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Useful Quotes (250 quotes)

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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Deliberare utilia, mora est tutissima.
To deliberate about useful things, is the safest delay.
In 'Ornamenta Rationalia, or, Elegant Sentences' (1625). As given in Essays, Moral, Economical, and Political: A New Edition, With the Latin Quotations Translated (1813), No. 6, 362.
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Engineering, too, owes its most useful materials to the achievements of chemists in identifying, separating, and transforming materials: structural steel for the framework of bridges and buildings, portland cement for roadways and aqueducts, pure copper for the electrical industries, aluminum alloys for automobiles and airplanes, porcelain for spark plugs and electrical insulators. The triumphs of engineering skill rest on a chemical foundation.
In Fundamental Chemistry, and Elementary Textbook for College Classes (1936), 8.
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Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 15.
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L’Astronomie est utile, parce qu’elle nous élève au-dessus de nous-mêmes; elle est utile, parce qu’elle est grande; elle est utile, parce qu’elle est belle… C’est elle qui nous montre combien l’homme est petit par le corps et combien il est grand par l’esprit, puisque cette immensité éclatante où son corps n’est qu’un point obscur, son intelligence peut l’embrasser tout entière et en goûter la silencieuse harmonie.
Astronomy is useful because it raises us above ourselves; it is useful because it is grand[; it is useful because it is beautiful]… It shows us how small is man’s body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.
In La Valeur de la Science (1904), 276, translated by George Bruce Halsted, in The Value of Science (1907), 84. Webmaster added the meaning of “elle est utile, parce qu’elle est belle,” in brackets, which was absent in Halsted’s translation.
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Nisi utile est quod facias, stulta est gloria.
All useless science is an empty boast.
Original Latin from 'Arbores in deorum tutela', Fabulae Aesopiae, Book 3, Poem 17, line 12. Translation by Samuel Johnson, used as an epigraph for an article on the thirst for collecting scientific curiosities, 'Numb. 83, Tuesday, January 1, 1755', The Rambler (1756), Vol. 2, 149. A mechanical translation of the Latin gives “Unless it is useful for what we do, it is the glory of the foolish.” In an 1874 collection by unnamed editor J.B.R., it is given as “nothing is truly valuable that is not useful.” It is given as “Unless what we do is useful, our pride is foolish,” in The Routledge Dictionary of Latin Quotations (2013), 74. Briefly summarizing, the fable is about the gods who choose trees to protect, but the wise Minerva alone picks a tree, the olive, that bears fruit which can be put to good use; moral, do what is useful. ( Webmaster found sources attributing the line in English to Shakespeare, but it cannot be found.)
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Omne tulit punctum qui miscuit utile dulci.
He gains everyone’s approval who mixes the pleasant with the useful.
Horace
In Ars Poetica (c. 18 BC), line 343. As translated and cited in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 123.
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A celebrated medical lecturer began one day “Fumigations, gentlemen, are of essential importance. They make such an abominable smell that they compel you to open the window.” I wish all the disinfecting fluids invented made such an “abominable smell” that they forced you to admit fresh air. That would be a useful invention.
In Notes on Nursing: What It Is and What It Is Not (1860), 28.
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A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.
From Address (1954) to Princeton Alumni, 'The Role of Mathematics in the Sciences and in Society', published in A.H. Taub (ed.), John von Neumann: Collected Works (1963), Vol. 6, 489. As quoted and cited in Rosemary Schmalz,Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993), 123.
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A life spent in making mistakes is not only more honorable but more useful than a life spent doing nothing.
In 'Preface on Doctors', The Doctor's Dilemma (1909, 1911), lxxxv.
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A person by study must try to disengage the subject from useless matter, and to seize on points capable of improvement. ... When subjects are viewed through the mists of prejudice, useful truths may escape.
In An Essay on Aërial Navigation, With Some Observations on Ships (1844), 80.
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A powerful telescope superior to and more powerful than any telescope ever yet made … and also, a suitable Observatory connected therewith … and shall be made useful in promoting science.
From Third Deed of Trust (1874). Excepted in 'Formal Recognition of the Transfer of the Lick Observatory to the Board of Regents of the University', Annual Report of the Secretary to the Board of Regents of the University of California For the Year Ending June 30, 1888, 125.
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A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113. Note that Hardy wrote these words while World War II was raging.
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A science or an art may be said to be “useful” if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.
In A Mathematician's Apology (1940, 2012), 115.
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A sense of duty is useful in work but offensive in personal relations.
In The Conquest of Happiness (1930), Chap. 9, 156.
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A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes.
As quoted by William Ramsay, in 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52. The first part, about suppositions, appears in a paper read by G. Johnson Stoney to the American Philosophical Society, Philadelphia (3 Apr 1903), printed in 'On the Dependence of What Apparently Takes Place in Nature Upon What Actually Occurs in the Universe of Real Existences', Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge (Apr-May 1903) 42, No. 173, 107. If you know a primary source for the part on fictions and mistakes, please contact Webmaster.
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A young man passes from our public schools to the universities, ignorant almost of the elements of every branch of useful knowledge.
Reflections on the Decline of Science in England and on Some of its Causes (1830), 3.
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Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
In 'General Prospectus', The Development of Mathematics (1940, 2017), Chap. 1, 9.
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Abstruse mathematical researches … are … often abused for having no obvious physical application. The fact is that the most useful parts of science have been investigated for the sake of truth, and not for their usefulness. A new branch of mathematics, which has sprung up in the last twenty years, was denounced by the Astronomer Royal before the University of Cambridge as doomed to be forgotten, on account of its uselessness. Now it turns out that the reason why we cannot go further in our investigations of molecular action is that we do not know enough of this branch of mathematics.
In 'Conditions of Mental Development', Lectures and Essays (1901), Vol. 1, 115.
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Alchemy is the art that separates what is useful from what is not by transforming it into its ultimate matter and essence.
In Labyrinthus Medicorum. Cap. V. Von dem Buch der alchimei, wie on dasselbig der arzt kein arzt sein mag. Ed. Sudhoff, vol. XI, 188-189. As cited in Walter Pagel, Paracelsus: An Introduction to Philosophical Medicine in the Era of the Renaissance (2nd rev. ed., 1982), 113.
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All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions.
In 'Report of the Secretary', Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851 (1852), 10.
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All science is full of statements where you put your best face on your ignorance, where you say: … we know awfully little about this, but more or less irrespective of the stuff we don’t know about, we can make certain useful deductions.
From Assumption and Myth in Physical Theory (1967), 11.
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Although I was four years at the University [of Wisconsin], I did not take the regular course of studies, but instead picked out what I thought would be most useful to me, particularly chemistry, which opened a new world, mathematics and physics, a little Greek and Latin, botany and and geology. I was far from satisfied with what I had learned, and should have stayed longer.
[Enrolled in Feb 1861, left in 1863 without completing a degree, and began his first botanical foot journey.]
John Muir
The Story of My Boyhood and Youth (1913), 286.
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Although my Aachen colleagues and students at first regarded the “pure mathematician” with suspicion, I soon had the satisfaction of being accepted a useful member not merely in teaching but also engineering practice; thus I was requested to render expert opinions and to participate in the Ingenieurverein [engineering association].
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 527. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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Analogy is a wonderful, useful and most important form of thinking, and biology is saturated with it. Nothing is worse than a horrible mass of undigested facts, and facts are indigestible unless there is some rhyme or reason to them. The physicist, with his facts, seeks reason; the biologist seeks something very much like rhyme, and rhyme is a kind of analogy.... This analogizing, this fine sweeping ability to see likenesses in the midst of differences is the great glory of biology, but biologists don't know it.... They have always been so fascinated and overawed by the superior prestige of exact physical science that they feel they have to imitate it.... In its central content, biology is not accurate thinking, but accurate observation and imaginative thinking, with great sweeping generalizations.
In Science is a Sacred Cow (1950), 98-100.
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And I believe there are many Species in Nature, which were never yet taken notice of by Man, and consequently of no use to him, which yet we are not to think were created in vain; but it’s likely … to partake of the overflowing Goodness of the Creator, and enjoy their own Beings. But though in this sense it be not true, that all things were made for Man; yet thus far it is, that all the Creatures in the World may be some way or other useful to us, at least to exercise our Wits and Understandings, in considering and contemplating of them, and so afford us Subject of Admiring and Glorifying their and our Maker. Seeing them, we do believe and assert that all things were in some sense made for us, we are thereby obliged to make use of them for those purposes for which they serve us, else we frustrate this End of their Creation.
John Ray
The Wisdom of God Manifested in the Works of the Creation (1691), 169-70.
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And indeed I am not humming,
Thus to sing of Cl-ke and C-ming,
Who all the universe surpasses
in cutting up and making gases;
With anatomy and chemics,
Metaphysics and polemics,
Analyzing and chirugery,
And scientific surgery …
H-slow's lectures on the cabbage
Useful are as roots of Babbage;
Fluxions and beet-root botany,
Some would call pure monotony.
Magazine
Punch in Cambridge (28 Jan 1834). In Mark Weatherall, Gentlemen, Scientists, and Medicine at Cambridge 1800-1940 (2000), Vol. 3,77. The professors named were William Clark (anatomy), James Cumming (chemistry) and Johns Stephens Henslow (botany).
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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 was not free from the prevailing notion that geometry was degraded by being employed to produce anything useful. It was with difficulty that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science.
In Lord Bacon', Edinburgh Review (Jul 1887), in Critical and Miscellaneous Essays (1879), Vol. 1, 395.
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As an answer to those who are in the habit of saying to every new fact, “ What is its use ?” Dr. Franklin says to such, “What is the use of an infant?” The answer of the experimentalist would be, “Endeavour to make it useful.”
From 5th Lecture in 1816, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 218.
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As long as an individual mollusk remains unregistered it is deprived of its full usefulness; but even then it may reveal an important fact—as the trilobite speaks of the Palaeozoic period, and a nummulite of the Tertiary.
In 'A Brief Account of the Thesaurus Siluricus with a Few Facts and Inferences', Proceedings op the Royal Society (1867), No. 90, 373.
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As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer. But Euclid for children is barbarous.
Electro-Magnetic Theory (1893), Vol. 1, 148. In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.
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At first he who invented any art that went beyond the common perceptions of man was naturally admired by men, not only because there was something useful in the inventions, but because he was thought wise and superior to the rest. But as more arts were invented, and some were directed to the necessities of life, others to its recreation, the inventors of the latter were always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility.
