.
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Sometime in my early teens, I started feeling an inner urgency, ups and downs of excitement and frustration, caused by such unlikely occupations as reading Granville’s course of calculus ... I found this book in the attic of a friend’s apartment. Among other standard stuff, it contained the notorious epsilon-delta definition of continuous functions. After struggling with this definition for some time (it was the hot Crimean summer, and I was sitting in the shadow of a dusty apple tree), I got so angry that I dug a shallow grave for the book between the roots, buried it there, and left in disdain. Rain started in an hour. I ran back to the tree and exhumed the poor thing. Thus, I discovered that I loved it, regardless.
'Mathematics as Profession and vocation', in V. Arnold et al. (eds.), Mathematics: Frontiers and Perspectives (2000), 153. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 79.
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Study actively. Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
In I Want to be a Mathematician: An Automathography (1985), 69.
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The art of discovering the causes of phenomena, or true hypothesis, is like the art of deciphering, in which an ingenious conjecture greatly shortens the road.
In Gottfried Leibniz and Alfred Fideon Langley (trans.), 'Leibniz’s Critique of Locke', New Essays Concerning Human Understanding (1896), Book 4, Chap. 12, 526.
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The best men are always first discovered by their enemies: it is the adversary who turns on the searchlight, and the proof of excellence lies in being able to stand the gleam.
Aphorism in The Philistine (Dec 1904), 20, No. 1, 18.
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The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others.
In Positive Philosophy, Bk. 1, chap. 2.
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The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.
Epigraph, without citation, in Morris Kline, Mathematical Thought from Ancient to Modern Times (1972), 231. Need primary source. Can you help?
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The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 94. Also in Science (1912), New Series, 35, 107.
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The future of humanity is uncertain, even in the most prosperous countries, and the quality of life deteriorates; and yet I believe that what is being discovered about the infinitely large and the infinitely small is sufficient to absolve this end of the century and millennium. What a very few are acquiring in knowledge of the physical world will perhaps cause this period not to be judged as a pure return to barbarism.
In 'News from the Sky', Other People’s Trades (1989), 23-24.
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The greatest achievements in the science of this [twentieth] century are themselves the sources of more puzzlement than human beings have ever experienced. Indeed, it is likely that the twentieth century will be looked back at as the time when science provided the first close glimpse of the profundity of human ignorance. We have not reached solutions; we have only begun to discover how to ask questions.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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The greatest and noblest pleasure which we can have in this world is to discover new truths; and the next is to shake off old prejudices.
Epigraph, without citation, in Sir Richard Gregory, Discovery: Or, The Spirit and Service of Science (1916), 23.
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The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
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The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
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The hope that new experiments will lead us back to objective events in time and space is about as well founded as the hope of discovering the end of the world in the unexplored regions of the Antarctic.
…...
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The imagination is … the most precious faculty with which a scientist can be equipped. It is a risky possession, it is true, for it leads him astray a hundred times for once that it conducts him to truth; but without it he has no chance at all of getting at the meaning of the facts he has learned or discovered.
In Respiratory Proteids: Researches in Biological Chemistry (1897), Preface, iv.
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The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me—both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.
In I Want to be a Mathematician: An Automathography (1985), 3.
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The major gift of science to the world is a mighty increase of power. Did science then create that power? Not a bit of it! Science discovered that power in the universe and set it free. Science found out the conditions, fulfilling which, the endless dynamic forces of the cosmos are liberated. Electricity is none of man’s making, but man has learned how to fulfill the conditions that release it. Atomic energy is a force that man did not create, but that some day man may liberate. Man by himself is still a puny animal; a gorilla is much the stronger. Man's significance lies in another realm—he knows how to fulfill conditions so that universal power not his own is set free. The whole universe as man now sees it is essentially a vast system of power waiting to be released.
In 'When Prayer Means Power', collected in Living Under Tension: Sermons On Christianity Today (1941), 78-79.
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The method of definition is the method of discovering what the thing under consideration is by means of the definition of that thing in so far as it makes it known. This method involves two procedures, one being by composition and the other by resolution.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 63.
