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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index S > Category: Substitution

Substitution Quotes (13 quotes)

Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. It appears that it must some day serve as a universal motor, and be substituted for animal power, waterfalls, and air currents.
'Réflexions sur la puissance motrice du feu' (1824) translated by R.H. Thurston in Reflections on the Motive Power of Fire, and on Machines Fitted to Develop that Power (1890), 38.
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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I have always considered that the substitution of the internal combustion engine for the horse marked a very gloomy milestone in the progress of mankind.
Speaking in the House of Commons (24 Jun 1952), as cited in Jack House (ed.), Winston Churchill, His Wit and Wisdom: Selections from His (1965), 115.
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I have considered the two terms you want to substitute for eisode and exode, and upon the whole I am disposed to recommend instead of them anode and cathode. These words may signify eastern and western way, just as well as the longer compounds which you mention … I may mention too that anodos and cathodos are good, genuine Greek words, and not compounds coined for the purpose.
Letter to Michael Faraday (25 Apr 1834). Quoted in I. Todhunter (ed.), William Whewell: An Account of His Writings with Selections From His Literary and Scientific Correspondence (1876), Vol. 2, 179.
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I was an impostor, the worthy associate of a brigand, &c., &c., and all this for an atom of chlorine put in the place of an atom of hydrogen, for the simple correction of a chemical formula!
Chemical Method (1855), 203.
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In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group, invariant, differential invariant and differential parameter, appear more and more clearly as the most important conceptions of mathematics.
In Lapziger Berichte, No. 47 (1896), 261.
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Kepler’s suggestion of gravitation with the inverse distance, and Bouillaud’s proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I have discovered two anagrams on his name, which are quite conclusive: the notion of gravitation was not new; but Newton went on.
In Budget of Paradoxes (1872), 82.
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Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.
In A Scrap-book of Elementary Mathematics (1908), 215.
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Science is now the craft of the manipulation, substitution and deflection of the forces of nature. What I see coming is a gigantic slaughterhouse, an Auschwitz, in which valuable enzymes, hormones, and so on will be extracted instead of gold teeth.
In Columbia Forum (Summer 1969). As quoted and cited in Rob Kaplan, Science Says (2000), 58.
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The law of conservation rigidly excludes both creation and annihilation. Waves may change to ripples, and ripples to waves,—magnitude may be substituted for number, and number for magnitude,—asteroids may aggregate to suns, suns may resolve themselves into florae and faunae, and florae and faunae melt in air,—the flux of power is eternally the same. It rolls in music through the ages, and all terrestrial energy,—the manifestations of life, as well as the display of phenomena, are but the modulations of its rhythm.
Conclusion to lecture 12 (10 Apr 1862) at the Royal Institution, collected in Heat Considered as a Mode of Motion: Being a Course of Twelve Lectures (1863), 449.
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The mathematics of the twenty-first century may be very different from our own; perhaps the schoolboy will begin algebra with the theory of substitution groups, as he might now but for inherited habits.
From Address before the New York Mathematical Society, Bulletin of the New York Mathematical Society (1893), 3, 107. As cited in G.A. Miller, 'Appreciative Remarks on the Theory of Groups', The American Mathematical Monthly (1903), 10, No. 4, 89. https://books.google.com/books?id=hkM0AQAAMAAJ 1903
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The Post Office Committee of the House has referred to a sub-committee all the bills authorizing the building or buying of telegraph lines for the purpose of establishing a postal telegraph—that is, of sending mails by electricity … All is done by contract … with the carriage of mails by steam power [railroads] … It does not appear why there should be any difference of principle because of the substitution of electricity for steam.
[Foreshadowing email.]
In 'Mails by Electricity', New York Times (26 Apr 1884), 4. A previous proposal for U.S. Government ownership of a test postal telegraph received an adverse Report of the House Post Office Committee, reported in 'Postal Telegraph', New York Times (25 Feb 1869).
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Who does not know Maxwell’s dynamic theory of gases? At first there is the majestic development of the variations of velocities, then enter from one side the equations of condition and from the other the equations of central motions, higher and higher surges the chaos of formulas, suddenly four words burst forth: “Put n = 5.” The evil demon V disappears like the sudden ceasing of the basso parts in music, which hitherto wildly permeated the piece; what before seemed beyond control is now ordered as by magic. There is no time to state why this or that substitution was made, he who cannot feel the reason may as well lay the book aside; Maxwell is no program-musician who explains the notes of his composition. Forthwith the formulas yield obediently result after result, until the temperature-equilibrium of a heavy gas is reached as a surprising final climax and the curtain drops.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 29-30, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 187. From the original German, “Wer kennt nicht seine dynamische Gastheorie? – Zuerst entwickeln sich majestätisch die Variationen der Geschwindigkeiten, dann setzen von der einen Seite die Zustands-Gleichungen, von der anderen die Gleichungen der Centralbewegung ein, immer höher wogt das Chaos der Formeln; plötzlich ertönen die vier Worte: „Put n=5.“Der böse Dämon V verschwindet, wie in der Musik eine wilde, bisher alles unterwühlende Figur der Bässe plötzlich verstummt; wie mit einem Zauberschlage ordnet sich, was früher unbezwingbar schien. Da ist keine Zeit zu sagen, warum diese oder jene Substitution gemacht wird; wer das nicht fühlt, lege das Buch weg; Maxwell ist kein Programmmusiker, der über die Noten deren Erklärung setzen muss. Gefügig speien nun die Formeln Resultat auf Resultat aus, bis überraschend als Schlusseffect noch das Wärme-Gleichgewicht eines schweren Gases gewonnen wird und der Vorhang sinkt.” A condensed alternate translation also appears on the Ludwig Boltzmann Quotes page of this website.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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