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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Discover Quotes (571 quotes)
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... there is an external world which can in principle be exhaustively described in scientific language. The scientist, as both observer and language-user, can capture the external facts of the world in prepositions that are true if they correspond to the facts and false if they do not. Science is ideally a linguistic system in which true propositions are in one-to-one relation to facts, including facts that are not directly observed because they involve hidden entities or properties, or past events or far distant events. These hidden events are described in theories, and theories can be inferred from observation, that is the hidden explanatory mechnism of the world can be discovered from what is open to observation. Man as scientist is regarded as standing apart from the world and able to experiment and theorize about it objectively and dispassionately.
'Introduction', Revolutions and Reconstructions in the Philosophy of Science (1981), xii. In John Templeton and Robert L. Herrmann, Is God the Only Reality (1994), 11-12.
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...a man estimable for his learning, amiable for his life, and venerable for his piety. Arbuthnot was a man of great comprehension, skilful in his profession, versed in the sciences, acquainted with ancient literature, and able to animate his mass of knowledge by a bright and active imagination; a scholar with great brilliance of wit; a wit who, in the crowd of life, retained and discovered a noble ardour of religious zeal.
The Lives of the English Poets (1826), vol. 2, 257.
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...He cannot conclude however, without observing, that from the contemplation of so great a variety of extraneous fossils discovered in the cliffs which were evidently the produce of very different climates, he thinks himself rationally induced to believe that nothing short of an universal deluge could be a cause adequate to this effect.
Plantae Favershamiensis, Appendix, 'Establishing a short view of the fossil bodies of the adjacent island of Sheppey.' Quoted in David Beerling, The Emerald Planet: How Plants Changed Earth's History (2007), 145.
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...neither is it possible to discover the more remote and deeper parts of any science, if you stand but upon the level of the same science, and ascend not to a higher science.
Francis Bacon, Basil Montagu (Ed.), The Works of Francis Bacon (1852), Vol. 1, 173.
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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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...to invent is to discover that we know not, and not to recover or resummon that which we already know.
The Second Book of Francis Bacon of the Proficience and Advancement of Learning (1605). In Francis Bacon and Basil Montagu, The Works of Francis Bacon, Lord Chancellor of England (1852), 209
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“Talent is a long patience.” We must look on what we wish to express long enough and with enough attention to discover an aspect that has not been seen and portrayed by another. There is, in everything, something unexplored, because we always use our eyes only with the recollection of what has been thought before on the subject we are contemplating.
From Pierre et Jean (1888), as translated by Alexina Loranger in 'Introduction', Pierre et Jean (Peter and John) (1890), 38-39. The opening words are quoted from Gustave Flaubert. From the original French, “Le talent est une longue patience. — Il s’agit de regarder tout ce qu’on veut exprimer assez longtemps et avec assez d’attention pour en découvrir un aspect qui n’ait été vu et dit par personne. Il y a, dans tout, de l’inexploré, parce que nous sommes habitués à ne nous servir de nos yeux qu’avec le souvenir de ce qu’on a pensé avant nous sur ce que nous contemplons.”
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“Yes,” he said. “But these things (the solutions to problems in solid geometry such as the duplication of the cube) do not seem to have been discovered yet.” “There are two reasons for this,” I said. “Because no city holds these things in honour, they are investigated in a feeble way, since they are difficult; and the investigators need an overseer, since they will not find the solutions without one. First, it is hard to get such an overseer, and second, even if one did, as things are now those who investigate these things would not obey him, because of their arrogance. If however a whole city, which did hold these things in honour, were to oversee them communally, the investigators would be obedient, and when these problems were investigated continually and with eagerness, their solutions would become apparent.”
Plato
In The Republic 7 528bc, trans. R.W. Sharples.
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[1665-06-11] I out of doors a little to show forsooth my new suit, and back again; and in going, saw poor Dr Burnets door shut. But he hath, I hear, gained goodwill among his neighbours; for he discovered it himself first, and caused himself to be shut up of his own accord - which was very handsome.
Diary of Samuel Pepys (11 Jun 1665)
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[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
Unpublished Manuscript. Quoted In Frank Edward Manuel and Fritzie Prigohzy Manuel, Utopian Thought in the Western World (1979, 2009), 493.
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[As a youth, fiddling in my home laboratory] I discovered a formula for the frequency of a resonant circuit which was 2π x sqrt(LC) where L is the inductance and C the capacitance of the circuit. And there was π, and where was the circle? … I still don’t quite know where that circle is, where that π comes from.
From address to the National Science Teachers’ Association convention (Apr 1966), 'What Is Science?', collected in Richard Phillips Feynman and Jeffrey Robbins (ed.), The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman (1999, 2005), 177.
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[Concerning] phosphorescent bodies, and in particular to uranium salts whose phosphorescence has a very brief duration. With the double sulfate of uranium and potassium ... I was able to perform the following experiment: One wraps a Lumière photographic plate with a bromide emulsion in two sheets of very thick black paper, such that the plate does not become clouded upon being exposed to the sun for a day. One places on the sheet of paper, on the outside, a slab of the phosphorescent substance, and one exposes the whole to the sun for several hours. When one then develops the photographic plate, one recognizes that the silhouette of the phosphorescent substance appears in black on the negative. If one places between the phosphorescent substance and the paper a piece of money or a metal screen pierced with a cut-out design, one sees the image of these objects appear on the negative. One can repeat the same experiments placing a thin pane of glass between the phosphorescent substance and the paper, which excludes the possibility of chemical action due to vapors which might emanate from the substance when heated by the sun's rays. One must conclude from these experiments that the phosphorescent substance in question emits rays which pass through the opaque paper and reduces silver salts.
[Although the sun is irrelevant, and he misinterprets the role of phosphorescence, he has discovered the effect of radioactivity.]
Read at French Academy of Science (24 Feb 1896). In Comptes Rendus (1896), 122, 420. As translated by Carmen Giunta on the Classic Chemistry web site.
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[Davy's] March of Glory, which he has run for the last six weeks—within which time by the aid and application of his own great discovery, of the identity of electricity and chemical attractions, he has placed all the elements and all their inanimate combinations in the power of man; having decomposed both the Alkalies, and three of the Earths, discovered as the base of the Alkalies a new metal... Davy supposes there is only one power in the world of the senses; which in particles acts as chemical attractions, in specific masses as electricity, & on matter in general, as planetary Gravitation... when this has been proved, it will then only remain to resolve this into some Law of vital Intellect—and all human knowledge will be Science and Metaphysics the only Science.
In November 1807 Davy gave his famous Second Bakerian Lecture at the Royal Society, in which he used Voltaic batteries to “decompose, isolate and name” several new chemical elements, notably sodium and potassium.
Letter to Dorothy Wordsworth, 24 November 1807. In Earl Leslie Griggs (ed.), The Collected Letters of Samuel Taylor Coleridge (1956), Vol. 3, 38.
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[E.H.] Moore was presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting—to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group—an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.
In Obituary, 'Eliakim Hastings Moore', The American Mathematical Monthly (Apr 1933), 40, 191.
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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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[Oppenheimer is] tense, dedicated, deeper than deep, somewhat haunted, uncertain, calm, confident, and full, full, full of knowledge, not only of particles and things but of men and motives, and of the basic humanity that may be the only savior we have in this strange world he and his colleagues have discovered.
In Due to Circumstances Beyond Our Control by Fred W. Friendly (1967).
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[The more science discovers and] the more comprehension it gives us of the mechanisms of existence, the more clearly does the mystery of existence itself stand out.
Julian Huxley and Aldous Huxley, Aldous Huxley, 1894-1963: A Memorial Volume (1965), 21.
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[W]hen Galileo discovered he could use the tools of mathematics and mechanics to understand the motion of celestial bodies, he felt, in the words of one imminent researcher, that he had learned the language in which God recreated the universe. Today we are learning the language in which God created life. We are gaining ever more awe for the complexity, the beauty, the wonder of God's most devine and sacred gift.
From White House Announcement of the Completion of the First Survey of the Entire Human Genome Project, broadcast on the day of the publication of the first draft of the human genome. Quoted in transcript on the National Archives, Clinton White House web site, 'Text of Remarks on the Completion of the First Survey of the Entire Human Genome Project' (26 Jun 2000).
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[Of the Laputans:] They have likewise discovered two lesser stars, or satellites, which revolve about Mars, whereof the innermost is distant from the centre of the primary planet exactly three of his diameters, and the outermost five; the former revolves in the space of ten hours, and the latter in twenty one and a half.
Gulliver's Travels (1726, Penguin ed. 1967), Part III, Chap. 3, 213.
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[When asked “Dr. Einstein, why is it that when the mind of man has stretched so far as to discover the structure of the atom we have been unable to devise the political means to keep the atom from destroying us?”] That is simple, my friend. It is because politics is more difficult than physics.
Einstein’s answer to a conferee at a meeting at Princeton, N.J. (Jan 1946), as recalled by Greenville Clark in 'Letters to the Times', in New York Times (22 Apr 1955), 24.
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Connaître, découvrir, communiquer—telle est, au fond, notre honorable destinée.
To get to know, to discover, to publish—this is the destiny of a scientist.
From 'De L’Utiliteé des Pensions', Œuvres complètes de François Arago (1855), Vol. 3, 621. Translation as given in Alan L. MacKay in A Harvest of a Quiet Eye (1977), 10.
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Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. Kepler is said to have discovered the laws of planetary motion named after him, but no the many other 'laws' which he formulated. ... Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge.
Discovery in the Physical Sciences (1969). In Rodney P. Carlisle, Scientific American Inventions and Discoveries (2004), 179.
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Dogbert: Scientists have discovered the gene that makes some people love golf.
Dilbert: How can they tell it’s the golf gene?
Dogbert: It’s plaid and it lies.
Dilbert comic strip (28 Oct 1989).
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Forging differs from hoaxing, inasmuch as in the later the deceit is intended to last for a time, and then be discovered, to the ridicule of those who have credited it; whereas the forger is one who, wishing to acquire a reputation for science, records observations which he has never made.
Reflections on the Decline of Science in England (1830). In Calyampudi Radhakrishna Rao, Statistics and Truth (1997), 84.
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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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On se persuade mieux, pour l’ordinaire, par les raisons qu’on a soi-même trouvées, que par celles qui sont venues dans l’esprit des autres.
We are generally more effectually persuaded by reasons we have ourselves discovered than by those which have occurred to others.
Pensées (1670), Section 1, aphorism 18. In H. F. Stewart (ed.), Pascal's Pensées (1950), 11. Original French text in Pensées de Pascal: publiées dans leur texte authentique (1866), Vol. 1, 99.
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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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Question: Explain why, in order to cook food by boiling, at the top of a high mountain, you must employ a different method from that used at the sea level.
Answer: It is easy to cook food at the sea level by boiling it, but once you get above the sea level the only plan is to fry it in its own fat. It is, in fact, impossible to boil water above the sea level by any amount of heat. A different method, therefore, would have to be employed to boil food at the top of a high mountain, but what that method is has not yet been discovered. The future may reveal it to a daring experimentalist.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 178-9, Question 11. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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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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~~[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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230(231-1) ... is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for; as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it.
In An Elementary Investigation of the Theory of Numbers (1811), 43. The stated number, which evaluates as 2305843008139952128 was discovered by Euler in 1772 as the eighth known perfect number. It has 19 digits. By 2013, the 48th perfect number found had 34850340 digits.
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A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one’s ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop these laws is based entirely on a fact, whose existence has hitherto been vaguely discerned rather than demonstrated. This fact is that in all minerals which belong to the same species, these little solids, which are the crystal elements and which I call their integrant molecules, have an invariable form, in which the faces lie in the direction of the natural fracture surfaces corresponding to the mechanical division of the crystals. Their angles and dimensions are derived from calculations combined with observation.
Traité de mineralogie … Publié par le conseil des mines (1801), Vol. 1, xiii-iv, trans. Albert V. and Marguerite Carozzi.
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A cell of a higher organism contains a thousand different substances, arranged in a complex system. This great organized system was not discovered by chemical or physical methods; they are inadequate to its refinement and delicacy and complexity.
'The Cell in Relation to its Environment', Journal of the Maryland Academy of Sciences (1931), 2, 25.
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A drop from the nose of Fleming, who had a cold, fell onto an agar plate where large yellow colonies of a contaminant had grown, and lysosyme was discovered. He made this important discovery because when he saw that the colonies of the contaminant were fading, his mind went straight to the right cause of the phenomenon he was observing—that the drop from his nose contained a lytic substance. And also immediately, he thought that this substance might be present in many secretions and tissues of the body. And he found this was so—the substance was in tears, saliva, leucocytes, skin, fingernails, mother's milk—thus very widely distributed in amounts and also in plants.
Personal recollections of Alexander Fleming by Lady Amelia Fleming. Quoted in Molecular Cloning (2001), Vol. 1, 153.
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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 fossil hunter needs sharp eyes and a keen search image, a mental template that subconsciously evaluates everything he sees in his search for telltale clues. A kind of mental radar works even if he isn’t concentrating hard. A fossil mollusk expert has a mollusk search image. A fossil antelope expert has an antelope search image. … Yet even when one has a good internal radar, the search is incredibly more difficult than it sounds. Not only are fossils often the same color as the rocks among which they are found, so they blend in with the background; they are also usually broken into odd-shaped fragments. … In our business, we don’t expect to find a whole skull lying on the surface staring up at us. The typical find is a small piece of petrified bone. The fossil hunter’s search therefore has to have an infinite number of dimensions, matching every conceivable angle of every shape of fragment of every bone on the human body.
Describing the skill of his co-worker, Kamoya Kimeu, who discovered the Turkana Boy, the most complete specimen of Homo erectus, on a slope covered with black lava pebbles.
Richard Leakey and Roger Lewin, Origins Reconsidered: In Search of What Makes Us Human (1992), 26.
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A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
Quoted in H. Eves, Mathematical Circles (1977) .
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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 man of science rises ever, in seeking truth; and if he never finds it in its wholeness, he discovers nevertheless very significant fragments; and these fragments of universal truth are precisely what constitutes science.
From An Introduction to the Study of Experimental Medicine (1927, 1957), as translated by Henry Copley Greene (1927, 1957), 222. From the original French by Claude Bernard: “le savant monte toujours en cherchant la vérité, et s'il ne la trouve jamais tout entière, il en découvre néanmoins des fragments très-importants, et ce sont précisément ces fragments de la vérité générale qui constituent la science.” (1865), 389. A Google translation gives: “The scientist always rises by seeking the truth, and if he never finds it entirely, he nevertheless discovers very important fragments of it, and it is precisely these fragments of the general truth which constitute science.”
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A man who dares to waste one hour of time has not discovered the value of life.
In a Letter to his sister Susan (Aug 1836), collected in Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters, Volume 5 (1892), 137.
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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 proposal…to bore a hole in the crust of the Earth and discover the conditions deep down below the surface…may remind us that the most secret places of Nature are, perhaps, not 10 to the n-th miles above our heads, but 10 miles below our feet.
From Presidential address to Section A of the British Association at Cardiff (24 Aug 1920). Published in 'The Internal Constitution of the Stars', The Observatory: A Monthly Review of Astronomy (Oct 1920), 43, No. 557, 341.
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A scientist can discover a new star but he cannot make one. He would have to ask an engineer to do it for him.
The Design of Design (1969), 1
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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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A teacher … is never a giver of "truth”; he is a guide, a pointer to the truth that the student must discover for himself. … For example, a skillful teacher might spur his student’s growth by confronting him with certain frustrations. A good teacher is a catalyst.
Bruce Lee
In 'Liberate Yourself From Classical Karate', Black Belt (Sep 1971), 27.
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About eight days ago I discovered that sulfur in burning, far from losing weight, on the contrary, gains it; it is the same with phosphorus; this increase of weight arises from a prodigious quantity of air that is fixed during combustion and combines with the vapors. This discovery, which I have established by experiments, that I regard as decisive, has led me to think that what is observed in the combustion of sulfur and phosphorus may well take place in the case of all substances that gain in weight by combustion and calcination; and I am persuaded that the increase in weight of metallic calxes is due to the same cause... This discovery seems to me one of the most interesting that has been made since Stahl and since it is difficult not to disclose something inadvertently in conversation with friends that could lead to the truth I have thought it necessary to make the present deposit to the Secretary of the Academy to await the time I make my experiments public.
Sealed note deposited with the Secretary of the French Academy 1 Nov 1772. Oeuvres de Lavoisier, Correspondance, Fasc. II. 1770-75 (1957), 389-90. Adapted from translation by A. N. Meldrum, The Eighteenth-Century Revolution in Science (1930), 3.
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About medications that are drunk or applied to wounds it is worth learning from everyone; for people do not discover these by reasoning but by chance, and experts not more than laymen.
Affections, in Hippocrates, trans. P. Potter (1988), Vol. 5, 69. Littré VI, 254.
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About the year 1772, being then an apprentice to a wheel-wright, or wagon maker, I laboured to discover some means of propelling land carriages without animal power. … one of my brothers [told me of] blacksmith’s boys, who, for amusement, had stopped up the touch hole of a gun barrel, then put in about a gill of water, and rammed down a tight wad; after which they put the breech in the smith’s fire, when it discharged itself with as loud a crack as if it had been loaded with powder. It immediately occurred to me, that here was the power to propel any wagon, if I could only apply it.
From 'On the Origin of Steam Boats and Steam Wagons', Thomas Cooper (ed.), The Emporium of Arts and Sciences (Feb 1814), 2, No. 2, 205.
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According to the historian D. B. McIntyre (1963), James Hutton, often known as the father of geology, said in a lecture before the Royal Society of Edinburgh in the 1790s that he thought of the Earth as a superorganism and that its proper study would be by physiology. Hutton went on to make the analogy between the circulation of the blood, discovered by Harvey, and the circulation of the nutrient elements of the Earth and of the way that sunlight distills water from the oceans so that it may later fall as rain and so refresh the earth.
In 'The Earth as a Living Organism', Essay collected in E. O. Wilson and F. M. Peter (eds.), Biodiversity (1988), Chap. 56, 488. [Notes: Donald Bertram McIntyre (1923–2009) was a geologist. Hutton had medical training early in his life. According to Mirriam-Webster’s dictionary, the first known use of the word “superorganism” was “circa 1899”—so Hutton did not use that word. However, McIntyre did adopt that sophisticated word to describe Hutton’s thought, twice, in Philosophy of Geology (1963), 7 & 10. Thus, McIntyre and Lovelock freely embroidered whatever Hutton actually wrote, perhaps over-stepping. Cándido Manuel García Cruz criticizes that these “assertions are merely a misinterpretation” although “Hutton has nevertheless an holistic view which is closer to the Alfred N. Whitehead’s organic mechanicism than the James Lovelock’s Gaia Hypothesis,” as quoted from the abstract of his article 'From James Hutton’s «Theory of the Earth» to James Lovelock’s «Gaia Hypothesis»', Asclepio; Archivo Iberoamericano de Historia de la Medicina y Antropología Médica (Jun 2007), 59, No. 1, 65-100. Thus, it is best to read his own words in James Hutton, Theory of the Earth, which at length describes the “terrestrial system” as a “machine of a peculiar construction.” —Webmaster]
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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 appearances to the contrary, the only watchmaker in nature is the blind forces of physics, albeit deployed in very special way. A true watchmaker has foresight: he designs his cogs springs, and plans their interconnections, with a future purpose in his mind's eye. Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind's eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.
The Blind Watchmaker (1986), 5.
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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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All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.
Lettre Prétendue de M. De Leibnitz, à M. Hermann dont M. Koenig a Cité le Fragment (1753), cxi-cxii, trans. in A. O. Lovejoy, Great Chain of Being: A Study of the History of an Idea (1936), 144-5.
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All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.
In Lectures on the Logic of Arithmetic (1903), Preface, 18-19.
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Although Rick [Richard Smalley] made enormous contributions to science, I believe his worldwide contributions in making so many of us aware of the huge energy problem is even greater and longer-lasting than the beautiful science that he discovered.
As quoted in Eric Berger, Houston Chronicle (28 Oct 2005).
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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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An eye critically nice can only be formed by observing well-colored pictures with attention; and by close attention … discover … expedients by which good colorists have raised the value of their tints, and by which nature has been so happily imitated.
