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 ...

Lamarck (1800 – 1811) was one of the first scholars to note thedependence of the weather on its previous state, see for example t. 5, pp. 5and 8 and t. 11, p. 143 of that source.Quetelet (1852; 1853, p. 68; 1849 – 1857, 1857, pt 5, pp. 29 and 83)analysed lasting periods of fair or foul weather by applying elementarystochastic considerations and concluded that the chances of the weatherpersisting (or changing) were not independent. Köppen’s analysis (1872)was more mathematically oriented. Quetelet also compiled and systematizedmeteorological observations. In many letters of 1841 – 1860 Faraday (1991– 2008), see for example vol. 3, No. 1367 and vol. 4, No. 2263, praisedQuetelet’s observations of atmospheric electricity. In the first instance hewrote:You are indeed a worthy example in activity & power to all workers inscience and, if I cannot imitate your example, I can at least appreciate &value it.10.8.4. Astronomy. Already Daniel Bernoulli (§ 6.1.1) and Laplace (§7.1-2) stochastically studied regularities in the Solar system. They actuallyconsidered planets as elements of a single population, and this approach wasvividly revealed in the later investigations of the asteroids. Newcomb(1861a and elsewhere) compared the theoretical (calculated in accordancewith the uniform distribution) and the actual parameters of the orbits ofasteroids but was yet unable to appraise quantitatively his results.Concerning their distribution, he (1862; 1881) seems to have intuitivelyarrived at the following proposition: a large number of independent pointsA 1 = (B 1 + b 1 t), A 2 = (B 2 + b 2 t), … where t denoted time, and the othermagnitudes were constant, will become almost uniformly distributed over acircumference.In 1881 Newcomb remarked that the first pages of logarithmic tableswore out much faster than the last ones and set out to derive the probabilitythat the first significant digits of empirically obtained numbers will be n 1 , n 2 ,… Without any proof he indicated that, if numbers s 1 , s 2 , …, s n wereselected at random, the positive fractional parts of the differences (s 1 – s 2 ),(s 2 – s 3 ), … will tend, as n → ∞, to a uniform distribution over acircumference, and that the empirical magnitudes, to which these differencesconform, will have equally probable mantissas of their logarithms.Newcomb’s reasoning heuristically resembled the Weyl celebrated theoremthat states that the terms of the sequence {nx}, where x is irrational, n = 1,2, …, and the braces mean drop the integral part, are uniformly distributedon a unit interval. In the sense of the information theory, Newcomb’sstatement means that each empirical number tends to provide one and thesame information. Several authors independently one from another provedthat Newcomb was right. One of them called his statement an inspired guessbut reasonably noted that it was not universally valid (Raimi 1976, p. 536).By the mid-century, after processing observations made over about acentury, a rough periodicity of the number of sunspots was established.Newcomb (1901), who studied their observations from 1610 onward,arrived at T = 11.13 years which did not, however, essentially differ fromthe previous results. The present-day figure is T ≈ 11 years but a strictperiodicity is denied. In any case, it might be thought that the numbers of102

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