Aristotle
Metaphysics, 981b, 13-20. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1553.
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At the beginning of this debate Stephen [Hawking] said that he thinks that he is a positivist, whereas I am a Platonist. I am happy with him being a positivist, but I think that the crucial point here is, rather, that I am a realist. Also, if one compares this debate with the famous debate of Bohr and Einstein, some seventy years ago, I should think that Stephen plays the role of Bohr, whereas I play Einstein's role! For Einstein argued that there should exist something like a real world, not necessarily represented by a wave function, whereas Bohr stressed that the wave function doesn't describe a 'real' microworld but only 'knowledge' that is useful for making predictions.
Debate at the Isaac Newton Institute of the Mathematical Sciences, Cambridge University (1994), transcribed in Stephen Hawking and Roger Penrose, The Nature of Space and Time (1996), 134-135.
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At the entrance to the observatory Stjerneborg located underground, Tycho Brahe built a Ionic portal. On top of this were three sculptured lions. On both sides were inscriptions and on the backside was a longer inscription in gold letters on a porfyr stone: Consecrated to the all-good, great God and Posterity. Tycho Brahe, Son of Otto, who realized that Astronomy, the oldest and most distinguished of all sciences, had indeed been studied for a long time and to a great extent, but still had not obtained sufficient firmness or had been purified of errors, in order to reform it and raise it to perfection, invented and with incredible labour, industry, and expenditure constructed various exact instruments suitable for all kinds of observations of the celestial bodies, and placed them partly in the neighbouring castle of Uraniborg, which was built for the same purpose, partly in these subterranean rooms for a more constant and useful application, and recommending, hallowing, and consecrating this very rare and costly treasure to you, you glorious Posterity, who will live for ever and ever, he, who has both begun and finished everything on this island, after erecting this monument, beseeches and adjures you that in honour of the eternal God, creator of the wonderful clockwork of the heavens, and for the propagation of the divine science and for the celebrity of the fatherland, you will constantly preserve it and not let it decay with old age or any other injury or be removed to any other place or in any way be molested, if for no other reason, at any rate out of reverence to the creator’s eye, which watches over the universe. Greetings to you who read this and act accordingly. Farewell!
(Translated from the original in Latin)
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Botany,—the science of the vegetable kingdom, is one of the most attractive, most useful, and most extensive departments of human knowledge. It is, above every other, the science of beauty.
Using pseudonym Peter Parley, in Peter Parley’s Cyclopedia of Botany (1838), ix. [This is a correction. Earlier on this website, the quote was identified as by Joseph Paxton, because that author’s name was on Google’s (erroneous) cover image of the book search result.]
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But concerning vision alone is a separate science formed among philosophers, namely, optics, and not concerning any other sense ... It is possible that some other science may be more useful, but no other science has so much sweetness and beauty of utility. Therefore it is the flower of the whole of philosophy and through it, and not without it, can the other sciences be known.
Opus Majus [1266-1268], Part V, distinction I, chapter I, trans. R. B. Burke, The Opus Maius of Roger Bacon (1928), Vol. 2, 420.
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But of this I can assure you that there is not a movement of any body of Men however small whether on Horse-back or on foot, nor an operation or March of any description nor any Service in the field that is not formed upon some mathematical principle, and in the performance of which the knowledge and practical application of the mathematicks will be found not only useful but necessary. The application of the Mathematicks to Gunnery, Fortification, Tactics, the survey and knowledge of formal Castrenantion etc. cannot be acquired without study.
Duke of Wellington to his son Douro (1826). Quoted in A Selection of the Private Correspondence of the First Duke of Wellington (1952), 44.
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By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more.
From Address (1954) to Princeton Alumni, 'The Role of Mathematics in the Sciences and in Society', published in A.H. Taub (ed.), John von Neumann: Collected Works (1963), Vol. 6, 489. As quoted and cited in Rosemary Schmalz,Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993), 123.
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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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Chance... in the accommodation peculiar to sensorimotor intelligence, plays the same role as in scientific discovery. It is only useful to the genius and its revelations remain meaningless to the unskilled.
The Origin of Intelligence in the Child (1936), trans. Margaret Cook (1953), 303.
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Chemistry is an art that has furnished the world with a great number of useful facts, and has thereby contributed to the improvement of many arts; but these facts lie scattered in many different books, involved in obscure terms, mixed with many falsehoods, and joined to a great deal of false philosophy; so that it is not great wonder that chemistry has not been so much studied as might have been expected with regard to so useful a branch of knowledge, and that many professors are themselves but very superficially acquainted with it. But it was particularly to be expected, that, since it has been taught in universities, the difficulties in this study should have been in some measure removed, that the art should have been put into form, and a system of it attempted—the scattered facts collected and arranged in a proper order. But this has not yet been done; chemistry has not yet been taught but upon a very narrow plan. The teachers of it have still confined themselves to the purposes of pharmacy and medicine, and that comprehends a small branch of chemistry; and even that, by being a single branch, could not by itself be tolerably explained.
John Thomson, An Account of the Life, Lectures and Writings of William Cullen, M.D. (1832), Vol. 1, 40.
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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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Committees are dangerous things that need most careful watching. I believe that a research committee can do one useful thing and one only. It can find the workers best fitted to attack a particular problem, bring them together, give them the facilities they need, and leave them to get on with the work. It can review progress from time to time, and make adjustments; but if it tries to do more, it will do harm.
Attributed.
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Common sense … may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do.
In Science and Common Sense (1951), 32-33.
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Concepts that have proven useful in ordering thi ngs easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens.
…...
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Data isn't information. ... Information, unlike data, is useful. While there’s a gulf between data and information, there’s a wide ocean between information and knowledge. What turns the gears in our brains isn't information, but ideas, inventions, and inspiration. Knowledge—not information—implies understanding. And beyond knowledge lies what we should be seeking: wisdom.
In High-Tech Heretic: Reflections of a Computer Contrarian (2000), 185-186.
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Defenders of the short-sighted men who in their greed and selfishness will, if permitted, rob our country of half its charm by their reckless extermination of all useful and beautiful wild things sometimes seek to champion them by saying the “the game belongs to the people.” So it does; and not merely to the people now alive, but to the unborn people. The “greatest good for the greatest number” applies to the number within the womb of time, compared to which those now alive form but an insignificant fraction. Our duty to the whole, including the unborn generations, bids us restrain an unprincipled present-day minority from wasting the heritage of these unborn generations. The movement for the conservation of wild life and the larger movement for the conservation of all our natural resources are essentially democratic in spirit, purpose, and method.
'Bird Reserves at the Mouth of the Mississippi', A Book-Lover's Holidays in the Open (1920), 300-301.
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During the eighteenth and nineteenth centuries we can see the emergence of a tension that has yet to be resolved, concerning the attitude of scientists towards the usefulness of science. During this time, scientists were careful not to stress too much their relationships with industry or the military. They were seeking autonomy for their activities. On the other hand, to get social support there had to be some perception that the fruits of scientific activity could have useful results. One resolution of this dilemma was to assert that science only contributed at the discovery stage; others, industrialists for example, could apply the results. ... Few noted the ... obvious paradox of this position; that, if scientists were to be distanced from the 'evil' effects of the applications of scientific ideas, so too should they receive no credit for the 'good' or socially beneficial, effects of their activities.
Co-author with Philip Gummett (1947- ), -British social scientist
Science, Technology and Society Today (1984), Introduction, 4.
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During this [book preparation] time attacks have not been wanting—we must always be prepared for them. If they grow out of a scientific soil, they cannot but be useful, by laying bare weak points and stimulating to their correction; but if they proceed from that soil, from which the lilies of innocence and the palms of conciliation should spring up, where, however, nothing but the marsh-trefoil of credulity and the poisonous water-hemlock of calumniation grow, they deserve no attention.
Carl Vogt
From Carl Vogt and James Hunt (ed.), Lectures on Man: His Place in Creation, and in the History of the Earth (1861), Author's Preface, 2-3.
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Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.
Reflections: Mathematics and Creativity', New Yorker (1972), 47, No. 53, 39-45. In Douglas M. Campbell, John C. Higgins (eds.), Mathematics: People, Problems, Results (1984), Vol. 2, 3.
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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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Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge.
The Great Equations: Breakthroughs in Science: from Pythagoras to Heisenberg (2009), 17.
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Every common mechanic has something to say in his craft about good and evil, useful and useless, but these practical considerations never enter into the purview of the mathematician.
Quoted in Robert Drew Hicks, Stoic and Epicurean (1910), 210.
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Fine sense and exalted sense are not half as useful as common sense.
'Thoughts On Various Subjects', The Works of Alexander Pope (1806), Vol. 6, 406.
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Firm support has been found for the assertion that electricity occurs at thousands of points where we at most conjectured that it was present. Innumerable electrical particles oscillate in every flame and light source. We can in fact assume that every heat source is filled with electrons which will continue to oscillate ceaselessly and indefinitely. All these electrons leave their impression on the emitted rays. We can hope that experimental study of the radiation phenomena, which are exposed to various influences, but in particular to the effect of magnetism, will provide us with useful data concerning a new field, that of atomistic astronomy, as Lodge called it, populated with atoms and electrons instead of planets and worlds.
'Light Radiation in a Magnetic Field', Nobel Lecture, 2 May 1903. In Nobel Lectures: Physics 1901-1921 (1967), 40.
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Food may be defined as material which, when taken into the body, serves to either form tissue or yield energy, or both. This definition includes all the ordinary food materials, since they both build tissue and yield energy. It includes sugar and starch, because they yield energy and form fatty tissue. It includes alcohol, because the latter is burned to yield energy, though it does not build tissue. It excludes creatin, creatininin, and other so-called nitrogeneous extractives of meat, and likewise thein or caffein of tea and coffee, because they neither build tissue nor yield energy, although they may, at times, be useful aids to nutrition.
Methods and Results of Investigations on the Chemistry and Economy of Food, Bulletin 21, US Department of Agriculture (1895). Quoted in Ira Wolinsky, Nutrition in Exercise and Sport (1998), 36.
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For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium—the extreme rarity of which renders it commercially unimportant—as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 20.
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For it may safely be said, not that the habit of ready and correct observation will by itself make us useful nurses, but that without it we shall be useless with all our devotion.
