The Relevance of Computation Irreducibility as Computation Universality in Economics

Abstract

Stephen Wolfram’s A New Kind of Science [26] should have made a greater impact in economics—at least in its theorising and computational modes—than it seems to have. There are those who subscribe to varieties of agent-based modelling, who do refer to Wolfram’s paradigms–a word I use with the utmost trepidation–whenever simulational exercises within a framework of cellular automata is invoked to make claims on complexity, emergence, holism, reduction and many such ‘buzz words’. Very few of these exercises, and their practitioners, seem to be aware of the deep mathematical–and even metamathematical–underpinnings of Wolfram’s innovative concepts, particularly of computational equivalence and computational irreducibility in the works of Turing and Ulam. Some threads of these foundational underpinnings are woven together to form a possible tapestry for economic theorising and modelling in computable modes.

I am greatly indebted to my friend, Hector Zenil, for the kind invitation to contribute to this important commemorative volume. One minor caveat should be added here. I subscribe to the entirely sensible view of Chris Moore & Stephan Mertens that ‘old fashioned topics, like formal languages and automata’ are better left out of discussions at the frontiers of the theory of computation ([7], p. xvii).