  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 employing a principled, well-defined measure of
intrinsic cause-effect power - integrated information ({\Phi}), and showing
that, according to this measure, it is possible for a macro level to "beat" the
micro level. Simple systems were evaluated for {\Phi} 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 updates. Cause-effect power was evaluated based on the inputs and
outputs of the black boxes, ignoring the internal micro elements that support
their input-output function. We show how black-box elements can have more
common inputs and outputs than the corresponding micro elements, revealing the
emergence of high-order mechanisms and joint constraints that are not apparent
at the micro level. As a consequence, a macro, black-box system can have higher
{\Phi} than its micro constituents by having more mechanisms (higher
composition) that are more interconnected (higher integration). We also show
that, for a given micro system, one can identify local maxima of {\Phi} across
several spatiotemporal scales. The framework is demonstrated on a simple
biological system, the Boolean network model of the fission-yeast cell-cycle,
for which we identify stable local maxima during the course of its simulated
biological function. These local maxima correspond to macro levels of
organization at which emergent cause-effect properties of physical systems come
into focus, and provide a natural vantage point for scientific inquiries.