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The methods of science aren’t foolproof, but they are indefinitely perfectible. Just as important: there is a tradition of criticism that enforces improvement whenever and wherever flaws are discovered. The methods of science, like everything else under the sun, are themselves objects of scientific scrutiny, as method becomes methodology, the analysis of methods. Methodology in turn falls under the gaze of epistemology, the investigation of investigation itself—nothing is off limits to scientific questioning. The irony is that these fruits of scientific reflection, showing us the ineliminable smudges of imperfection, are sometimes used by those who are suspicious of science as their grounds for denying it a privileged status in the truth-seeking department—as if the institutions and practices they see competing with it were no worse off in these regards. But where are the examples of religious orthodoxy being simply abandoned in the face of irresistible evidence? Again and again in science, yesterday’s heresies have become today’s new orthodoxies. No religion exhibits that pattern in its history.
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The ordinary patient goes to his doctor because he is in pain or some other discomfort and wants to be comfortable again; he is not in pursuit of the ideal of health in any direct sense. The doctor on the other hand wants to discover the pathological condition and control it if he can. The two are thus to some degree at cross purposes from the first, and unless the affair is brought to an early and happy conclusion this diversion of aims is likely to become more and more serious as the case goes on.
Address, opening of 1932-3 session of U.C.H. Medical School (4 Oct 1932), 'Art and Science in Medicine', The Collected Papers of Wilfred Trotter, FRS (1941), 98.
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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The progress of science requires more than new data; it needs novel frameworks and contexts. And where do these fundamentally new views of the world arise? They are not simply discovered by pure observation; they require new modes of thought. And where can we find them, if old modes do not even include the right metaphors? The nature of true genius must lie in the elusive capacity to construct these new modes from apparent darkness. The basic chanciness and unpredictability of science must also reside in the inherent difficulty of such a task.
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The pure scientist discovers the universe. The applied scientist exploits existing scientific discoveries to create a usable product.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 181.
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The reptilian idea of fun
Is to bask all day in the sun.
A physiological barrier,
Discovered by Carrier,
Says they can't breathe, if they run.
Written about David Carrier’s rule concerning a vertebrate’s breathing when lungs are affected because the rib structure distorts during locomotion. Thus sprawling vertebrates cannot run and breathe at the same time. In sidebar to 'Respiration, Metabolism, and Locomotion', History of Life (1991), 177. Carrier’s constraint idea was published in 'The evolution of locomotor stamina in tetrapods: circumventing a mechanical constraint' Paleobiology (1987), 13, 326-341.
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The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.
In 'Imagination in Mathematics', North American Review, 85, 228.
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The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.
In On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function (1833), 7-8. [The spelling as “groupe” in the original text, has her been corrected to “group” to avoid an intrusive “sic”.]
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The science of Psychiatry is now where the science of Medicine was before germs were discovered.
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The Scientific Revolution turns us away from the older sayings to discover the lost authorization in Nature. What we have been through in these last four millennia is the slow inexorable profaning of our species. And in the last part of the second millennium A.D., that process is apparently becoming complete. It is the Great Human Irony of our noblest and greatest endeavor on this planet that in the quest for authorization, in our reading of the language of God in Nature, we should read there so clearly that we have been so mistaken.
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The Senses place before us the Characters of the Book of Nature; but these convey no knowledge to us, till we have discovered the Alphabet by which they are to be read.
In 'Aphorisms Concerning Ideas', The Philosophy of the Inductive Sciences (1840), Vol. 1, xvii.
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The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 67.
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The Synthesis consists in assuming the Causes discovered and established as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 380-381.
