Complexity Fits the Fittest

Abstract

In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality. It seems sustainable to equate universal systems to complex systems or at least to potentially complex systems. Post's problem on the existence of (natural) intermediate degrees (between decidable and universal RE) then finds its analog in the Principle of Computional Equivalence (PCE). In this paper we address possible driving forces --if any-- behind PCE. Both the natural aspects as well as the cognitive ones are investigated. We postulate a principle GNS that we call the Generalized Natural Selection principle that together with the Church-Turing thesis is seen to be in close correspondence to a weak version of PCE. Next, we view our cognitive toolkit in an evolutionary light and postulate a principle in analogy with Fodor's language principle. In the final part of the paper we reflect on ways to provide circumstantial evidence for GNS by means of theorems, experiments or, simulations.