An Algorithmic Approach to Emergence

Emergence is a concept often referred to in the study of complex systems. Coined in 1875 by the philosopher George H. Lewes in his book Problems of Life and Mind [1], the term has ever since mainly been used in qualitative discussions [2, 3]. In most contexts, emergence refers to the phenomenon by which novel properties arise in a complex system which is composed of a large quantity of simpler subsystems that do not exhibit those novel properties by themselves, but rather through their collective interactions. The following citation from Wikipedia [4] reflects this popular idea: "For instance, the phenomenon of life as studied in biology is an emergent property of chemistry, and psychological phenomena emerge from the neurobiological phenomena of living things". For claims such as the above to have a precise meaning, an objective definition of emergence must be provided. Current definitions are framed around a qualitative evaluation of the "novelty" of properties exhibited by a system with respect