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Who said: “Nature does nothing in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.”
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Decimal Quotes (20 quotes)

As plants convert the minerals into food for animals, so each man converts some raw material in nature to human use. The inventors of fire, electricity, magnetism, iron, lead, glass, linen, silk, cotton; the makers of tools; the inventor of decimal notation, the geometer, the engineer, the musician, severally make an easy way for all, through unknown and impossible confusions.
In 'Uses of Great Men', Representative Men (1850), 5-6.
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Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
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Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent (with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
In Men of Mathematics (1937), 256.
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I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours I found it quite enthralling.
In Agatha Christie: An Autobiography (1977), 89.
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I never could make out what those damned dots meant.
Referring to decimal points. “But this was surely only to tease.” Quoted in W.S. Churchill, Lord Randolph Churchill (1906), Vol. 2, 184.
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In 1905, a physicist measuring the thermal conductivity of copper would have faced, unknowingly, a very small systematic error due to the heating of his equipment and sample by the absorption of cosmic rays, then unknown to physics. In early 1946, an opinion poller, studying Japanese opinion as to who won the war, would have faced a very small systematic error due to the neglect of the 17 Japanese holdouts, who were discovered later north of Saipan. These cases are entirely parallel. Social, biological and physical scientists all need to remember that they have the same problems, the main difference being the decimal place in which they appear.
In William G. Cochran, Frederick Mosteller and John W. Tukey, 'Principles of Sampling', Journal of the American Statistical Society, 1954, 49, 31. Collected in Selected Papers of Frederick Mosteller (2006), 290.
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In modern Europe, the Middle Ages were called the Dark Ages. Who dares to call them so now? … Their Dante and Alfred and Wickliffe and Abelard and Bacon; their Magna Charta, decimal numbers, mariner’s compass, gunpowder, glass, paper, and clocks; chemistry, algebra, astronomy; their Gothic architecture, their painting,—are the delight and tuition of ours. Six hundred years ago Roger Bacon explained the precession of the equinoxes, and the necessity of reform in the calendar; looking over how many horizons as far as into Liverpool and New York, he announced that machines can be constructed to drive ships more rapidly than a whole galley of rowers could do, nor would they need anything but a pilot to steer; carriages, to move with incredible speed, without aid of animals; and machines to fly into the air like birds.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
Science and Hypothesis (1902), trans. W. J. G. and preface by J. Larmor (1905), 181.
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William Cecil Dampier quote: It seemed as though the main framework had been put together once and for all
It seemed as though the main framework had been put together once and for all, and that little remained to be done but to measure physical constants to the increased accuracy represented by another decimal point.
A History of Science and Its Relations with Philosophy and Religion (1931), 882.
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Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The comparatively small progress toward universal acceptance made by the metric system seems to be due not altogether to aversion to a change of units, but also to a sort of irrepressible conflict between the decimal and binary systems of subdivision.
[Remarking in 1892 (!) that although decimal fractions were introduced about 1585, America retains measurements in halves, quarters, eights and sixteenths in various applications such as fractions of an inch, the compass or used by brokers.]
'Octonary Numeration', Bulletin of the New York Mathematical Society (1892),1, 1.
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The judicial mind is too commonly characterized by a regard for a fourth decimal as the equal of a whole number.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”
In Light Waves and Their Uses (1903), 23-4. Michelson had some years earlier referenced “an eminent physicist” that he did not name who had “remarked that the future truths of physical science are to be looked for in the sixth place of decimals,” near the end of his Convocation Address at the Dedication of the Ryerson Physical Laboratory at the University of Chicago, 'Some of the Objects and Methods of Physical Science' (4 Jul 1894), published in University of Chicago Quarterly Calendar (Aug 1894), 3, No.2, 15. Also
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The natural philosophers are mostly gone. We modern scientists are adding too many decimals.
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The whole history of physics proves that a new discovery is quite likely lurking at the next decimal place.
In 'The Romance of the Next Decimal Place', Science (1 Jan 1932), 75, No. 1931, 3.
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This characteristic of modern experiments–that they consist principally of measurements,–is so prominent, that the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry these measurements to another place of decimals … But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured.
Maxwell strongly disagreed with the prominent opinion, and was attacking it. Thus, he was saying he did not believe in such a future of merely making “measurements to another place of decimals.” In 'Introductory Lecture on Experimental Physics', (Oct 1871). In W.D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 244. Note that his reference to making measurements to another place of decimals is often seen extracted as a short quote without the context showing - obscuring the fact that he actually despised that opinion.
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To what heights would science now be raised if Archimedes had made that discovery [of decimal number notation]!
As quoted, without citation, in Eric Temple Bell, Men of Mathematics (1937), 256.
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While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established, and that further advances are to be sought chiefly in the rigorous applications of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance—where the quantitative results are more to be desired than qualitative work. An eminent physicist has remarked that the future truths of Physical Science are to be looked for in the sixth place of decimals.
University of Chicago, Annual Register 1894-1895 (1894), 150. Michelson also incorporated these lines in his address, 'Some of the Objects and Methods of Physical Science', at the opening of the Physics and Electrical Engineering Laboratory at the University of Kansas, reprinted in The Electrical Engineer (1 Jan 1896), 21, No. 400, 9.
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[Decimal currency is desirable because] by that means all calculations of interest, exchange, insurance, and the like are rendered much more simple and accurate, and, of course, more within the power of the great mass of people. Whenever such things require much labor, time, and reflection, the greater number who do not know, are made the dupes of the lesser number who do.
Letter to Congress (15 Jan 1782). 'Coinage Scheme Proposed by Robert Morris, Superintendent of Finance', from MS. letters and reports of the Superintendent of Finance, No, 137, Vol. 1, 289-300. Reprinted as Appendix, in Executive Documents, Senate of the U.S., Third Session of the Forty-Fifth Congress, 1878-79 (1879), 430.
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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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