Perspectives on Multi-Level Dynamics

TL;DR

This paper explores a unified framework for understanding multi-level systems across various fields, emphasizing the importance of dimensionality reduction and the challenges in establishing accurate simplified models.

Contribution

It proposes a foundational approach for analyzing multi-level systems and illustrates it with cross-disciplinary examples, addressing key difficulties and limitations.

Findings

A common framework for multi-level systems is proposed.

Examples from different fields illustrate the framework.

Discussion of challenges in model reduction and correspondence.

Abstract

As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters, linked together by causal equations of evolution whose structure may reveal hidden principles. This requires a huge reduction of dimensionality (number of degrees of freedom) and a change in the level of description. Beyond the mere necessity of developing accurate techniques affording this reduction, there is the question of the correspondence between the initial system and the reduced one. In this paper, we offer a perspective towards a common framework for discussing and understanding multi-level systems exhibiting structures at various spatial and temporal levels. We propose a common foundation and illustrate it with examples from different fields. We also point out the difficulties in constructing such a general setting and its limitations.