Can the macro beat the micro? Integrated information across spatiotemporal scales.

Causal interactions within complex systems such as the brain can be analyzed at multiple spatiotemporal levels. It is widely assumed that the micro level is causally complete, thus excluding causation at the macro level. However, by measuring effective information-how much a system's mechanisms constrain its past and future states-we recently showed that causal power can be stronger at macro rather than micro levels. In this work, we go beyond effective information and consider additional requirements of a proper measure of causal power from the intrinsic perspective of a system: composition (the cause-effect power of the parts), state-dependency (the cause-effect power of the system in a specific state); integration (the causal irreducibility of the whole to its parts), and exclusion (the causal borders of the system). A measure satisfying these requirements, called Φ Max, was developed in the context of integrated information theory. Here, we evaluate Φ Max systematically at micro and macro levels in space and time using simplified neuronal-like systems. We show that for systems characterized by indeterminism and/or degeneracy, Φ can indeed peak at a macro level. This happens if coarse-graining micro elements produces macro mechanisms with high irreducible causal selectivity. These results are relevant to a theoretical account of consciousness, because for integrated information theory the spatiotemporal maximum of integrated information fixes the spatiotemporal scale of consciousness. More generally, these results show that the notions of macro causal emergence and micro causal exclusion hold when causal power is assessed in full and from the intrinsic perspective of a system.