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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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The union of philosophical and mathematical productivity, which besides in Plato we find only in Pythagoras, Descartes and Leibnitz, has always yielded the choicest fruits to mathematics; To the first we owe scientific mathematics in general, Plato discovered the analytic method, by means of which mathematics was elevated above the view-point of the elements, Descartes created the analytical geometry, our own illustrious countryman discovered the infinitesimal calculus—and just these are the four greatest steps in the development of mathematics.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 149-150. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 210. From the original German, “Die Verbindung philosophischer und mathematischer Productivität, wie wir sie ausser in Platon wohl nur noch in Pythagoras, Descartes, Leibnitz vorfinden, hat der Mathematik immer die schönsten Früchte gebracht: Ersterem verdanken wir die wissenschaftliche Mathematik überhaupt, Platon erfand die analytische Methode, durch welche sich die Mathematik über den Standpunct der Elemente erhob, Descartes schuf die analytische Geometrie, unser berühmter Landsmann den Infinitesimalcalcül—und eben daß sind die vier grössten Stufen in der Entwickelung der Mathematik.”
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The work of a pioneer in science of technique often consists of finding a correct solution, or creating a working mechanism, based on laws that are not yet discovered.
In The Story of the Winged-S: The Autobiography of Igor I. Sikorsky (2011).
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The X-ray spectrometer opened up a new world. It proved to be a far more powerful method of analysing crystal structure…. One could examine the various faces of a crystal in succession, and by noting the angles at which and the intensity with which they reflected the X-rays, one could deduce the way in which the atoms were arranged in sheets parallel to these faces. The intersections of these sheets pinned down the positions of the atoms in space.… It was like discovering an alluvial gold field with nuggets lying around waiting to be picked up.… It was a glorious time when we worked far into every night with new worlds unfolding before us in the silent laboratory.
In The History of X-ray Analysis (1943), 9.
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There are no shortcuts to moral insight. Nature is not intrinsically anything that can offer comfort or solace in human terms–if only because our species is such an insignificant latecomer in a world not constructed for us. So much the better. The answers to moral dilemmas are not lying out there, waiting to be discovered. They reside, like the kingdom of God, within us–the most difficult and inaccessible spot for any discovery or consensus.
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There are three leading objects in the study of truth:—one, to discover it; another, to demonstrate it when discovered; the last, to separate it from all admixture of falsehood.
As translated in Blaise Pascal and M.P. Faugère (trans.), 'On The Geometrical Spirit', collected in The Miscellaneous Writings of Pascal; Consisting of Letters, Essays, Conversations, and Miscellaneous Thoughts (1849), 73. From the original French, “On peut avoir trois principaux objets dans l’etude de la vérité: l’un, de la découvrir quand on la cherche; l’autre, de la démontrer quand on la possède; le dernier, de la discerner d'avec le faux quand on l’examine,” in 'De l'Esprit Géométrique', Pascal: Opuscules Philosophiques (1887), 82. For an alternative translation, see the quote beginning, “We may have three principal objects…” on the Blaise Pascal Quotes page of this website.
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There are two avenues from the little passions and the drear calamities of earth; both lead to the heaven and away from hell—Art and Science. But art is more godlike than science; science discovers, art creates.
Spoken by fictional character Zanoni in novel, Zanoni (1842), 6.
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There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered. Theon called this analysis.
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There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is anybody’s guess. …
In 'Mathematical Knowledge: Internal, Social, and Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 4.
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There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
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There is always more in one of Ramanujan’s formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface; but there is not one which is not curious and entertaining.
Commenting on the formulae in the letters sent by Ramanujan from India, prior to going to England. Footnote in obituary notice by G.H. Hardy in the Proceedings of the London Mathematical Society (2) (1921), 19, xl—lviii. The same notice was printed, with slight changes, in the Proceedings of the Royal Society (A) (1921), 94, xiii—xxix. Reprinted in G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson (eds.) Collected Papers of Srinivasa Ramanujan (1927), xxi.
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There is nothing that haz bin diskovered yet, that iz so skarse as good Hoss sense, about 28 hoss power.
In The Complete Works of Josh Billings (1876), 78.
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There is scarce a single Humour in the Body of a Man, or of any other Animal, in which our Glasses do not discover Myriads of living Creatures.
In The Spectator (25 Oct 1712), No. 519, as collected in Vol. 7 (1729, 10th ed.), 84.
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There will still be things that machines cannot do. They will not produce great art or great literature or great philosophy; they will not be able to discover the secret springs of happiness in the human heart; they will know nothing of love and friendship.
