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

Conclusion. Some Problemsof the Current Development of the Theory of ProbabilityThe examples provided in Chapter 2 were aimed at illustrating theidea that the problem concerning the boundaries of applicability of thetheory of probability can not be solved speculatively, by logicaljustification (or by justifying the opposite). Neither does a singlepractical success scientifically assure us in the correctness of atheoretical concept. [...]Only prolonged studies lasting many years (almost 20 years in theFramingham investigation (§ 2.2)) and even carried out by manygenerations of scientists (like the study of problems of heredityoriginated by Mendel) provide a reliable result. In a purely methodicalsense such studies ensure complete possibility of experimental checksof many stochastic assumptions. In particular, checks of statisticalhomogeneity (for example, by non-parametric criteria fordistinguishing two empirical distribution functions), of confidenceintervals (recall my rejection of that interval for the mass of Jupiter in§ 1.1) and of much more.And so, it is wrong that no experimental checks are threateningthose premises (Alimov’s objection). However, if simply collecting the(statistical or not) ensemble of all the instances in which stochasticmethods are applied, and find out in how many cases Alimov and Iwere in the right, then, as I fear, he would have collected anoverwhelming majority of votes. I would have to take cover behind theargument that in science a numerical majority of votes might meannothing.All the circumstances concern one aspect of the problem, of whatand under which conditions can theory give to practice. Let us try tothink what, on the contrary, can practice give to theory. Formathematics, this is a venerable question and most extremely pertinentopinions had been voiced. I begin by quoting the opinion of thecelebrated French mathematician Dieudonne (1966, p. 11; translatednow from Russian):In concluding, I would wish to stress how little does the most recenthistory exonerate the pious banalities of the soothsayers of a break-upwho are regularly warning us about the pernicious consequences thatmathematics will unavoidably attract to itself by abandoningapplications to other sciences. I do not wish to say that a close contactwith other fields such as theoretical physics is not beneficial for bothsides. It is absolutely clear, however, that among all the astonishingachievements described, not a single one, possibly excepting thetheory of distributions, is at all suitable for being applied in physics.Even in the theory of partial differential equations the emphasis is nowmuch more on the internal and structural problems than on thosehaving a direct physical significance.Even if mathematics be cut off forcibly from all the other streams ofhuman activity, it will still have food enough for centuries of thoughtabout great problems which we still ought to solve in our own science.116