Notes on Nursing: What it is and what it is not (1860), 160.
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For my part, I must say that science to me generally ceases to be interesting as it becomes useful.
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493.
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For this we must make automatic and habitual, as early as possible, as many useful actions as we can, and guard against the growing into ways that are likely to be disadvantageous to us, as we should guard against the plague?
'The Laws of Habit', The Popular Science Monthly (Feb 1887), 434.
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From common salt are obtained chemically as primary derivatives chlorine—both a war gas and a means of purifying water; and 'caustic soda.' … [O]n the chlorine side there is obtained chloride of lime, (a bleaching powder and a disinfectant), chloroform (an anesthetic), phosgene (a frightful ware gas), chloroacetophenone (another war gas), and an indigo and a yellow dye. [O]n the soda side we get metallic sodium, from which are derived sodium cyanide (a disinfectant), two medicines with [long] names, another war gas, and a beautiful violet dye. Thus, from a healthful, preservative condiment come things useful and hurtful—according to the intent or purpose.
Anonymous
The Homiletic Review, Vol. 83-84 (1922), Vol. 83, 209.
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From my earliest childhood I nourished and cherished the desire to make a creditable journey in a new country, and write such a respectable account of its natural history as should give me a niche amongst the scientific explorers of the globe I inhabit, and hand my name down as a useful contributor of original matter.
Letter to Charles Darwin (1854), in Francis Darwin, More Letters of Charles Darwin (1903).
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Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.
Doctrine of Chances (1718), Preface, v.
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Guard well your spare moments. They are like uncut diamonds. Discard them and their value will never be known. Improve them and they will become the brightest gems in a useful life.
…...
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Had I been present at the Creation, I would have given some useful hints for the better ordering of the universe.
Remarking on the complexity of Ptolemaic model of the universe after it was explained to him.
Footnote: Carlyle says, in his History of Frederick the Great, book ii. chap. vii. that this saying of Alphonso about Ptolemy's astronomy, 'that it seemed a crank machine; that it was pity the Creator had not taken advice,' is still remembered by mankind, — this and no other of his many sayings.
In John Bartlett and Nathan Haskell Dole (Ed.), Familiar Quotations: A Collection of Passages, Phrases, and Proverbs Traced to Their Sources (1914), 954.
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HEART, n. An automatic, muscular blood- pump. Figuratively, this useful organ is said to be the seat of emotions and sentiments—a very pretty fancy which, however, is nothing but a survival of a once universal belief. It is now known that the sentiments and emotions reside in the stomach, being evolved from food by chemical action of the gastric fluid. The exact process by which a beefsteak becomes a feeling—tender or not, according to the age of the animal from which it was cut; the successive stages of elaboration through which a caviar sandwich is transmuted to a quaint fancy and reappears as a pungent epigram; the marvelous functional methods of converting a hard-boiled egg into religious contrition, or a cream-puff into a sigh of sensibility—these things have been patiently ascertained by M. Pasteur, and by him expounded with convincing lucidity. 
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  133-134.
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His Majesty has, with great skill, constructed a cart, containing a corn mill, which is worked by the motion of the carriage. He has also contrived a carriage of such a magnitude as to contain several apartments, with a hot bath; and it is drawn by a single elephant. This movable bath is extremely useful, and refreshing on a journey. … He has also invented several hydraulic machines, which are worked by oxen. The pulleys and wheels of some of them are so adjusted that a single ox will at once draw water out of two wells, and at the same time turn a millstone.
From Ain-i-Akbery (c.1590). As translated from the original Persian, by Francis Gladwin in 'Akbar’s Conduct and Administrative Rules', 'Of Machines', Ayeen Akbery: Or, The Institutes of the Emperor Akber (1783), Vol. 1, 284. Note: Akbar (Akber) was a great ruler and enlightened statesman.
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Human societies increased the abundance and distribution of useful species. This can also be used to preserve the forest, I think. We can use this as an opportunity to reduce the impacts of deforestation. Now we have huge plantations of soybeans that are destroying the Amazon—while in the forest we have lots of plants that can be used while maintaining the forest as it is.
As quoted in Robinson Meyer, 'The Amazon Rainforest Was Profoundly Changed by Ancient Humans', The Atlantic (2 Mar 2017).
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Hypotheses may be useful, though involving much that is superfluous, and even erroneous: for they may supply the true bond of connexion of the facts; and the superfluity and error may afterwards be pared away.
Aphorism 11, 'Aphorisms Concerning Science', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvi.
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I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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I can certainly wish for new, large, and properly constructed instruments, and enough of them, but to state where and by what means they are to be procured, this I cannot do. Tycho Brahe has given Mastlin an instrument of metal as a present, which would be very useful if Mastlin could afford the cost of transporting it from the Baltic, and if he could hope that it would travel such a long way undamaged… . One can really ask for nothing better for the observation of the sun than an opening in a tower and a protected place underneath.
As quoted in James Bruce Ross and Mary Martin McLaughlin, The Portable Renaissance Reader (1968), 605.
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I confess, that after I began … to discern how useful mathematicks may be made to physicks, I have often wished that I had employed about the speculative part of geometry, and the cultivation of the specious Algebra I had been taught very young, a good part of that time and industry, that I had spent about surveying and fortification (of which I remember I once wrote an entire treatise) and other parts of practick mathematicks.
In 'The Usefulness of Mathematiks to Natural Philosophy', Works (1772), Vol. 3, 426.
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I consider that a man’s brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things so that he has a difficulty in laying his hands upon it. Now the skilful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones.
In 'The Science Of Deduction', A Study In Scarlet (1887, 1904), 15-16.
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I distinguish two kinds of "applied" research: problem-solving research — government or commercially initiated, centrally managed and institutionally coupled to a plan for application of the results, useful science—investigator-initiated, competitively evaluated and widely communicated. Then we have basic science—useful also, also investigator-initiated, competitively evaluated and widely communicated.
In Confessions of a Technophile (1994), 31.
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I do not believe there is anything useful which men can know with exactitude that they cannot know by arithmetic and algebra.
Oeuvres, Vol. 2, 292g. Trans. J. L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics (1979), 42.
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I have been branded with folly and madness for attempting what the world calls impossibilities, and even from the great engineer, the late James Watt, who said ... that I deserved hanging for bringing into use the high-pressure engine. This has so far been my reward from the public; but should this be all, I shall be satisfied by the great secret pleasure and laudable pride that I feel in my own breast from having been the instrument of bringing forward new principles and new arrangements of boundless value to my country, and however much I may be straitened in pecuniary circumstances, the great honour of being a useful subject can never be taken from me, which far exceeds riches.
From letter to Davies Gilbert, written a few months before Trevithick's last illness. Quoted in Francis Trevithick, Life of Richard Trevithick: With an Account of his Inventions (1872), Vol. 2, 395-6.
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I have called this principle, by which each slight variation, if useful, is preserved, by the term Natural Selection, in order to mark its relation to man's power of selection. But the expression often used by Mr. Herbert Spencer of the Survival of the Fittest is more accurate, and is sometimes equally convenient.
from Origin of Species (1859, 1888), 49.
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I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.
A Mathematician's Apology (1940), 90-1.
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I have never done anything “useful.” No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value. [The things I have added to knowledge do not differ from] the creations of the other artists, great or small, who have left some kind of memorial beind them.
Concluding remarks in A Mathmatician's Apology (1940, 2012), 150-151.
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I suspect that the most important effect of World War II on physical science lay in the change in the attitude of people to science. The politicians and the public were convinced that science was useful and were in no position to argue about the details. A professor of physics might be more sinister than he was in the 1930s, but he was no longer an old fool with a beard in a comic-strip. The scientists or at any rate the physicists, had changed their attitude. They not only believed in the interest of science for themselves, they had acquired also a belief that the tax-payer should and would pay for it and would, in some unspecified length of run, benefit by it.
'The Effect of World War II on the Development of Knowledge in the Physical Sciences', Proceedings of the Royal Society of London, 1975, Series A, 342, 532.
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I would like to start by emphasizing the importance of surfaces. It is at a surface where many of our most interesting and useful phenomena occur. We live for example on the surface of a planet. It is at a surface where the catalysis of chemical reactions occur. It is essentially at a surface of a plant that sunlight is converted to a sugar. In electronics, most if not all active circuit elements involve non-equilibrium phenomena occurring at surfaces. Much of biology is concerned with reactions at a surface.
'Surface properties of semiconductors', Nobel Lecture (11 Dec 1956). In Nobel Lectures, Physics 1942-1962 (1967), 377.
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If any student comes to me and says he wants to be useful to mankind and go into research to alleviate human suffering, I advise him to go into charity instead. Research wants real egotists who seek their own pleasure and satisfaction, but find it in solving the puzzles of nature.
In Science Today (May 1980), 35. In Vladimir Burdyuzha, The Future of Life and the Future of Our Civilization (2006), 374.
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If every drug in the world were abolished a physician would still be a useful member of society.
As quoted in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xxv.
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In an age of egoism, it is so difficult to persuade man that of all studies, the most important is that of himself. This is because egoism, like all passions, is blind. The attention of the egoist is directed to the immediate needs of which his senses give notice, and cannot be raised to those reflective needs that reason discloses to us; his aim is satisfaction, not perfection. He considers only his individual self; his species is nothing to him. Perhaps he fears that in penetrating the mysteries of his being he will ensure his own abasement, blush at his discoveries, and meet his conscience. True philosophy, always at one with moral science, tells a different tale. The source of useful illumination, we are told, is that of lasting content, is in ourselves. Our insight depends above all on the state of our faculties; but how can we bring our faculties to perfection if we do not know their nature and their laws! The elements of happiness are the moral sentiments; but how can we develop these sentiments without considering the principle of our affections, and the means of directing them? We become better by studying ourselves; the man who thoroughly knows himself is the wise man. Such reflection on the nature of his being brings a man to a better awareness of all the bonds that unite us to our fellows, to the re-discovery at the inner root of his existence of that identity of common life actuating us all, to feeling the full force of that fine maxim of the ancients: 'I am a man, and nothing human is alien to me.'
Considerations sur les diverses méthodes à suivre dans l'observation des peuples sauvages (1800) The Observation of Savage Peoples, trans. F. C. T. Moore (1969), 61.
