Unifying science through computation: Reflections on computability and physics

Abstract

Many activities of a contemporary working scientist involve the idea of the unity of science. There are countless examples where the ideas and methods of one subject find application in another. There are subjects that comfortably straddle the border between disciplines. There are problems that can only be tackled by multidisciplinary approaches. Science is a loose federation of diverse intellectual, experimental and material communities and cultures. However, these cultures are strong. In this paper we reflect upon an area of research that is attracting the attention of computer scientists, mathematicians, physicists and philosophers: the relationship between theories of computation and physical systems. There are intriguing questions about the computability of physics, and the physical foundations of computability, that can set the agenda for a new subject, and that will not go away. Research is in an early phase of its development, but has considerable potential and ambition. First, we will argue that concepts of computability theory have a natural place in physical descriptions. We will look at incomputability and (1) the idea that computers “exist” in Nature, (2) models of physical systems and notions of prediction, and (3) hypercomputation. We will reflect upon computability and physics as an example of work crossing the frontiers of two disciplines, introducing new questions and ways of argument in physics, and enabling a reappraisal of computers and computation.We will also notice the social phenomenon of suspicion and resistance, as the theories are unbalanced by their encounter with one another.