Symmetry and Contextuality

TL;DR

This paper offers a broad, unified conceptualization of symmetry across various domains, emphasizing its context dependence, virtuality, and aesthetic aspects, and explores its role in life and creativity.

Contribution

It introduces a general, context-sensitive definition of symmetry based on non-essential substitutions, linking symmetry to virtuality, creativity, and aesthetic considerations.

Findings

Symmetry is context-dependent and often involves virtual substitutions.

Detection of hidden symmetries can lead to new insights.

Symmetry and its breaking are fundamental to life and aesthetics.

Abstract

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common ground for this variedness a very general conceptualization of symmetry is proposed: Existence of substitutions, which, in the given context, do not lead to an essential change. This simple definition has multiple consequences: -The context dependence of the notion of symmetry is evident in the humanities but by no means irrelevant yet often neglected in science. The subtle problematic of concept formation and the ontological status of similarities opens up. -In general, the substitutions underlying the concept of symmetry are not really performed but remain in a state of virtuality. Counterfactuality, freedom and creativity come into focus. The detection of previously hidden symmetries may provide deep and surprising insights. -Related to this, due attention is devoted to the aesthetic dimension of symmetry and the breaking of it. -Finally, we point out to what extent life is based on the interplay between order and freedom, between full and broken symmetry.