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In destroying the predisposition to anger, science of all kind is useful; but the mathematics possess this property in the most eminent degree.
Quoted in Day, Collacon (no date).
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In Japan, an exceptional dexterity that comes from eating with chopsticks … is especially useful in micro-assembly. (This … brings smiles from my colleagues, but I stand by it. Much of modern assembly is fine tweezer work, and nothing prepares for it better than eating with chopsticks from early childhood.)
In The Wealth and Poverty of Nations: Why Some Are So Rich and Some So Poor (1998, 1999), 475.
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In my own view, some advice about what should be known, about what technical education should be acquired, about the intense motivation needed to succeed, and about the carelessness and inclination toward bias that must be avoided is far more useful than all the rules and warnings of theoretical logic.
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), 6.
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In place of infinity we usually put some really big number, like 15.
Perhaps referring to the programmer’s hexadecimal counting scheme which has 16 digits (0-9 followed by digits A-F), useful in binary context as a power of 2.
Anonymous
Attributed to a Computer Science Professor on various web pages. Webmaster has found no print source for this wording and comments, but its originality makes it worthy of inclusion here. Webmaster comments: perhaps one of those infinite number of monkeys typed it! Please make contact if you know a primary print source.
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In science the primary duty of ideas is to be useful and interesting even more than to be “true.”
Lecture delivered to Anthropological Society of University College, London (25 Jan 1929). Published in 'The Functions of the Human Skull', Nature (6 Apr 1929), 123, No. 3101, 533-537. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 73.
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In the Choice of … Things, neglect not any, tho’ the most ordinary and trivial; the Commonest Peble or Flint, Cockle or Oyster-shell, Grass, Moss, Fern or Thistle, will be as useful, and as proper to be gathered and sent, as any the rarest production of the Country. Only take care to choose of each the fairest of its kind, and such as are perfect or whole.
In Brief Instructions for Making Observations in all Parts of the World (1696), 10.
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In the spring of 1760, [I] went to William and Mary college, where I continued two years. It was my great good fortune, and what probably fixed the destinies of my life, that Dr. William Small of Scotland, was then Professor of Mathematics, a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and an enlarged and liberal mind. He, most happily for me, became soon attached to me, and made me his daily companion when not engaged in the school; and from his conversation I got my first views of the expansion of science, and of the system of things in which we are placed.
In Thomas Jefferson and Andrew Adgate Lipscomb (ed.), The Writings of Thomas Jefferson (1904), Vol. 1, 3.
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In working out physical problems there should be, in the first place, no pretence of rigorous formalism. The physics will guide the physicist along somehow to useful and important results, by the constant union of physical and geometrical or analytical ideas. The practice of eliminating the physics by reducing a problem to a purely mathematical exercise should be avoided as much as possible. The physics should be carried on right through, to give life and reality to the problem, and to obtain the great assistance which the physics gives to the mathematics.
In Electromagnetic Theory (1892), Vol. 2, 5.
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Instinct is defined as the untaught ability to perform actions of all kinds, and more especially such as are necessary or useful to the animal.
The Senses and the Intellect (1855, 1974), p. 246.
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Instrumental or mechanical science is the noblest and above all others, the most useful.
(Sul volo degli Uccelli, 3 r.) In Edward McCurdy (ed., trans.), Leonardo da Vinci’s Note-Books: Arranged and Rendered into English (1908), 47.
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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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It has been demonstrated that a species of penicillium produces in culture a very powerful antibacterial substance which affects different bacteria in different degrees. Generally speaking it may be said that the least sensitive bacteria are the Gram-negative bacilli, and the most susceptible are the pyogenic cocci ... In addition to its possible use in the treatment of bacterial infections penicillin is certainly useful... for its power of inhibiting unwanted microbes in bacterial cultures so that penicillin insensitive bacteria can readily be isolated.
'On the Antibacterial Action of Cultures of a Penicillium, with Special Reference to their Use in the Isolation of B. Influenzae', British Journal of Experimental Pathology, 1929, 10, 235-6.
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It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them.
Epigraph in Richard Rhodes, The Making of the Atomic Bomb (1986), 11.
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It is by the aid of iron that we construct houses, cleave rocks, and perform so many other useful offices of life. But it is with iron also that wars, murders, and robberies are effected, and this, not only hand to hand, but from a distance even, by the aid of missiles and winged weapons, now launched from engines, now hurled by the human arm, and now furnished with feathery wings. This last I regard as the most criminal artifice that has been devised by the human mind; for, as if to bring death upon man with still greater rapidity, we have given wings to iron and taught it to fly. ... Nature, in conformity with her usual benevolence, has limited the power of iron, by inflicting upon it the punishment of rust; and has thus displayed her usual foresight in rendering nothing in existence more perishable, than the substance which brings the greatest dangers upon perishable mortality.
Natural History of Pliny, translation (1857, 1898) by John Bostock and H. T. Riley, 205-6.
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It is folly to use as one's guide in the selection of fundamental science the criterion of utility. Not because (scientists)... despise utility. But because. .. useful outcomes are best identified after the making of discoveries, rather than before.
Concerning the allocation of research funds.
Speech to the Canadian Society for the Weizmann Institute of Science, Toronto (2 Jun 1996)
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It is important to go into work you would like to do. Then it doesn't seem like work. You sometimes feel it's almost too good to be true that someone will pay you for enjoying yourself. I've been very fortunate that my work led to useful drugs for a variety of serious illnesses. The thrill of seeing people get well who might otherwise have died of diseases like leukemia, kidney failure, and herpes virus encephalitis cannot be described in words.
From her lecture notes.
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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Quoted in Return to Mathematical Circles H. Eves (Boston 1988).
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It is like the difference between a specialist and a philosopher. A specialist is someone who knows more and more about less and less until at last he knows everything about nothing. A philosopher is someone who knows less and less about more and more until at last he knows nothing about everything. Physics is now too philosophical. In my work I would like to reverse the process, and to try to limit the things to be found out and to make some modest discoveries which may later be useful.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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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 enough to teach man a specialty. Through it he may become a kind of useful machine, but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he—with his specialized knowledge—more closely resembles a well-trained dog than a harmoniously developed person.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
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It is the function of notions in science to be useful, to be interesting, to be verifiable and to acquire value from anyone of these qualities. Scientific notions have little to gain as science from being forced into relation with that formidable abstraction, “general truth.”
In paper delivered before the Royal College of Surgeons of England (15 Feb 1932), in 'The Commemoration of Great Men', British Medical Journal (1932), 1, 32. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 29.
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It is the triumph of civilization that at last communities have obtained such a mastery over natural laws that they drive and control them. The winds, the water, electricity, all aliens that in their wild form were dangerous, are now controlled by human will, and are made useful servants.
In Tryon Edwards, A Dictionary of Thoughts (1908), 75.
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It must be for truth’s sake, and not for the sake of its usefulness to humanity, that the scientific man studies Nature. The application of science to the useful arts requires other abilities, other qualities, other tools than his; and therefore I say that the man of science who follows his studies into their practical application is false to his calling. The practical man stands ever ready to take up the work where the scientific man leaves it, and adapt it to the material wants and uses of daily life.
Methods of Study in Natural History (1863),24.
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It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
Ars conjectandi (1713). In F. Maseres, The Doctrine of Permutations and Combinations (1795), 36.
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It seems to me what is called for is an exquisite balance between two conflicting needs: the most skeptical scrutiny of all hypotheses that are served up to us and at the same time a great openness to new ideas … If you are only skeptical, then no new ideas make it through to you … On the other hand, if you are open to the point of gullibility and have not an ounce of skeptical sense in you, then you cannot distinguish the useful ideas from the worthless ones.
In 'The Burden of Skepticism', Skeptical Inquirer (Fall 1987), 12, No. 1.
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It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
Sections and Views Illustrative of Geological Phenomena (1830), viii.
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Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 32.
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Let us dismiss the question, “Have you proven that your model is valid?” with a quick NO. Then let us take up the more rewarding and far more challenging question: “Have you proven that your model is useful for learning more… ” [Co-author]
In J.B. Mankin, R.V. O’Neill, H.H. Shugart and B.W. Rust, 'The Importance of Validation in Ecosystem Analysis', in: G.S. Innis (ed.), New Directions in the Analysis of Ecological Systems (1977), Part I, 69.
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Magnetic lines of force convey a far better and purer idea than the phrase magnetic current or magnetic flood: it avoids the assumption of a current or of two currents and also of fluids or a fluid, yet conveys a full and useful pictorial idea to the mind.
Diary Entry for 10 Sep 1854. In Thomas Martin (ed.), Faraday's Diary: Being the Various Philosophical Notes of Experimental Investigation (1935), Vol. 6, 315.
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Man does not live by bread alone, there are other wants to be supplied, and even in a practical point of view, a single thought may be fraught with a thousand useful inventions.
Presidential Address (Aug 1853) to the American Association for the Advancement of Education, in Proceedings of the Third Session of the American Association for the Advancement of Education (1854), 29.
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Man is a classifying animal: in one sense it may be said that the whole process of speaking is nothing but distributing phenomena, of which no two are alike in every respect, into different classes on the strength of perceived similarities and dissimilarities. In the name-giving process we witness the same ineradicable and very useful tendency to see likenesses and to express similarity in the phenomena through similarity in name.
Language: Its Nature, Development and Origin (1922), 388-9.
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Man is a free moral agent and can be magnanimous and deal disinterestedly, humanity is a definite goal, social justice is desirable and possible, individual lives may be gloriously diversified, uniquely individualized, and yet socially useful; or, these are mere phrases, snares to catch gulls, soothing syrup for our troubled souls.
From Why We Behave Like Human Beings (1925), 476.
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Measurement has too often been the leitmotif of many investigations rather than the experimental examination of hypotheses. Mounds of data are collected, which are statistically decorous and methodologically unimpeachable, but conclusions are often trivial and rarely useful in decision making. This results from an overly rigorous control of an insignificant variable and a widespread deficiency in the framing of pertinent questions. Investigators seem to have settled for what is measurable instead of measuring what they would really like to know.
'Patient Care—Mystical Research or Researchable Mystique/', Clinical Research (1964), 12, no. 4, 422.
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Medicine, like every useful science, should be thrown open to the observation and study of all. It should, in fact, like law and every important science, be made part of the primary education of the people. … We should at once explode the whole machinery of mystification and concealment—wigs, gold canes, and the gibberish of prescriptions—which serves but as a cloak to ignorance and legalized murder.
