Emergence : an algorithmic formulation 1

When the microequations of a dynamical system generate complex macrobehaviour, there can be an explanatory gap between the small-scale and large-scale descriptions of the same system. The microdynamics may be simple, but its relationship to the macrobehaviour may seem impenetrable. This phenomenon, known as emergence, poses problems for the nature of scientific understanding. How do we reconcile two radically different modes of description? Emergence is formulated using the powerful tools of algorithmic information and computational theory. This provides the ground for an extension and generalisation of the phenomenon. Mathematics itself is analysed as an emergent system, linking formalist notions of mathematics as a string manipulation game with the more abstract ideas and proofs that occupy mathematicians. A philosophical problem that has plagued emergence is whether the whole can be more than the sum of its parts. This possibility, known as strong emergence, manifests when emergent macrostructures introduce brand new causal dynamics into a system. A new perspective on this problem is gained by analysing strong emergence through algorithmic terms.