In The Life and Discourses of Sir Joshua Reynolds (1853), 24.
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Anaximander son of Praxiades, of Miletus: he said that the principle and element is the Indefinite, not distinguishing air or water or anything else. … he was the first to discover a gnomon, and he set one up on the Sundials (?) in Sparta, according to Favorinus in his Universal History, to mark solstices and equinoxes; and he also constructed hour indicators. He was the first to draw an outline of earth and sea, but also constructed a [celestial] globe. Of his opinions he made a summary exposition, which I suppose Apollodorus the Athenian also encountered. Apollodorus says in his Chronicles that Anaximander was sixty-four years old in the year of the fifty-eighth Olympiad [547/6 B.C.], and that he died shortly afterwards (having been near his prime approximately during the time of Polycrates, tyrant of Samos).
Diogenes Laërtius II, 1-2. In G.S. Kirk, J.E. Raven and M. Schofield (eds), The Presocratic Philosophers: A Critical History with a Selection of Texts (1957), 99. The editors of this translation note that Anaximander may have introduced the gnomon into Greece, but he did not discover it—the Babylonians used it earlier, and the celestial sphere, and the twelve parts of the day.
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Another argument of hope may be drawn from this–that some of the inventions already known are such as before they were discovered it could hardly have entered any man's head to think of; they would have been simply set aside as impossible. For in conjecturing what may be men set before them the example of what has been, and divine of the new with an imagination preoccupied and colored by the old; which way of forming opinions is very fallacious, for streams that are drawn from the springheads of nature do not always run in the old channels.
Translation of Novum Organum, XCII. In Francis Bacon, James Spedding, The Works of Francis Bacon (1864), Vol. 8, 128.
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Applied research generates improvements, not breakthroughs. Great scientific advances spring from pure research. Even scientists renowned for their “useful” applied discoveries often achieved success only when they abandoned their ostensible applied-science goal and allowed their minds to soar—as when Alexander Fleming, “just playing about,” refrained from throwing away green molds that had ruined his experiment, studied them, and discovered penicillin. Or when C. A. Clarke, a physician affiliated with the University of Liverpool, became intrigued in the 1950s by genetically created color patterns that emerged when he cross-bred butterflies as a hobby. His fascination led him—“by the pleasant route of pursuing idle curiosity”—to the successful idea for preventing the sometimes fatal anemia that threatened babies born of a positive-Rhesus-factor father and a negative-Rhesus-factor mother.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 214-215.
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Archimedes said Eureka,
Cos in English he weren't too aversed in,
when he discovered that the volume of a body in the bath,
is equal to the stuff it is immersed in,
That is the law of displacement,
Thats why ships don't sink,
Its a shame he weren't around in 1912,
The Titanic would have made him think.
From lyrics of song Sod’s Law.
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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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Aristotle discovered all the half-truths which were necessary to the creation of science.
From Dialogue XLII in Alfred North Whitehead and Lucien Price (ed.), Dialogues of Alfred North Whitehead (1954, 1977), 344.
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Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.
The Principles of Mathematics (1903), 451.
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Art is more godlike than science. Science discovers; art creates.
John Opie
As given, without citation, in Maturin Murray Ballo, Edge-Tools of Speech (1851), 25. Also in a fictional conversation in novel by Baron Edward Bulwer Lytton, Zanoni (1842), 89.
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As a boy I had liked both drawing and physics, and I always abhorred the role of being a spectator. In 1908, when I was 15, I designed, built and flew a toy model airplane which won the then-famous James Gordon Bennett Cup. By 16 I had discovered that design could be fun and profitable, and this lesson has never been lost on me.
On the official Raymond Loewry website.
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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 regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, “If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.” And again, “Without this theory no one can have a correct insight into truth.” And he says also, “I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.” And Again, “It is clear that whosoever passes these by, has lost the knowledge of all learning.”
Opus Majus [1266-1268], Part IV, distinction I, chapter I, trans. R. B. Burke, The Opus Majus of Roger Bacon (1928), Vol. I, 117.
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As the component parts of all new machines may be said to be old[,] it is a nice discriminating judgment, which discovers that a particular arrangement will produce a new and desired effect. ... Therefore, the mechanic should sit down among levers, screws, wedges, wheels, etc. like a poet among the letters of the alphabet, considering them as the exhibition of his thoughts; in which a new arrangement transmits a new idea to the world.
A Treatise on the Improvement of Canal Navigation (1796), preface, x.
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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 them. 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 my urgent request the Curie laboratory, in which radium was discovered a short time ago, was shown to me. The Curies themselves were away travelling. It was a cross between a stable and a potato-cellar, and, if I had not seen the worktable with the chemical apparatus, I would have thought it a practical joke.
Wilhelm Ostwald on seeing the Curie's laboratory facilities.
In R. Reid, Marie Curie (1974), 95.
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At the voice of comparative anatomy, every bone, and fragment of a bone, resumed its place. I cannot find words to express the pleasure I have in seeing, as I discovered one character, how all the consequences, which I predicted from it, were successively confirmed; the feet were found in accordance with the characters announced by the teeth; the teeth in harmony with those indicated beforehand by the feet; the bones of the legs and thighs, and every connecting portion of the extremities, were found set together precisely as I had arranged them, before my conjectures were verified by the discovery of the parts entire: in short, each species was, as it were, reconstructed from a single one of its component elements.
Geology and Mineralogy (1836), Vol. I, 83-4.
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At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
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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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Balard did not discover bromine, rather bromine discovered Balard.
Justus von Liebig comment on Antonie Jerome Balard.
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 124.
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Before the promulgation of the periodic law the chemical elements were mere fragmentary incidental facts in nature; there was no special reason to expect the discovery of new elements, and the new ones which were discovered from time to time appeared to be possessed of quite novel properties. The law of periodicity first enabled us to perceive undiscovered elements at a distance which formerly were inaccessible to chemical vision, and long ere they were discovered new elements appeared before our eyes possessed of a number of well-defined properties.
In Faraday Lecture, delivered before the Fellows of the Chemical Society in the Theatre of the Royal Institution (4 Jun 1889), printed in Professor Mendeléeff, 'The Periodic Law of the Chemical Elements', Transactions of the Chemical Society (1889), 55, 648.
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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 from the time I was in college I learned that there is nothing one could imagine which is so strange and incredible that it was not said by some philosopher; and since that time, I have recognized through my travels that all those whose views are different from our own are not necessarily, for that reason, barbarians or savages, but that many of them use their reason either as much as or even more than we do. I also considered how the same person, with the same mind, who was brought up from infancy either among the French or the Germans, becomes different from what they would have been if they had always lived among the Chinese or among the cannibals, and how, even in our clothes fashions, the very thing that we liked ten years ago, and that we may like again within the next ten years, appears extravagant and ridiculous to us today. Thus our convictions result from custom and example very much more than from any knowledge that is certain... truths will be discovered by an individual rather than a whole people.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 14-5.
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But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule, therefore, throughout the universe, bears impressed on it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the Temple of Karnac ... the exact quantity of each molecule to all others of same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article and precludes the idea of its being external and self-existent.
'Molecules', 1873. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 375-6.
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But it is just this characteristic of simplicity in the laws of nature hitherto discovered which it would be fallacious to generalize, for it is obvious that simplicity has been a part cause of their discovery, and can, therefore, give no ground for the supposition that other undiscovered laws are equally simple.
From Herbert Spencer lecture delivered at Oxford (1914) 'On Scientific Method in Philosophy', collected in Mysticism and Logic and Other Essays (1919), 102.
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But medicine has long had all its means to hand, and has discovered both a principle and a method, through which the discoveries made during a long period are many and excellent, while full discovery will be made, if the inquirer be competent, conduct his researches with knowledge of the discoveries already made, and make them his starting-point. But anyone who, casting aside and rejecting all these means, attempts to conduct research in any other way or after another fashion, and asserts that he has found out anything, is and has been victim of deception.
Ancient Medicine, in Hippocrates, trans. W. H. S. Jones (1923), Vol. I, 15.
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But neither thirty years, nor thirty centuries, affect the clearness, or the charm, of Geometrical truths. Such a theorem as “the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides” is as dazzlingly beautiful now as it was in the day when Pythagoras first discovered it, and celebrated its advent, it is said, by sacrificing a hecatomb of oxen—a method of doing honour to Science that has always seemed to me slightly exaggerated and uncalled-for. One can imagine oneself, even in these degenerate days, marking the epoch of some brilliant scientific discovery by inviting a convivial friend or two, to join one in a beefsteak and a bottle of wine. But a hecatomb of oxen! It would produce a quite inconvenient supply of beef.
Written without pseudonym as Charles L. Dodgson, in Introduction to A New Theory of Parallels (1888, 1890), xvi. Note: a hecatomb is a great public sacrifice, originally of a hundred oxen.
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But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.
Memoirs of Dr. Joseph Priestley, in the Year 1795 (1806), Vol. 1, 61-2.
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But shall gravity be therefore called an occult cause, and thrown out of philosophy, because the cause of gravity is occult and not yet discovered? Those who affirm this, should be careful not to fall into an absurdity that may overturn the foundations of all philosophy. For causes usually proceed in a continued chain from those that are more compounded to those that are more simple; when we are arrived at the most simple cause we can go no farther ... These most simple causes will you then call occult and reject them? Then you must reject those that immediately depend on them.
Mathematical Principles (1729), 27.
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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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But there is another alchemy, operative and practical, which teaches how to make the noble metals and colours and many other things better and more abundantly by art than they are made in nature. And science of this kind is greater than all those preceding because it produces greater utilities. For not only can it yield wealth and very many other things for the public welfare, but it also teaches how to discover such things as are capable of prolonging human life for much longer periods than can be accomplished by nature … Therefore this science has special utilities of that nature, while nevertheless it confirms theoretical alchemy through its works.
Opus Tertium [1266-1268], chapter 12, quoted in A. C. Crombie, Augustine to Galileo (1959), Vol. I, 69.
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But what exceeds all wonders, I have discovered four new planets and observed their proper and particular motions, different among themselves and from the motions of all the other stars; and these new planets move about another very large star [Jupiter] like Venus and Mercury, and perchance the other known planets, move about the Sun. As soon as this tract, which I shall send to all the philosophers and mathematicians as an announcement, is finished, I shall send a copy to the Most Serene Grand Duke, together with an excellent spyglass, so that he can verify all these truths.
Letter to the Tuscan Court, 30 Jan 1610. Quoted in Albert van Heiden (ed.), Siderius Nuncius or The Sidereal Messenger (1989), 18.
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By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.
In Speech made on behalf of a delegation from the Conjoint Board of Scientific Studies in 1916 to Lord Crewe, then Lord President of the Council. In George Paget Thomson, J. J. Thomson and the Cavendish Laboratory in His Day (1965), 167-8.
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By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on ...Today even our clocks are not made of clockwork. ... With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law.
Does God Play Dice?: The New Mathematics of Chaos (2002). xi.
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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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Common sense … has the very curious property of being more correct retrospectively than prospectively. It seems to me that one of the principal criteria to be applied to successful science is that its results are almost always obvious retrospectively; unfortunately, they seldom are prospectively. Common sense provides a kind of ultimate validation after science has completed its work; it seldom anticipates what science is going to discover.
Quoted in A. De Reuck, M. Goldsmith and J. Knight (eds.), Decision Making in National Science Policy (1968), 96.
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Complexity is the prodigy of the world. Simplicity is the sensation of the universe. Behind complexity, there is always simplicity to be revealed. Inside simplicity, there is always complexity to be discovered
Gang Yu
In course Syllabus for 'Algorithm Design and Implementations' (2004) on mccombs.utexas.edu web site.
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Concerning alchemy it is more difficult to discover the actual state of things, in that the historians who specialise in this field seem sometimes to be under the wrath of God themselves; for, like those who write of the Bacon-Shakespeare controversy or on Spanish politics, they seem to become tinctured with the kind of lunacy they set out to describe.
The Origins of Modern Science (1949), 115.
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Consider a cow. A cow doesn’t have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain’s ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.
In John Tierney, 'For Decades, Puzzling People With Mathematics', New York Times (20 Oct 2009), D2.
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Considering, therefore, that the metal which has been examined is to different from those hitherto discovered, it appeared proper that it should be distinguished by a peculiar name; and, having consulted with several of the eminent and ingenious chemists of this country, I have been induced to give it the name of Columbium.
Opening paragraph from Paper (26 Nov 1801) read to the Royal Society, printed in 'Analysis of a Mineral Substance From North America, Containing a Metal Hitherto Unknown', Philosophical Transactions (1802), 92, 65.
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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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Cosmology is a science which has only a few observable facts to work with. The discovery of the cosmic microwave background radiation added one—the present radiation temperature of the universe. This, however, was a significant increase in our knowledge since it requires a cosmology with a source for the radiation at an early epoch and is a new probe of that epoch. More sensitive measurements of the background radiation in the future will allow us to discover additional facts about the universe.
'Discovery of the Cosmic Microwave Background', in B. Bertotti (ed.) Modern Cosmology in Retrospect (1990), 304.
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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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Divers of Hermetic Books have such involv’d Obscuritys that they may justly be compar’d to Riddles written in Cyphers. For after a Man has surmounted the difficulty of decyphering the Words & Terms, he finds a new & greater difficulty to discover ye meaning of the seemingly plain Expression.
Fragment In Boyle papers. Cited by Lawrence Principe, 'Boyle's Alchemical Pursuits', In M. Hunter (ed.), Robert Boyle Reconsidered (1994), 95
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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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During the time that [Karl] Landsteiner gave me an education in the field of imununology, I discovered that he and I were thinking about the serologic problem in very different ways. He would ask, What do these experiments force us to believe about the nature of the world? I would ask, What is the most. simple and general picture of the world that we can formulate that is not ruled by these experiments? I realized that medical and biological investigators were not attacking their problems the same way that theoretical physicists do, the way I had been in the habit of doing.
‘Molecular Disease’, Pfizer Spectrum (1958), 6:9, 234.
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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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ENGINEER, in the military art, an able expert man, who, by a perfect knowledge in mathematics, delineates upon paper, or marks upon the ground, all sorts of forts, and other works proper for offence and defence. He should understand the art of fortification, so as to be able, not only to discover the defects of a place, but to find a remedy proper for them; as also how to make an attack upon, as well as to defend, the place. Engineers are extremely necessary for these purposes: wherefore it is requisite that, besides being ingenious, they should be brave in proportion. When at a siege the engineers have narrowly surveyed the place, they are to make their report to the general, by acquainting him which part they judge the weakest, and where approaches may be made with most success. Their business is also to delineate the lines of circumvallation and contravallation, taking all the advantages of the ground; to mark out the trenches, places of arms, batteries, and lodgments, taking care that none of their works be flanked or discovered from the place. After making a faithful report to the general of what is a-doing, the engineers are to demand a sufficient number of workmen and utensils, and whatever else is necessary.
In Encyclopaedia Britannica or a Dictionary of Arts and Sciences (1771), Vol. 2, 497.
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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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Every great anthropologic and paleontologic discovery fits into its proper place, enabling us gradually to fill out, one after another, the great branching lines of human ascent and to connect with the branches definite phases of industry and art. This gives us a double means of interpretation, archaeological and anatomical. While many branches and links in the chain remain to be discovered, we are now in a position to predict with great confidence not only what the various branches will be like but where they are most like to be found.
In Henry Fairfield Osborn, 'Osborn States the Case For Evolution', New York Times (12 Jul 1925), XX1
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Every great scientific truth goes through three states: first, people say it conflicts with the Bible; next, they say it has been discovered before; lastly, they say they always believed it.
Attributed; it does not appear directly in this form in any writings by Agassiz. This version of the quote comes from the Saturday Evening Post (1890), as cited in Ralph Keyes, The Quote Verifier (2006), 226. Since the quote was not printed within quotation marks, it is unlikely that this is a verbatim statement. Keyes discusses variations of the “three stages of truth” that have been attributed to a various other authors, but provides some substantiation with examples of similar quotes linked to Agassiz as related in second-person accounts.
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Every science has for its basis a system of principles as fixed and unalterable as those by which the universe is regulated and governed. Man cannot make principles; he can only discover them.
In The Age of Reason (1794, 1834), 30-31.
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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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Exercises in being obedient can not begin too early, and I have, during an almost daily observation of six years, discovered no harm from an early, consistent guiding of the germinating will, provided only this guiding be done with the greatest mildness and justice, as if the infant had already an insight into the benefits of obedience.
In W. Preyer and H.W. Brown (trans.), The Mind of the Child: The Senses and the Will: Observations Concerning the Mental Development of the Human Being in the First Years of Life (1888, 1890), Vol. 1, 345.
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Facts, and facts alone, are the foundation of science... When one devotes oneself to experimental research it is in order to augment the sum of known facts, or to discover their mutual relations.
Precis elementaire de Physiologie (1816), ii. Trans. J. M. D. Olmsted, François Magendie: Pioneer in Experimental Physiology and Scientific Medicine in XIX Century France (1944), 62.
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First... a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.
'Pragmatism's Conception of Truth', in Pragmatism: A New Name for some Old Ways of Thinking, Popular Lectures on Philosophy (1907), 198.
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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 he who knows not mathematics cannot know any other science; what is more, he cannot discover his own ignorance, or find its proper remedy.
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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.
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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.
Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.
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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 more than ten years, my theory was in limbo. Then, finally, in the late 1980s, physicists at Princeton said, “There’s nothing wrong with this theory. It’s the only one that works, and we have to open out minds to hyperspace.” We weren’t destined to discover this theory for another 100 years because it’s so bizarre, so different from everything we’d been doing. We didn’t use the normal sequence of discoveries to get to it.
Describing reaction to his superstring theory of hyperspace which mathematically relates the universe’s basic forces.
Quoted in Nina L. Diamond, Voices of Truth (2000), 326.
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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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For there are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience; since many have the arguments relating to what can be known, but because they lack experience they neglect the arguments, and neither avoid what is harmful nor follow what is good. For if a man who has never seen fire should prove by adequate reasoning that fire burns and injures things and destroys them, his mind would not be satisfied thereby, nor would he avoid fire, until he placed his hand or some combustible substance in the fire, so that he might prove by experience that which reasoning taught. But when he has had actual experience of combustion his mind is made certain and rests in the full light of truth. Therefore reasoning does not suffice, but experience does.
Opus Majus [1266-1268], Part VI, chapter I, trans. R. B. Burke, The Opus Majus of Roger Bacon (1928), Vol. 2, 583.
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For, every time a certain portion is destroyed, be it of the brain or of the spinal cord, a function is compelled to cease suddenly, and before the time known beforehand when it would stop naturally, it is certain that this function depends upon the area destroyed. It is in this way that I have recognized that the prime motive power of respiration has its seat in that part of the medulla oblongata that gives rise to the nerves of the eighth pair [vagi]; and it is by this method that up to a certain point it will be possible to discover the use of certain parts of the brain.
Expériences sur le Principe de la Vie, Notamment sur celui des Mouvements du Coeur, et sur le Siege de ce Principe (1812), 148-149. Translated in Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts (1987), 247.
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Fortunately Nature herself seems to have prepared for us the means of supplying that want which arises from the impossibility of making certain experiments on living bodies. The different classes of animals exhibit almost all the possible combinations of organs: we find them united, two and two, three and three, and in all proportions; while at the same time it may be said that there is no organ of which some class or some genus is not deprived. A careful examination of the effects which result from these unions and privations is therefore sufficient to enable us to form probable conclusions respecting the nature and use of each organ, or form of organ. In the same manner we may proceed to ascertain the use of the different parts of the same organ, and to discover those which are essential, and separate them from those which are only accessory. It is sufficient to trace the organ through all the classes which possess it, and to examine what parts constantly exist, and what change is produced in the respective functions of the organ, by the absence of those parts which are wanting in certain classes.
Letter to Jean Claude Mertrud. In Lectures on Comparative Anatomy (1802), Vol. I, xxiii--xxiv.
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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.
From Cours d’Economie Politique (1896-97), as given in Archives Internationales d’Histoire des Sciences (1993), Issues 131-133, 67.
