“[R]andom spinning being assumed, the distribution of chance in the game depends upon the mechanical perfection of the teetotum; it must be equally likely to fall on all its thirty-seven sides, i.e. the frequency of all the numbers must in the long run be very nearly the same.”

"The Scientific Aspect of Monte Carlo Roulette" (1894)

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Karl Pearson65

English mathematician and biometrician 1857–1936

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“This means that if in a city seven accidents occur each week, then (assuming that all possible distributions are equally likely) practically all weeks will contain days with two or more accidents, and on the average only one week out of 165 will show a uniform distribution of one accident per day.”

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“The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible”

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Philosophical Essay on Probabilities (1902)
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“If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.”

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“Bohr had… discovered that the frequencies corresponding to very large integers could be calculated accurately from the classical mechanics; they were simply the number of times that an ordinary electron would complete the circuit of its orbit in one second when it was at a very great distance from the nucleus of the atom to which it belonged. This could only mean that when an electron receded to a great distance from the nucleus of its atom, it not only assumed the properties of an ordinary electron, but also behaved as directed by the classical mechanics. Yet the classical mechanics failed completely for the calculation of frequencies corresponding to small orbits.”

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“We must recover the element of quality in our traditional pursuit of equality. We must not, in opening our schools to everyone, confuse the idea that all should have equal chance with the notion that all have equal endowments.”

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“That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.”

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“The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance.”

Richard von Mises (1883–1953) Austrian physicist and mathematician

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Probability, Statistics And Truth - Second Revised English Edition - (1957)

“It must be all the same to the citizens ("ressortissants", Fr.) of a country that their governing (those in power) speak such language or such other ("telle langue ou telle autre", Fr.); likewise that it must be all the same to them that these adhere to such or such religion, so long as a full (or complete) liberty is equally garantee for everyone.”

African Spir (1837–1890) Russian philosopher

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“[R]andom spinning being assumed, the distribution of chance in the game depends upon the mechanical perfection of the teetotum; it must be equally likely to fall on all its thirty-seven sides, i.e. the frequency of all the numbers must in the long run be very nearly the same.”

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Karl Pearson65

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