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

He concludes that since the action of the great moral principles isconstant, and, as the CLT teaches us, they will in any case prevail overrandomness, it is better to keep to them, otherwise you will experiencebad times. That conclusion is really commendable, but from thescientific viewpoint it is obviously not better than converting theChinese emperor to Christianity desired by Leibniz. At the end of theEssai (p. 123) we find the celebrated phrase:It is remarkable that a science that began by considering games ofchance should itself be raised to the rank of the most importantsubjects of human knowledge.He means exactly those political applications of the theory ofprobability.All the strangeness of metaphysics in the philosophical andemotional spheres notwithstanding, Laplace shows an amazing insightwhen concretely applying the probability theory. I have lookedthrough the ATP with a special aim, to find at least one wrong definitestatement. It seemed that supporting myself with a hundred and fiftyyears during which science has been since developing and given suchstrangeness of his general philosophical views, it will not be difficultto find there definite errors as well. Indeed, he considered somedubious problems on the probability of judicial decisions etc.It occurred, however, that it was not at all easy to find at least onewrong statement 9 . A great many applications that he considered can beseparated into three parts:1. Obvious and absolutely unquestionable problems such as partialcensuses of population or the change of the frequency of male births inParis due to foundlings.2. Treatment of the results of astronomical observations. It isdifficult to discuss those applications since vast material ought to bestudied.3. Obviously dubious problems like the probabilities of judicialdecisions. Here, however, Laplace’s conclusions are so careful thatpurely scientific errors are simply impossible.There is nothing to say here about the first group, but somethinginstructive can be noted concerning the second one. There, Laplace (p.46) quotes the result of the treatment of observations: the ratio of themasses of Jupiter and the Sun is equal to 1:1071 and states that hisprobabilistic method gives odds of 1 000 000 to 1 that this result is nota hundredth in error 10 . According to modern data, that ratio is a littlemore than 2% larger so that the odds are obviously wrong.The great question here is, however, was that occasioned by amistaken treatment of the observations or by a systematic error ofthose observations impossible to eliminate by any statistical treatment.I was unable to answer that question. In general, it is very easy tocommit such an error, and it is relevant to remark that quite recentlythe mass of the Moon was corrected in its third significant digit so thatthe precision of modern numbers should be carefully considered. If,however, we tend to believe that the observations were treatedcorrectly, and modern numbers are also correct, we arrive at an91