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From whence it is obvious to conclude that, since our Faculties are not fitted to penetrate into the internal Fabrick and real Essences of Bodies; but yet plainly discover to us the Being of a GOD, and the Knowledge of our selves, enough to lead us into a full and clear discovery of our Duty, and great Concernment, it will become us, as rational Creatures, to imploy those Faculties we have about what they are most adapted to, and follow the direction of Nature, where it seems to point us out the way.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 11, 646.
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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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Genetics has enticed a great many explorers during the past two decades. They have labored with fruit-flies and guinea-pigs, with sweet peas and corn, with thousands of animals and plants in fact, and they have made heredity no longer a mystery but an exact science to be ranked close behind physics and chemistry in definiteness of conception. One is inclined to believe, however, that the unique magnetic attraction of genetics lies in the vision of potential good which it holds for mankind rather than a circumscribed interest in the hereditary mechanisms of the lowly species used as laboratory material. If man had been found to be sharply demarcated from the rest of the occupants of the world, so that his heritage of physical form, of physiological function, and of mental attributes came about in a superior manner setting him apart as lord of creation, interest in the genetics of the humbler organisms—if one admits the truth—would have flagged severely. Biologists would have turned their attention largely to the ways of human heredity, in spite of the fact that the difficulties encountered would have rendered progress slow and uncertain. Since this was not the case, since the laws ruling the inheritance of the denizens of the garden and the inmates of the stable were found to be applicable to prince and potentate as well, one could shut himself up in his laboratory and labor to his heart's content, feeling certain that any truth which it fell to his lot to discover had a real human interest, after all.
Mankind at the Crossroads (1923), v-vi.
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God was always invented to explain mystery. God is always invented to explain those things that you do not understand. Now, when you finally discover how something works … you don't need him anymore. But … you leave him to create the universe because we haven't figured that out yet.
Interview, collected in Paul C. W. Davies and Julian R. Brown (eds.) Superstrings: A Theory of Everything? (1988), 208-209.
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GOOSE, n. A bird that supplies quills for writing. These, by some occult process of nature, are penetrated and suffused with various degrees of the bird's intellectual energies and emotional character, so that when inked and drawn mechanically across paper by a person called an "author," there results a very fair and accurate transcript of the fowl's thought and feeling. The difference in geese, as discovered by this ingenious method, is considerable: many are found to have only trivial and insignificant powers, but some are seen to be very great geese indeed.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  119-120.
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Gradually, at various points in our childhoods, we discover different forms of conviction. There’s the rock-hard certainty of personal experience (“I put my finger in the fire and it hurt,”), which is probably the earliest kind we learn. Then there’s the logically convincing, which we probably come to first through maths, in the context of Pythagoras’s theorem or something similar, and which, if we first encounter it at exactly the right moment, bursts on our minds like sunrise with the whole universe playing a great chord of C Major.
In short essay, 'Dawkins, Fairy Tales, and Evidence', 2.
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Had we lived, I should have had a tale to tell of the hardihood, endurance and courage of my companions which would have stirred the heart of every Englishman. These rough notes and our dead bodies must tell the tale, but surely, a great rich country like ours will see that those who are dependent on us are properly provided for.
[Final words in a 'Message to the Public' left written in his diary dated 25 March 1912, shortly before he died on the Ross Ice Barrier, Antarctica. When searchers found his body, on 12 Nov 1912, Scott was discovered sitting upright against the pole of the tent with the diary behind his head, as if for a pillow.]
Final words in a 'Message to the Public' left written in his diary dated 25 March 1912, shortly before he died on the Ross Ice Barrier, Antarctica. In Logan Marshall, The Story of Polar Conquest: The Complete History of Arctic and Antarctic (1913), 24-25. by Logan Marshall - Polar regions - 1913
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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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Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the problem. He did not delay, but in his joy leaped out of the bath. Rushing naked through the streets towards his home, he cried out in a loud voice that he had found what he sought. For, as he ran, he repeatedly shouted in Greek; “Eureka! Eurekal I’ve found it! I’ve found it!”
Vitrivius Pollio, De Architectura, ix, prologue, section 10.
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His genius now began to mount upwards apace & shine out with more strength, & as he told me himself, he excelled particularly in making verses... In everything he undertook he discovered an application equal to the pregnancy of his parts & exceeded the most sanguine expectations his master had conceived of him.
[About Newton's recollection of being a schoolboy at Grantham, written by Conduitt about 65 years after that time.]
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 65. Footnoted Keynes MS 130.2, p. 32-3, in the collection at King's College, Cambridge.
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How did I discover saccharin? Well, it was partly by accident and partly by study. I had worked a long time on the compound radicals and substitution products of coal tar... One evening I was so interested in my laboratory that I forgot about my supper till quite late, and then rushed off for a meal without stopping to wash my hands. I sat down, broke a piece of bread, and put it to my lips. It tasted unspeakably sweet. I did not ask why it was so, probably because I thought it was some cake or sweetmeat. I rinsed my mouth with water, and dried my moustache with my napkin, when, to my surprise the napkin tasted sweeter than the bread. Then I was puzzled. I again raised my goblet, and, as fortune would have it, applied my mouth where my fingers had touched it before. The water seemed syrup. It flashed on me that I was the cause of the singular universal sweetness, and I accordingly tasted the end of my thumb, and found it surpassed any confectionery I had ever eaten. I saw the whole thing at once. I had discovered some coal tar substance which out-sugared sugar. I dropped my dinner, and ran back to the laboratory. There, in my excitement, I tasted the contents of every beaker and evaporating dish on the table.
Interview with American Analyst. Reprinted in Pacific Record of Medicine and Surgery (1886), 1, No. 3, 78.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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How is it, one fine morning, Duchenne discovered a disease which probably existed in the time of Hippocrates.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1929), 15.
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How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?
In Dreams of a Final Theory (1992), 235.
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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 accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured for himself immortal fame among a few but stepped down among the great crowd (for this is how foolish people are to be numbered), only to be derided and dishonoured. I would dare publish my thoughts if there were many like you; but since there are not, I shall forbear.
Letter to Johannes Kepler, 4 Aug 1597. Quoted in G. de Santillana, Crime of Galileo (1955), 11.
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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 am told that the wall paintings which we had the happiness of admiring in all their beauty and freshness [in the chapel she discovered at Abu Simbel] are already much injured. Such is the fate of every Egyptian monument, great or small. The tourist carves it over with names and dates, and in some instances with caricatures. The student of Egyptology, by taking wet paper “squeezes” sponges away every vestige of the original colour. The “Collector” buys and carries off everything of value that he can, and the Arab steals it for him. The work of destruction, meanwhile goes on apace. The Museums of Berlin, of Turin, of Florence are rich in spoils which tell their lamentable tale. When science leads the way, is it wonderful that ignorance should follow?
Quoted in Margaret S. Drower, The Early Years, in T.G.H. James, (ed.), Excavating in Egypt: The Egypt Exploration Society, 1882-1982 (1982), 10. As cited in Wendy M.K. Shaw, Possessors and Possessed: Museums, Archaeology, and the Visualization of History in the Late Ottoman Empire (2003), 37. Also quoted in Margaret S. Drower, Flinders Petrie: A Life in Archaeology (1995), 57.
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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 believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations,” are simply the notes of our observations.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113.
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I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realised that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me.
The italicized phrase refers to “no new source” of energy. Concerning a Lecture by Rutherford, at the Royal Institution, dealing with the energy of subterranean radium, which had an effect prolonging the heat of the Earth. Arthur S. Eve wrote that Rutherford “used to tell humorous stories about this lecture long afterwards:” — followed by the subject quote above, as its own paragraph. As given in Arthur S. Eve, Rutherford: Being the Life and Letters of the Rt. Hon. Lord Rutherford, O.M. (1939), 107. The story lacks quotation marks, and thus should be regarded as perhaps Eve’s own words giving a faithful recollection, rather than Rutherford’s verbatim words. (However, note that the style used throughout the book is to omit quotation marks from their own separate paragraph.)
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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 conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Religion and Science (1935), 243.
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I discovered that Johns Hopkins [University] was a lot like Bell Labs, where the doors were always open and we were free to collaborate with researchers in other disciplines. I like the fact that I won’t be locked into one small niche here.
Quoted in Johns Hopkins University News Release (9 Jan 2003) after he retired from Bell Labs and joined the faculty in Fall 2002. On jh.edu web site.
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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 feel very strongly indeed that a Cambridge education for our scientists should include some contact with the humanistic side. The gift of expression is important to them as scientists; the best research is wasted when it is extremely difficult to discover what it is all about ... It is even more important when scientists are called upon to play their part in the world of affairs, as is happening to an increasing extent.
From essay in Thomas Rice Henn, The Apple and the Spectroscope: Being Lectures on Poetry Designed (in the Main) for Science Students (1951), 142.
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I found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems. … Very soon I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.
In Adventures of a Mathematician (1976), 147.
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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 had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.
[Concerning his calculations on the orbital motion of the Moon.]
Private note (29 Sep 1890). In George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.
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I had made up my mind to find that for which I was searching even if it required the remainder of my life. After innumerable failures I finally uncovered the principle for which I was searching, and I was astounded at its simplicity. I was still more astounded to discover the principle I had revealed not only beneficial in the construction of a mechanical hearing aid but it served as well as means of sending the sound of the voice over a wire. Another discovery which came out of my investigation was the fact that when a man gives his order to produce a definite result and stands by that order it seems to have the effect of giving him what might be termed a second sight which enables him to see right through ordinary problems. What this power is I cannot say; all I know is that it exists and it becomes available only when a man is in that state of mind in which he knows exactly what he wants and is fully determined not to quit until he finds it.
As quoted, without citation, in Mack R. Douglas, Making a Habit of Success: How to Make a Habit of Succeeding, How to Win With High Self-Esteem (1966, 1994), 38. Note: Webmaster is dubious of a quote which seems to appear in only one source, without a citation, decades after Bell’s death. If you know a primary source, please contact Webmaster.
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I had no books as a child. I had real machines, and I went out to work in the fields. I was driving farm machinery at five, and fixing it at age seven or eight. It’s no accident that I worked on Hubble 50 to 60 years later. My books were nature; it was very important to how I related to the Earth, and the Earth from space. No doubt when I go into space, I go back into the cool soil of Earth. I’m always thinking of it. Nature was my book. Other people come from that tradition - Emerson, Thoreau, and especially Whitman. Look at what they said in their philosophy - go out and have a direct relationship with nature.
When asked by Discover magazine what books helped inspire his passion as an astronaut.
'The 1998 Discover Science Gift Guide: Fantastic Voyages Children's Books That Mattered', Discover (Dec 1998).
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I had observed that there were different lines exhibited in the spectra of different metals when ignited in the voltaic arc; and if I had had any reasonable amount of wit I ought to have seen the converse, viz., that by ignition different bodies show in their spectral lines the materials of which they are formed. If that thought had occured to my mind, I should have discovered the spectroscope before Kirchoff; but it didn’t.
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493. Words as in original text, occured and Kirchoff are sic.
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I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich.
Letter to Christian Schönbein (13 Nov 1845), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 148.
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I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.
(1891) As quoted in translation in Leo Koenigsberger and Frances A. Welby (trans.), Hermann von Helmholtz (1906), 180-181.
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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 not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
Principia. In Isaac Newton, Andrew Motte and N. W. Chittenden, Newton’s Principia (1847), 506-507.
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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 here present the reader with a new sign which I have discovered for detecting diseases of the chest. This consists in percussion of the human thorax, whereby, according to the character of the particular sounds then elicited, an opinion is formed of the internal state of that cavity.
New Invention by Means of Percussing the Human Thorax for Detecting Signs of Obscure Disease of the Interior of the Chest, Inventum novum ex percussione (31 Dec 1761).
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I now saw very distinctly that these were little eels or worms... Lying huddled together and wriggling, just as if you saw with your naked eye a whole tubful of very little eels and water, the eels moving about in swarms; and the whole water seemed to be alive with the multitudinous animalcules. For me this was among all the marvels that I have discovered in nature the most marvellous of all, and I must say that, for my part, no more pleasant sight has yet met my eye than this of so many thousands of living creatures in one small drop of water, all huddling and moving, but each creature having its own motion.
Letter to H. Oldenburg, 9 Oct 1676. In The Collected Letters of Antoni van Leeuwenhoek (l957), Vol. 2, 115.
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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 said that there is something every man can do, if he can only find out what that something is. Henry Ford has proved this. He has installed in his vast organization a system for taking hold of a man who fails in one department, and giving him a chance in some other department. Where necessary every effort is made to discover just what job the man is capable of filling. The result has been that very few men have had to be discharged, for it has been found that there was some kind of work each man could do at least moderately well. This wonderful system adopted by my friend Ford has helped many a man to find himself. It has put many a fellow on his feet. It has taken round pegs out of square holes and found a round hole for them. I understand that last year only 120 workers out of his force of 50,000 were discharged.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 10.
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I see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
Letter to S. F. Lacroix, 1792. Quoted in S. F. Lacroix, Traité du calcul differentiel et du calcul integral (1797), Vol. 1, xxiv, trans. Ivor Grattan-Guinness.
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I specifically paused to show that, if there were such machines with the organs and shape of a monkey or of some other non-rational animal, we would have no way of discovering that they are not the same as these animals. But if there were machines that resembled our bodies and if they imitated our actions as much as is morally possible, we would always have two very certain means for recognizing that, none the less, they are not genuinely human. The first is that they would never be able to use speech, or other signs composed by themselves, as we do to express our thoughts to others. For one could easily conceive of a machine that is made in such a way that it utters words, and even that it would utter some words in response to physical actions that cause a change in its organs—for example, if someone touched it in a particular place, it would ask what one wishes to say to it, or if it were touched somewhere else, it would cry out that it was being hurt, and so on. But it could not arrange words in different ways to reply to the meaning of everything that is said in its presence, as even the most unintelligent human beings can do. The second means is that, even if they did many things as well as or, possibly, better than anyone of us, they would infallibly fail in others. Thus one would discover that they did not act on the basis of knowledge, but merely as a result of the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need a specific disposition for every particular action.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 5, 40.
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I think chemistry is being frittered away by the hairsplitting of the organic chemists; we have new compounds discovered, which scarcely differ from the known ones and when discovered are valueless—very illustrations perhaps of their refinements in analysis, but very little aiding the progress of true science.
Letter to William Grove (5 Jan 1845), The Letters of Faraday and Schoenbein, 1836-1862 (1899), Footnote, 209.
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I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]
'"Unified Theory" Is Getting Closer, Hawking Predicts', interview in San Jose Mercury News (23 Jan 2000), 29A. Answer quoted in Ashok Sengupta, Chaos, Nonlinearity, Complexity: The Dynamical Paradigm of Nature (2006), vii. Question included in Hans-Joachim Schellnhuber, Nicholas Stern and Mario Molina , Global Sustainability: a Nobel Cause (2010), 13. Cite from Brent Davis and Dennis J. Sumara, Complexity and Education: Inquiries Into Learning, Teaching, and Research (2006), 171.
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I think there will always be something interesting left to be discovered.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 739.
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I trust ... I have succeeded in convincing you that modern chemistry is not, as it has so long appeared, an ever-growing accumulation of isolated facts, as impossible for a single intellect to co-ordinate as for a single memory to grasp.
The intricate formulae that hang upon these walls, and the boundless variety of phenomena they illustrate, are beginning to be for us as a labyrinth once impassable, but to which we have at length discovered the clue. A sense of mastery and power succeeds in our minds to the sort of weary despair with which we at first contemplated their formidable array. For now, by the aid of a few general principles, we find ourselves able to unravel the complexities of these formulae, to marshal the compounds which they represent in orderly series; nay, even to multiply their numbers at our will, and in a great measure to forecast their nature ere we have called them into existence. It is the great movement of modern chemistry that we have thus, for an hour, seen passing before us. It is a movement as of light spreading itself over a waste of obscurity, as of law diffusing order throughout a wilderness of confusion, and there is surely in its contemplation something of the pleasure which attends the spectacle of a beautiful daybreak, something of the grandeur belonging to the conception of a world created out of chaos.
Concluding remark for paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
In 'Reflections on my Eightieth Birthday', Portraits from Memory (1956), 54.
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I was often humiliated to see men disputing for a piece of bread, just as animals might have done. My feelings on this subject have very much altered since I have been personally exposed to the tortures of hunger. I have discovered, in fact, that a man, whatever may have been his origin, his education, and his habits, is governed, under certain circumstances, much more by his stomach than by his intelligence and his heart.
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'The History of My Youth: An Autobiography of Francis Arago', Biographies of Distinguished Scientific Men (1859), Vol. 1, 55.
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I went to the woods because I wished to live deliberately, to front only the essential facts of life, and see if I could not learn what it had to teach, and not, when I came to die, discover that I had not lived.
Walden (1854), 143.
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I wish I had my beta-blockers handy.
[Comment when told that he had won a Nobel prize, referring to the drug he discovered for the treatment of heart disease.]
As quoted in Obituary, The Times (24 Mar 2010)
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I would liken science and poetry in their natural independence to those binary stars, often different in colour, which Herschel’s telescope discovered to revolve round each other. “There is one light of the sun,” says St. Paul, “and another of the moon, and another of the stars: star differeth from star in glory.” It is so here. That star or sun, for it is both, with its cold, clear, white light, is SCIENCE: that other, with its gorgeous and ever-shifting hues and magnificent blaze, is POETRY. They revolve lovingly round each other in orbits of their own, pouring forth and drinking in the rays which they exchange; and they both also move round and shine towards that centre from which they came, even the throne of Him who is the Source of all truth and the Cause of all beauty.
'The Alleged Antagonism between Poetry and Chemistry.' In Jesse Aitken Wilson, Memoirs of George Wilson. Quoted in Natural History Society of Montreal, 'Reviews and Notices of Books,' The Canadian Naturalist and Geologist (1861) Vol. 6, 393.
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I would rather discover one scientific fact than become King of Persia.
Dionysius cited by Eusebius, Preparation for the Gospel, 14.27-4. Democritus fr 118. Diels--Kranz.
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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 a given scientist had not made a given discovery, someone else would have done so a little later. Johann Mendel dies unknown after having discovered the laws of heredity: thirty-five years later, three men rediscover them. But the book that is not written will never be written. The premature death of a great scientist delays humanity; that of a great writer deprives it.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 89.
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If and when all the laws governing physical phenomena are finally discovered, and all the empirical constants occurring in these laws are finally expressed through the four independent basic constants, we will be able to say that physical science has reached its end, that no excitement is left in further explorations, and that all that remains to a physicist is either tedious work on minor details or the self-educational study and adoration of the magnificence of the completed system. At that stage physical science will enter from the epoch of Columbus and Magellan into the epoch of the National Geographic Magazine!
'Any Physics Tomorrow', Physics Today, January 1949, 2, 17.
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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 not animated with the desire to discover laws, they would escape the most enlightened attention.
Maurice Crosland, Gay-Lussac, Scientist and Bourgeois (1978), 54.
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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 the man of science chose to follow the example of historians and pulpit-orators, and to obscure strange and peculiar phenomena by employing a hollow pomp of big and sounding words, this would be his opportunity; for we have approached one of the greatest mysteries which surround the problem of animated nature and distinguish it above all other problems of science. To discover the relations of man and woman to the egg-cell would be almost equivalent of the egg-cell in the body of the mother, the transfer to it by means of the seed, of the physical and mental characteristics of the father, affect all the questions which the human mind has ever raised in regard to existence.
Quoted in Ernst Heinrich Philipp August Haeckel, The Evolution of Man (1897), vol 1, 148.
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If Watson and I had not discovered the [DNA] structure, instead of being revealed with a flourish it would have trickled out and that its impact would have been far less. For this sort of reason Stent had argued that a scientific discovery is more akin to a work of art than is generally admitted. Style, he argues, is as important as content. I am not completely convinced by this argument, at least in this case.
What Mad Pursuit (1990), 76.
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If we do discover a complete unified theory, it should be in time understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.
A Brief History of Time (1988), 191.
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If we look into ourselves we discover propensities which declare that our intellects have arisen from a lower form; could our minds be made visible we should find them tailed.
In The Martyrdom of Man (1876), 242.