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This frustration of reading the tabloid press… it would easy to become convinced that the human race is on a mission to divide things into two clean columns… Good or evil, healthy or deadly or natural or chemical… everything organic and natural is good, ignoring the fact that organic natural substances include arsenic… Everything chemical is bad, ignoring that fact the everything is chemicals. Everything is chemicals! The day they discover yoga mats are carcinogenic will be the happiest day of my life.
Introducing his song, 'The Fence', on DVD, Live at the Royal Albert Hall (2011).
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Those intervening ideas, which serve to show the agreement of any two others, are called proofs; and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration; it being shown to the understanding, and the mind made to see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or disagreement of any other) and to apply them right, is, I suppose, that which is called sagacity.
In An Essay concerning Human Understanding, Bk. 6, chaps. 2, 3.
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Till Algebra, that great Instrument and Instance of Humane Sagacity, was discovered, Men, with amazement, looked on several of the Demonstrations of ancient Mathematicians, and could scarce forbear to think the finding some of those Proofs, more than humane.
In 'Of Reason', Essay Concerning Humane Understanding (1690), Book 4, Ch. 17, Sec. 11, 345. Note: humane (obsolete) = human.
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To discover and to teach are distinct functions; they are also distinct gifts, and are not commonly found united in the same person.
Discourses on the Scope and Nature of University Education. Addressed to the Catholics of Dublin (1852), Preface, xii.
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To discover not more and more things but the truth or real relation of things is what distinguishes men from the animals.
In On Love & Psychological Exercises: With Some Aphorisms & Other Essays (1998), 57.
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To-day we no longer beg of nature; we command her, because we have discovered certain of her secrets and shall discover others each day. We command her in the name of laws she can not challenge because they are hers; these laws we do not madly ask her to change, we are the first to submit to them. Nature can only be governed by obeying her.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 85.
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Twenty years from now you will be more disappointed by the things you didn’t do than by the ones you did. So throw off the bowlines, Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.
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Unfortunately, the study of organic remains is beset with two evils, which, though of an opposite character, do not neutralize each other so much as at first sight might be anticipated: the one consisting of a strong desire to find similar organic remains in supposed equivalent deposits, even at great distances; the other being an equally strong inclination to discover new species, often as it would seem for the sole purpose of appending the apparently magical word nobis.
In Geological Manual (1832), Preface, iii.
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We do whatever we can to deny intuition of the invisible realms. We clog up our senses with smog, jam our minds with media overload. We drown ourselves in alcohol or medicate ourselves into rigidly artificial states... we take pride in our cynicism and detachment. Perhaps we are terrified to discover that our “rationality” is itself a kind of faith, an artifice, that beneath it lies the vast territory of the unknown.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 29
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We live only to discover beauty. All else is a form of waiting.
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We love to discover in the cosmos the geometrical forms that exist in the depths of our consciousness. The exactitude of the proportions of our monuments and the precision of our machines express a fundamental character of our mind. Geometry does not exist in the earthly world. It has originated in ourselves. The methods of nature are never so precise as those of man. We do not find in the universe the clearness and accuracy of our thought. We attempt, therefore, to abstract from the complexity of phenomena some simple systems whose components bear to one another certain relations susceptible of being described mathematically.
In Man the Unknown (1935), 8.
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We may discover resources on the moon or Mars that will boggle the imagination, that will test our limits to dream. And the fascination generated by further exploration will inspire our young people to study math, and science, and engineering and create a new generation of innovators and pioneers.
Speech, NASA Headquarters (14 Jan 2004). In Office of the Federal Register (U.S.) Staff (eds.), Public Papers of the Presidents of the United States, George W. Bush (2007), 58-59.
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We may have three principal objects in the study of truth: one to discover it when it is sought; another to demonstrate it when it is possessed; and a third, to discriminate it from the false when it is examined.
