7. Probability and Statistics Soviet Essays - Sheynin, Oscar

it seems to me, in such cases we should study some approximate functional dependencesbetween several magnitudes, x, y, z, and establish whether the hypothetical functionsconstructed on the basis of economic considerations are indeed sufficiently stable and littledepend on time or place. The role of the theory of probability in such matters is far fromsimple and its formulas should be applied with great care. When comparing dynamical series,the very concept of correlation should be replaced, as some authors do, by the termcovariation with a purely technical descriptive meaning attached to it. In any case, thenumerous studies concerning covariations are until now of a purely empirical nature and donot belong to the province of the theory of probability. In restricting the field of applicationof the correlation theory by more or less stationary populations, we lessen its practicalimportance; however, its conclusions in this {smaller} domain possess indisputable valueand in some cases the correlation dependences express the same regularities as the functionaldependences.The need to complete my report which has already dragged on for an extremely long time,makes it impossible to dwell on purely mathematical and not yet fully solved problemsconnected with correlation theory. I hope that I was able to show that the methods ofprobability theory have now attained a sufficient degree of flexibility and perfection so as notto be afraid of most severe scientific criticism and to serve as a solid foundation for thefurther development of science. It should only be remembered that the concept of probabilityis a precise mathematical idea and that it should not be abused in the absence of strictpreconditions for its application. Because, as apparently Poincaré put it, the theory did notoffer us a wonderful gift of deriving something out of nothing 15 ; it only embodies adistinctive method of stating, combining and uniting our knowledge into an harmoniousmathematical system.Notes1. {Bernstein hardly had much knowledge of the (then not yet studied) history ofprobability. Thus, he did not mention De Moivre at all. And Bertrand (1888) had indeedseverely criticized the theory of probability, – not only in its Préface,– but in many cases hewas mistaken, see Sheynin (1994).}2. {Its application became necessary, above all, owing to Darwin’s Origin of Species.}3. {This statement seems too optimistic: the Kolmogorov axiomatics was yet to appear (in1933).}4. I think that it is unnecessary to repeat that, owing to the generally accepted continuity ofspace, the values of the angles are supposed here to be physically measured rather thanabsolutely precise and determined arithmetically.5. {The Editors inserted here a reference to the Russian translation of Borel (1914).}6. {Bernstein did not mention Mises.}7. {Possibly Marbe (1899).}8. {The reader will encounter this coefficient time and time again. Bernstein also devotedmuch attention to it much later, in his treatise (1946) but in either case he did not mentionthat Markov and Chuprov had all but rejected the coefficient of dispersion as a reliable tool.See Sheynin (1996, §§14.3 – 14.5).}9. {Boris Sergeevich Yastremsky (1877 – 1962). See Yastremsky (1964) and Anonymous(1962).}10. {The second reference is perhaps to Poincaré’s remark (1912, p. 171) that he borrowedfrom G. Lippmann to the effect that experimenters believe that the normal law is amathematical theorem whereas the latter think that it is an experimental fact.}11. {On Liapunov’s alleged use of the discontinuity factor see his note (1901).}