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If we make a couple of discoveries here and there we need not believe things will go like this for ever. An acrobat can leap higher than a farm-hand, and one acrobat higher than another, yet the height no man can overleap is still very low. Just as we hit water when we dig in the earth, so we discover the incomprehensible sooner or later.
Aphorisms, trans. R. J. Hollingdale (1990), 92.
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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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If you plan it out, and it seems logical to you, then you can do it. I discovered the power of a plan.
Quoted in biography on website of the National Geographic Channel, Australia.
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Imagination is the Discovering Faculty, pre-eminently. … It is that which feels & discovers what is, the REAL which we see not, which exists not for our senses. … Mathematical science shows what is. It is the language of unseen relations between things. … Imagination too shows what is. … Hence she is or should be especially cultivated by the truly Scientific, those who wish to enter into the worlds around us!
Lovelace Papers, Bodleian Library, Oxford University, 175, folio 199, journal entry for 5 Jan 1841. As quoted and cited in Dorothy Stein (ed.), 'In Time I Will Do All, I Dare Say', Ada: A Life and a Legacy (1985), 128.
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In 1905, a physicist measuring the thermal conductivity of copper would have faced, unknowingly, a very small systematic error due to the heating of his equipment and sample by the absorption of cosmic rays, then unknown to physics. In early 1946, an opinion poller, studying Japanese opinion as to who won the war, would have faced a very small systematic error due to the neglect of the 17 Japanese holdouts, who were discovered later north of Saipan. These cases are entirely parallel. Social, biological and physical scientists all need to remember that they have the same problems, the main difference being the decimal place in which they appear.
In William G. Cochran, Frederick Mosteller and John W. Tukey, 'Principles of Sampling', Journal of the American Statistical Society, 1954, 49, 31. Collected in Selected Papers of Frederick Mosteller (2006), 290.
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In 1945 J.A. Ratcliffe … suggested that I [join his group at Cavendish Laboratory, Cambridge] to start an investigation of the radio emission from the Sun, which had recently been discovered accidentally with radar equipment. … [B]oth Ratcliffe and Sir Lawrence Bragg, then Cavendish Professor, gave enormous support and encouragement to me. Bragg’s own work on X-ray crystallography involved techniques very similar to those we were developing for “aperture synthesis,” and he always showed a delighted interest in the way our work progressed.
From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)
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In 2056, I think you’ll be able to buy T-shirts on which are printed equations describing the unified laws of our universe. All the laws we have discovered so far will be derivable from these equations.
Quoted in 'Brilliant Minds Forecast the Next 50 Years', New Scientist (18 Nov 2006).
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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 attempting to discover how much blood passes from the veins into the arteries I made dissections of living animals, opened up arteries in them, and carried out various other investigations. I also considered the symmetry and size of the ventricles of the heart and of the vessels which enter and leave them (since Nature, who does nothing purposelessly, would not purposelessly have given these vessels such relatively large size). I also recalled the elegant and carefully contrived valves and fibres and other structural artistry of the heart; and many other points. I considered rather often and with care all this evidence, and took correspondingly long trying to assess how much blood was transmitted and in how short a time. I also noted that the juice of the ingested food could not supply this amount without our having the veins, on the one hand, completely emptied and the arteries, on the other hand, brought to bursting through excessive inthrust of blood, unless the blood somehow flowed back again from the arteries into the veins and returned to the right ventricle of the heart. In consequence, I began privately to consider that it had a movement, as it were, in a circle.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth j. Franklin (1957), Chapter 8, 57-8.
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In design, people like Buckminster Fuller amazed me at the levels at which he could think. He could think molecularly. And he could think at the almost galactic scale. And the idea that somebody could actually talk about molecules and talk about buildings and structures and talk about space just amazed me. As I get older–I’ll be 60 next year–what I’ve discovered is that I find myself in those three realms too.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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In experimenting on the arc, my aim was not so much to add to the large number of isolated facts that had already been discovered, as to form some idea of the bearing of these upon one another, and thus to arrive at a clear conception of what takes place in each part of the arc and carbons at every moment. The attempt to correlate all the known phenomena, and to bind them together into one consistent whole, led to the deduction of new facts, which, when duly tested by experiment, became parts of the growing body, and, themselves, opened up fresh questions, to be answered in their turn by experiment.
In The Electric Arc (1902), Preface, iii. Ayrton described the growth of her published work on the electric arc, from a series of articles in The Electrician in 1895-6, to the full book, which “has attained to its present proportions almost with the growth of an organic body.”
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In going on with these Experiments, how many pretty systems do we build, which we soon find ourselves oblig’d to destroy! If there is no other Use discover’d of Electricity, this, however, is something considerable, that it may help to make a vain Man humble.
Letter to Peter Collinson, 14 Aug 1747. In I. Bernard Cohen (ed.), Benjamin Franklin’s Experiments (1941), 63.
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In my personal view, a failure to discover unimagined objects and answer unasked questions, once HST functions properly, would indicate a lack of imagination in stocking the Universe on the part of the Deity.
In Hubble Space Telescope flaw: hearing before the Committee on Science, Space, and Technology, U.S. House of Representatives, One Hundred First Congress, second session, July 13, 1990 (1990), 105.
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In order that an inventory of plants may be begun and a classification of them correctly established, we must try to discover criteria of some sort for distinguishing what are called “species”. After a long and considerable investigation, no surer criterion for determining species had occurred to me than distinguishing features that perpetuate themselves in propagation from seed. Thus, no matter what variations occur in the individuals or the species, if they spring from the seed of one and the same plant, they are accidental variations and not such as to distinguish a species. For these variations do not perpetuate themselves in subsequent seeding. Thus, for example, we do not regard caryophylli with full or multiple blossoms as a species distinct from caryophylli with single blossoms, because the former owe their origin to the seed of the latter and if the former are sown from their own seed, they once more produce single-blossom caryophylli. But variations that never have as their source seed from one and the same species may finally be regarded as distinct species. Or, if you make a comparison between any two plants, plants which never spring from each other's seed and never, when their seed is sown, are transmuted one into the other, these plants finally are distinct species. For it is just as in animals: a difference in sex is not enough to prove a difference of species, because each sex is derived from the same seed as far as species is concerned and not infrequently from the same parents; no matter how many and how striking may be the accidental differences between them; no other proof that bull and cow, man and woman belong to the same species is required than the fact that both very frequently spring from the same parents or the same mother. Likewise in the case of plants, there is no surer index of identity of species than that of origin from the seed of one and the same plant, whether it is a matter of individuals or species. For animals that differ in species preserve their distinct species permanently; one species never springs from the seed of another nor vice versa.
John Ray
Historia Plantarum (1686), Vol. 1, 40. Trans. Edmund Silk. Quoted in Barbara G. Beddall, 'Historical Notes on Avian Classification', Systematic Zoology (1957), 6, 133-4.
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In order to discover Truth in this manner by observation and reason, it is requisite we should fix on some principles whose certainty and effects are demonstrable to our senses, which may serve to explain the phenomena of natural bodies and account for the accidents that arise in them; such only are those which are purely material in the human body with mechanical and physical experiments … a physician may and ought to furnish himself with, and reason from, such things as are demonstrated to be true in anatomy, chemistry, and mechanics, with natural and experimental philosophy, provided he confines his reasoning within the bounds of truth and simple experiment.
As quoted in selection from the writings of Herman Boerhaave, collected in Oliver Joseph Thatcher (ed.), The Ideas that Have Influenced Civilization, in the Original Documents (1800), Vol. 6, 242.
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In order to survive, an animal must be born into a favoring or at least tolerant environment. Similarly, in order to achieve preservation and recognition, a specimen of fossil man must be discovered in intelligence, attested by scientific knowledge, and interpreted by evolutionary experience. These rigorous prerequisites have undoubtedly caused many still-births in human palaeontology and are partly responsible for the high infant mortality of discoveries of geologically ancient man.
Apes, Men and Morons (1938), 106.
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In reality, all Arguments from Experience are founded on the Similarity which we discover among natural Objects, and by which we are induc'd to expect effects similar to those which we have found to follow from such Objects. And tho' none but a Fool or Madman will ever pretend to dispute the Authority of Experience, or to reject that great Guide of human Life, it may surely be allow'd a Philosopher to have so much Curiosity at least as to examine the Principle of human Nature, which gives this mighty Authority to Experience, and makes us draw Advantage from that Similarity which Nature has plac'd among different Objects. From Causes which appear similar we expect similar Effects. This is the Sum of our experimental Conclusions.
An Enquiry Concerning Human Understanding (1748), 63.
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In recent years several new particles have been discovered which are currently assumed to be “elementary,” that is, essentially structureless. The probability that all such particles should be really elementary becomes less and less as their number increases. It is by no means certain that nucleons, mesons, electrons, neutrinos are all elementary particles.
Opening statement, Enrico Fermi and C.N. Yang, 'Are Mesons Elementary Particles?', Physical Review (1949), 76, 1739. As cited in James Gleick, Genius: The Life and Science of Richard Feynman (1992), 283.
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In science men have discovered an activity of the very highest value in which they are no longer, as in art, dependent for progress upon the appearance of continually greater genius, for in science the successors stand upon the shoulders of their predecessors; where one man of supreme genius has invented a method, a thousand lesser men can apply it. … In art nothing worth doing can be done without genius; in science even a very moderate capacity can contribute to a supreme achievement.
Essay, 'The Place Of Science In A Liberal Education.' In Mysticism and Logic: and Other Essays (1919), 41.
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In science, law is not a rule imposed from without, but an expression of an intrinsic process. The laws of the lawgiver are impotent beside the laws of human nature, as to his disillusion many a lawgiver has discovered.
Attributed. Peter McDonald, In The Oxford Dictionary of Medical Quotations (2004), 2.
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In science, probably ninety-nine percent of the knowable has to be discovered. We know only a few streaks about astronomy. We are only beginning to imagine the force and composition of the atom. Physics has not yet found any indivisible matter, or psychology a sensible soul.
'This World Depression of Ours is Chock-full of Good News', Hearst's International Combined with Cosmopolitan, (Oct 1932), 26. Reprinted in Ella Winter and Herbert Shapiro The World of Lincoln Steffens (1962), 216.
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In science, the more discovered, the more new paths open for exploration. It is usual in science, when things are vague and unclear, for the path to be like that of a drunkard, wandering in a zigzag. As we stagger back from what lastly dawns upon our befuddled wits is the wrong way, we cross over the true path and move nearly as far to the, equally wrong, opposite side. If all goes well, our deviations lessen and the path converges towards, but never completely follows, the true one. It gives a new insight to the old tag in vino veritas.
In The Ages of Gaia: A Biography of Our Living Earth (1999), 199.
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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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In the early seventies my mother [Mary Leakey] returned to Laetoli, a site in Tanzania that my parents had discovered in the thirties. In 1976, she discovered footprints of ancient hominids. These three-and-a-half-million- year-old footprints provide evidence of bipedality.
In Pamela Weintraub, The Omni Interviews (1984), 60.
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In the heavens we discover [stars] by their light, and by their light alone ... the sole evidence of the existence of these distant worlds ... that each of them is built up of molecules of the same kinds we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the royal cubit of the Temple of Karnac.
[Footnote: Where Maxwell uses the term “molecule” we now use the term “atom.”]
Lecture to the British Association at Bradford (1873), 'Atoms and Molecules'. Quoted by Ernest Rutherford, in 'The Constitution of Matter and the Evolution of the Elements', The Popular Science Monthly (Aug 1915), 112.
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In the history of scientific development the personal aspects of the process are usually omitted or played down to emphasize that the thing discovered is independent of the discoverer and that the result can be checked. But, as Einstein has pointed out, scientific concepts are 'created in the minds of men,' and in some way the nonprofessional aspects of life and mind are inevitably related to the professional.
American Institute of Physics, Center for History of Physics Newsletter (Fall 2004).
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In war, science has proven itself an evil genius; it has made war more terrible than it ever was before. Man used to be content to slaughter his fellowmen on a single plane—the earth’s surface. Science has taught him to go down into the water and shoot up from below and to go up into the clouds and shoot down from above, thus making the battlefield three times as bloody as it was before; but science does not teach brotherly love. Science has made war so hellish that civilization was about to commit suicide; and now we are told that newly discovered instruments of destruction will make the cruelties of the late war seem trivial in comparison with the cruelties of wars that may come in the future.
Proposed summation written for the Scopes Monkey Trial (1925), in Genevieve Forbes Herrick and John Origen Herrick, The Life of William Jennings Bryan (1925), 405. This speech was prepared for delivery at the trial, but was never heard there, as both sides mutually agreed to forego arguments to the jury.
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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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Investigating the conditions under which mutations occur … requires studies of mutation frequency under various methods of handling the organisms. As yet, extremely little has been done along this line. That is because, in the past, a mutation was considered a windfall, and the expression “mutation frequency” would have seemed a contradiction in terms. To attempt to study it would have seemed as absurd as to study the conditions affecting the distribution of dollar bills on the sidewalk. You were simply fortunate if you found one. … Of late, however, we may say that certain very exceptional banking houses have been found, in front of which the dollars fall more frequently—in other words, specially mutable genes have been discovered, that are beginning to yield abundant data at the hands of Nilsson-Ehle, Zeleny, Emerson, Anderson and others.
In 'Variation Due to Change in the Individual Gene', The American Naturalist (Jan-Feb 1922), 56, No. 642, 44.
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IODINE
It was Courtois discover'd Iodine
(In the commencement of this century),
Which, with its sisters, bromine and chlorine,
Enjoys a common parentage - the sea;
Although sometimes 'tis found, with other things,
In minerals and many saline springs.

But yet the quantity is so minute
In the great ocean, that a chemist might,
With sensibilities the most acute,
Have never brought this element to light,
Had he not thought it were as well to try
Where ocean's treasures concentrated lie.

And Courtois found that several plants marine,
Sponges, et cetera, exercise the art
Of drawing from the sea its iodine
In quantities sufficient to impart
Its properties; and he devised a plan
Of bringing it before us - clever man!
Anonymous
Discursive Chemical Notes in Rhyme (1876) by the Author of the Chemical Review, a B.
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Is it not evident, in these last hundred years (when the Study of Philosophy has been the business of all the Virtuosi in Christendome) that almost a new Nature has been revealed to us? that more errours of the School have been detected, more useful Experiments in Philosophy have been made, more Noble Secrets in Opticks, Medicine, Anatomy, Astronomy, discover'd, than in all those credulous and doting Ages from Aristotle to us? So true it is that nothing spreads more fast than Science, when rightly and generally cultivated.
Of Dramatic Poesie (1684 edition), lines 258-67, in James T. Boulton (ed.) (1964), 44
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Is it not true that electricity, and all the prodigies it has hitherto discovered, have only served to excite curiosity?
Letter to Jean le Rond D'Alembert (7 Jan 1768). Collected in Correspondence: Letters Between Frederick II and M. D’Alembert (1789), 79, as translated by Thomas Holcroft.
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Is no one inspired by our present picture of the universe? This value of science remains unsung by singers: you are reduced to hearing not a song or poem, but an evening lecture about it. This is not yet a scientific age.
Perhaps one of the reasons for this silence is that you have to know how to read music. For instance, the scientific article may say, “The radioactive phosphorus content of the cerebrum of the rat decreases to one-half in a period of two weeks.” Now what does that mean?
It means that phosphorus that is in the brain of a rat—and also in mine, and yours—is not the same phosphorus as it was two weeks ago. It means the atoms that are in the brain are being replaced: the ones that were there before have gone away.
So what is this mind of ours: what are these atoms with consciousness? Last week’s potatoes! They now can remember what was going on in my mind a year ago—a mind which has long ago been replaced. To note that the thing I call my individuality is only a pattern or dance, that is what it means when one discovers how long it takes for the atoms of the brain to be replaced by other atoms. The atoms come into my brain, dance a dance, and then go out—there are always new atoms, but always doing the same dance, remembering what the dance was yesterday.
'What do You Care What Other People Think?' Further Adventures of a Curious Character (1988), 244.
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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 behooves us always to remember that in physics it has taken great men to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows of a cup.
In On Growth and Form (1917).
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It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active.
From Novum Organum (1620), Book 1, Aphorism 24. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 51.
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It has been shown to be possible, by deliberately planned and chemotherapeutic approach, to discover curative agents which act specifically and aetiologically against diseases due to protozoal infections, and especially against the spirilloses, and amongst these against syphilis in the first place. Further evidence for the specificity of the action of dihydroxydiaminoarsenobenzene [Salvarsan ‘606’] is the disappearance of the Wasserman reaction, which reaction must … be regarded as indicative of a reaction of the organism to the constituents of the spirochaetes.
P. Ehrlich and S. Hata, 'Closing Notes to the Experimental Chemotherapy of Spirilloses', 1910. Reprinted in F. Himmelweit (ed.), The Collected Papers of Paul Ehrlich (1957), Vol. 3, 302.
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It is a curious and painful fact that almost all the completely futile treatments that have been believed in during the long history of medical folly have been such as caused acute suffering to the patient. When anesthetics were discovered, pious people considered them an attempt to evade the will of God. It was pointed out, however, that when God extracted Adam's rib He put him into a deep sleep. This proved that anesthetics are all right for men; women, however, ought to suffer, because of the curse of Eve.
In An Outline of Intellectual Rubbish (1943), 13.
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It is a happy world after all. The air, the earth, the water teem with delighted existence. In a spring noon, or a summer evening, on whichever side I turn my eyes, myriads of happy beings crowd upon my view. “The insect youth are on the wing.” Swarms of new-born flies are trying their pinions in the air. Their sportive motions, their wanton mazes, their gratuitous activity testify their joy and the exultation they feel in their lately discovered faculties … The whole winged insect tribe, it is probable, are equally intent upon their proper employments, and under every variety of constitution, gratified, and perhaps equally gratified, by the offices which the author of their nature has assigned to them.
Natural Theology: or, Evidences of the Existence and Attributes of The Deity, Collected from the Appearances of Nature (1802), 490-1.
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It is a peculiar feature in the fortune of principles of such high elementary generality and simplicity as characterise the laws of motion, that when they are once firmly established, or supposed to be so, men turn with weariness and impatience from all questionings of the grounds and nature of their authority. We often feel disposed to believe that truths so clear and comprehensive are necessary conditions, rather than empirical attributes of their subjects: that they are legible by their own axiomatic light, like the first truths of geometry, rather than discovered by the blind gropings of experience.
In An Introduction to Dynamics (1832), x.
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It is a vulgar belief that our astronomical knowledge dates only from the recent century when it was rescued from the monks who imprisoned Galileo; but Hipparchus…who among other achievements discovered the precession of the eqinoxes, ranks with the Newtons and the Keplers; and Copernicus, the modern father of our celestial science, avows himself, in his famous work, as only the champion of Pythagoras, whose system he enforces and illustrates. Even the most modish schemes of the day on the origin of things, which captivate as much by their novelty as their truth, may find their precursors in ancient sages, and after a careful analysis of the blended elements of imagination and induction which charaterise the new theories, they will be found mainly to rest on the atom of Epicurus and the monad of Thales. Scientific, like spiritual truth, has ever from the beginning been descending from heaven to man.
Lothair (1879), preface, xvii.
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It is by logic that we prove, but by intuition that we discover.
In Science and Method (1908) translated by Francis Maitland (1914, 2007), 129.
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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 curious to observe with what different degrees of architectonic skill Providence has endowed birds of the same genus, and so nearly correspondent in their general mode of life! for while the swallow and the house-martin discover the greatest address in raising and securely fixing crusts or shells of loam as cunabula for their young, the bank-martin terebrates a round and regular hole in the sand or earth, which is serpentine, horizontal, and about two feet deep. At the inner end of this burrow does this bird deposit, in a good degree of safety, her rude nest, consisting of fine grasses and feathers, usually goose-feathers, very inartificially laid together.
In Letter to Daines Barrington, (26 Feb 1774), in The Natural History and Antiquities of Selborne (1789), 176.
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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 no way derogatory to Newton, or Kepler, or Galileo, that Science in these days should have advanced far beyond them. Rather is this itself their crown of glory. Their works are still bearing fruit, and will continue to do so. The truths which they discovered are still living in our knowledge, pregnant with infinite consequences.
