Observations on Determinism and Order

Abstract

According to Plato, rational phenomena are regular or consistent with laws; in other words, phenomena are fortuitous only if they are rationally inexplicable. Facts subject to chance are not the object of science. That which is random cannot be known. In privileging deterministic models Thom could be drawing on a philosophical tradition that goes back to Plato and that identifies rationality and legality. Since Newton, it has been customary to consider chance as one of the names for ignorance. When, in a class K of events, we discover a statistical regularity, that is, one which can be described in terms of a probability distribution, we say that the events K obey a law of chance. The use of probability is not incompatible with an underlying determinism. It was even orthodox to want to be able to use probabilities only in those domains where the existence of a determinism had been established. According to this doctrine, chance, having no intrinsic consistency, constitutes a negative notion. Mr. Morin cites Rene Thom on this subject, yet neglects to reproduce a fairly substantial portion of the context: Chance can never be completely simulated. This results from the only possible way in which it can be defined: a strictly random event is a process whose evolution cannot be simulated by any mechanism.' Unfortunately the great geometrician does not indicate how the word is to be understood. If probabilistic laws could not be simulated by physical apparatuses,2 the probability theory would lack natural applications. No such simulation is yet possible by mechanical, by which I mean calculable, processes. But empirical phenomena, which follow laws that cannot be simulated mechanically, need not be random. Moreover, mathematicians know of phenomena whose irregular motion externally resembles randomness, yet which are engendered by deterministic equations.3