Chance and Necessity

Abstract

Chance appears to have a considerable effect on natural behaviour. We have seen examples regarding irreversibility, phase transitions, traffic flow, “noise” and percolation. Now we shall look at the general properties of chance and the notion of probability. This task was started by physicists Carl Gauss (1777) and Andrey Kolmogorov (1903), who together with Laplace and others have provided a robust theory. Basic elements of this theory that make it relevant in many applications are the law of large numbers and the central limit theorem. It is worthwhile reviewing them now. Thus, we shall reveal that the concept of probability seems to reflect essential characteristics in many phenomena and that there are implications of this fact whose scope must still be assessed. And we shall encounter motivation for that thesis of the biologist Jacques L. Monod (1910) following observations of the philosophers Democritus (460 BC) and Epicurus (341 BC) that all that exists is the fruit of chance and necessity.