Anonymous
Populist philosophy, of Samuel Thomson (1769-1843), founder of the Thomsonian System of medicine, as stated in New York Evening Star (27 Dec 1833)., as cited in the Thomsonian Recorder (17 Jan 1835), 3, 127. Quoted in Paul Starr The Social Transformation of American Medicine (1984), 56.
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Mistakes are at the very base of human thought feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.
In The Medusa and the Snail (1979), 37.
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Models so constructed, though of no practical value, serve a useful academic function. The oldest problem in economic education is how to exclude the incompetent. The requirement that there be an ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
In Economics, Peace, and Laughter (1981), 40-41.
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Much is said about the progress of science in these centuries. I should say that the useful results of science had accumulated, but that there had been no accumulation of knowledge, strictly speaking, for posterity; for knowledge is to be acquired only by corresponding experience. How can be know what we are told merely? Each man can interpret another’s experience only by his own.
In A Week on the Concord and Merrimack Rivers (1862), 384.
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My own thinking (and that of many of my colleagues) is based on two general principles, which I shall call the Sequence Hypothesis and the Central Dogma. The direct evidence for both of them is negligible, but I have found them to be of great help in getting to grips with these very complex problems. I present them here in the hope that others can make similar use of them. Their speculative nature is emphasized by their names. It is an instructive exercise to attempt to build a useful theory without using them. One generally ends in the wilderness.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
'On Protein Synthesis', Symposia of the Society for Experimental Biology: The Biological Replication of Macromolecules, 1958, 12, 152-3.
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Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ’d, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 15, 113.
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Next came the patent laws. These began in England in 1624, and in this country with the adoption of our Constitution. Before then any man [might] instantly use what another man had invented, so that the inventor had no special advantage from his own invention. The patent system changed this, secured to the inventor for a limited time exclusive use of his inventions, and thereby added the fuel of interest to the fire of genius in the discovery and production of new and useful things.
Lecture 'Discoveries, Inventions and Improvements' (22 Feb 1860) in John George Nicolay and John Hay (eds.), Complete Works of Abraham Lincoln (1894), Vol. 5, 113. In Eugene C. Gerhart, Quote it Completely! (1998), 802.
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No body can desire more ardently than myself to concur in whatever may promote useful science, and I view no science with more partiality than Natural history.
Letter (24 May 1807) from Jefferson in Washington to G.C. de la Coste.
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No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without regard to any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of the most important laws of nature.
In Introduction to Mathematics (1911), 136-137.
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Nothing could be more admirable than the manner in which for forty years he [Joseph Black] performed this useful and dignified office. His style of lecturing was as nearly perfect as can well be conceived; for it had all the simplicity which is so entirely suited to scientific discourse, while it partook largely of the elegance which characterized all he said or did … I have heard the greatest understandings of the age giving forth their efforts in its most eloquent tongues—have heard the commanding periods of Pitt’s majestic oratory—the vehemence of Fox’s burning declamation—have followed the close-compacted chain of Grant’s pure reasoning—been carried away by the mingled fancy, epigram, and argumentation of Plunket; but I should without hesitation prefer, for mere intellectual gratification (though aware how much of it is derived from association), to be once more allowed the privilege which I in those days enjoyed of being present while the first philosopher of his age was the historian of his own discoveries, and be an eyewitness of those experiments by which he had formerly made them, once more performed with his own hands.
In 'Philosophers of the Time of George III', The Works of Henry, Lord Brougham, F.R.S. (1855), Vol. I, 19-21.
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Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
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One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various facts that make it up.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 122.
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One of the many useful properties of giant nerve fibres is that samples of protoplasm or axoplasm as it is usually called can be obtained by squeezing out the contents from a cut end … As in many other cells there is a high concentration of potassium ions and relatively low concentration of sodium and chloride ions. This is the reverse of the situation in the animals’ blood or in sea water, where sodium and chloride are the dominant ions and potassium is relatively dilute.
The Conduction of the Nervous Impulse (1964), 27.
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Only about seventy years ago was chemistry, like a grain of seed from a ripe fruit, separated from the other physical sciences. With Black, Cavendish and Priestley, its new era began. Medicine, pharmacy, and the useful arts, had prepared the soil upon which this seed was to germinate and to flourish.
Familiar Letters on Chemistry (1851),5.
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Only the applied scientist sets out to find a “useful” pot of gold. The pure scientist sets out to find nothing. Anything. Everything. The applied scientist is a prospector. The pure scientist is an explorer.
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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Psychology must not only strive to become a useful basis for the other mental sciences, but it must also turn again and again to the historical sciences, in order to obtain an understanding for the more highly developed metal processes.
An Introduction to Psychology (1912)
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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George E.P. Box quote: Remember that all models are wrong; the practical question is how wrong do they have to be to not
[Co-author with Norman R. Draper] (source)
Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful. [Co-author with Norman R. Draper]
In George E.P. Box and Norman R. Draper, Empirical Model-Building and Response Surfaces (1987), 74.
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Rules of Thumb
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Anonymous
In Arthur Bloch, The Complete Murphy's Law: A Definitive Collection (1991), 126.
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Science by itself produces a very badly deformed man who becomes rounded out into a useful creative being only with great difficulty and large expenditure of time. … It is a much smaller matter to both teach and learn pure science than it is to intelligently apply this science to the solution of problems as they arise in daily life.
As quoted in Gary W. Matkin, Technology Transfer and the University (1990), 24.
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Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it.
Anonymous
This, and variations, appear in various places attributed (highly likely incorrectly) to Richard Feynman, but without any primary source citation. For example, see John Lloyd and John Mitchinson, If Ignorance Is Bliss, Why Aren't There More Happy People? : Smart Quotes for Dumb Times (2009), 274. It is also very suspicious that no example, readily found on the internet, is dated earlier than 2000, yet such a salacious remark surely would have seen the light of day long before that! Also seen worded beginning with: "Physics is….” If you know any instance of this quote published before 2000, please contact Webmaster.
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Science only means knowledge; and for [Greek] ancients it did only mean knowledge. Thus the favorite science of the Greeks was Astronomy, because it was as abstract as Algebra. ... We may say that the great Greek ideal was to have no use for useful things. The Slave was he who learned useful things; the Freeman was he who learned useless things. This still remains the ideal of many noble men of science, in the sense they do desire truth as the great Greeks desired it; and their attitude is an external protest against vulgarity of utilitarianism.
'About Beliefs', in As I was Saying: A Book of Essays (1936), 65-66. Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 318.
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Scientific knowledge is the most reliable and useful knowledge that human beings possess.
Anonymous
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Several of my young acquaintances are in their graves who gave promise of making happy and useful citizens and there is no question whatever that cigarettes alone were the cause of their destruction. No boy living would commence the use of cigarettes if he knew what a useless, soulless, worthless thing they would make of him.
Quoted in Henry Ford, The Case Against the Little White Slaver (1914), Vol. 1, 20.
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Signs and symptoms indicate the present, past and future states of the three states of the body (health, illness, neutrality). According to Galen, knowledge of the present state is of advantage only to the patient as it helps him to follow the proper course of management. Knowledge of the past state is useful only to the physician inasmuch as its disclosure by him to the patient brings him a greater respect for his professional advice. Knowledge of the future state is useful to both. It gives an opportunity to the patient to be forewarned to adopt necessary preventative measures and it enhances the reputation of the physician by correctly forecasting the future developments.
Avicenna
'The Signs and Symptoms (Diagnosis): General Remarks,' in The Canon of Medicine, adapted by L. Bakhtiar (1999), 259.
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Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.
Particle Physics and an Introduction to Field Theory (1981), 177.
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Skepticism is a useful tool of the inquisitive mind, but it is scarcely a method of investigation.
(1928). As quoted, without source, in James P. Vanyo, 'The Legal System: Can it be Analyzed to Suit the Scientist?', Jurimetric Journal (Winter 1973), 14, No. 2, 106.
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Sometimes a hunch, right or wrong, is sufficient theory to lead to a useful observation.
In On the Management of Statistical Techniques for Quality and Productivity (1981), 86.
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Speaking one day to Monsieur de Buffon, on the present ardor of chemical inquiry, he affected to consider chemistry but as cookery, and to place the toils of the laboratory on the footing with those of the kitchen. I think it, on the contrary, among the most useful of sciences, and big with future discoveries for the utility and safety of the human race.
Letter to Rev. James Madison (Paris, 19 Jul 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 431.
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Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations.
In Probability, Statistics, and Truth (1939), 1. In the 1957 edition, this was rewritten as, “Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and “truth-full” and quite as practically useful as those obtained in any other exact science.”
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Stem cells are probably going to be extremely useful. But it isn’t a given, and even if it were, I don’t think the end justifies the means. I am not against stem cells, I think it’s great. Blanket objection is not very reasonable to me—any effort to control scientific advances is doomed to fail. You cannot stop the human mind from working.
From Cornelia Dean, 'A Conversation with Joseph E. Murray', New York Times (25 Sep 2001), F5.
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Such explosives [atomic bombs] in men’s hands, while their moral and intellectual status is declining, is about as useful as giving out firearms to all inmates of a gaol and then saying that you hope ‘this will ensure peace’.
From Letter (No. 102) to Christopher Tolkien (9 Aug 1945). In Humphrey Carpenter (ed.) assisted by Christopher Tolkien, The Letters of J.R.R. Tolkien (1995, 2014), 116, Letter No. 102.
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Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
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That form of popular science which merely recites the results of investigations, which merely communicates useful knowledge, is from this standpoint bad science, or no science at all. … Apply this test to every work professing to give a popular account of any branch of science. If any such work gives a description of phenomena that appeals to his imagination rather than to his reason, then it is bad science.
From The Grammar of Science (1892), 12.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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That scientific work should be more useful the more it has been used, while mechanical work is expended in use, may seem strange to us.
From 'The Economy of Science' in The Science of Mechanics: A Critical and Historical Exposition of its Principles (1893), 488.
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The advancement of agriculture, commerce and manufactures, by all proper means, will not, I trust, need recommendation. But I cannot forbear intimating to you the expediency of giving effectual encouragement as well to the introduction of new and useful inventions from abroad, as to the exertions of skill and genius in producing them at home.
