Greater than the parts: a review of the information decomposition approach to causal emergence

Abstract

Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept, the study of emergence has suffered from a lack of formalisms that could be used to guide discussions and advance theories. Here, we summarize, elaborate on, and extend a recent formal theory of causal emergence based on information decomposition, which is quantifiable and amenable to empirical testing. This theory relates emergence with information about a system's temporal evolution that cannot be obtained from the parts of the system separately. This article provides an accessible but rigorous introduction to the framework, discussing the merits of the approach in various scenarios of interest. We also discuss several interpretation issues and potential misunderstandings, while highlighting the distinctive benefits of this formalism. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Keywords: emergence; information decomposition; synergy.

Figure 1.

Schematic of the $\mathrm{\Phi }\text{ID}$ approach to causal emergence. (a) Lattice of $\mathrm{\Phi }\text{ID}$ information atoms, with atoms corresponding to causal decoupling ($\mathcal{G}$) and downward causation ($\mathcal{D}$) highlighted. (b) Relationship between system variables ${\mathit{X}}_t$, supervenient variables $V_t$ and emergent properties (cf. equation (3.2)). Images adapted from [7,27,28]. (Online version in colour.)

Figure 2.

Example published applications of the $\mathrm{\Phi }\text{ID}$ approach to causal emergence. Examples include (a) Conway’s Game of Life, (b) a bird flocking model, (c) macaque ECoG during motor control [7], (d) human resting-state fMRI brain activity [34] and (e) human fMRI during loss of consciousness [35]. Images reproduced from [7,34,35] and the Neurotycho database. (Online version in colour.)