As translated in Blaise Pascal and G.W. Wight (trans.), Of the Geometrical Spirit, collected in Charles William Eliot, The Harvard Classics (1910), Vol. 48, 427. From the original French, “On peut avoir trois principaux objets dans l’etude de la vérité: l’un, de la découvrir quand on la cherche; l’autre, de la démontrer quand on la possède; le dernier, de la discerner d'avec le faux quand on l’examine,” in 'De l'Ésprit Géométrique', Pascal: Opuscules Philosophiques (1887), 82. For an alternative translation, see the quote beginning, “There are three leading objects…” on the Blaise Pascal Quotes page of this website.
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We may regard [Scheele] not only as having given the first indication of the rich harvest to be reaped by the investigation of the compounds of organic chemistry, but as having been the first to discover and make use of characteristic reactions by which closely allied substances can be detected and separated, so that he must be considered one of the chief founders of analytical chemistry.
In Treatise on Chemistry (1877, 1890), Vol. 1, 23.
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We praise the eighteenth century for concerning itself chiefly with analysis. The task remaining to the nineteenth is to discover the false syntheses which prevail, and to analyse their contents anew.
In The Maxims and Reflections of Goethe (1906), 198.
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We see not only thought as participating in evolution as an anomaly or as an epiphenomenon; but evolution as so reducible to and identifiable with a progress towards thought that the movement of our souls expresses and measures the very stages of progress of evolution itself. Man discovers that he is nothing else than evolution become conscious of itself.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 221. Originally published in French as Le Phénomene Humain (1955).
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What I chiefly admired, and thought altogether unaccountable, was the strong disposition I observed in them [the mathematicians of Laputa] towards news and politics; perpetually inquiring into public affairs; giving their judgments in matters of state; and passionately disputing every inch of party opinion. I have indeed observed the same disposition among most of the mathematicians I have known in Europe, although I could never discover the least analogy between the two sciences.
In Gulliver's Travels, Part 8, chap. 2.
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What is a weed? A plant whose virtues have not been discovered.
From Lecture delivered at the Old South Church (30 Mar 1878), published as a booklet, Fortune of the Republic (1878), 3.
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What strange wonder is this? Our prayer to thee was for water,
Earth! What is this that thou now send’st from thy womb in reply?
In the abyss is there life ? Or hidden under the lava
Dwelleth some race now unknown? Does what hath fled e’er return?
Greeks and Romans, oh come! Oh, see the ancient Pompeii
Here is discover’d again,—Hercules’ town is rebuilt!
Beginning lines of poem, 'Pompeii and Herculaneum', in Edgar A. Bowring (trans.), The Poems of Schiller (1875), 237.
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When all the trees have been cut down,
when all the animals have been hunted,
when all the waters are polluted,
when all the air is unsafe to breathe,
only then will you discover you cannot eat money.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 28
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When Aloisio Galvani first stimulated the nervous fiber by the accidental contact of two heterogeneous metals, his contemporaries could never have anticipated that the action of the voltaic pile would discover to us, in the alkalies, metals of a silvery luster, so light as to swim on water, and eminently inflammable; or that it would become a powerful instrument of chemical analysis, and at the same time a thermoscope and a magnet.
In 'Introduction' Cosmos: A Sketch of a Physical Description of the Universe (1860), Vol. 1, 52, as translated by E.C. Otté.
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When first I applied my mind to Mathematics I read straight away most of what is usually given by the mathematical writers, and I paid special attention to Arithmetic and Geometry because they were said to be the simplest and so to speak the way to all the rest. But in neither case did I then meet with authors who fully satisfied me. I did indeed learn in their works many propositions about numbers which I found on calculation to be true. As to figures, they in a sense exhibited to my eyes a great number of truths and drew conclusions from certain consequences. But they did not seem to make it sufficiently plain to the mind itself why these things are so, and how they discovered them. Consequently I was not surprised that many people, even of talent and scholarship, should, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very outset from learning them. … But when I afterwards bethought myself how it could be that the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom any one who was not versed in Mathematics … I was confirmed in my suspicion that they had knowledge of a species of Mathematics very different from that which passes current in our time.
