1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

1. PrehistoryI trace the prehistory of statistics until Kepler and Galileo inclusively anddescribe the appearance of randomness and probability as philosophicalnotions. Statistical considerations were mostly based on generalimpressions. The arithmetic mean appeared in astronomy as a universalestimator. Kepler rejected the Ptolemaic system of the world.Key words: randomness, probability, cause vs chance, qualitativecorrelation, expectation1.1. RandomnessIs an infinite (a much more difficult question: a finite) number sequencerandom or not? This is a fundamental problem. Another point is the role ofrandomness in natural sciences, for example in evolution of species or thekinetic theory of gases. Then, in statistics, a random variable should bestatistically stable, but in natural science this restriction is not necessary, cf.Poincaré (1896/1912, p. 3), so how to check stability? All this exoneratesthe need to study the history of randomness, and, incidentally, to see how aphilosophical concept becomes a mathematical notion.Early scientists threw light upon randomness. Aristotle’s examples ofrandom events are a sudden meeting of two acquaintances (Phys. 196b30)and a sudden unearthing of a buried treasure (Metaphys. 1025a). Lack ofaim or intersection of chains of events is also seen in Hobbes’ remark(1646/1840, p. 259):When a traveller meets with a shower, the journey had a cause, and therain had a cause […], but because the journey caused not the rain, nor therain the cause, we say that they were contingent one to another.Cournot (1843, § 40) revived the first example due to Aristotle as anintersection of two independent chains of events and both illustrate one ofPoincaré’s interpretations of randomness (1896/1912, p. 4): if equilibriumwas unstable, a small cause determined a considerable effect. Again, anevent was random if its causes were complicated and numerous.I continue to dwell on Aristotle, but leave aside several other ancientphilosophers because their understanding of randomness seems difficult toexplain. Aristotle’s special example (Phys. 199b1; also see De generationeanimalium 767b5) mentioned deviations from law, monstrosities. The firstdeparture of nature from the type is that the offspring should become femaleinstead of male; […] as it is possible for the male sometimes not to prevailover the female. […] He did not consider such events random; indeed, he (e.g., De Caelo 283b) stated that chance did not occur always or usually.Possibly, however, the sex of the offspring is determined either by small, orby complicated and numerous causes, so that the birth of a female (or amale) is a random event.An addition is necessary. A chaotic process engendered by a smallcorruption of the initial conditions of motion can lead to exponentialdeviation of the appropriate path. A coin toss has a constant number ofoutcomes whose probabilities persist, whereas chaotic motions imply a7

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