Optima and Simplicity in Nature

TL;DR

This paper argues that natural shapes are simple and symmetric because they are optimal solutions to energy and physics-based optimization problems, and that such optimality suggests cross-objective similarities.

Contribution

It introduces an information-theoretic framework linking optimal natural shapes to simplicity and symmetry, and predicts cross-objective optimality likelihood.

Findings

Optimal geometries in nature tend to be simple, regular, and symmetric.

A null model predicts that geometries optimal for one objective are likely near-optimal for others.

The approach connects physics, engineering laws, and algorithmic information theory to explain natural shapes.

Abstract

Why are simple, regular, and symmetric shapes common in nature? Many natural shapes arise as solutions to energy minimisation or other optimisation problems, but is there a general relation between optima and simple, regular shapes and geometries? Here we argue from algorithmic information theory that for objective functions common in nature -- based on physics and engineering laws -- optimal geometries will be simple, regular, and symmetric. Further, we derive a null model prediction that if a given geometry is an optimal solution for one natural objective function, then it is a priori more likely to be optimal or close to optimal for another objective function.