Page 452: I didn't mention what tune it was that AMT played to Arnold on the violin. It was the traditional air Cockles and Mussels. Page 453: I was struck by AMT's reference to quantum mechanics in his 1951 radio talk, but confined my comment to the way it harked back to his reading of 20 years before. Now, stimulated by Roger Penrose, I would give more attention to what AMT was saying about the connection between computability and physics in this one sentence. AMT was actually questioning whether a quantummechanical system could be modelled by a universal Turing machine, i.e. whether it might fail to be computable. In fact, I think this sentence gives an important if tantalising link between his logical work and the late interest in the wavefunction reduction process. which he developed in 19534 (see chapter 8). It is the reduction process, not the evolution of the wave function according to Schrödinger's equation, which introduces an unpredictable element. This sentence also gives a link between Turing's thought and the arguments Roger Penrose published from 1988 onwards, (see The Emperor's New Mind) although this is not to say that Turing would have thought there must be an uncomputable element in quantum mechanics. More likely he was trying to make quantum mechanics into a computable theory by finding a new account of the reduction process. I wrote a short piece for the last volume of the Turing Collected Works which includes these remarks as an aspect of Turing's relationship with physics; this is available on this site. I would also now comment that his reference to the 'Mathematical Objection' was in this talk less conclusive than his Mind article had been a year earlier. However Turing drew no connection drawn between these two problematic areas, as Roger Penrose has done. B. J. Copeland's 1999 preface to this 1951 talk (see the bibliography) also draws attention to this sentence of Turing's but interprets 'unpredictable' in the context of his claim (not based on anything in Turing's writing) about randomness having a connection with 'oraclemachines.' Copeland does not draw the connection with Turing's developing interest in fundamental physics. In Psyche you can read a series of objections to Roger Penrose's thesis, and a response from Roger Penrose, Beyond the Doubting of a Shadow. There is further material in the Alan Turing Internet Scrapbook: Machines and Men's Minds and Growth, Form and Crisis Update Index  Intro  Parts 1  2  3  4  BP  5  6  7  8  Authors Note