Co-author with his brother Augustus William Hare Guesses At Truth, By Two Brothers: Second Edition: With Large Additions (1848), Second Series, 251. (The volume is introduced as “more than three fourths new.” This quote is identified as by Julius; Augustus had died in 1833.)
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It is not enough to discover and prove a useful truth previously unknown, but that it is necessary also to be able to propagate it and get it recognized.
Philosophie Zoologique (1809), Vol. 2, 450, trans. Hugh Elliot (1914), 404
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It is not hard to learn more. What is hard is to unlearn when you discover yourself wrong
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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 not, indeed, strange that the Greeks and Romans should not have carried ... any ... experimental science, so far as it has been carried in our time; for the experimental sciences are generally in a state of progression. They were better understood in the seventeenth century than in the sixteenth, and in the eighteenth century than in the seventeenth. But this constant improvement, this natural growth of knowledge, will not altogether account for the immense superiority of the modern writers. The difference is a difference not in degree, but of kind. It is not merely that new principles have been discovered, but that new faculties seem to be exerted. It is not that at one time the human intellect should have made but small progress, and at another time have advanced far; but that at one time it should have been stationary, and at another time constantly proceeding. In taste and imagination, in the graces of style, in the arts of persuasion, in the magnificence of public works, the ancients were at least our equals. They reasoned as justly as ourselves on subjects which required pure demonstration.
History (May 1828). In Samuel Austin Allibone, Prose Quotations from Socrates to Macaulay (1880), 36.
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It is only by historical analysis that we can discover what makes up man, since it is only in the course of history that he is formed.
'The Dualism of Human Nature and its Social Conditions' (1914), trans. Charles Blend, in Kurt H. Wolff (ed.), Emile Durkheim, 1858-1917 (1960), 325.
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It is only when science asks why, instead of simply describing how, that it becomes more than technology. When it asks why, it discovers Relativity. When it only shows how, it invents the atom bomb, and then puts its hands over its eye and says, 'My God what have I done?
The Stalin in Soul (1973). Quoted in Gary Westfahl, Science Fiction Quotations (2005), 322.
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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 seems to me farther, that these Particles have not only a Vis inertiae, accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles, such as that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies. These Principles I consider, not as occult Qualities, supposed to result from the specifick Forms of Things, but as general Laws of Nature, by which the Things themselves are form'd; their Truth appearing to us by Phaenomena, though their Causes be not yet discover'd. For these are manifest Qualities, and their Causes only are occult.
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 376-377.
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It takes two of us to discover truth: one to utter it and one to understand it.
In Kahlil Gibran - The Collected Works (2007), 176.
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It was a standing joke of [Dr. Chapman] to quote old Leuwenhoeck as having discovered 'twenty thousand devils playing upon the point of a needle' thus foreshadowing some of the most remarkable discoveries of the present day, especially disease germs.
Opening address to American Medical Association, Cleveland, Ohio, 5 Jun 1883. In The Chicago Medical Journal and Examiner (1883), 47 4.
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It was my Uncle George who discovered that alcohol was a food well in advance of modern medical thought.
'The Delayed Exit of Claude and Eustace', The Inimitable Jeeves (2011), 193.
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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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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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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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July 11, 1656. Came home by Greenwich ferry, where I saw Sir J. Winter’s project of charring sea-coal to burn out the sulphur and render it sweet [coke]. He did it by burning the coals in such earthen pots as the glassmen melt their metal, so firing them without consuming them, using a bar of iron in each crucible, or pot, which bar has a hook at one end, that so the coals being melted in a furnace with other crude sea-coals under them, may be drawn out of the pots sticking to the iron, whence they are beaten off in great half-exhausted cinders, which being rekindled make a clear pleasant chamber-fire deprived of their sulphur and arsenic malignity. What success it may have, time will discover.
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Just as Americans have discovered the hidden energy costs in a multitude of products—in refrigerating a steak, for example, on its way to the butcher—they are about to discover the hidden water costs. Beginning with the water that irrigated the corn that was fed to the steer, the steak may have accounted for 3,500 gallons. The water that goes into a 1,000-pound steer would float a destroyer. It takes 14,935 gallons of water to grow a bushel of wheat, 60,000 gallons to produce a ton of steel, 120 gallons to put a single egg on the breakfast table.
From 'The Browning of America: Drought, Waste and Pollution Threaten a Water Shortage', Newsweek (23 Feb 1981), 26-30. In long excerpt in William Shurtleff and Akiko Aoyagi, History of Soymilk and Other Non-Dairy Milks (1226-2013) (2013), 1126-1127.
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Just as Darwin discovered the law of evolution in organic nature, so Marx discovered the law of evolution in human history; he discovered the simple fact, hitherto concealed by an overgrowth of idealogy [sic], that mankind must first of all eat and drink, have shelter and clothing, before it can pursue politics, science, religion, art etc.
Engels' Speech over the Grave of Karl Marx, delivered at Highgate Cemetery, London, 17 Mar 1883. Quoted in Karl Marx 1818-1883, for the Anniversary of his Death (1942), 27.
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Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future ... If someone can hit on the right lines along which to make this development, it m may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply the ... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.
'The Evolution of the Physicist's Picture of Nature', Scientific American, May 1963, 208, 47. In Steve Adams, Frontiers (2000), 57.
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Keep discovering…
…...
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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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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Laws of Serendi[ity:
(1) In order to discover anything, you must be looking for something.
(2) If you wish to make an improved product, you must already be engaged in making an inferior one.
In Dr. N Sreedharan, Quotations of Wit and Wisdom (2007), 18.
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Learn the leading precognita of all things—no need to turn over leaf by leaf, but grasp the trunk hard and you will shake all the branches.
Advice cherished by Samuel Johnson that that, if one is to master any subject, one must first discover its general principles.
Advice from Rev. Cornelius Ford, a distant cousin, quoted in John P. Hardy, Samuel Johnson: A Critical Study (1979), 29.
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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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Let us suppose that an ichthyologist is exploring the life of the ocean. He casts a net into the water and brings up a fishy assortment. Surveying his catch, he proceeds in the usual manner of a scientist to systematise what it reveals. He arrives at two generalisations:
(1) No sea-creature is less than two inches long.
(2) All sea-creatures have gills.
These are both true of his catch, and he assumes tentatively that they will remain true however often he repeats it.
In applying this analogy, the catch stands for the body of knowledge which constitutes physical science, and the net for the sensory and intellectual equipment which we use in obtaining it. The casting of the net corresponds to observation; for knowledge which has not been or could not be obtained by observation is not admitted into physical science.
An onlooker may object that the first generalisation is wrong. “There are plenty of sea-creatures under two inches long, only your net is not adapted to catch them.” The icthyologist dismisses this objection contemptuously. “Anything uncatchable by my net is ipso facto outside the scope of icthyological knowledge. In short, what my net can't catch isn't fish.” Or—to translate the analogy—“If you are not simply guessing, you are claiming a knowledge of the physical universe discovered in some other way than by the methods of physical science, and admittedly unverifiable by such methods. You are a metaphysician. Bah!”
In 'Selective Subjectivism', The Philosophy of Physical Science (1938, 2012), 16.
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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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Look at those animals and remember the greatest scientists in the world have never discovered how to make grass into milk.
As quoted in Dorothy Caruso, Enrico Caruso: His Life and Death (1963), 41.
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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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Man is a little germ that lives on an unimportant rock ball that revolves about a small star at the outskirts of an ordinary galaxy. ... I am absolutely amazed to discover myself on this rock ball rotating around a spherical fire. It’s a very odd situation. And the more I look at things I cannot get rid of the feeling that existence is quite weird.
From lecture, 'Images of God,' available as a podcast, and part of The Tao of Philosophy six-CD collection of lectures by Watts.
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Man may be excused for feeling some pride at having risen, though not through his own exertions, to the very summit of the organic scale; and the fact of his having thus risen, instead of having been aboriginally placed there, may give him hopes for a still higher destiny in the distant future. But we are not here concerned with hopes or fears, only with the truth as far as our reason allows us to discover it. I have given the evidence to the best of my ability; and we must acknowledge, as it seems to me, that man with all his noble qualities, with sympathy which feels for the most debased, with benevolence which extends not only to other men but to the humblest living creature, with his god-like intellect which has penetrated into the movements and constitution of the solar system—with all these exalted powers—Man still bears in his bodily frame the indelible stamp of his lowly origin.
Concluding remarks. The Descent of Man (1871), Vol. 2, 405.
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Many people know everything they know in the way we know the solution of a riddle after we have read it or been told it, and that is the worst kind of knowledge and the kind least to be cultivated; we ought rather to cultivate that kind of knowledge which enables us to discover for ourselves in case of need that which others have to read or be told of in order to know it.
Aphorism 89 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 58.
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Many psychologists ... thought by turning their attention to their own consciousness to be able to explain what happened when we were thnking. Or they sought to attain the same end by asking another person a question, by means of which certain processes of thought would be excited, and then by questioning the person about the introspection he had made. It is obvious ... that nothing can be discovered in such experiments.
An Introduction to Psychology (1912)
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Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell’s equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein’s field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that “there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.”
In 'Introduction', The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (2009), 12.
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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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Mathematics … belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by observation. In its pure and simple form the syllogism cannot be directly compared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law.
From Memoir (1870) read before the National Academy of Sciences, Washington, printed in 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97-98.
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Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show that its Method is the same: that, like other sciences, having observed or discovered properties, which it classifies, generalises, co-ordinates and subordinates, it proceeds to extend discoveries by means of Hypothesis, Induction, Experiment and Deduction.
In Problems of Life and Mind: The Method of Science and its Application (1874), 423-424. [The reals are the relations of magnitude.]
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May there not be methods of using explosive energy incomparably more intense than anything heretofore discovered? Might not a bomb no bigger than an orange be found to possess a secret power to destroy a whole block of buildings—nay, to concentrate the force of a thousand tons of cordite and blast a township at a stroke? Could not explosives even of the existing type be guided automatically in flying machines by wireless or other rays, without a human pilot, in ceaseless procession upon a hostile city, arsenal, camp or dockyard?
'Shall We All Commit Suicide?' Pall Mall (Sep 1924). Reprinted in Thoughts and Adventures (1932), 250.
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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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Medicine in its present state is, it seems to me, by now completely discovered, insofar as it teaches in each instance the particular details and the correct measures. For anyone who has an understanding of medicine in this way depends very little upon good luck, but is able to do good with or without luck. For the whole of medicine has been established, and the excellent principles discovered in it clearly have very little need of good luck.
Places in Man, in Hippocrates, trans. P. Potter (1995), Vol. 8, 93.
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Men cannot help feeling a little ashamed of their cousin-german the Ape. His close yet grotesque and clumsy semblance of the human form is accompanied by no gleams of higher instinct. Our humble friend the dog, our patient fellow-labourer the horse, are nearer to us in this respect. The magnanimous and sagacious elephant, doomed though he be to all fours, is godlike compared with this spitefully ferocious creature. Strangely enough, too, the most repulsive and ferocious of all apekind, the recently discovered Gorilla is, the comparative anatomist assures us, nearest to us all: the most closely allied in structure to the human form.
In 'Our Nearest Relation', All Year Round (28 May 1859), 1, No. 5, 112. Charles Dickens was both the editor and publisher of this magazine. The author of the article remains unknown. The articles were by custom printed without crediting the author. Biographers have been able to use extant office records to identify various authors of other articles, but not this specific one. Dickens and Richard Owen were friends; they read each other’s work. Owen is known to have found at least a little time to write a few articles for Dickens’ magazines. Owen had given a talk at the Royal Institution (4 Feb 1859) titled 'On the Gorilla.' This would suggest why Dickens may have had a definite interest in publishing on this subject, regardless of who in fact wrote the article.
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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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Natural Magick therefore is that, which considering well the strength and force of Natural and Celestial beings, and with great curiosity labouring to discover their affections, produces into open Act the hidden and concealed powers of Nature.
In The Vanity of the Arts and Sciences (1530), translation (1676), 111.
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Neither the natives of Munsa [chief of the Mangbetu] nor the people of Kifan who came to me knew anything of the existence of a great lake, even though I undertook a positively detective investigation in order to discover any possible political intrigues. All of the statements of different people were noted and then compared; they agree as to names etc., which put my mind at rest.
On the necessity of compiling map data by comparisons between interviews with locals. In August Petermann, Petermann’s Geographische Mittheilungen (1871), 13. As quoted and cited in Kathrin Fritsch, '"You Have Everything Confused And Mixed Up…!" Georg Schweinfurth, Knowledge And Cartography Of Africa In The 19th Century', History in Africa (2009), 36, 93.
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New sources of power … will surely be discovered. Nuclear energy is incomparably greater than the molecular energy we use today. The coal a man can get in a day can easily do five hundred times as much work as himself. Nuclear energy is at least one million times more powerful still. If the hydrogen atoms in a pound of water could be prevailed upon to combine and form helium, they would suffice to drive a thousand-horsepower engine for a whole year. If the electrons, those tiny planets of the atomic systems, were induced to combine with the nuclei in hydrogen, the horsepower would be 120 times greater still. There is no question among scientists that this gigantic source of energy exists. What is lacking is the match to set the bonfire alight, or it may be the detonator to cause the dynamite to explode. The scientists are looking for this.
[In his last major speech to the House of Commons on 1 Mar 1955, Churchill quoted from his original printed article, nearly 25 years earlier.]
'Fifty Years Hence'. Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57:3, 395.
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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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NEWTONIAN, adj. Pertaining to a philosophy of the universe, invented by Newton, who discovered that an apple will fall to the ground, but was unable to say why. His successors and disciples have advanced so far as to be able to say when.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  228.
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No anatomist ever discovered a system of organization, calculated to produce pain and disease; or, in explaining the parts of the human body, ever said, this is to irritate; this is to inflame; this duct is to convey the gravel to the kidneys; this gland to secrete the humour which forms the gout: if by chance he come at a part of which he knows not the use, the most he can say is, that it is useless; no one ever suspects that it is put there to incommode, to annoy, or torment.
The Principles of Moral and Political Philosophy (1785), Vol. 1, 79.
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No man of science wants merely to know. He acquires knowledge to appease his passion for discovery. He does not discover in order to know, he knows in order to discover.
In 'Technical Education and Its Relation to Science and Literature', The Aims of Education: & Other Essays (1917), 74.
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No medieval schoolman has been singled out as a precursor more often than the French scholastic Nicole Oresme.This brilliant scholar has been credited with … the framing of Gresham’s law before Gresham, the invention of analytic geometry before Descartes, with propounding structural theories of compounds before nineteenth century organic chemists, with discovering the law of free fall before Galileo, and with advocating the rotation of the Earth before Copernicus. None of these claims is, in fact, true, although each is based on discussion by Oresme of some penetration and originality …
In Nicole Oresme and the Medieval Geometry of Quantities and Motions (1968).
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No one can take from us the joy of the first becoming aware of something, the so-called discovery. But if we also demand the honor, it can be utterly spoiled for us, for we are usually not the first. What does discovery mean, and who can say that he has discovered this or that? After all it’s pure idiocy to brag about priority; for it’s simply unconscious conceit, not to admit frankly that one is a plagiarist.
Epigraph to Lancelot Law Whyte, The Unconscious before Freud (1960).
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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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Now when you cut a forest, an ancient forest in particular, you are not just removing a lot of big trees and a few birds fluttering around in the canopy. You are drastically imperiling a vast array of species within a few square miles of you. The number of these species may go to tens of thousands. … Many of them are still unknown to science, and science has not yet discovered the key role undoubtedly played in the maintenance of that ecosystem, as in the case of fungi, microorganisms, and many of the insects.
From On Human Nature (2000). As quoted in John H. Morgan, Naturally Good: A Behavioral History of Moral Development (2005), 251-252.
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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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Nurse, it was I who discovered that leeches have red blood.
(1832). Attributed - on his deathbed when the nurse came to apply leeches. In Barnaby Conrad, Famous Last Words (1961), 78.
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O. Hahn and F. Strassmann have discovered a new type of nuclear reaction, the splitting into two smaller nuclei of the nuclei of uranium and thorium under neutron bombardment. Thus they demonstrated the production of nuclei of barium, lanthanum, strontium, yttrium, and, more recently, of xenon and caesium. It can be shown by simple considerations that this type of nuclear reaction may be described in an essentially classical way like the fission of a liquid drop, and that the fission products must fly apart with kinetic energies of the order of hundred million electron-volts each.
'Products of the Fission of the Urarium Nucleus', Nature (1939), 143, 471.
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Oersted would never have made his great discovery of the action of galvanic currents on magnets had he stopped in his researches to consider in what manner they could possibly be turned to practical account; and so we would not now be able to boast of the wonders done by the electric telegraphs. Indeed, no great law in Natural Philosophy has ever been discovered for its practical implications, but the instances are innumerable of investigations apparently quite useless in this narrow sense of the word which have led to the most valuable results.
From Silvanus Phillips Thompson, 'Introductory Lecture to the Course on Natural Philosophy', The Life of Lord Kelvin (1910), Vol. 1, Appendix to Chap. 5, 249.
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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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Oh! But I have better news for you, Madam, if you have any patriotism as citizen of this world and wish its longevity. Mr. Herschel has found out that our globe is a comely middle-aged personage, and has not so many wrinkles as seven stars, who are evidently our seniors. Nay, he has discovered that the Milky Way is not only a mob of stars, but that there is another dairy of them still farther off, whence, I conclude, comets are nothing but pails returning from milking, instead of balloons filled with inflammable air.
Letter to the Countess of Upper Ossory (4 Jul 1785) in W. S. Lewis (ed.), Horace Walpole's Correspondence with the Countess of Upper Ossory (1965), Vol. 33, 474.
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On coming down the stairs at dinner Tris [Trismegistus = Frankland] who walked before me seemed impressed by a mechanical impulse which impelled him along the corridor with a fervid velocity. On reaching the stair bottom I discovered the cause of the attraction. Miss Edmondson, like a pure planet, had checked his gravitating tendencies and lo! He stood radiant with smiles dropping joysparkes from his eyes as he clasped her hand. His countenance became a transparency through which the full proportions of his soul shone manifest; his blood tingled from his eyebrows to his finger ends, and wealthy with rich emotions his face became the avenue of what he felt.
Journals of John Tyndall, 18 Jan 1848. Royal Institution Archives.
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On one occasion, when he was giving a dinner to some friends at the university, he left the table to get them a bottle of wine; but, on his way to the cellar, he fell into reflection, forgot his errand and his company, went to his chamber, put on his surplice, and proceeded to the chapel. Sometimes he would go into the street half dressed, and on discovering his condition, run back in great haste, much abashed. Often, while strolling in his garden, he would suddenly stop, and then run rapidly to his room, and begin to write, standing, on the first piece of paper that presented itself. Intending to dine in the public hall, he would go out in a brown study, take the wrong turn, walk a while, and then return to his room, having totally forgotten the dinner. Once having dismounted from his horse to lead him up a hill, the horse slipped his head out of the bridle; but Newton, oblivious, never discovered it till, on reaching a tollgate at the top of the hill, he turned to remount and perceived that the bridle which he held in his hand had no horse attached to it. His secretary records that his forgetfulness of his dinner was an excellent thing for his old housekeeper, who “sometimes found both dinner and supper scarcely tasted of, which the old woman has very pleasantly and mumpingly gone away with”. On getting out of bed in the morning, he has been discovered to sit on his bedside for hours without dressing himself, utterly absorbed in thought.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 257.
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On the contrary, God was always invented to explain mystery. God is always invented to explain those things that you do not understand. Now when you finally discover how something works, you get some laws which you're taking away from God; you don't need him anymore. But you need him for the other mysteries. So therefore you leave him to create the universe because we haven't figured that out yet; you need him for understanding those things which you don't believe the laws will explain, such as consciousness, or why you only live to a certain length of time—life and death—stuff like that. God is always associated with those things that you do not understand. Therefore, I don't think that the laws can be considered to be like God because they have been figured out.
Quoted in P. C. W. Davies and Julian Brown (eds.), Superstrings: A Theory of Everything? (1988), 208-9.
