Computable Foundations for Economics

Introduction to The joes special Issue On nonlinearity, Randomness and Complexity

“…It was Velupillai's early insight (already explicitly expressed in Velupillai, 2000 and elaborated further in Velupillai, 2010a) that all three of these concepts should – and could – be underpinned in a theory of computability. It is this insight that led him to develop the idea of computationally universal dynamical systems , within a computable economics context, even before he delivered the Arne Ryde Lectures of 1994 7 .…”

Simulation, computation and dynamics in economics

“…3. Agent-based computational economics (cf., Tesfatsion, 2006, Epstein, 2006 That CGE in the Scarf Tradition is not underpinned by either computable or constructive mathematics is, by now, fairly well known (cf., Velupillai, 2010) But it is less well documented that the claims of computability of the Johansen -Stone tradition is equally untenable. Therefore some comments may be in order.…”

“…Smooth (Infinitesimal) Analysis (cf., Bell, 1998) . Numerical Analysis (cf., Stuart & Humphries, 1996) We have, in a series of writings over the past decade (see many of the essays in Velupillai, 2010 andVelupillai, 2009), reflected on the nuanced differences in these mathematical theories, and their applications in economics. The interested reader is referred to them for more detailed information on these mathematical theories, their alternative logical foundations, the nature of their algorithmic underpinnings, and much else -for example, in particular, on the role (or non-role, as the case may be) of the Church -Turing Thesis in the different theories.…”

Agent-based Modeling: The Right Mathematics for the Social Sciences?

“…For example, social system modelers using classical mathematics typically assume (explicitly or implicitly) that all modeled decision makers share common knowledge about an objective reality, even if there is no constructive way in which these decision makers could attain this common knowledge. In contrast, social system modelers advocating a constructive mathematics approach have argued that the "reality" of each modeled decision maker ought to be limited to whatever that decision maker is able to compute (Velupillai 2010).…”