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Home > Category Index for Science Quotations > Category Index D > Category: Derivative

Derivative Quotes (6 quotes)

Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
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In reality the origin of the notion of derivatives is in the vague feeling of the mobility of things, and of the greater or less speed with which phenomena take place; this is well expressed by the terms fluent and fluxion, which were used by Newton and which we may believe were borrowed from the ancient mathematician Heraclitus.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 407.
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In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.
In 'Mathematics Is an Edifice, Not a Toolbox', Notices of the AMS (Oct 1996), 43, No. 10, 1108.
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We divorced ourselves from the materials of the earth, the rock, the wood, the iron ore; we looked to new materials which were cooked in vats, long complex derivatives of urine which we called plastic. They had no odor of the living, ... their touch was alien to nature. ... [They proliferated] like the matastases of cancer cells.
The Idol and the Octopus: political writings (1968), 83 and 118.
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When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science, the vulgarized derivative from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.
'The Art of Being Ruled'. Revolution and Progress (1926), 4.
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Who has not be amazed to learn that the function y = ex, like a phoenix rising again from its own ashes, is its own derivative?
In Franηois Le Lionnais (ed.), Great Currents of Mathematical Thought: Mathematics in the Arts and Sciences (1971), Vol. 2, 126.
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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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