Statistical frequencies as dynamic equilibria.

Abstract

A plea for clearer understanding of the implications and use of statistical methods in physics and social sciences is made, specifically, a demand for more determinism in statistics, for a causal interpretation of probabilities in science, and an unwillingness to resort to indeterminacy except when de-terminacy is known to be, for the time being, impossible. (1) "The Principle of Indifference, when it is used to predict frequencies in the absence of observation, is only ignorance masquerading as knowledge." (2) "The Principle of Independence .... can exist, if the series converges upon a given frequency, only if the number of cases is indeterminate or infinite, and .... the number of cases in the law of large numbers must be finite and determinate if the statistical model is to be of scientific use, since a model must have definite dimensions." Hence, the investigator must discover the nature of the interaction among the events causing the series to converge. (3) 7 classical instances of actual supposed convergence are discussed, and all imply the existence of interaction among the events. Indication is given of the general nature of the equilibrating forces which would make the events tend toward a limiting frequency.