Explaining Emergence

TL;DR

This paper explores the concept of emergence in systems, emphasizing that emergent behavior can arise from simple deterministic rules and introducing computational irreducibility as a key to understanding such phenomena objectively.

Contribution

It defines computational irreducibility as a fundamental concept for understanding emergence without relying on subjective observer perspectives.

Findings

Emergence can occur in simple deterministic systems.

Computational irreducibility explains unpredictable behavior.

Objective understanding of emergence is possible through computational irreducibility.

Abstract

Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often been said that emergence is a subjective property relative to the observer. Some mathematical systems having very simple and deterministic rules nevertheless show emergent behavior. Studying these systems shed a new light on the subject and allows to define a new concept, computational irreducibility, which deals with behaviors that even though they are totally deterministic cannot be predicted without simulating them. Computational irreducibility is then a key for understanding emergent phenomena from an objective point of view that does not need the mention of any observer.