3.45 pm First Lecture: Sir Roger Penrose FRS (Oxford)

Non-computability in Physics?

Abstract: Three lecture courses I attended in Cambridge, in the early 1950s (not part of my official PhD topic in algebraic geometry) had a profound influence on my later research. These were by Steen, on mathematical logic, Bondi, on general relativity, and Dirac on quantum mechanics. Steen showed, in effect, via Godel’s theorems and Turing computability, why conscious understanding could not be a purely computational process. But if our brains and bodies are, in essence, just physical systems, albeit very sophisticated ones, how could they be capable of non-computable tasks, as seem to be implied by an ability to appreciate the truth of Godel’s statements?

Elsewhere I have made a case that a missing ingredient lies in an incompleteness of quantum theory, namely that the process referred to as “wave-function collapse” may objectively underlie this essential missing ingredient, allowing non-computable conscious actions. In this talk, I explore an alternative possibility, arising from a gap occurring in the behaviour of classical systems, pointed out by Dirac in 1938.          
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