Symmetry-simplicity, broken-symmetry-complexity

Author: Krakauer, David C.
Source: Interface Focus; Vol.: 13; Article No.: 20220075; Issue: 3; DOI: 10.1098/rsfs.2022.0075; 14 April 2023

SFI Taxonomy: Information Theory, Machine Learning and Statistics

Abstract:
Complex phenomena are made possible when: (i) fundamental physical symmetries are broken and (ii) from the set of broken symmetries historically selected ground states are applied to performing mechanical work and storing adaptive information. Over the course of several decades Philip Anderson enumerated several key principles that can follow from broken symmetry in complex systems. These include emergence, frustrated random functions, autonomy and generalized rigidity. I describe these as the four Anderson Principles all of which are preconditions for the emergence of evolved function. I summarize these ideas and discuss briefly recent extensions that engage with the related concept of functional symmetry breaking, inclusive of information, computation and causality.