Quantifying Complexity: An Object-Relations Approach to Complex Systems

TL;DR

This paper introduces a novel object-relations based model and the Complex Information Entropy (CIE) equation to quantify complexity across diverse systems, providing a unified framework for understanding complex information structures.

Contribution

It develops a generalized object-relations model and the CIE equation for measuring complexity, along with algorithms for system analysis across multiple disciplines.

Findings

CIE effectively quantifies complexity in various systems.

Algorithms improve approximation and inference of system composition.

Applications span engineering, physics, biology, and social sciences.

Abstract

The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates this question. With ideas drawn from the object-relations theory of psychology, this paper develops an object-relations model of complex systems which generalizes to systems of all types, including mathematical operations, machines, biological organisms, and social structures. The resulting Complex Information Entropy (CIE) equation is a robust method to quantify complexity across various contexts. The paper also describes algorithms to iteratively update and improve approximate solutions to the CIE equation, to recursively infer the composition of complex systems, and to discover the connections among objects across different lengthscales and timescales. Applications are discussed in the fields of engineering design, atomic and molecular physics, chemistry, materials science, neuroscience, psychology, sociology, ecology, economics, and medicine.