1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

only a small number of monographs are more voluminous, so thathuman capability of writing great books has not changed much.The TAP is separated into two parts utterly different in style. Thefirst part, the Essai, is an Introduction and summary of the book and itobeys an indispensable condition of having no formulas. Thus, theformula21 xf ( x ) = exp( − )2π 2is expressed by words together with the definition of the numbers πand e. Such phrases are certainly little adaptable for perception.However, the Essai also contains many materials of philosophical,general scientific and applied nature described, as I see it, in a mostwonderful style 5 . Had that style not been so beautiful, we wouldperhaps have no need to counter, after a century and a half, attempts atapplying the theory of probability universally and indiscriminately.The Essai is about 12 lists long; the rest consists of the TAP properwhere Laplace applied mathematical analysis in plenty and, for us,rather strangely. This strangeness extremely impedes theunderstanding of the second part of the book (whereas the same is trueconcerning the Essai owing to the complete absence there of analyticalformulas). It is apparently difficult to find someone nowadays whocould be able to boast about having read (and understood) the TAPproper. However, many people have read the Essai whereas theattempts to understand the second, mathematical part led to thecreation of more rigorous (and therefore more easily understandable)methods of proving limit theorems of the theory of probability. We arehere only interested in the Essai.As stated above, it is a work of a rather free style. A scientist’spsychology is doubtlessly such that he builds a superstructure abovehis concrete scientific results. It consists of general ideas and emotionsemerging out of those results and providing new faith, will and energy.The concrete results are usually published whereas the superstructureremains the property of a narrow circle of students and friends 6 .Laplace, however, published both and thus, as I see it, rendered hisreaders an inestimable service.In his Essai, not being shy of the boundaries of a purely scientificpublication, Laplace carried out a wide polemic. Many scientistsendured quite a lot: Pascal (pp. 70 and 110) 7 for a number ofunfounded statements in his Pensées about the estimation ofprobabilities of testimonies; the author of the Novum Organum(Bacon, p. 113) for his inductive reasoning which led him to believethat the Earth was motionless (and thus to deny the Copernicanteaching); and many others, but the great Leibniz endured the most.Leibniz is mentioned in connection with summing the series (p. 96)11+ x = − + − +2 31 x x x ...(1.1)88