Computing the uncomputable; or, the discrete charm of second-order simulacra

Matthew W. Parker

pp. 447-463

in: Roman Frigg, Stephan Hartmann, Cyrille Imbert (eds), Models and simulations, Synthese 169 (3), 2009.

Abstract

We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove.