Measuring emergence via nonlinear Granger causality

The concept of emergence is central to artificial life and complexity science, yet quantitative, intuitive, and easy-to-apply measures of emergence are surprisingly lacking. Here, I introduce a just such a measure, G-emergence, which operationalizes the notion that an emergent process is both dependent upon and autonomous from its underlying causal factors. G-emergence is based on a nonlinear time series analysis adapted from ‘Granger causality’ and it provides a measure not only of emergence but also of apparent ‘downward causation’. I illustrate the measure by application to a canonical example of emergence, an agent-based simulation of bird flocking, and I discuss its potential impact on perhaps the most challenging of all scientific problems involving emergence: consciousness.

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