In Elizabeth S. Haldane (trans.) and G.R.T. Ross (trans.), 'Rules for the Direction of the Mind', The Philosophical Works of Descartes (1911, 1973), Vol. 1, Rule 4, 11.
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When I discover who I am, I’ll be free.
…...
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When scientists discovered that liquid water, which brought forth life on Earth, exists nowhere else in great quantities in the solar system, the most significant lesson they taught was not that water, or the life that depends on it, is necessarily the result of some chemical accident in space; their most important revelation was that water is rare in infinity, that we should prize it, preserve it, conserve it.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 201-202.
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When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
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When the first mathematical, logical, and natural uniformities, the first laws, were discovered, men were so carried away by the clearness, beauty and simplification that resulted, that they believed themselves to have deciphered authentically the eternal thoughts of the Almighty.
From Lecture (Nov 1906) at the Lowell Institute, Boston. Published in 'The Present Dilemma in Philosophy',Pragmatism: A New Name for Some Old Ways of Thinking: Popular Lectures on Philosophy (1907), 56.
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When we have fully discovered the scientific laws that govern life, we shall realise that one person who has more illusions than the dreamer is the man of action.
In Epigrams of Oscar Wilde (2007), 111.
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When you recover or discover something that nourishes your soul and brings joy, care enough about yourself to make room for it in your life.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 253
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Whenever … a controversy arises in mathematics, the issue is not whether a thing is true or not, but whether the proof might not be conducted more simply in some other way, or whether the proposition demonstrated is sufficiently important for the advancement of the science as to deserve especial enunciation and emphasis, or finally, whether the proposition is not a special case of some other and more general truth which is as easily discovered.
In Mathematical Essays and Recreations (1898), 88.
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While there is still much to learn and discover through space exploration, we also need to pay attention to our unexplored world here on earth. Our next big leap into the unknown can be every bit as exciting and bold as our pioneering work in space. It possesses the same “wow” factor: alien worlds, dazzling technological feats and the mystery of the unknown.
In 'Why Exploring the Ocean is Mankind’s Next Giant Leap', contributed to CNN 'Lightyears Blog' (13 Mar 2012)
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You can't really discover the most interesting conflicts and problems in a subject until you've tried to write about them. At that point, one discovers discontinuities in the data, perhaps, or in one's own thinking; then the act of writing forces you to work harder to resolve these contradictions.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 109.
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[Herbert Spencer] has discovered a great law of evolution in nature, which underlies all phenomena, & which is as important & more comprehensive than Newton’s law of gravitation.
In letter to his mother, after reading (Jul 1861) Herbert Spencer, The Principles of Psychology (1855). Fiske called the book, “the profoundest work I ever read”. It ignited his enthusiasm for Spencer’s philosophy of evolution. As quoted in Milton Berman, John Fiske: The Evolution of a Popularizer (1961), 36-37.
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[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 265-266.
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~~[Orphan ?]~~ Reason is the slow and tortuous method by which those who do not know the truth discover it.
Webmaster presently believes this is an orphan quote, best attributed to Anonymous. It seem to be unsupported when attributed to Blaise Pascal, for example, as quoted, without citation, in Morris Kline, 'Ancients versus Moderns, A New Battle of the Books', The Mathematics Teacher (Oct 1958), 51, No. 6, 423. Also later published, without citation, in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972), 296. Webmaster has not yet found a primary source for this as a quote by Pascal - not in English, not in French, and not in any earlier books. This is suspicious. (Can you help?) Furthermore, this sentence is also often seen in more recent books and online quotes pages as a first sentence, followed by a second sentence, “The heart has its reasons, which reason does not know.” The second sentence is a known Pascal quote verified in original French texts. However, Webmaster has not yet found, in any original French text, any instance of these two sentences together. Thus, putting them together more definitely appears to be a misquote. Can you help? [It is included on the Blaise Pascal page to link it with this cautionary note. —Webmaster]
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…tis a dangerous thing to ingage the authority of Scripture in disputes about the Natural World, in opposition to Reason; lest Time, which brings all things to light, should discover that to be evidently false which we had made Scripture to assert.
The Sacred Theory of the Earth (1681)
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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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