Computability, G\"odel's Incompleteness Theorem, and an inherent limit on the predictability of evolution

TL;DR

This paper demonstrates that due to the digital inheritance in evolution, there are fundamental limits on predicting evolutionary outcomes, akin to G"odel's Incompleteness Theorem, unless evolution exhibits progressiveness.

Contribution

It proves a theorem linking computability limits to evolutionary theory, showing that open-ended evolution cannot be fully predicted without progressiveness.

Findings

Inherent limits on predicting open-ended evolution.

Complete theory unattainable unless evolution is progressive.

Connection to G"odel's Incompleteness and Halting Problem.

Abstract

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to G\"odel's Incompleteness Theorem and to the Halting Problem from computability theory.