Predictability of Tao

 

CONVERGENT SEQUENCES ARE PREDICTABLE

This generality is the converse of the generality examined in the previous, and the relation between the two depends on the contrast between the concepts of divergence and convergence. This contrast is a special case, although a very fundamental one, of the difference between successive levels in a Russellian hierarchy, ... For the moment, it should be noted that the components of a Russellian hierarchy are to each other as member to class, as class to class of classes, or as thing named to name.

What is important about divergent sequences is that our description of them concerns individuals, especially individual molecules. The crack in the glass, the first step in the beginning of the boiling of water, and all the rest are cases in which the location and instant of the event is determined by some momentary constellation of a small number of individual molecules. Similarly, any description of the pathways of individual molecules in Brownian movement allows no extrapolation. What happens at one moment, even if we could know it, would not give us data to predict that will happen at the next.

In contrast, the movement of planets in the solar system, the trend of a chemical reaction in an ionic mixture of salts, the impact of billiard balls, which involves millions of molecules – all are predictable because our description of the events has as its subject matter the behavior of immense crowds or classes of individuals. It is this that gives science some justification for statistics, providing the statistician always remembers that his statements have reference only to aggregates.

In this sense, the so-called laws of probability mediate between descriptions of that of the gross crowd. We shall see later that this particular sort of conflict between the individual and the statistical has dogged the development of evolutionary theory from the time of Lamarck onward. If Lamarck had asserted that changes in environment would affect the general characteristics of whole populations, he would have been in step with the latest genetic assimilation, ... But Lamarck and, indeed, his followers ever since have seemed to have an innate proclivity for confusion of logical types.

Be all that as it may, in the stochastic processes (from the greek "stochazein", "shooting the target with a bow", that is spreading the events in a partially randomly way, so that some have more favorable outcome. If a sequence of events combines a random component with a selective process in so that only certain outcomes of the random can continue, such a sequence is called "stochastic") either of evolution or of thought, the new can be plucked from nowhere but the random. And to pluck the new from the random, if and when it happens to show itself, requires some sort of selective machinery to account for the ongoing persistence of the new idea. Something like natural selection, in all its truism and tautology, must obtain. To persist, the new must be of such a sort that it will endure longer than the alternatives. What lasts longer among the ripples of the random must last longer than those ripples that last not so long. That is the theory of natural selection in a nutshell.

The Marxian view of history – which in its crudest form would argue that if Darwin had not written The Origin of Species, somebody else would have produced a similar book within the next five years – is an unfortunate effort to apply a theory that would view social process as convergent to events involving unique human beings. The error is, again, of logical typing.