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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index E > Category: Exceptional

Exceptional Quotes (18 quotes)

Question: On freezing water in a glass tube, the tube sometimes breaks. Why is this? An iceberg floats with 1,000,000 tons of ice above the water line. About how many tons are below the water line?
Answer: The water breaks the tube because of capallarity. The iceberg floats on the top because it is lighter, hence no tons are below the water line. Another reason is that an iceberg cannot exceed 1,000,000 tons in weight: hence if this much is above water, none is below. Ice is exceptional to all other bodies except bismuth. All other bodies have 1090 feet below the surface and 2 feet extra for every degree centigrade. If it were not for this, all fish would die, and the earth be held in an iron grip.
P.S.—When I say 1090 feet, I mean 1090 feet per second.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 179-80, Question 13. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
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A single tree by itself is dependent upon all the adverse chances of shifting circumstances. The wind stunts it: the variations in temperature check its foliage: the rains denude its soil: its leaves are blown away and are lost for the purpose of fertilisation. You may obtain individual specimens of line trees either in exceptional circumstances, or where human cultivation had intervened. But in nature the normal way in which trees flourish is by their association in a forest. Each tree may lose something of its individual perfection of growth, but they mutually assist each other in preserving the conditions of survival. The soil is preserved and shaded; and the microbes necessary for its fertility are neither scorched, nor frozen, nor washed away. A forest is the triumph of the organisation of mutually dependent species.
In Science and the Modern World (1926), 296-7.
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Although few expressions are more commonly used in writing about science than “science revolution,” there is a continuing debate as to the propriety of applying the concept and term “revolution” to scientific change. There is, furthermore, a wide difference of opinion as to what may constitute a revolution. And although almost all historians would agree that a genuine alteration of an exceptionally radical nature (the Scientific Revolution) occurred in the sciences at some time between the late fifteenth (or early sixteenth) century and the end of the seventeenth century, the question of exactly when this revolution occurred arouses as much scholarly disagreement as the cognate question of precisely what it was.
The Newtonian Revolution (1980), 3.
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Common to all these types is the anthropomorphic character of their conception of God. In general, only individuals of exceptional endowments, and exceptionally high-minded communities, rise to any considerable extent above this level. But there is a third stage of religious experience which belongs to all of them, even though it is rarely found in a pure form: I shall call it cosmic religious feeling. It is very difficult to elucidate this feeling to anyone who is entirely without it, especially as there is no anthropomorphic conception of God corresponding to it.
…...
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I came from Paris in the Spring of 1884, and was brought in intimate contact with him [Thomas Edison]. We experimented day and night, holidays not excepted. His existence was made up of alternate periods of work and sleep in the laboratory. He had no hobby, cared for no sport or amusement of any kind and lived in utter disregard of the most elementary rules of hygiene. There can be no doubt that, if he had not married later a woman of exceptional intelligence, who made it the one object of her life to preserve him, he would have died many years ago from consequences of sheer neglect. So great and uncontrollable was his passion for work.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25.
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I would be the last to deny that the greatest scientific pioneers belonged to an aristocracy of the spirit and were exceptionally intelligent, something that we as modest investigators will never attain, no matter how much we exert ourselves. Nevertheless … I continue to believe that there is always room for anyone with average intelligence … to utilize his energy and … any man could, if he were so inclined, be the sculptor of his own brain, and that even the least gifted may, like the poorest land that has been well-cultivated and fertilized, produce an abundant harvest..
From Preface to the second edition, 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), xv.
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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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Investigating the conditions under which mutations occur … requires studies of mutation frequency under various methods of handling the organisms. As yet, extremely little has been done along this line. That is because, in the past, a mutation was considered a windfall, and the expression “mutation frequency” would have seemed a contradiction in terms. To attempt to study it would have seemed as absurd as to study the conditions affecting the distribution of dollar bills on the sidewalk. You were simply fortunate if you found one. … Of late, however, we may say that certain very exceptional banking houses have been found, in front of which the dollars fall more frequently—in other words, specially mutable genes have been discovered, that are beginning to yield abundant data at the hands of Nilsson-Ehle, Zeleny, Emerson, Anderson and others.
In 'Variation Due to Change in the Individual Gene', The American Naturalist (Jan-Feb 1922), 56, No. 642, 44.
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It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way. Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
In 'The Mathematician', Works of the Mind (1947), 1, No. 1. Collected in James Roy Newman (ed.), The World of Mathematics (1956), Vol. 4, 2053.
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It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase. Professor Eddington has recently remarked that “The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature.” It is not a little instructive that so similar a law should hold the supreme position among the biological sciences. While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.
The Genetical Theory of Natural Selection (1930), 36.
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Life exists in the universe only because the carbon atom possesses certain exceptional properties.
In The Mysterious Universe (1930, 1932), 22.
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Mr. Hillaire Belloc has pointed out that science has changed greatly, and for the worse, since it became popular. Some hundred years ago, or more, only very unusual, highly original spirits were attracted to science at all; scientific work was therefore carried out by men of exceptional intelligence. Now, scientists are turned out by mass production in our universities.
In Science is a Sacred Cow (1950), 23-24.
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Round about the accredited and orderly facts of every science there ever floats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to … Anyone will renovate his science who will steadily look after the irregular phenomena, and when science is renewed, its new formulas often have more of the voice of the exceptions in them than of what were supposed to be the rules.
In 'The Hidden Self', Scribner’s Magazine (1890), Vol. 7, 361.
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Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
The Fractal Geometry of Nature (1977, 1983), 28.
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The majority of evolutive movements are degenerative. Progressive cases are exceptional. Characters appear suddenly that have no meaning in the atavistic series. Evolution in no way shows a general tendency toward progress… . The only thing that could be accomplished by slow changes would be the accumulation of neutral characteristics without value for survival. Only important and sudden mutations can furnish the material which can be utilized by selection.
As quoted in Isaac Asimov's Book of Science and Nature Quotations (1988), 91. Please contact Webmaster if you know the primary source.
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Thus died Negro Tom [Thomas Fuller], this untaught arithmetician, this untutored scholar. Had his opportunities of improvement been equal to those of thousands of his fellow-men, neither the Royal Society of London, the Academy of Science at Paris, nor even a Newton himself need have been ashamed to acknowledge him a brother in science.
[Thomas Fuller (1710-1790), although enslaved from Africa at age 14, was an arithmetical prodigy. He was known as the Virginia Calculator because of his exceptional ability with arithmetic calculations. His intellectual accomplishments were related by Dr. Benjamin Rush in a letter read to the Pennsylvania Society for the Abolition of Slavery.]
Obituary
From obituary in the Boston Columbian Centinal (29 Dec 1790), 14, No. 31. In George Washington Williams, History of the Negro Race in America from 1619 to 1880 (1882), Vol. 1, 400
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What I then got hold of, something frightful and dangerous, a problem with horns but not necessarily a bull, in any case a new problem—today I should say that it was the problem of science itself, science considered for the first time as problematic, as questionable. But the book in which my youthful courage and suspicion found an outlet—what an impossible book had to result from a task so uncongenial to youth! Constructed from a lot of immature, overgreen personal experiences, all of them close to the limits of communication, presented in the context of art—for the problem of science cannot be recognized in the context of science—a book perhaps for artists who also have an analytic and retrospective penchant (in other words, an exceptional type of artist for whom one might have to look far and wide and really would not care to look) …
In The Birth of Tragedy (1872). Collected in Friedrich Nietzsche and Walter Kaufmann (trans.), The Birth of Tragedy and The Case of Wagner (1967), 18.
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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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