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Part 2 — Matter and Spirit |
| Turing's private notes on the theory of
relativity showed a degree-level appreciation, yet he was almost
prevented from taking the School Certificate lest he shame the
school with failure. But it appears that the stimulus for effective
communication and competition came only from contact with another
very able youth, a year ahead of him at Sherborne, to whom Alan
Turing found himself powerfully attracted in 1928. He, Christopher
Morcom, gave Turing a vital period of intellectual companionship —
which ended with Morcom's sudden death in February 1930.
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| Turing's conviction that he must now do what Morcom
could not, apparently sustained him through a long crisis. For three
years at least, as we know from his letters to Morcom's mother, his
thoughts turned to the question of how the human mind, and
Christopher's mind in particular, was embodied in matter; and
whether accordingly it could be released from matter by death.
This question led him deeper into the area of twentieth century
physics, first helped by A. S. Eddington's book The Nature of
the Physical World, wondering whether quantum-mechanical
theory affected the traditional problem of mind and matter.
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Alan Turing, 1931 |
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As an undergraduate at King's College, Cambridge from 1931, he
entered a world more encouraging to free-ranging thought. His 1932
reading of the then new work of von Neumann on the logical
foundations of quantum mechanics, helped the transition from
emotional to rigorous intellectual enquiry. At the same time, this
was when his homosexuality became a definitive part of his identity.
The special ambience of King's College gave him a first real home.
His association with the so-called anti-War movement of 1933 did not
develop into Marxism, nor into the pacifism of his friend and
occasional lover James Atkins, then a fellow undergraduate
mathematician, later musician. He was closer in thought to the
liberal-left economists J. M. Keynes and A. C. Pigou. His
relaxations were found not in the literary circles generally
associated with the King's College homosexual milieu, but in rowing,
running, and later in sailing a small boat.
Turing's progress seemed assured, A distinguished degree in 1934
followed by a Fellowship of King's College in 1935 and a Smith's
Prize in 1936 for work on probability theory, and he might then have
seemed on course for a successful career as a mildly eccentric
King's don engaged in pure mathematics. His uniqueness of mind,
however, drove him in a direction none could have foreseen.
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| By 1933 Turing had already introduced himself to
Russell and Whitehead's Principia Mathematica and so to
the then arcane area of mathematical logic. Bertrand Russell had
thought of logic as a solid foundation for mathematical truth, but
many questions had since been raised about how truth could be
captured by any formalism. In particular, in 1931 Gödel had
shattered Russell's picture by showing the incompleteness of
mathematics: the existence of true statements about numbers which
could not be proved by the formal application of set rules of
deduction. In 1935, Turing learnt from the lecture course of the
Cambridge topologist M. H. A. Newman that a further question, posed
by Hilbert, still lay open. It was the question of Decidability, the
Entscheidungsproblem. Could there exist, at least in
principle, a definite method or process by which it could be decided
whether any given mathematical assertion was provable? |
Alan Turing in 1934 |
| To answer such a question needed a
definition of 'method' which would be not only precise but
compelling. This is what Turing supplied. He analysed what could be
achieved by a person performing a methodical process, and seizing on
the idea of something done 'mechanically', expressed the analysis in
terms of a theoretical machine able to perform certain precisely
defined elementary operations on symbols on paper tape. He presented
convincing arguments that the scope of such a machine was sufficient
to encompass everything that would count as a 'definite method.'
Daringly he included an argument based on the transitions between
'states of mind' of a human being performing a mental process.
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© Andrew Hodges
1995 |
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