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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 important object of this original spectroscopic investigation of the light of the stars and other celestial bodies, namely to discover whether the same chemical elements as those of our earth are present throughout the universe, was most satisfactorily settled in the affirmative. (1909)
In Publications of Sir William Huggins's Observatory (1909), Vol. 2, 49, footnote added to emphasize the significance of the results shown in this collection’s reprint of William Huggins and Dr. Miller, 'On the Spectra of Some of the Fixed Stars', Philosophical Transactions (1864), 64, 413-435.
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One must credit an hypothesis with all that has had to be discovered in order to demolish it.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 89.
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One of the chiefest triumphs of modern mathematics consists in having discovered what mathematics really is.
International Monthly (1901), 4, 84. In Robert Édoward Moritz, Memorabilia Mathematica (1914), 109.
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One of the most immediate consequences of the electrochemical theory is the necessity of regarding all chemical compounds as binary substances. It is necessary to discover in each of them the positive and negative constituents... No view was ever more fitted to retard the progress of organic chemistry. Where the theory of substitution and the theory of types assume similar molecules, in which some of the elements can be replaced by others without the edifice becoming modified either in form or outward behaviour, the electrochemical theory divides these same molecules, simply and solely, it may be said, in order to find in them two opposite groups, which it then supposes to be combined with each other in virtue of their mutual electrical activity... I have tried to show that in organic chemistry there exist types which are capable, without destruction, of undergoing the most singular transformations according to the nature of the elements.
Traité de Chemie Appliquée aux Arts, Vol. I (1828), 53. Trans. J. R. Partington, A History of Chemistry, Vol. 4, 366.
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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 experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to understanding nature… In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed in Discovery (Jul 1933), 14, 227. Also quoted in Stefano Zambelli and Donald A. R. George, Nonlinearity, Complexity and Randomness in Economics (2012).
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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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Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Preface to the first edition, 382.
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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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Philosophy is not a science of things in general, but a science that investigates the presuppositions of experience and discovers the nature of the first principle.
Epigram to 'Philosophy in Outline', The Journal of Speculative Philosophy (Jul 1883), 17, No. 3, 296.
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Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover.
In The World within the World by John D. Barrow (1988).
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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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Placed in a universe of constant change, on an isolated globe surrounded by distant celestial objects on all sides, subjected to influences of various kinds, it is a sublime occupation to measure the earth and weigh the planets, to predict their changes, and even to discover the materials of which they are composed; to investigate the causes of the tempest and volcano; to bring the lightning from the clouds; to submit it to experiment by which it shall reveal its character; and to estimate the size and weight of those invisible atoms which constitute the universe of things.
In Letter (3 Feb 1873) to the Committee of Arrangements, in Proceedings of the Farewell Banquet to Professor Tyndall (4 Feb 1873), 19. Reprinted as 'On the Importance of the Cultivation of Science', The Popular Science Monthly (1873), Vol. 2, 645.
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Poetry, mythology, and religion represent the world as man would like to have it, while science represents the world as he gradually comes to discover it.
In The Modern Temper: a Study and a Confession (1929), 6.
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Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
In letter (1 May 1935), Letters to the Editor, 'The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician', New York Times (4 May 1935), 12.
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Pure mathematics was discovered by Boole in a work which he called “The Laws of Thought” (1854).… His book was in fact concerned with formal logic, and this is the same thing as mathematics.
In 'Recent Work on the Principles of Mathematics', The International Monthly (Jul-Dec 1901), 4, 83. Relevant context appears in a footnote in William Bragg Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics (1996), Vol. 1, 442, which gives: “Russell’s essay was written for a popular audience, and (as he notes) for an editor who asked him to make the essay ‘as romantic as possible’. Russell’s considered appraisal of Boole was more sober. For instance, in Our Knowledge of the External World, Lecture II, he says of Boole: ‘But in him and his successors, before Peano and Frege, the only thing really achieved, apart from certain details, was the invention of a mathematical symbolism for deducing consequences from the premises which the newer methods shared with Aristotle.’”
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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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Rejoice when other scientists do not believe what you know to be true. It will give you extra time to work on it in peace. When they start claiming that they have discovered it before you, look for a new project.
'Resolution and Reconstitution of Biological Pathways from 1919 to 1984', Federation Proceedings (1983), 12, 2902.
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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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Research is industrial prospecting. The oil prospectors use every scientific means to find new paying wells. Oil is found by each one of a number of methods. My own group of men are prospecting in a different field, using every possible scientific means. We believe there are still things left to be discovered. We have only stumbled upon a few barrels of physical laws from the great pool of knowledge. Some day we are going to hit a gusher.
'Industrial Prospecting', an address to the Founder Societies of Engineers (20 May 1935). In National Research Council, Reprint and Circular Series of the National Research Council (1933), No. 107, 1.
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Researchers keep identifying new species, but they have no idea about the life cycle of a given species or its other hosts. They cut open an animal and find a new species. Where did it come from? What effect does it have on its host? What is its next host? They don't know and they don't have time to find out, because there are too many other species waiting to be discovered and described.
Talk at Columbia University, 'The Power of Parasites.'
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Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”
In History of Mathematics (1893), 67.
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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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 is Christian, not when it condemns itself to the letter of things, but when, in the infinitely little, it discovers as many mysteries and as much depth and power as in the infinitely great.
In Fourth Lecture, 'The Roman Church and Science: Galileo', (7 May 1844). Collected in Edgar Quinet and C. Cocks (trans.), Ultramontanism: Or, The Roman Church and Modern Society (1845), 73.
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Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality... And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover—discover. Like Bacon, we might describe our own contemporary science—'the method of reasoning which men now ordinarily apply to nature'—as consisting of 'anticipations, rash and premature' and as 'prejudices'.
The Logic of Scientific Discovery (1959), 278.
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Science is the organised attempt of mankind to discover how things work as causal systems. The scientific attitude of mind is an interest in such questions. It can be contrasted with other attitudes, which have different interests; for instance the magical, which attempts to make things work not as material systems but as immaterial forces which can be controlled by spells; or the religious, which is interested in the world as revealing the nature of God.
In The Scientific Attitude (1941), Foreword, 9.
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Science is wonderful: for years uranium cost only a few dollars a ton until scientists discovered you could kill people with it.
Anonymous
In Evan Esar, 20,000 Quips and Quotes, 703.
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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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Scientific method, although in its more refined forms it may seem complicated, is in essence remarkably simply. It consists in observing such facts as will enable the observer to discover general laws governing facts of the kind in question. The two stages, first of observation, and second of inference to a law, are both essential, and each is susceptible of almost indefinite refinement. (1931)
In The Scientific Outlook (1931, 2009), 3.
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Scientific practice is above all a story-telling practice. ... Biology is inherently historical, and its form of discourse is inherently narrative. ... Biology as a way of knowing the world is kin to Romantic literature, with its discourse about organic form and function. Biology is the fiction appropriate to objects called organisms; biology fashions the facts “discovered” about organic beings.
Primate Visions: Gender, Race and Nature in the World of Modern Science(1989), 4-5.
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Scientific truth is universal, because it is only discovered by the human brain and not made by it, as art is.
In On Aggression (2002), 279.
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Scientists are going to discover many subtle genetic factors in the makeup of human beings. Those discoveries will challenge the basic concepts of equality on which our society is based. Once we can say that there are differences between people that are easily demonstrable at the genetic level, then society will have to come to grips with understanding diversity—and we are not prepared for that.
(1983).
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Scientists don’t really ever grow up. I read, as a 10-or-so-year-old, a book for kids by Einstein. I think it was The Meaning of Relativity. It was exciting! Science was compared to a detective story, replete with clues, and the solution was the search for a coherent account of all the known events. Then I remember some very entrapping biographies: Crucibles, by Bernard Jaffe, was the story of chemistry told through the lives of great chemists; Microbe Hunters, by Paul de Kruif, did the same for biologists. Also, the novel Arrowsmith, by Sinclair Lewis, about a medical researcher. These books were a crucial component of getting hooked into science.
When asked by Discover magazine what books helped inspire his passion as a scientist.
In 'The 1998 Discover Science Gift Guide: Fantastic Voyages Children's Books That Mattered', Discover (Dec 1998).
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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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She [Rosalind Franklin] discovered in a series of beautifully executed researches the fundamental distinction between carbons that turned on heating into graphite and those that did not. Further she related this difference to the chemical constitution of the molecules from which carbon was made. She was already a recognized authority in industrial physico-chemistry when she chose to abandon this work in favour of the far more difficult and more exciting fields of biophysics.
Comment in The Times, 19 Apr 1958, shortly after Franklin's death. In Jenifer Glynn, 'Rosalind Franklin', in E. Shils and C. Blacker (eds.), Cambridge Women: Twelve Portraits (1996), 206.
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Shortly after electrons were discovered it was thought that atoms were like little solar systems, made up of a … nucleus and electrons, which went around in “orbits,” much like the planets … around the sun. If you think that’s the way atoms are, then you’re back in 1910.
In QED: The Strange Theory of Light and Matter (1985, 2006), 84.
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Should the research worker of the future discover some means of releasing this [atomic] energy in a form which could be employed, the human race will have at its command powers beyond the dream of scientific fiction, but the remotest possibility must always be considered that the energy once liberated will be completely uncontrollable and by its intense violence detonate all neighbouring substances. In this event, the whole of the hydrogen on earth might be transformed at once and the success of the experiment published at large to the universe as a new star.
'Mass Spectra and Isotopes', Nobel Lecture, 12 December 1922. In Nobel Lectures, Chemistry, 1922-1941 (1966), 20.
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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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Since my logic aims to teach and instruct the understanding, not that it may with the slender tendrils of the mind snatch at and lay hold of abstract notions (as the common logic does), but that it may in very truth dissect nature, and discover the virtues and actions of bodies, with their laws as determined in matter; so that this science flows not merely from the nature of the mind, but also from the nature of things.
In Novum Organum (1620), Book 2, Aphorism 42.
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Sir Humphrey Davy
Abominated gravy.
He lived in the odium
Of having discovered sodium.
.
Said to have been written as a schoolboy during a chemistry class at St. Paul’s School. Fromn Edmund Clerihew Bentley, 'Sir Humphrey [sic] Davy', Biography for Beginners (1905). An example of a clerihew, an irregular form of biographical humorous verse, devised by the author. Collected in Complete Clerihews (2008), 38. Schoolboy comment as quoted in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 26. Note the correct spelling for Davy’s name is Humphry.
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So far no chemist has ever discovered exchange-value either in a pearl or a diamond.
Karl Marx
Capital: A Critique of Political Economy (1867), trans. Ben Fowkes (1976), Vol. 1, 177.
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Some day when you have time, look into the business of prayer, amulets, baths, and poultices, and discover much valuable therapy the profession has cast on the dump
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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Some months ago we discovered that certain light elements emit positrons under the action of alpha particles. Our latest experiments have shown a very striking fact: when an aluminium foil is irradiated on a polonium preparation [alpha ray emitter], the emission of positrons does not cease immediately when the active preparation is removed: the foil remains radioactive and the emission of radiation decays exponentially as for an ordinary radio-element. We observed the same phenomenon with boron and magnesium.
[Co-author with Irène Joliot-Curie. This one-page paper reported their discovery of artificial radioactivity for which they were awarded the 1935 Nobel Prize for Chemistry.]
Letter to the Editor, 'Artificial Production of a New Kind of Radio-Element'(10 Jan 1934) published in Nature (1934), 133, 201-2. Cited in Mauro Dardo, Nobel Laureates and Twentieth-Century Physics (2004), 187.
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Some of my cousins who had the great advantage of University education used to tease me with arguments to prove that nothing has any existence except what we think of it. … These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless. ... I always rested on the following argument. … We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is this great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason that a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making “a cross bearing.” When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, “no.” They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about the calculations and use our ears for that purpose, I reply that the mathematical process has a reality and virtue in itself, and that onie discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot— in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
In My Early Life (1930).
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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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Suppose [an] imaginary physicist, the student of Niels Bohr, is shown an experiment in which a virus particle enters a bacterial cell and 20 minutes later the bacterial cell is lysed and 100 virus particles are liberated. He will say: “How come, one particle has become 100 particles of the same kind in 20 minutes? That is very interesting. Let us find out how it happens! How does the particle get in to the bacterium? How does it multiply? Does it multiply like a bacterium, growing and dividing, or does it multiply by an entirely different mechanism ? Does it have to be inside the bacterium to do this multiplying, or can we squash the bacterium and have the multiplication go on as before? Is this multiplying a trick of organic chemistry which the organic chemists have not yet discovered ? Let us find out. This is so simple a phenomenon that the answers cannot be hard to find. In a few months we will know. All we have to do is to study how conditions will influence the multiplication. We will do a few experiments at different temperatures, in different media, with different viruses, and we will know. Perhaps we may have to break into the bacteria at intermediate stages between infection and lysis. Anyhow, the experiments only take a few hours each, so the whole problem can not take long to solve.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
From 'Experiments with Bacterial Viruses (Bacteriophages)', Harvey Lecture (1946), 41, 161-162. As cited in Robert Olby, The Path of the Double Helix: The Discovery of DNA (1974, 1994), 237.
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Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same time, with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions. And the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment.
A Reply to the Animadversions of the Edinburgh Reviewers on Some Papers Published in the Philosophical Transactions (1804), 17-8.
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Sure Prometheus discovered fire, but what has he done since?
Anonymous
In A Dictionary of Scientific Quotations by Alan L. Mackay (1991).
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Take the living human brain endowed with mind and thought. …. The physicist brings his tools and commences systematic exploration. All that he discovers is a collection of atoms and electrons and fields of force arranged in space and time, apparently similar to those found in inorganic objects. He may trace other physical characteristics, energy, temperature, entropy. None of these is identical with thought. … How can this collection of ordinary atoms be a thinking machine? … The Victorian physicist felt that he knew just what he was talking about when he used such terms as matter and atoms. … But now we realize that science has nothing to say as to the intrinsic nature of the atom. The physical atom is, like everything else in physics, a schedule of pointer readings.
From a Gifford Lecture, University of Edinburgh (1927), published in 'Pointer Readings: Limits of Physical Knowledge', The Nature of the Physical World (1929), 258-259.
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Taking advantage of the method, found by me, of the black staining of the elements of the brain, staining obtained by the prolonged immersion of the pieces, previously hardened with potassium or ammonium bichromate, in a 0.50 or 1.0% solution of silver nitrate, I happened to discover some facts concerning the structure of the cerebral gray matter that I believe merit immediate communication.
'On the Structure of the Gray Matter of the Brain', Gazetta Medica Italiana, 2 Aug 1873. Trans. Maurizio Santini (ed.), Golgi Centennial Symposium: Perspectives in Neurobiology (1975), 647.
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Talent deals with the actual, with discovered and realized truths, any analyzing, arranging, combining, applying positive knowledge, and, in action, looking to precedents. Genius deals with the possible, creates new combinations, discovers new laws, and acts from an insight into new principles.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203.
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That there is no such thing as the scientific method, one might easily discover by asking several scientists to define it. One would find, I am sure, that no two of them would exactly agree. Indeed, no two scientists work and think in just the same ways.
In Science in the Making (1957), 8-9.
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The Qualities then that are in Bodies rightly considered, are of Three sorts.
First, the Bulk, Figure, Number, Situation, and Motion, or Rest of their solid Parts; those are in them, whether we perceive them or no; and when they are of that size, that we can discover them, we have by these an Idea of the thing, as it is in it self, as is plain in artificial things. These I call primary Qualities.
Secondly, The Power that is in any Body, by Reason of its insensible primary Qualities, to operate after a peculiar manner on any of our Senses, and thereby produce in us the different Ideas of several Colours, Sounds, Smells, Tastes, etc. These are usually called sensible Qualities.
Thirdly, The Power that is in any Body, by Reason of the particular Constitution of its primary Qualities, to make such a change in the Bulk, Figure, Texture, and Motion of another Body, as to make it operate on our Senses, differently from what it did before. Thus the Sun has a Power to make Wax white, and Fire to make Lead fluid. These are usually called Powers.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 8, Section 23, 140-1.
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The 4th sort of creatures... which moved through the 3 former sorts, were incredibly small, and so small in my eye that I judged, that if 100 of them lay [stretched out] one by another, they would not equal the length of a grain of course Sand; and according to this estimate, ten hundred thousand of them could not equal the dimensions of a grain of such course Sand. There was discover’d by me a fifth sort, which had near the thickness of the former, but they were almost twice as long.
The first time bacteria were observed.
Letter to H. Oldenburg, 9 Oct 1676. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 95.
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The aim of science is to discover and illuminate truth. And that, I take it, is the aim of literature, whether biography or history or fiction. It seems to me, then, that there can be no separate literature of science.
Address upon receiving National Book Award at reception, Hotel Commodore, New York (27 Jan 1952). As cited in Linda Lear, Rachel Carson: Witness for Nature (1997), 219.
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The alchemists in their search for gold discovered other things [of greater value].
With the phrase “of greater value” in James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 415. The more specific description '—gunpowder, china, medicines, the laws of nature' is given for 'of greater value' in Counsels and Maxims: Being the Second Part of Arthur Schopenhauer's Aphorismen Zur Lebensweisheit translated by Thomas Bailey Saunders (2nd Ed., 1890), 16.
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The alternative to the Big Bang is not, in my opinion, the steady state; it is instead the more general theory of continuous creation. Continuous creation can occur in bursts and episodes. These mini-bangs can produce all the wonderful element-building that Fred Hoyle discovered and contributed to cosmology. This kind of element and galaxy formation can take place within an unbounded, non-expanding universe. It will also satisfy precisely the Friedmann solutions of general relativity. It can account very well for all the facts the Big Bang explains—and also for those devastating, contradictory observations which the Big Bang must, at all costs, pretend are not there
In 'Letters: Wrangling Over the Bang', Science News (27 Jul 1991), 140, No. 4, 51. Also quoted in Roy C. Martin, Astronomy on Trial: A Devastating and Complete Repudiation of the Big Bang Fiasco (1999), Appendix I, 217.
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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 best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 350.
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The body of science is not, as it is sometimes thought, a huge coherent mass of facts, neatly arranged in sequence, each one attached to the next by a logical string. In truth, whenever we discover a new fact it involves the elimination of old ones. We are always, as it turns out, fundamentally in error.
In 'On Science and Certainty', Discover Magazine (Oct 1980)
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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 cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plants and of numerical constants; and since in them nothing occurs without supreme reason—not, to be sure, such as discursive reasoning discovers, but such as existed from the first in the Creators's design and is preserved from that origin to this day in the wonderful nature of animal faculties, I do not believe that even in a snowflake this ordered pattern exists at random.
Di Nive Sexangula, On the Six-Cornered Snowflake (1611), K18, 1. 6-12. Trans. and ed. Colin Hardie (1966), 33.
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The century after the Civil War was to be an Age of Revolution—of countless, little-noticed revolutions, which occurred not in the halls of legislatures or on battlefields or on the barricades but in homes and farms and factories and schools and stores, across the landscape and in the air—so little noticed because they came so swiftly, because they touched Americans everywhere and every day. Not merely the continent but human experience itself, the very meaning of community, of time and space, of present and future, was being revised again and again, a new democratic world was being invented and was being discovered by Americans wherever they lived.
In The Americans: The Democratic Experience (1973, 1974), ix.
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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 day will come when, after harnessing space, the winds, the tides, and gravitation, we shall harness for God the energies of love. And on that day, for the second time in the history of the world, we shall have discovered fire.
From 'The Evolution of Chastity' (Feb 1934), as translated by René Hague in Toward the Future (1975), 86-87.
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The development of an organism … may be considered as the execution of a 'developmental program' present in the fertilized egg. … A central task of developmental biology is to discover the underlying algorithm from the course of development.
Aristid Lindenmayer and Grzegorz Rozenberg, Automata, Languages, Development (1976), v.
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The development of statistics are causing history to be rewritten. Till recently the historian studied nations in the aggregate, and gave us only the story of princes, dynasties, sieges, and battles. Of the people themselves—the great social body with life, growth, sources, elements, and laws of its own—he told us nothing. Now statistical inquiry leads him into the hovels, homes, workshops, mines, fields, prisons, hospitals, and all places where human nature displays its weakness and strength. In these explorations he discovers the seeds of national growth and decay, and thus becomes the prophet of his generation.
