On the Mathematical Structure of Cascade Effects and Emergent Phenomena

TL;DR

This paper explores the mathematical foundations of cascade and emergent phenomena, linking them to Galois connections and introducing generative effects to formalize their emergence.

Contribution

It introduces the concept of generative effects and connects them to Galois connections, providing a new mathematical framework for studying emergent phenomena.

Findings

Generative effects arise from concealing mechanisms or forgetting characteristics.

These effects are linked to a loss of exactness in the system.

Homological algebra can be used to characterize generative effects.

Abstract

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We establish that these effects arise, via a notion of a veil, from either concealing mechanisms in a system or forgetting characteristics from it. The goal of the work is to initiate a mathematical base that enables us to further study such phenomena. In particular, generative effects can be further linked to a certain loss of exactness. Homological algebra, and related algebraic methods, may then be used to characterize the effects.