Early suggestion for awarding patent protection. In First Annual Message to Congress on the State of the Union (8 Jan 1790).
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The anatomist presents to the eye the most hideous and disagreeable objects, but his science is useful to the painter in delineating even a Venus or a Helen.
Inquiry Concerning the Human Understanding collected in The Philosophical Works of David Hume (1826), Vol. 4, 8.
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The beginning of civilisation is the discovery of some useful arts, by which men acquire property, comforts, or luxuries. The necessity or desire of preserving them leads to laws and social institutions. The discovery of peculiar arts gives superiority to particular nations ... to subjugate other nations, who learn their arts, and ultimately adopt their manners;— so that in reality the origin as well as the progress and improvement of civil society is founded in mechanical and chemical inventions.
Consolations In Travel; or, the Last Days of a Philosopher (1830), 228.
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The Congress shall have power to ... promote the progress of science and useful arts, by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries.
Founding U.S. Patents.
Constitution of the United States, Art. 1, Sec.8, Par. 8. In George Sewall Boutwell, The Constitution of the United States at the End of the First Century (1895), 219.
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The earliest of my childhood recollections is being taken by my grandfather when he set out in the first warm days of early spring with a grubbing hoe (we called it a mattock) on his shoulder to seek the plants, the barks and roots from which the spring medicine for the household was prepared. If I could but remember all that went into that mysterious decoction and the exact method of preparation, and with judicious advertisement put the product upon the market, I would shortly be possessed of wealth which might be made to serve the useful purpose of increasing the salaries of all pathologists. … But, alas! I remember only that the basic ingredients were dogwood bark and sassafras root, and to these were added q.s. bloodroot, poke and yellow dock. That the medicine benefited my grandfather I have every reason to believe, for he was a hale, strong old man, firm in body and mind until the infection came against which even spring medicine was of no avail. That the medicine did me good I well know, for I can see before me even now the green on the south hillside of the old pasture, the sunlight in the strip of wood where the dogwood grew, the bright blossoms and the delicate pale green of the leaf of the sanguinaria, and the even lighter green of the tender buds of the sassafras in the hedgerow, and it is good to have such pictures deeply engraved in the memory.
From address, 'A Medical Retrospect'. Published in Yale Medical Journal (Oct 1910), 17, No. 2, 57. [Note: q.s. in an abbreviation for quantum sufficit meaning “as much as is sufficient,” when used as a quantity specification in medicine and pharmacology. -Webmaster]
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The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.
In 'Education as a Political Institution', Atlantic Monthly, (Jun 1916), 117 755. Also in Principles of Social Reconstruction (1916, 2013), 113.
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The fear of meeting the opposition of envy, or the illiberality of ignorance is, no doubt, the frequent cause of preventing many ingenious men from ushering opinions into the world which deviate from common practice. Hence for want of energy, the young idea is shackled with timidity and a useful thought is buried in the impenetrable gloom of eternal oblivion.
A Treatise on the Improvement of Canal Navigation (1796), preface, ix.
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The first steps in Agriculture, Astronomy, Zoology, (those first steps which the farmer, the hunter, and the sailor take,) teach that nature's dice are always loaded; that in her heaps and rubbish are concealed sure and useful results.
In Nature (1849), 36.
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The game of Chess is not merely an idle amusement. Several very valuable qualities of the mind, useful in the course of human life, are to be acquired or strengthened by it so as to become habits ready on all occasions.
In The Morals of Chess. As quoted in The Gentleman's Magazine, and Historical Chronicle (1787), 590.
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The game of status seeking, organized around committees, is played in roughly the same fashion in Africa and in America and in the Soviet Union. Perhaps the aptitude for this game is a part of our genetic inheritance, like the aptitude for speech and for music. The game has had profound consequences for science. In science, as in the quest for a village water supply, big projects bring enhanced status; small projects do not. In the competition for status, big projects usually win, whether or not they are scientifically justified. As the committees of academic professionals compete for power and influence, big science becomes more and more preponderant over small science. The large and fashionable squeezes out the small and unfashionable. The space shuttle squeezes out the modest and scientifically more useful expendable launcher. The Great Observatory squeezes out the Explorer. The centralized adduction system squeezes out the village well. Fortunately, the American academic system is pluralistic and chaotic enough that first-rate small science can still be done in spite of the committees. In odd corners, in out-of the-way universities, and in obscure industrial laboratories, our Fulanis are still at work.
From a Danz lecture at University of Washington, 'Six Cautionary Tales for Scientists' (1988), collected in From Eros to Gaia (1992), Vol. 5, 19.
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The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
In 'Review of “Théorie Analytique des Probabilites” par M. le Marquis de Laplace, 3eme edition. Paris. 1820', Dublin Review (1837), 2, 348.
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The genotypic constitution of a gamete or a zygote may be parallelized with a complicated chemico-physical structure. This reacts exclusively in consequence of its realized state, but not in consequence of the history of its creation. So it may be with the genotypical constitution of gametes and zygotes: its history is without influence upon its reactions, which are determined exclusively by its actual nature. The genotype-conception is thus an 'ahistoric' view of the reactions of living beings—of course only as far as true heredity is concerned. This view is an analog to the chemical view, as already pointed out; chemical compounds have no compromising ante-act, H2O is always H2O, and reacts always in the same manner, whatsoever may be the 'history' of its formation or the earlier states of its elements. I suggest that it is useful to emphasize this 'radical' ahistoric genotype-conception of heredity in its strict antagonism to the transmission—or phenotype-view.
'The Genotype Conception of Heredity', The American Naturalist (1911), 45, 129.
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The greatest service which can be rendered any country is to add an useful plant to its culture; especially, a bread grain; next in value to bread is oil.
In Memoir, Correspondence, and Miscellanies from the Papers of T. Jefferson (1829), Vol. 1, 144.
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The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.
Philosophy of the Inductive Sciences (1847), Vol. 2, 62-63.
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The inspired and expired air may be sometimes very useful, by condensing and cooling the blood that passeth through the lungs; I hold that the depuration of the blood in that passage, is not only one of the ordinary, but one of the principal uses of respiration.
New Experiments ... Touching the Spring of Air. In Works, Vol 1, 113. Quoted in Barbara Kaplan (ed.), Divulging of Useful Truths in Physick: The Medical Agenda of Robert Boyle (1993), 85.
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The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.
In 'Calculus of Functions', Encyclopaedia of Pure Mathematics (1847), Addition to Article 26, 388.
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The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
From 'Electrical Units of Measurement', a lecture delivered at the Institution of Civil Engineers, London (3 May 1883), Popular Lectures and Addresses Vol. 1 (1891), 86-87.
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The more experiences and experiments accumulate in the exploration of nature, the more precarious the theories become. But it is not always good to discard them immediately on this account. For every hypothesis which once was sound was useful for thinking of previous phenomena in the proper interrelations and for keeping them in context. We ought to set down contradictory experiences separately, until enough have accumulated to make building a new structure worthwhile.
Lichtenberg: Aphorisms & Letters (1969), 61.
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The most humble research scientist in the Department of Agriculture is at this time contributing more to this country than the most useful member of Congress.
Speaking (29 Dec 1932) as a member of the 72nd Congress, early in the Great Depression, in opposition to curtailing the agricultural appropriation. As quoted in 'Mayor-Elect La Guardia on Research', Science (1933), New Series, 78, No. 2031, 511. Also in A. Hunter Dupree, under subtitle 'Impact of the Great Depression' in Science in the Federal Government: A History of Policies and Activities to 1940, 344.
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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 old fashioned family physician and general practitioner ... was a splendid figure and useful person in his day; but he was badly trained, he was often ignorant, he made many mistakes, for one cannot by force of character and geniality of person make a diagnosis of appendicitis, or recognize streptococcus infection.
New York Medical Journal (1913), 97, 1.
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The origin of an adaptive structure and the purposes it comes to fulfill are only chance combinations. Purposefulness is a very human conception for usefulness. It is usefulness looked at backwards. Hard as it is to imagine, inconceivably hard it may appear to many, that there is no direct relation between the origin of useful variations and the ends they come to serve, yet the modern zoologist takes his stand as a man of science on this ground. He may admit in secret to his father confessor, the metaphysician, that his poor intellect staggers under such a supposition, but he bravely carries forward his work of investigation along the only lines that he has found fruitful.
'For Darwin', The Popular Science Monthly (1909), 74, 380.
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The powerful notion of entropy, which comes from a very special branch of physics … is certainly useful in the study of communication and quite helpful when applied in the theory of language.
From 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 67.
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The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
Disquisitiones Arithmeticae (1801), Article 329
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The process of natural selection has been summed up in the phrase “survival of the fittest.” This, however, tells only part of the story. “Survival of the existing” in many cases covers more of the truth. For in hosts of cases the survival of characters rests not on any special usefulness or fitness, but on the fact that individuals possessing these characters have inhabited or invaded a certain area. The principle of utility explains survivals among competing structures. It rarely accounts for qualities associated with geographic distribution.
The nature of animals which first colonize a district must determine what the future fauna will be. From their specific characters, which are neither useful nor harmful, will be derived for the most part the specific characters of their successors.
It is not essential to the meadow lark that he should have a black blotch on the breast or the outer tail-feather white. Yet all meadow larks have these characters just as all shore larks have the tiny plume behind the ear. Those characters of the parent stock, which may be harmful in the new relations, will be eliminated by natural selection. Those especially helpful will be intensified and modified, but the great body of characters, the marks by which we know the species, will be neither helpful nor hurtful. These will be meaningless streaks and spots, variations in size of parts, peculiar relations of scales or hair or feathers, little matters which can neither help nor hurt, but which have all the persistence heredity can give.
Foot-notes to Evolution. A Series of Popular Addresses on the Evolution of Life (1898), 218.
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The Religion that is afraid of science dishonours God and commits suicide. It acknowledges that it is not equal to the whole of truth, that it legislates, tyrannizes over a village of God's empires but is not the immutable universal law. Every influx of atheism, of skepticism is thus made useful as a mercury pill assaulting and removing a diseased religion and making way for truth.
(4 Mar 1831). In William H. Gilman (ed.) The Journals and Miscellaneous Notebooks of Ralph Waldo Emerson: Vol III, 1826-1832 (1963), 239.