Speech (16 Dec 1867) given while a member of the U.S. House of Representatives, introducing resolution for the appointment of a committee to examine the necessities for legislation upon the subject of the ninth census to be taken the following year. Quoted in John Clark Ridpath, The Life and Work of James A. Garfield (1881), 217.
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The effect of a concept-driven revolution is to explain old things in new ways. The effect of a tool-driven revolution is to discover new things that have to be explained.
In Imagined Worlds (1997), 50-51.
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The errors of a wise man are literally more instructive than the truths of a fool. The wise man travels in lofty, far-seeing regions; the fool in low-lying, high-fenced lanes; retracing the footsteps of the former, to discover where he diviated, whole provinces of the universe are laid open to us; in the path of the latter, granting even that he has not deviated at all, little is laid open to us but two wheel-ruts and two hedges.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 425:26.
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The facts obtained in this study may possibly be sufficient proof of the causal relationship, that only the most sceptical can raise the objection that the discovered microorganism is not the cause but only an accompaniment of the disease... It is necessary to obtain a perfect proof to satisfy oneself that the parasite and the disease are ... actually causally related, and that the parasite is the... direct cause of the disease. This can only be done by completely separating the parasite from the diseased organism [and] introducing the isolated parasite into healthy organisms and induce the disease anew with all its characteristic symptoms and properties.
Berliner Klinische Wochenschrift (1882), 393. Quoted in Edward J. Huth and T. Jock Murray (eds.), Medicine in Quotations: Views of Health and Disease Through the Ages (2000), 52.
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The famous set of pictures taken from the moon, [celebrate] the birth of a global consciousness that will help build a peaceful future for humankind. That future is in the hands of those who dedicate their lives to explore Teilhard de Chardin’s three infinities: the infinitely big, the infinitely small, and the infinitely complex. And from all the beauty they discover while crossing perpetually receding frontiers, they develop for nature and for humankind an infinite love.
From concluding paragraph written for 'Foreword' to Kevin W. Kelley (ed.), The Home Planet (1988), paragraph 8 (unpaginated).
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The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.
How to Solve it: A New Aspect of Mathematical Method (1957), 206.
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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 gentleman [Mr. Taber] from New York says [agricultural research] is all foolish. Yes; it was foolish when Burbank was experimenting with wild cactus. It was foolish when the Wright boys went down to Kitty Hawk and had a contraption there that they were going to fly like birds. It was foolish when Robert Fulton tried to put a boiler into a sail boat and steam it up the Hudson. It was foolish when one of my ancestors thought the world was round and discovered this country so that the gentleman from New York could become a Congressman. (Laughter.) ... Do not seek to stop progress; do not seek to put the hand of politics on these scientific men who are doing a great work. As the gentleman from Texas points out, it is not the discharge of these particular employees that is at stake, it is all the work of investigation, of research, of experimentation that has been going on for years that will be stopped and lost.
Speaking (28 Dec 1932) as a member of the 72nd Congress, early in the Great Depression, in opposition to an attempt to eliminate a small amount from the agricultural appropriation bill. As quoted in 'Mayor-Elect La Guardia on Research', Science (1933), New Series, 78, No. 2031, 511.
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The glory of science is not that it discovers “truth”; rather it advances inexorably by discovering and correcting error.
In Francis Bello, Lawrence Lessing and George A.W. Boehm, Great American Scientists (1960, 1961), 116.
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The great revelation of the quantum theory was that features of discreteness were discovered in the Book of Nature, in a context in which anything other than continuity seemed to be absurd according to the views held until then.
What is Life? (1944), 48.
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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 hypothesis that man is not free is essential to the application of scientific method to the study of human behavior. The free inner man who is held responsible for the behavior of the external biological organism is only a prescientific substitute for the kinds of causes which are discovered in the course of a scientific analysis.
In Science and Human Behavior (1953), 447.
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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 important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.
This is a paraphrase from Bragg’s actual quote, beginning: “The fun in science lies not in discovering facts…” (q.v.) included with citation elsewhere on this web page. The paraphrased quote is as given in Alan Lindsay Mackay, A Dictionary of Scientific Quotations (1991), 38. It is cited by Mackay as collected from Arthur Koestler and J.R. Smithies, Beyond Reductionism (1958), 115. It is mentioned therein without quotation marks. Webmaster finds the source is actually: Arthur Koestler and John Raymond Smythies (eds.), Beyond Reductionism: New Perspectives in the Life Sciences: Proceedings of the Alpbach Symposium (1968) (1969, 1971), 115. (This corrects date from 1958 to 1968, and the spelling of Smythies name.)
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The indescribable pleasure—which pales the rest of life's joys—is abundant compensation for the investigator who endures the painful and persevering analytical work that precedes the appearance of the new truth, like the pain of childbirth. It is true to say that nothing for the scientific scholar is comparable to the things that he has discovered. Indeed, it would be difficult to find an investigator willing to exchange the paternity of a scientific conquest for all the gold on earth. And if there are some who look to science as a way of acquiring gold instead of applause from the learned, and the personal satisfaction associated with the very act of discovery, they have chosen the wrong profession.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 50.
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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 landed classes neglected technical education, taking refuge in classical studies; as late as 1930, for example, long after Ernest Rutherford at Cambridge had discovered the atomic nucleus and begun transmuting elements, the physics laboratory at Oxford had not been wired for electricity. Intellectuals neglect technical education to this day.
Describing C.P. Snow’s observations on the neglect of technical education in Visions of Technology (1999), 23.
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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 man who discovers a new scientific truth has previously had to smash to atoms almost everything he had learnt, and arrives at the new truth with hands blood stained from the slaughter of a thousand platitudes.
The Revolt of the Masses: Authorised Translation From the Spanish (1950), 116
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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 momentous laws of induction between currents and between currents and magnets were discovered by Michael Faraday in 1831-32. Faraday was asked: “What is the use of this discovery?” He answered: “What is the use of a child—it grows to be a man.” Faraday’s child has grown to be a man and is now the basis of all the modern applications of electricity.
In An Introduction to Mathematics (1911), 34-35.
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The more I learned about the use of pesticides, the more appalled I became. I realized that here was the material for a book. What I discovered was that everything which meant most to me as a naturalist was being threatened, and that nothing I could do would be more important.
Explaining her motivation for writing the book Silent Spring (1962), quoted in Always, Rachel: The Letters of Rachel Carson and Dorothy Freeman, 1952-1964 (1995), xxvii.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.
In Light Waves and Their Uses (1903), 23-4.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”
In Light Waves and Their Uses (1903), 23-4. Michelson had some years earlier referenced “an eminent physicist” that he did not name who had “remarked that the future truths of physical science are to be looked for in the sixth place of decimals,” near the end of his Convocation Address at the Dedication of the Ryerson Physical Laboratory at the University of Chicago, 'Some of the Objects and Methods of Physical Science' (4 Jul 1894), published in University of Chicago Quarterly Calendar (Aug 1894), 3, No.2, 15. Also
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The name chronic alcoholism applies to the collective symptoms of a disordered condition of the mental, motor, and sensory functions of the nervous system, these symptoms assuming a chronic form, and without their being immediately connected with any of those (organic) modifications of the central or peripheric portions of the nervous system which may be detected during life, or discovered after death by ocular inspection; such symptoms, moreover, affecting individuals who have persisted for a considerable length of time in the abuse of alcoholic liquors.
Published in Swedish in 1849. Translation quoted in William Marcet On Chronic Alcoholic Intoxication (1868), 21.
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The natural scientists of the previous age knew less than we do and believed they were very close to the goal: we have taken very great steps in its direction and now discover we are still very far away from it. With the most rational philosophers an increase in their knowledge is always attended by an increased conviction of their ignorance.
Aphorisms, trans. R. J. Hollingdale (1990), 89.
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The next care to be taken, in respect of the Senses, is a supplying of their infirmities with Instruments, and, as it were, the adding of artificial Organs to the natural; this in one of them has been of late years accomplisht with prodigious benefit to all sorts of useful knowledge, by the invention of Optical Glasses. By the means of Telescopes, there is nothing so far distant but may be represented to our view; and by the help of Microscopes, there is nothing so small, as to escape our inquiry; hence there is a new visible World discovered to the understanding. By this means the Heavens are open'd, and a vast number of new Stars, and new Motions, and new Productions appear in them, to which all the ancient Astronomers were utterly Strangers. By this the Earth it self, which lyes so neer us, under our feet, shews quite a new thing to us, and in every little particle of its matter, we now behold almost as great a variety of creatures as we were able before to reckon up on the whole Universe it self.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), preface, sig. A2V.
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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 originator of a new concept … finds, as a rule, that it is much more difficult to find out why other people do not understand him than it was to discover the new truths.
From address on Michael Faraday. As given in Michael Pupin, From Immigrant to Inventor (1923), 225.
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The other experiment (which I shall hardly, I confess, make again, because it was cruel) was with a dog, which, by means of a pair of bellows, wherewith I filled his lungs, and suffered them to empty again, I was able to preserve alive as long as I could desire, after I had wholly opened the thorax, and cut off all the ribs, and opened the belly. Nay, I kept him alive above an hour after I had cut off the pericardium and the mediastinum, and had handled and turned his lungs and heart and all the other parts of its body, as I pleased. My design was to make some enquiries into the nature of respiration. But though I made some considerable discovery of the necessity of fresh air, and the motion of the lungs for the continuance of the animal life, yet I could not make the least discovery in this of what I longed for, which was, to see, if I could by any means discover a passage of the air of the lungs into either the vessels or the heart; and I shall hardly be induced to make any further trials of this kind, because of the torture of this creature: but certainly the enquiry would be very noble, if we could any way find a way so to stupify the creature, as that it might not be sensible.
Letter from Robert Hooke to Robert Boyle (10 Nov 1664). In M. Hunter, A. Clericuzio and L. M. Principe (eds.), The Correspondence of Robert Boyle (2001), Vol. 2, 399.
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The philosophy of mathematics still consists essentially in discerning the rational order of dependence of as many abstract truths as the sagacity of inventive minds has successfully and laboriously discovered, often by very roundabout means.
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), Vol. 2, 235, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 475. From the original French: “La philosophie des mathématiques consiste encore essentiellement à discerner l'ordre et la dépendance rationnelle de tant de vérités abstraites que la sagacité des inventeurs a successivement et laborieusement découvertes, souvent par des voies si détournées.”
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The point [is] largely scientific in character …[concerning] the methods which can be invented or adopted or discovered to enable the Earth to control the Air, to enable defence from the ground to exercise control—indeed dominance—upon aeroplanes high above its surface. … science is always able to provide something. We were told that it was impossible to grapple with submarines, but methods were found … Many things were adopted in war which we were told were technically impossible, but patience, perseverance, and above all the spur of necessity under war conditions, made men’s brains act with greater vigour, and science responded to the demands.
[Remarks made in the House of Commons on 7 June 1935. His speculation was later proved correct with the subsequent development of radar during World War II, which was vital in the air defence of Britain.]
Quoting himself in The Second World War: The Gathering Storm (1948, 1986), Vol. 1, 134.
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The principal goal of education is to create men who are capable of doing new things, not simply of repeating what other generations have done—men who are creative, inventive, and discovers. The second goal of education is to form minds which can be critical, can verify, and not accept everything they are offered.
From remarks at a conference on cognitive development, Cornell University (1964). In Philip Hampson Taylor, New Directions in Curriculum Studies (1979), 90.
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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 depends less than is usually believed on the efforts and performance of the individual genius ... many important discoveries have been made by men of ordinary talents, simply because chance had made them, at the proper time and in the proper place and circumstances, recipients of a body of doctrines, facts and techniques that rendered almost inevitable the recognition of an important phenomenon. It is surprising that some historian has not taken malicious pleasure in writing an anthology of 'one discovery' scientists. Many exciting facts have been discovered as a result of loose thinking and unimaginative experimentation, and described in wrappings of empty words. One great discovery does not betoken a great scientist; science now and then selects insignificant standard bearers to display its banners.
Louis Pasteur, Free Lance of Science (1986), 368
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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 scientist discovers a new type of material or energy and the engineer discovers a new use for it.
The Development of Design (1981), 19.
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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 subject matter of the scientist is a crowd of natural events at all times; he presupposes that this crowd is not real but apparent, and seeks to discover the true place of events in the system of nature. The subject matter of the poet is a crowd of historical occasions of feeling recollected from the past; he presupposes that this crowd is real but should not be, and seeks to transform it into a community. Both science and art are primarily spiritual activities, whatever practical applications may be derived from their results. Disorder, lack of meaning, are spiritual not physical discomforts, order and sense spiritual not physical satisfactions.
The Dyer’s Hand and Other Essays (1965), 66.
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The suppression of uncomfortable ideas may be common in religion or in politics, but it is not the path to knowledge; it has no in the endeavor of science. We do not know in advance who will discover fundamental insights.
In Cosmos (1985), 74.
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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 technology [semiconductors] which has transformed practical existence is largely an application of what was discovered by these allegedly irresponsible [natural] philosophers.
Address on the Tercentenary of the Royal Society (1960). In Michael Dudley Sturge, Statistical and Thermal Physics (2003), 251.
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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 use of every organ has been discovered by starting from the assumption that it must have been some use.
In History of the Inductive Sciences (1857), Vol. 3, 385.
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The visible universe is subject to quantification, and is so by necessity. … Between you and me only reason will be the judge … since you proceed according to the rational method, so shall I. … I will also give reason and take it. … This generation has an innate vice. It can’t accept anything that has been discovered by a contemporary!
As quoted in James Burke, The Day the Universe Changed (1985), 41. Burke also quotes the first sentence in The Axemaker's Gift (1995), 112, but after the first ellipsis, is substituted “If you wish to hear more from me, give and take reason, because I am not the kind of man to satisfy his hunger on the picture of a steak!”
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The way a child discovers the world constantly replicates the way science began. You start to notice what’s around you, and you get very curious about how things work. How things interrelate. It’s as simple as seeing a bug that intrigues you. You want to know where it goes at night; who its friends are; what it eats.
In David Chronenberg and Chris Rodley (ed.), Chronenberg on Chronenberg (1992), 5.
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The whole aim of comparative anatomy is to discover what structures are homologous.
A Laboratory Manual for Comparative Vertebrate Anatomy (1922), 3.
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The whole inherent pride of human nature revolts at the idea that the lord of the creation is to be treated like any other natural object. No sooner does the naturalist discover the resemblance of some higher mammals, such as the ape, to man, than there is a general outcry against the presumptuous audacity that ventures to touch man in his inmost sanctuary. The whole fraternity of philosophers, who have never seen monkeys except in zoological gardens, at once mount the high horse, and appeal to the mind, the soul, to reason, to consciousness, and to all the rest of the innate faculties of man, as they are refracted in their own philosophical prisms.
Carl Vogt
From Carl Vogt and James Hunt (ed.), Lectures on Man: His Place in Creation, and in the History of the Earth (1861), 10.
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The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects; and it is only so far, therefore, as we can discover and register resemblances that we can turn our observations to account.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 1.
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The winds, the sea, and the moving tides are what they are. If there is wonder and beauty and majesty in them, science will discover these qualities. If they are not there, science cannot create them. If there is poetry in my book about the sea, it is not because I deliberately put it there, but because no one could write truthfully about the sea and leave out the poetry.
Address upon receiving National Book Award at reception, Hotel Commodore, New York (27 Jan 1952). As cited in Linda Lear, Rachel Carson: Witness for Nature (1997), 219. She was referring to her book being recognized, The Sea Around Us.
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The word “electromagnetic” which is used to characterize the phenomena produced by the conducting wires of the voltaic pile, … were those which M. Oersted discovered, exhibited by an electric current and a magnet. I have determined to use the word electrodynamic in order to unite under a common name all these phenomena, and particularly to designate those which I have observed between two voltaic conductors. It expresses their true character, that of being produced by electricity in motion: while the electric attractions and repulsions, which have been known for a long time, are electrostatic phenomena produced by the unequal distribution of electricity at rest in the bodies in which they are observed.
New terminology introduced in 'Experiments on the New Electrodynamical Phenomena', Annales de Chemie et de Physique (1822), Series 2, Vol. 20, 60. As translated in Dagobert David Runes (ed.), A Treasury of World Science (1962), 5.
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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 60 sub-atomic particles they’ve discovered that can explain the thousands of other sub-atomic particles, and the model is too ugly. This is my analogy: it’s like taking Scotch tape and taping a giraffe to a mule to a whale to a tiger and saying this is the ultimate theory of particles. … We have so many particles that Oppenheimer once said you could give a Nobel Prize to the physicist that did not discover a particle that year. We were drowning in sub-atomic particles.
Now we realize that this whole zoo of sub-atomic particles, thousands of them coming out of our accelerators, can be explained by little vibrating strings.
Quoted in Nina L. Diamond, Voices of Truth (2000), 334.
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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 are, I believe, very few maxims in philosophy that have laid firmer hold upon the mind, than that air, meaning atmospherical air (free from various foreign matters, which were always supposed to be dissolved, and intermixed with it) is a simple elementary substance, indestructible, and unalterable, at least as much so as water is supposed to be. In the course of my enquiries, I was, however, soon satisfied that atmospherical air is not an unalterable thing; for that the phlogiston with which it becomes loaded from bodies burning in it, and animals breathing it, and various other chemical processes, so far alters and depraves it, as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in water, the process of vegetation, and probably other natural processes, by taking out the superfluous phlogiston, restore it to its original purity.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 6.
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There have been men, like Dalton, of humble origin and retiring habits, unable to command the advantages of a public position, and scantily provided with the means for private research, who by speculation and experiment confined to some one branch have reached the highest eminence in science, and discovered laws of nature with which their names are thenceforth connected.
In obituary, Benjamin Silliman, Benjamin Silliman Jr., and James D. Dana (eds.), Art. XXXI, 'Heinrich Rose', American Journal of Science and Arts (Nov 1864), s2-38, No. 114, 305. The article title gives no author name, but it ends with a one-letter signature, “D.”, [For attribution, Webmaster has assumed this is the initial identifying one of the journal editors, of which only the name James Dana corresponds.]
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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.
In The Restaurant at the End of the Universe (1980), facing p. 1.
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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 another form of temptation even more fraught with danger. This is the disease of curiosity. ... It is this which drives us on to try to discover the secrets of nature, those secrets which are beyond our understanding, which can avail us nothing and which men should not wish to learn.
In Dragons of Eden by Carl Sagan (1977).
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There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.
Webmaster has searched for a primary print source without success. Walter Isaacson likewise found no direct evidence, as he reports in Einstein (2007), 575. However, these sentences are re-quoted in a variety of books and other sources (often citing them as a remark reportedly made by Kelvin in an Address at the British Association for the Advancement of Science in 1900). Although the quote appears noteworthy, it is not included in the major biographical work, the two volumes by Silvanus P. Thomson, The Life of Lord Kelvin (1976). The quote is included here so that this caveat should be read with it.
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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 is, then, one great purpose for man and for us today, and that is to try to discover man’s purpose by every means in our power. That is the ultimate relevance of science, and not only of science, but of every branch of learning which can improve our understanding. In the words of Tolstoy, “The highest wisdom has but one science, the science of the whole, the science explaining the Creation and man’s place in it.”
In The Times, June 21,1975.
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There must be some bond of union between mass and the chemical elements; and as the mass of a substance is ultimately expressed (although not absolutely, but only relatively) in the atom, a functional dependence should exist and be discoverable between the individual properties of the elements and their atomic weights. But nothing, from mushrooms to a scientific dependence can be discovered without looking and trying. So I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and soon this convinced me that the properties of the elements are in periodic dependence upon their atomic weights; and although I had my doubts about some obscure points, yet I have never doubted the universality of this law, because it could not possibly be the result of chance.
Principles of Chemistry (1905), Vol. 2, 18.
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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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They were very different men. Or boys. Someone said they were both like curious children—Einstein the merry boy, Rutherford the boisterous one. They were looking and working in different directions—Einstein looking outward, rather dreamily trying to discover where we came from, and Rutherford drilling deep to discover what we were.
A Force of Nature: The Frontier Genius of Ernest Rutherford (2007), 66.
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Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.
In 'On the Origin and Significance of Geometrical Axioms,' Popular Scientific Lectures< Second Series (1881), 57-59. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 357-358.
