RANDOMNESS

Randomness is a term with two principal meanings, one mathematical and the other physical. In the mathematics of probability and statistics, the term can refer to either the notion of "random variable" or the more imprecise concept signified by "random sampling," "at random," or "random distribution." A random variable, best defined as "a function defined on a given sample space" (Feller, 204), is less important than the imprecise "at random" notion it helps to clarify. The latter, in the purely theoretical formulation of probability, is roughly equivalent to the equal likelihood presumed in the basic postulates of probability (ibid. 29). As such, it is a purely theoretical model for the explanation of experimental results that are often neither perfectly random nor truly equally likely.

In the physical world randomness is closely associated with chance and with the data of such theories as quantum and statistical mechanics, which presuppose random motion of particles for the very formulation of their laws. Randomness thus seems to be a given, or datum, in at least some of the most important areas of science; J. von Neumann has attempted to demonstrate the radical character of this randomness. Nevertheless, it is a peculiarity of statistical theory that the most unexpected experimental results—equally probable or not—can be (approximately) reduced to some sort of statistical regularity. For example, consider the relations between Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac statistics in theoretical physics (ibid. 38–40). This suggests that there is some sort of order underlying even the most "random" of physical events, whether or not science ever in fact discovers it.

Bibliography: w. feller, An Introduction to Probability Theory and Its Applications, v.1 (New York 1957).

[p. r. durbin]