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The results have exhibited one striking feature which has been frequently emphasized, namely that at high pressures all twelve liquids become more nearly like each other. This suggests that it might be useful in developing a theory of liquids to arbitrarily construct a 'perfect liquid' and to discuss its properties. Certainly the conception of a 'perfect gas' has been of great service in the kinetic theory of gases; and the reason is that all actual gases approximate closely to the 'perfect gas.' In the same way, at high pressures all liquids approximate to one and the same thing, which may be called by analogy the 'perfect liquid.' It seems to offer at least a promising line of attack to discuss the properties of this 'perfect liquid,' and then to invent the simplest possible mechanism to explain them.
'Thermodynamic Properties of Twelve Liquids Between 200 and 800 and up to 1200 KGM. Per Sq. Cm.', Memoirs of the American Academy of Arts and Sciences, 1913, 49, 113.
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The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equations, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply mathematics, you have to live the life of differential equations. When you live this life, you can then go back to molecular biology with a new set of eyes that will see things you could not otherwise see.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 213.
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The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
On the Doctrine of Chances, with Later Reflections (1878), 61-2.
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The scientist or engineer—like every other human being bears also the responsibility of being a useful member of his community... and should speak on issues which can be addressed with competence—including joining hands with other citizens
Quoted in Thomas Hager, Force of Nature: The Life of Linus Pauling (1995), 347.
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The seemingly useless or trivial observation made by one worker leads on to a useful observation by another: and so science advances, “creeping on from point to point.”
Lecture 6, collected in Light Visible and Invisible: A Series of Lectures Delivered at the Royal Institution of Great Britain, at Christmas, 1896 (1897), 276.
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The sense for style … is an aesthetic sense, based on admiration for the direct attainment of a foreseen end, simply and without waste. Style in art, style in literature, style in science, style in logic, style in practical execution have fundamentally the same aesthetic qualities, namely, attainment and restraint. The love of a subject in itself and for itself, where it is not the sleepy pleasure of pacing a mental quarter-deck, is the love of style as manifested in that study. Here we are brought back to the position from which we started, the utility of education. Style, in its finest sense, is the last acquirement of the educated mind; it is also the most useful. It pervades the whole being. The administrator with a sense for style hates waste; the engineer with a sense for style economises his material; the artisan with a sense for style prefers good work. Style is the ultimate morality of the mind.
In 'The Aims of Education', The Aims of Education and Other Essays (1929), 23.
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The strangest thing of all is that our ulama these days have divided science into two parts. One they call Muslim science, and one European science. Because of this they forbid others to teach some of the useful sciences. They have not understood that science is that noble thing that has no connection with any nation, and is not distinguished by anything but itself. Rather, everything that is known is known by science, and every nation that becomes renowned becomes renowned through science. Men must be related to science, not science to men. How very strange it is that the Muslims study those sciences that are ascribed to Aristotle with the greatest delight, as if Aristotle were one of the pillars of the Muslims. However, if the discussion relates to Galileo, Newton, and Kepler, they consider them infidels. The father and mother of science is proof, and proof is neither Aristotle nor Galileo. The truth is where there is proof, and those who forbid science and knowledge in the belief that they are safeguarding the Islamic religion are really the enemies of that religion. Lecture on Teaching and Learning (1882).
In Nikki R. Keddie, An Islamic Response to Imperialism (1983), 107.
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The theory of medicine, therefore, presents what is useful in thought, but does not indicate how it is to be applied in practice—the mode of operation of these principles. The theory, when mastered, gives us a certain kind of knowledge. Thus we say, for example, there are three forms of fevers and nine constitutions. The practice of medicine is not the work which the physician carries out, but is that branch of medical knowledge which, when acquired, enables one to form an opinion upon which to base the proper plan of treatment.
Avicenna
'The Definition of Medicine', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 10.
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The true order of learning should be first, what is necessary; second, what is useful, and third, what is ornamental. To reverse this arrangement is like beginning to build at the top of the edifice.
Tryon Edwards and William Buell Sprague, The World’s Laconics: or, The Best Thoughts of the Best Authors (1853), 153.
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The vulgar opinion, then, which, on health reasons, condemns vegetable food and so much praises animal food, being so ill-founded, I have always thought it well to oppose myself to it, moved both by experience and by that refined knowledge of natural things which some study and conversation with great men have given me. And perceiving now that such my constancy has been honoured by some learned and wise physicians with their authoritative adhesion (della autorevole sequela), I have thought it my duty publicly to diffuse the reasons of the Pythagorean diet, regarded as useful in medicine, and, at the same time, as full of innocence, of temperance, and of health. And it is none the less accompanied with a certain delicate pleasure, and also with a refined and splendid luxury (non è privo nemmeno d’una certa delicate voluttà e d’un lusso gentile e splendido ancora), if care and skill be applied in selection and proper supply of the best vegetable food, to which the fertility and the natural character of our beautiful country seem to invite us. For my part I have been so much the more induced to take up this subject, because I have persuaded myself that I might be of service to intending diet-reformers, there not being, to my knowledge, any book of which this is the sole subject, and which undertakes exactly to explain the origin and the reasons of it.
From Dell Vitto Pitagorico (1743), (The Pythagorean Diet: for the Use of the Medical Faculty), as translated quotes in Howard Williams, The Ethics of Diet: A Catena of Authorities Deprecatory of the Practice of Flesh-Eating (1883), 158.
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The way of pure research is opposed to all the copy-book maxims concerning the virtues of industry and a fixed purpose, and the evils of guessing, but it is damned useful when it comes off. It is the diametrical opposite of Edison’s reputed method of trying every conceivable expedient until he hit the right one. It requires, not diligence, but experience, information, and a good nose for the essence of a problem.
Letter to Paul de Kruif (3 Aug 1933), as quoted in Nathan Reingold, Science in America: A Documentary History 1900-1939 (1981), 409.
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The wise man, however, will avoid partial views of things. He will not, with the miser, look to gold and silver as the only blessings of life; nor will he, with the cynic, snarl at mankind for preferring them to copper and iron. … That which is convenient is that which is useful, and that which is useful is that which is valuable.
From 13th Lecture in 1818, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 255.
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The work of Planck and Einstein proved that light behaved as particles in some ways and that the ether therefore was not needed for light to travel through a vacuum. When this was done, the ether was no longer useful and it was dropped with a glad cry. The ether has never been required since. It does not exist now; in fact, it never existed.
In Asimov on Physics (1976), 85. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 212.
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There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.
In 'The Unplanned Impact of Mathematics', Nature (14 Jul 2011), 475, No. 7355, 167.
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This is the geologist—this works with the scalpel—and this is a mathematician.
, Gentlemen! to you the first honors always:
Your facts are useful and real—and yet they are not my dwelling;
(I but enter by them to an area of my dwelling.)
In Leaves of Grass (1867), 49.
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This preservation of favourable variations and the destruction of injurious variations, I call Natural Selection, or the Survival of the Fittest. Variations neither useful nor injurious would not be affected by natural selection and would be left a fluctuating element.
From Origin of Species (fifth edition, 1869), 81. The phrase “survival of the fittest” was not added until the fifth edition (1869), and is absent from earlier editions. Also in the fifth edition, the word “destruction” replaced “rejection” used in the earlier editions (1859, 1860, 1861, 1866) to the fourth edition.
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This preservation of favourable variations and the rejection of injurious variations, I call Natural Selection. Variations neither useful nor injurious would not be affected by natural selection and would be left a fluctuating element.
From Origin of Species (first edition, 1859), 81. The phrase “survival of the fittest” was not added until the fifth edition (1869), when also “rejection” was replaced with “destruction.”
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Those who are fruitful in useful inventions and discoveries, in the practical mechanical arts, are men, not only of the greatest utility, but possess an understanding, which should be most highly estimated.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 143.
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Those who eat most, and who take the most exercise, are not in better health than they who eat just as much as is good for them; and in the same way it is not those who know a great many things, but they who know what is useful who are valuable men.
In Diogenes Laertius, translated by Charles Duke Yonge, 'Life of Aristippus', The Lives and Opinions of Eminent Philosophers (1853), 83.
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Though we must not without further consideration condemn a body of reasoning merely because it is easy, nevertheless we must not allow ourselves to be lured on merely by easiness; and we should take care that every problem which we choose for attack, whether it be easy or difficult, shall have a useful purpose, that it shall contribute in some measure to the up-building of the great edifice.
From 'On Some Recent Tendencies in Geometric Investigation', Rivista di Matematica (1891), 63. In Bulletin American Mathematical Society (1904), 465.
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To learn… the ordinary arrangement of the different strata of minerals in the earth, to know from their habitual colocations and proximities, where we find one mineral; whether another, for which we are seeking, may be expected to be in its neighborhood, is useful.
In The Writings of Thomas Jefferson (1854), Vol. 7, 443.
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To prove to an indignant questioner on the spur of the moment that the work I do was useful seemed a thankless task and I gave it up. I turned to him with a smile and finished, 'To tell you the truth we don't do it because it is useful but because it's amusing.' The answer was thought of and given in a moment: it came from deep down in my soul, and the results were as admirable from my point of view as unexpected. My audience was clearly on my side. Prolonged and hearty applause greeted my confession. My questioner retired shaking his head over my wickedness and the newspapers next day, with obvious approval, came out with headlines 'Scientist Does It Because It's Amusing!' And if that is not the best reason why a scientist should do his work, I want to know what is. Would it be any good to ask a mother what practical use her baby is? That, as I say, was the first evening I ever spent in the United States and from that moment I felt at home. I realised that all talk about science purely for its practical and wealth-producing results is as idle in this country as in England. Practical results will follow right enough. No real knowledge is sterile. The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously 'useless' equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand. With this faith in the ultimate usefulness of all real knowledge a man may proceed to devote himself to a study of first causes without apology, and without hope of immediate return.
A.V. Hill
Quoted in Larry R. Squire (ed.), The History of Neuroscience in Autobiography (1996), Vol. I, 351.
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To some men knowledge of the universe has been an end possessing in itself a value that is absolute: to others it has seemed a means of useful applications.
In The Structure of Physical Chemistry (1951, 2005), 2.
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To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree. When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei, as every philosopher knows, cannot be trusted in science. Reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real.
On The Origin of Species by Means of Natural Selection (1859, 1882), 143-144.