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This discovery, indeed, is almost of that kind which I call serendipity, a very expressive word, which as I have nothing better to tell you, I shall endeavour to explain to you: you will understand it better by the derivation than by the definition. I once read a silly fairy tale, called The Three Princes of Serendip: as their highnesses travelled, they were always making discoveries, by accidents and sagacity, of things which they were not in quest of: for instance, one of them discovered that a mule blind of the right eye had travelled the same road lately, because the grass was eaten only on the left side, where it was worse than on the right—now do you understand serendipity?
Letter to Sir Horace Mann (28 Jan 1754), in W. S. Lewis, Warren Hunting Smith and George L. Lam (eds.), Horace Walpole's Correspondence with Sir Horace Mann (1960), Vol. 20, 407-408.
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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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This is only one step in a much larger project. I discovered (no, not me: my team) the function of sugar nucleotides in cell metabolism. I want others to understood this, but it is not easy to explain: this is not a very noteworthy deed, and we hardly know even a little.
[replying when asked about the significance of his Nobel prize-winning achievement.]
As quoted in John H. Exto, Crucible of Science: The Story of the Cori Laboratory (2013), 52.
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This is our fifth White House Science Fair. And every year, I walk out smarter than I walked in, because … these young scientists and engineers teach us something beyond the specific topics that they’re exploring. They teach us how to question assumptions; to wonder why something is the way it is, and how we can make it better. And they remind us that there’s always something more to learn, and to try, and to discover, and to imagine—and that it’s never too early, or too late to create or discover something new.
From remarks at the fifth White House Science Fair, in Press Release (23 Mar 2015).
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This missing science of heredity, this unworked mine of knowledge on the borderland of biology and anthropology, which for all practical purposes is as unworked now as it was in the days of Plato, is, in simple truth, ten times more important to humanity than all the chemistry and physics, all the technical and indsutrial science that ever has been or ever will be discovered.
Mankind in the Making (1903), 72.
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This property of human languages—their resistance to algorithmic processing— is perhaps the ultimate reason why only mathematics can furnish an adequate language for physics. It is not that we lack words for expressing all this E = mc² and ∫eiS(Φ)DΦ … stuff … , the point is that we still would not be able to do anything with these great discoveries if we had only words for them. … Miraculously, it turns out that even very high level abstractions can somehow reflect reality: knowledge of the world discovered by physicists can be expressed only in the language of mathematics.
In 'Mathematical Knowledge: Internal, Social, And Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 5.
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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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Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 24.
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Throw out opium, which the Creator himself seems to prescribe, for we often see the scarlet poppy growing in the cornfields, as if it were foreseen that wherever there is hunger to be fed there must also be a pain to be soothed; throw out a few specifics which our art did not discover, and it is hardly needed to apply; throw out wine, which is a food, and the vapors which produce the miracle of anaesthesia, and I firmly believe that if the whole materia medica [medical drugs], as now used, could be sunk to the bottom of the sea, it would be all the better for mankind,—and all the worse for the fishes.
'Currents and Counter-Currents in Medical Science', Address to Massachusetts Medical Society (30 May 1860). In Medical Essays 1842-1882 (1891), 202-3.
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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 come very near to a true theory, and to grasp its precise application, are two different things, as the history of science teaches us. Everything of importance has been said before by someone who did not discover it.
In The Organisation of Thought (1917), 127. Collected in The Interpretation of Science: Selected Essays (1961), 33.
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To discover a Conception of the mind which will justly represent a train of observed facts is, in some measure, a process of conjecture, ... and the business of conjecture is commonly conducted by calling up before our minds several suppositions, selecting that one which most agrees with what we know of the observed facts. Hence he who has to discover the laws of nature may have to invent many suppositions before he hits upon the right one; and among the endowments which lead to his success, we must reckon that fertility of invention which ministers to him such imaginary schemes, till at last he finds the one which conforms to the true order of nature.
Philosophy of the Inductive Sciences (1847), Vol. 2, 54.
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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 discover the laws of operative power in material productions, whether formed by man or brought into being by Nature herself, is the work of a science, and is indeed what we more especially term Science.
Lecture (26 Nov 1851), to the London Society of Arts, 'The General Bearing of the Great Exhibition on the Progress of Art and Science', collected in Lectures on the Results of the Great Exhibition of 1851' (1852), 7.
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To seek in the great accumulation of the already-said the text that resembles "in advance" a later text, to ransack history in order to rediscover the play of anticipations or echoes, to go right back to the first seeds or to go forward to the last traces, to reveal in a work its fidelity to tradition or its irreducible uniqueness, to raise or lower its stock of originality, to say that the Port -Royal grammarians invented nothing, or to discover that Cuvier had more predecessors than one thought, these are harmless enough amusements for historians who refuse to grow up.
The Archaeology of Knowledge (1969), trans. M. Sheridan Smith (1972), 144.
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To study men, we must look close by; to study man, we must learn to look afar; if we are to discover essential characteristics, we must first observe differences.
Essai sur l'origine des langues (1781), 384
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To the Victorian scientist, science was the pursuit of truth about Nature. In imagination, each new truth discovered could be ticked off on a list kept perhaps in a celestial planning office, so reducing by one the total number of truths to be discovered. But the practising scientist now knows that he is dealing with a living, growing thing. His task is never done.
Opening remark in article 'Musical Acoustics Today', New Scientist (1 Nov 1962), 16 No. 311, 256.
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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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Truly the gods have not from the beginning revealed all things to mortals, but by long seeking, mortals discover what is better.
Fragment B18, from Diels and Kranz Die Fragmente der Vorsokratiker, as translated by Kathleen Freeman in Ancilla to the Pre-Socratic Philosophers (1948, 1983), 22.
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Truth is something that we can attempt to doubt, and then perhaps, after much exertion, discover that part of the doubt is not justified.
Quoted in Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52.
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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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Unless you expect the unexpected you will never find it, for it is hard to discover and hard to attain.
As quoted in Peter Pešic, Labyrinth: A Search for the Hidden Meaning of Science (2001), 2.
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We are very lucky to be living in an age in which we are still making discoveries. It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. It is very exciting, it is marvelous, but this excitement will have to go.
From transcript of the seventh Messenger Lecture, Cornell University (1964), 'Seeking New Laws.' Published in The Character of Physical Law (1965, reprint 2001), 172.
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We can distinguish three groups of scientific men. In the first and very small group we have the men who discover fundamental relations. Among these are van’t Hoff, Arrhenius and Nernst. In the second group we have the men who do not make the great discovery but who see the importance and bearing of it, and who preach the gospel to the heathen. Ostwald stands absolutely at the head of this group. The last group contains the rest of us, the men who have to have things explained to us.
'Ostwald', Journal of Chemical Education, 1933, 10, 612, as cited by Erwin N. Hiebert and Hans-Gunther Korber in article on Ostwald in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography Supplement 1, Vol 15-16, 466, which also says Wilder Bancroft "received his doctorate under Ostwald in 1892."
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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 learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a discovery.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 349.
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We live in a glass-soaked civilization, but as for the bird in the Chinese proverb who finds it so difficult to discover air, the substance is almost invisible to us. To use a metaphor drawn from glass, it may be revealing for us to re-focus, to stop looking through glass, and let our eyes dwell on it for a moment to contemplate its wonder. [Co-author with Gerry Martin.]
Glass: A World History (2002), 4.
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We live only to discover beauty. All else is a form of waiting.
In Kahlil Gibran, Kahlil Gibran - The Collected Works (2007), 178.
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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 best hope to understand the nature and conditions of real knowledge, by studying the nature and conditions of the most certain and stable portions of knowledge which we already possess: and we are most likely to learn the best methods of discovering truth, by examining how truths, now universally recognised, have really been discovered.
In The Philosophy of the Inductive Sciences (1840), Vol. I, 3-4.
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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 must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity.
Lecture at Vassar College, Poughkeepsie, New York (14 May 1921). In Cambridge Editorial Partnership, Speeches that Changed the World, 53.
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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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We sign treaties with all nations agreeing to give up war as an instrument of national policy, and then relax as if war had been made unlikely. The premises and the reasoning are very much like those underlying magical rain-making. That is, we want it to rain, therefore it should rain, therefore it will rain. We have discovered the invalidity of this reasoning in the case of rain, and our schools for the most part no longer teach magical methods of influencing physical events.
In 'Education in a Scientific Age', Can Science Save Us? (1947, 2nd ed. 1961), 68.
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We speak erroneously of “artificial” materials, “synthetics”, and so forth. The basis for this erroneous terminology is the notion that Nature has made certain things which we call natural, and everything else is “man-made”, ergo artificial. But what one learns in chemistry is that Nature wrote all the rules of structuring; man does not invent chemical structuring rules; he only discovers the rules. All the chemist can do is find out what Nature permits, and any substances that are thus developed or discovered are inherently natural. It is very important to remember that.
From 'The Comprehensive Man', Ideas and Integrities: A Spontaneous Autobiographical Disclosure (1963), 75-76.
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Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein’s theory of gravitation replaced Newton’s, but apples did not suspend themselves in mid-air pending the outcome. And human beings evolved from apelike ancestors whether they did so by Darwin’s proposed mechanism or by some other, yet to be discovered … Evolutionists make no claim for perpetual truth, though creationists often do (and then attack us for a style of argument that they themselves favor).
'Evolution as Fact and Theory', in Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983), 254-255.
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What about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven levels of hell, the seven primary colors, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.
The Magical Number Seven, Plus or Minus Two (1956), 42-3.
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What caused me to undertake the catalog was the nebula I discovered above the southern horn of Taurus on September 12, 1758, while observing the comet of that year. ... This nebula had such a resemblance to a comet in its form and brightness that I endeavored to find others, so that astronomers would not confuse these same nebulae with comets just beginning to shine. I observed further with suitable refractors for the discovery of comets, and this is the purpose I had in mind in compiling the catalog.
After me, the celebrated Herschel published a catalog of 2000 which he has observed. This unveiling the sky, made with instruments of great aperture, does not help in the perusal of the sky for faint comets. Thus my object is different from his, and I need only nebulae visible in a telescope of two feet [focal length].
Connaissance des Temps for 1800/1801. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 330.
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What hopes filled me when I discovered that there were laws behind so many obscure phenomena!
In Speech (27 Dec 1892) at the Golden Jubilee celebration for Pasteur's 70th birthday. As translated in Nature (1893), 47, 205.
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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 of the future of this adventure? What will happen ultimately? We are going along guessing the laws; how many laws are we going to have to guess? I do not know. Some of my colleagues say that this fundamental aspect of our science will go on; but I think there will certainly not be perpetual novelty, say for a thousand years. This thing cannot keep on going so that we are always going to discover more and more new laws … It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. Of course in the future there will be other interests … but there will not be the same things that we are doing now … There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.
In The Character of Physical Law (1965, 1994), 166.
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What politicians do not understand is that [Ian] Wilmut discovered not so much a technical trick as a new law of nature. We now know that an adult mammalian cell can fire up all the dormant genetic instructions that shut down as it divides and specializes and ages, and thus can become a source of new life. You can outlaw technique; you cannot repeal biology.
Writing after Wilmut's successful cloning of the sheep, Dolly, that research on the cloning of human beings cannot be suppressed.
'A Special Report on Cloning'. Charles Krauthammer in Time (10 Mar 1997).
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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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What the scientists have always found by physical experiment was an a priori orderliness of nature, or Universe always operating at an elegance level that made the discovering scientist’s working hypotheses seem crude by comparison. The discovered reality made the scientists’ exploratory work seem relatively disorderly.
As quoted by L.L. Larison Cudmore in The Center of Life: A Natural History of the Cell (1977), xi.
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What we have to discover for ourselves leaves behind in our mind a pathway that can be used on another occasion.
Aphorism 26 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 36.
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Wheeler hopes that we can discover, within the context of physics, a principle that will enable the universe to come into existence “of its own accord.” In his search for such a theory, he remarks: “No guiding principle would seem more powerful than the requirement that it should provide the universe with a way to come into being.” Wheeler likened this 'self-causing' universe to a self-excited circuit in electronics.
In God and the New Physics (1984), 39. Wheeler quotation footnoted 'From the Black Hole', in H. Woolf (Ed.),Some Strangeness in the Proportion (1980).
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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 discovered, [aluminum was a precious metal that] cost about 270 dollars a pound; then it fell to 27 dollars, and today a pound of aluminum is worth about nine dollars.
Answering the question, “Is not aluminum rather expensive?” to a fictional moon shot committee. In Jules Verne, Aaron Parrett (ed.) and Edward Roth (trans.), From the Earth to the Moon (1865, 2005), 50. In the original French edition, the costs were given in francs as about 1500, 150 and 48.75, respectively.
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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 Galileo caused balls, the weights of which he had himself previously determined, to roll down an inclined plane; when Torricelli made the air carry a weight which he had calculated beforehand to be equal to that of a definite volume of water; or in more recent times, when Stahl changed metal into lime, and lime back into metal, by withdrawing something and then restoring it, a light broke upon all students of nature. They learned that reason has insight only into that which it produces after a plan of its own, and that it must not allow itself to be kept, as it were, in nature's leading-strings, but must itself show the way with principles of judgement based upon fixed laws, constraining nature to give answer to questions of reason's own determining. Accidental observations, made in obedience to no previously thought-out plan, can never be made to yield a necessary law, which alone reason is concerned to discover.
Critique of Pure Reason (1781), trans. Norman Kemp Smith (1929), 20.
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When I discover who I am, I’ll be free.
…...
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When I investigate and when I discover that the forces of the heavens and the planets are within ourselves, then truly I seem to be living among the gods.
In Francesco De Sanctis, History of Italian literature (1959), Vol. 1, 418.
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When in many dissections, carried out as opportunity offered upon living animals, I first addressed my mind to seeing how I could discover the function and offices of the heart’s movement in animals through the use of my own eyes instead of through the books and writings of others, I kept finding the matter so truly hard and beset with difficulties that I all but thought, with Fracastoro, that the heart's movement had been understood by God alone.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth J. Franklin (1957), Chapter 1, author's motives for writing, 23.
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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 the most abstract and “useless” disciplines have been cultivated for a time, they are often seized upon as practical tools by other departments of science. I conceive that this is no accident, as if one bought a top hat for a wedding, and discovered later when a fire broke out, that it could be used as a water bucket.
In James R. Newman (ed.), 'Commentary on The Use of a Top Hat as a Water Bucket', The World of Mathematics (1956), Vol.4, 2051.
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When they have discovered truth in nature they fling it into a book, where it is in even worse hands.
Aphorism 62 in Notebook E (1775-1776), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 73.
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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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When you see the natural and almost universal craving in English sick for their 'tea,' you cannot but feel that nature knows what she is about. … [A] little tea or coffee restores them. … [T]here is nothing yet discovered which is a substitute to the English patient for his cup of tea.
'Tea, Coffee, and Cocoa for the Sick', Scientific American (2 Jul 1860), New Series, 3, No. 1, 3.
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When you start in science, you are brainwashed into believing how careful you must be, and how difficult it is to discover things. There’s something that might be called the “graduate student syndrome”; graduate students hardly believe they can make a discovery.
Quotation supplied by Professor Francis Crick.
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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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Whenever I meet in Laplace with the words “Thus it plainly appears”, I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.
Mécanique céleste (1829-39), Celestial mechanics (1966).
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Whereas there is nothing more necessary for promoting the improvement of Philosophical Matters, than the communicating to such, as apply their Studies and Endeavours that way, such things as are discovered or put in practice by others; it is therefore thought fit to employ the Press, as the most proper way to gratifie those, whose engagement in such Studies, and delight in the advancement of Learning and profitable Discoveries, doth entitle them to the knowledge of what this Kingdom, or other parts of the World, do, from time to time, afford as well of the progress of the Studies, Labours, and attempts of the Curious and learned in things of this kind, as of their compleat Discoveries and performances: To the end, that such Productions being clearly and truly communicated, desires after solid and usefull knowledge may be further entertained, ingenious Endeavours and Undertakings cherished, and those, addicted to and conversant in such matters, may be invited and encouraged to search, try, and find out new things, impart their knowledge to one another, and contribute what they can to the Grand design of improving Natural knowledge, and perfecting all Philosophical Arts, and Sciences. All for the Glory of God, the Honour and Advantage of these Kingdoms, and the Universal Good of Mankind.
'Introduction', Philosophical Transactions (1665), 1, 1-2.
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Wherever we seek to find constancy we discover change. Having looked at the old woodlands in Hutcheson Forest, at Isle Royale, and in the wilderness of the boundary waters, in the land of the moose and the wolf, and having uncovered the histories hidden within the trees and within the muds, we find that nature undisturbed is not constant in form, structure, or proportion, but changes at every scale of time and space. The old idea of a static landscape, like a single musical chord sounded forever, must be abandoned, for such a landscape never existed except in our imagination. Nature undisturbed by human influence seems more like a symphony whose harmonies arise from variation and change over many scales of time and space, changing with individual births and deaths, local disruptions and recoveries, larger scale responses to climate from one glacial age to another, and to the slower alterations of soils, and yet larger variations between glacial ages.
Discordant Harmonies (1990), 62.
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While reading in a textbook of chemistry, … I came across the statement, “nitric acid acts upon copper.” I was getting tired of reading such absurd stuff and I determined to see what this meant. Copper was more or less familiar to me, for copper cents were then in use. I had seen a bottle marked “nitric acid” on a table in the doctor’s office where I was then “doing time.” I did not know its peculiarities, but I was getting on and likely to learn. The spirit of adventure was upon me. Having nitric acid and copper, I had only to learn what the words “act upon” meant … I put one of them [cent] on the table, opened the bottle marked “nitric acid”; poured some of the liquid on the copper; and prepared to make an observation. But what was this wonderful thing which I beheld? The cent was already changed, and it was no small change either. A greenish blue liquid foamed and fumed over the cent and over the table. The air in the neighborhood of the performance became colored dark red. A great colored cloud arose. This was disagreeable and suffocating—how should I stop this? I tried to get rid of the objectionable mess by picking it up and throwing it out of the window, which I had meanwhile opened. I learned another fact—nitric acid not only acts upon copper but it acts upon fingers. The pain led to another unpremeditated experiment. I drew my fingers across my trousers and another fact was discovered. Nitric acid acts upon trousers. Taking everything into consideration, that was the most impressive experiment, and, relatively, probably the most costly experiment I have ever performed.
In F.H. Getman, The Life of Ira Remsen (1940), 9.
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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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Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
From Summa Theologiae Question 32, 'The Causes of Pleasure,' Article 8, 'Is Pleasure Caused by Wondering.'(1a2ae 32.8). As translated in James Vincent Cunningham, Tragic Effect and Tragic Process in Some Plays of Shakespeare (1945). Also in The Collected Essays of J.V. Cunningham (1976), 72-73.
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Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
From Summa Theologiae Question 32, 'The Causes of Pleasure,' Article 8, 'Is Pleasure Caused by Wondering.'(1a2ae 32.8). As translated in James Vincent Cunningham, Tragic Effect and Tragic Process in Some Plays of Shakespeare (1945). Also in The Collected Essays of J.V. Cunningham (1976), 72-73.
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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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You do not know what you will find, you may set out to find one thing and end up by discovering something entirely different.
About “pure fundamental research.” From Dedication Address opening the Oklahoma Medical Research Foundation, Fleming stressed training “to look for significance in scientific ‘accidents,’” and “the importance of serendipity in science,” as well as a “free atmosphere which will allow genius full play.” In 'Penicillin Discoverer Calls For Free Path for Research', New York Times (4 Jul 1949), 1.
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You may perceive something of the distinction which I think necessary to keep in view between art and science, between the artist and the man of knowledge, or the philosopher. The man of knowledge, the philosopher, is he who studies and acquires knowledge in order to improve his own mind; and with a desire of extending the department of knowledge to which he turns his attention, or to render it useful to the world, by discoveries, or by inventions, which may be the foundation of new arts, or of improvements in those already established. Excited by one or more of these motives, the philosopher employs himself in acquiring knowledge and in communicating it. The artist only executes and practises what the philosopher or man of invention has discovered or contrived, while the business of the trader is to retail the productions of the artist, exchange some of them for others, and transport them to distant places for that purpose.
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, 3.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 40 -
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