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

Reasoning based on common sense and the dimensionality theoremoccurred exceptionally successful although they can not be absolutelyprecise because some physical consideration oppose them. The entiretheory is of a purely statistical essence; its aim is to cover the mainfeatures of the statistics of the studied phenomenon by issuing fromrather rough considerations and to approach the possibility of anexperimental check. Now let us pass to a failed example.3.7. Statistical forecast. [...] We firmly believe in scientificpredictions, for example in calculations of the future situation of theplanets based on the law of universal gravitation. Actually, our beliefis certainty and it is never deceived, although the general theory ofrelativity is known to introduce corrections here. Are scientificmethods of forecasting stochastic processes able to provide areasonable if not firm certainty in predicting the future?Kolmogorov and somewhat later Wiener independently developedmethods of forecasting stationary stochastic processes. In hiscontribution on the theory of turbulence Kolmogorov clearly statesthat he considers his hypotheses about the structure of turbulence verylikely. It is curious to compare this with the absence in his works onthe prediction of stochastic processes of any hint on the possibility ofpractical applications.Both in his report (1952) and in Cybernetics (1969?) Wienerindicated that the theory of forecasting was practically important. Inthe first case he stated that he was prompted byThe problem of predicting the future position of an airplane byissuing from general statistical information on the methods of its flightand from more specific knowledge of its previous path. [...] My workwas concerned with instruments necessary for realizing the theory ofpredicted firing in an automatic device for shooting at the airplane(Translated back from Russian.)It is known, however, that such a method of shooting was notrealized, not because of calculational difficulties but first of all sincethe path of an airplane can not be described by a model of stationarystochastic process. There possibly is a statistical component in theairplane’s manoeuvre, but how can it be isolated? The manoeuvredepends so much on the concrete conditions that we can not at alldiscuss the statistical homogeneity of all the routes of the flight. Wecan attempt to isolate the statistical elements, but this problem is toodifficult for being solvable under war conditions.In all other processes, economic, technological, meteorological, etc.we usually encounter the fact that the statistical element, even ifpresent, does not cover the entire phenomenon. Thus, only the rapidcomponent on the small scale can yield to statistical description. Andeven that fact is only scientifically established in exceptional cases, forexample for the microstructure of turbulence. Another such exampleconcerns the change of the frequency of the generator of oscillationsduring very short periods of time, when the action of flicker and othertechnological causes of the change does not have enough time forbeing felt (Rytov 1966).81