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To the manufacturer, chemistry has lately become fruitful of instruction and assistance. In the arts of brewing, tanning, dying, and bleaching, its doctrines are important guides. In making soap, glass, pottery, and all metallic wares, its principles are daily applied, and are capable of a still more useful application, as they become better understood.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 9.
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To what purpose should People become fond of the Mathematicks and Natural Philosophy? … People very readily call Useless what they do not understand. It is a sort of Revenge… One would think at first that if the Mathematicks were to be confin’d to what is useful in them, they ought only to be improv'd in those things which have an immediate and sensible Affinity with Arts, and the rest ought to be neglected as a Vain Theory. But this would be a very wrong Notion. As for Instance, the Art of Navigation hath a necessary Connection with Astronomy, and Astronomy can never be too much improv'd for the Benefit of Navigation. Astronomy cannot be without Optics by reason of Perspective Glasses: and both, as all parts of the Mathematicks are grounded upon Geometry … .
Of the Usefulness of Mathematical Learning (1699)
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True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 32.
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Two forms or species are sympatric, if they occur together, that is if their areas of distribution overlap or coincide. Two forms (or species) are allapatric, if they do not occur together, that is if they exclude each other geographically. The term allopatric is primarily useful in denoting geographic representatives.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 148-9.
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Upon the whole, Chymistry is as yet but an opening science, closely connected with the usefull and ornamental arts, and worthy the attention of the liberal mind. And it must always become more and more so: for though it is only of late, that it has been looked upon in that light, the great progress already made in Chymical knowledge, gives us a pleasant prospect of rich additions to it. The Science is now studied on solid and rational grounds. While our knowledge is imperfect, it is apt to run into error: but Experiment is the thread that will lead us out of the labyrinth.
In Alexander Law, Notes of Black's Lectures, vol. 3, 88. Cited in Charles Coulston Gillispie, Dictionary of Scientific Biography: Volumes 1-2 (1981), 181.
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We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
'Concluding Remarks', Proceedings of the Royal Society of London, Series A, A Discussion of New Materials, 1964, 282, 152-3.
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We are a spectacular, splendid manifestation of life. We have language… We have affection. We have genes for usefulness, and usefulness is about as close to a “common goal” for all of nature as I can guess at.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 16-17.
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We cannot get more out of the mathematical mill than we put into it, though we may get it in a form infinitely more useful for our purpose.
From James Forrest Lecture (3 May 1894) at an Extra Meeting of the Institution of Civil Engineers, 'The Relation of Mathematics to Engineering', collected in Minutes of Proceedings of the Institution of Civil Engineers (1894), 346.
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We cannot hope to build a better world without improving the individual. Toward this end, each of us must work for his own highest development, accepting at the same time his share of responsibility in the general life of humanity—our particular duty being to aid those to whom we think we can be most useful.
Quoted in Eve Curie Labouisse and Eve Curie, trans. by Vincent Sheean, Madame Curie (1937), 53.
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We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens ... The diversity of the phenomena of Nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.
From Mysterium Cosmographicum. Quote as translated in Carl Sagan, Cosmos (1980, 1985), 32.
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We have no organ at all for knowledge, for ‘truth’: we ‘know’ (or believe or imagine) precisely as much as may be useful in the interest of the human herd, the species: and even what is here called ‘usefulness’ is in the end only a belief, something imagined and perhaps precisely that most fatal piece of stupidity by which we shall one day perish.
Sämtliche Werke: Kritische Studienausgabe, vol. 3, p. 593, eds. Giorgio Colli and Mazzino Montinari, Berlin, de Gruyter (1980). The Gay Science, second edition, 'Fifth Book: We Fearless Ones,' section 354 (1887).
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We have reason not to be afraid of the machine, for there is always constructive change, the enemy of machines, making them change to fit new conditions.
We suffer not from overproduction but from undercirculation. You have heard of technocracy. I wish I had those fellows for my competitors. I'd like to take the automobile it is said they predicted could be made now that would last fifty years. Even if never used, this automobile would not be worth anything except to a junkman in ten years, because of the changes in men's tastes and ideas. This desire for change is an inherent quality in human nature, so that the present generation must not try to crystallize the needs of the future ones.
We have been measuring too much in terms of the dollar. What we should do is think in terms of useful materials—things that will be of value to us in our daily life.
In 'Quotation Marks: Against Technocracy', New York Times (1 Han 1933), E4.
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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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Well, there’s no doubt about the fact that, that higher energy prices lead to greater conservation, greater energy efficiency, and they also, of course, play a useful role on the supply side.
John Snow
…...
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Well-established theories collapse under the weight of new facts and observations which cannot be explained, and then accumulate to the point where the once useful theory is clearly obsolete.
[Using Thomas S. Kuhn's theories to frame his argument about the relationship beween science and technology: as new facts continue to accumulate, a new, more accurate paradigm must replace the old one.]
Al Gore
Commencement address at M.I.T. (7 Jun 1996). In obituary, 'Thomas S. Kuhn', The Tech (26 Jun 1996), 9.
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Were I disposed to consider the comparative merit of each of them [facts or theories in medical practice], I should derive most of the evils of medicine from supposed facts, and ascribe all the remedies which have been uniformly and extensively useful, to such theories as are true. Facts are combined and rendered useful only by means of theories, and the more disposed men are to reason, the more minute and extensive they become in their observations.
Quoted in John Edmonds Stock, Memoirs of the life of Thomas Beddoes (1810), 401.
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What Art was to the ancient world, Science is to the modern: the distinctive faculty. In the minds of men the useful has succeeded to the beautiful. Instead of the city of the Violet Crown, a Lancashire village has expanded into a mighty region of factories and warehouses. Yet, rightly understood, Manchester is as great a human exploit; as Athens.
In Coningsby: Or The New Generation (1844), Vol. 2, Book 4, Ch.1, 2.
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What Art was to the ancient world, Science is to the modern: the distinctive faculty. In the minds of men the useful has succeeded to the beautiful. … There are great truths to tell, if we had either the courage to announce them or the temper to receive them.
In Coningsby: or the New Generation (1844), Vol. 2, Book 4, Chap. 1, 2.
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What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics?
In 'On the Usefulness of Mathematics', Works (1840), Vol. 2, 69.
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What, in fact, is mathematical discovery? It does not consist in making new combinations with mathematical entities that are already known. That can be done by anyone, and the combinations that could be so formed would be infinite in number, and the greater part of them would be absolutely devoid of interest. Discovery consists precisely in not constructing useless combinations, but in constructing those that are useful, which are an infinitely small minority. Discovery is discernment, selection.
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 50-51. Also seen elsewhere translated with “invention” in place of “discovery”.
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What, then, is it in particular that can be learned from teachers of special distinction? Above all, what they teach is high standards. We measure everything, including ourselves, by comparisons; and in the absence of someone with outstanding ability there is a risk that we easily come to believe that we are excellent and much better than the next man. Mediocre people may appear big to themselves (and to others) if they are surrounded by small circumstances. By the same token, big people feel dwarfed in the company of giants, and this is a most useful feeling. So what the giants of science teach us is to see ourselves modestly and not to overrate ourselves.
Reminiscences and Reflections (1981), 175.
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Whatever be the detail with which you cram your student, the chance of his meeting in after life exactly that detail is almost infinitesimal; and if he does meet it, he will probably have forgotten what you taught him about it. The really useful training yields a comprehension of a few general principles with a thorough grounding in the way they apply to a variety of concrete details. In subsequent practice the men will have forgotten your particular details; but they will remember by an unconscious common sense how to apply principles to immediate circumstances. Your learning is useless to you till you have lost your textbooks, burnt your lecture notes, and forgotten the minutiae which you learned by heart for the examination. What, in the way of detail, you continually require will stick in your memory as obvious facts like the sun and the moon; and what you casually require can be looked up in any work of reference. The function of a University is to enable you to shed details in favor of principles. When I speak of principles I am hardly even thinking of verbal formulations. A principle which has thoroughly soaked into you is rather a mental habit than a formal statement. It becomes the way the mind reacts to the appropriate stimulus in the form of illustrative circumstances. Nobody goes about with his knowledge clearly and consciously before him. Mental cultivation is nothing else than the satisfactory way in which the mind will function when it is poked up into activity.
In 'The Rhythm of Education', The Aims of Education: & Other Essays (1917), 41.
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When we no longer look at an organic being as a savage looks at a ship, as something wholly beyond his comprehension; when we regard every production of nature as one which has had a long history; when we contemplate every complex structure and instinct as the summing up of many contrivances, each useful to the possessor, in the same way as any great mechanical invention is the summing up of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, does the study of natural history become!
From the Conclusion of Origin of Species by Means of Natural Selection, Or the Preservation of Favoured Races in the Struggle for Life (3rd. ed., 1861), 521.
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When you are identifying science of the motion of water, remember to include under each subject its application and use, so that the science will be useful.
…...
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Whenever a man can get hold of numbers, they are invaluable: if correct, they assist in informing his own mind, but they are still more useful in deluding the minds of others. Numbers are the masters of the weak, but the slaves of the strong.
Passages From the Life of a Philosopher (1864), 410.
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While Occam’s razor is a useful tool in the physical sciences, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 138.
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William Blake called division the sin of man; Faraday was a great man because he was utterly undivided. His whole, very harmonious, very well balanced, … and used the brain in the limited way in which it is useful…. [H]e built up his few but precious speculations. Their simplicity rivals with their forcefulness.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 7.
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You have heard of the new chemical nomenclature endeavored to be introduced by Lavoisier, Fourcroy, &c. Other chemists of this country, of equal note, reject it, and prove in my opinion that it is premature, insufficient and false. These latter are joined by the British chemists; and upon the whole, I think the new nomenclature will be rejected, after doing more harm than good. There are some good publications in it, which must be translated into the ordinary chemical language before they will be useful.
Letter to Dr. Currie (Paris, 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 544.
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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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You, in this country [the USA], are subjected to the British insularity in weights and measures; you use the foot, inch and yard. I am obliged to use that system, but must apologize to you for doing so, because it is so inconvenient, and I hope Americans will do everything in their power to introduce the French metrical system. ... I look upon our English system as a wickedly, brain-destroying system of bondage under which we suffer. The reason why we continue to use it, is the imaginary difficulty of making a change, and nothing else; but I do not think in America that any such difficulty should stand in the way of adopting so splendidly useful a reform.
Journal of the Franklin Institute, Nov 1884, 118, 321-341
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