Black-boxing and cause-effect power

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by demonstrating that, once causal power is properly defined and measured, it is possible for a macro level to “beat” the micro level. Here, this was done through a principled, well-defined measure of intrinsic cause-effect power – integrated information (Φ). Simple systems were evaluated for Φ across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro time steps. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal mechanisms that support their function. We show that a macro, black-box system can have higher Φ than its micro constituents either by implementing more selective mechanisms (lower degeneracy) or by composing a system having more common inputs and outputs (higher integration). We also show that, for a given micro system, one can identify local maxima of Φ across several spatiotemporal scales. These local maxima correspond to macro levels of organization at which causal features of physical systems emerge, and provide a natural focus for scientific inquiries.