Software in the natural world: A computational approach to hierarchical emergence

TL;DR

This paper introduces a computational framework for understanding emergence in complex systems by analyzing their hierarchical software-like processes, enabling better prediction and control of such systems.

Contribution

It develops a novel formalism that characterizes macroscopic processes through their computational properties, revealing the functional architecture of complex systems.

Findings

Models from physics and neuroscience exhibit software-like macroscopic processes.

The framework delineates the computational hierarchy within complex systems.

Enables improved simulation, prediction, and control of emergent phenomena.

Abstract

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled.