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A Precise and Autonomous System for the Detection of Insect Emergence Patterns

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An Algorithmic Approach to Emergence.

Charles Alexandre Bédard¹, Geoffroy Bergeron²

¹Faculty of Informatics, Università della Svizzera Italiana, 6900 Lugano, Switzerland.

Entropy (Basel, Switzerland)

|July 27, 2022

Summary

We introduce a quantitative definition of emergence using algorithmic information theory. A key indicator is multiple drops in the Kolmogorov structure function, providing an objective measure for complex systems.

Keywords:

Kolmogorov’s structure function algorithmic information theory emergence

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Area of Science:

Complexity Science
Algorithmic Information Theory
Theoretical Physics

Background:

The concept of emergence in complex systems lacks a universally accepted quantitative definition.
Existing frameworks often rely on subjective interpretations or lack objective measurement criteria.
Algorithmic information theory provides tools for analyzing the complexity and information content of data.

Purpose of the Study:

To propose a novel, quantitative, and objective definition of emergence.
To establish a theoretical framework for emergence grounded in algorithmic information theory.
To extend existing concepts of coarse-graining and boundary conditions within this new framework.

Main Methods:

Utilizing algorithmic information theory to represent observational data as bit strings.
Analyzing the Kolmogorov structure function of these bit strings.
Identifying a plurality of drops in the Kolmogorov structure function as a signature of emergence.

Main Results:

A quantitative and objective definition of emergence is formally proposed.
The framework provides theoretical results extending coarse-graining and boundary condition concepts.
The proposed definition is validated through applications to dynamical systems and thermodynamics.

Conclusions:

Algorithmic information theory offers a robust foundation for defining and detecting emergence objectively.
The Kolmogorov structure function serves as a key indicator for emergent phenomena.
This approach provides a powerful new tool for analyzing complexity across scientific disciplines.