ABSTRACT. The relevance of the Turing universe as a model for complex physical situations (that is, those showing both computable and incomputable aspects) is discussed. Some well-known arguments concerning the nature of scientific reality are related to this theoretical context.
The close relationship between computability, mechanism and causal determinacy is basic to post-Newtonian science, and underpins the familiar notion of a Laplacian ‘clockwork’ Universe, which provided a clear mathematical model of physical reality for over a century and a half — the discovery in the 1930s of the possibility of an explicit mathematical description of the model providing a key ingredient in its eventual demise. Acceptance of such a model has never been total of course, even amongst scientists. But in recent times the need for a mathematical alternative to that of Laplace, subsuming and extending according to the changing theoretical and empirical environment, has become increasingly overdue. The purpose of this note is to argue that the genesis of such a precise and intuitively natural model lies in Alan Turing's response, in a more limited mathematical context, to the newly discovered incomputabilities of the decade 1927–1936.
A perceived algorithmic content for reality is peculiar to our time and culture. Its origins are commonly traced back to the ancient Greeks, as is the development of the notion of proof, providing a useful infrastructure for mathematical and scientific truth, having been rediscovered (largely via Arab texts) in the late Middle Ages and developed during and after the Renaissance.