Measuring autonomy and emergence via Granger causality

Concepts of emergence and autonomy are central to artificial life and related cognitive and behavioral sciences. However, quantitative and easy-to-apply measures of these phenomena are mostly lacking. Here, I describe quantitative and practicable measures for both autonomy and emergence, based on the framework of multivariate autoregression and specifically Granger causality. G-autonomy measures the extent to which the knowing the past of a variable helps predict its future, as compared to predictions based on past states of external (environmental) variables. G-emergence measures the extent to which a process is both dependent upon and autonomous from its underlying causal factors. These measures are validated by application to agent-based models of predation (for autonomy) and flocking (for emergence). In the former, evolutionary adaptation enhances autonomy; the latter model illustrates not only emergence but also downward causation. I end with a discussion of relations among autonomy, emergence, and consciousness.