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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 **of**randomness 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 **of**random events are a sudden meeting **of** two acquaintances (Phys. 196b30)and a sudden unearthing **of** a buried treasure (Metaphys. 1025a). Lack **of**aim 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 **of**Poincaré’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 **of**fspring 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 **of**fspring 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 **of**outcomes whose probabilities persist, whereas chaotic motions imply a7