Deconstructing Complex Systems with Mereology: Beyond Simple Causality
2025-02-06
This article presents a novel approach to understanding higher-order structure in complex systems, based on mereology, a branch of set theory. Using the Borromean rings as an example, it illustrates how the whole can be more than the sum of its parts. The author proposes that by constructing a system's mereology and applying the Möbius inversion formula, macroscopic quantities can be decomposed into sums of microscopic contributions, revealing the nature of higher-order interactions. Examples from gene interactions and mutual information in information theory demonstrate the method's application, with promising implications for machine learning and physics.