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Attempting to Model the Mathematical Mind

Prof. Sir Roger Penrose, Wadham College, University of Oxford

Date Icon Week 7, Tuesday 20 November MT 2012
Time Icon 8:15pm

Alan Turing’s ground-breaking 1937 paper introduced his concept of Universal Turing machine, which underlies the modern general-purpose computer. In 1939, he proposed generalizations based on ordinal logic and oracle machines, these being apparently motivated by attempts to model the mathematical mind in ways that evade the apparent limitations presented by Gödel’s incompleteness theorems. In this talk, I introduce the idea of a “cautious oracle” as a more human version of Turing’s oracles. Nevertheless, I show that even this fails to capture the essence of the full capabilities of our understanding. Are there possible physical processes that might circumvent these Gödel-type restrictions? I shall briefly report on some startling new experiments, which may shed light on possible physical processes underlying brain activity, and I speculate on its role relating to the power of human understanding.