On the necessity of complexity

TL;DR

This paper explores the reasons behind the abundance of universal phenomena in nature, proposing a principle GNS linked to PCE, and investigates why non-universal complexity is not observed, supported by a case study of pervasive rich structures.

Contribution

It introduces the Generalized Natural Selection principle and links it to the Principle of Computational Equivalence, offering a new perspective on the prevalence of universal complexity.

Findings

GNS principle is equivalent to a weak version of PCE

Rich structures are observed ubiquitously in nature

No phenomena of non-universal complexity are observed

Abstract

Wolfram's Principle of Computational Equivalence (PCE) implies that universal complexity abounds in nature. This paper comprises three sections. In the first section we consider the question why there are so many universal phenomena around. So, in a sense, we week a driving force behind the PCE if any. We postulate a principle GNS that we call the Generalized Natural Selection Principle that together with the Church-Turing Thesis is seen to be equivalent to a weak version of PCE. In the second section we ask the question why we do not observe any phenomena that are complex but not-universal. We choose a cognitive setting to embark on this question and make some analogies with formal logic. In the third and final section we report on a case study where we see rich structures arise everywhere.