Complexity fits the fittest

TL;DR

This paper explores the relationship between computational complexity and natural selection, proposing principles like GNS and PCE, and investigates their philosophical, natural, and cognitive implications through theoretical analysis.

Contribution

It introduces the GNS principle and links it to PCE, offering a philosophical and evolutionary perspective on complexity and universality in computation.

Findings

GNS aligns with a weak form of PCE

Cognitive evolution may support GNS

Potential for formal proofs and experiments

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.