ABSTRACT: This brief essay reviews an approach to defining and then detecting the emergence of complexity in nonlinear processes. It is, in fact, a synopsis of The Calculi of Emergence that leaves out the technical details in an attempt to clarify the motivations behind the approach.
The central puzzle addressed is how we as scientists -- or, for that matter, how adaptive agents evolving in populations -- ever "discover" anything new in our worlds, when it appears that all we can describe is expressed in the language of our current understanding. One resolution -- hierarchical machine reconstruction -- is proposed. Along the way, complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. The approach turns on a synthesis of tools from dynamical systems, computation, and inductive inference.