Undecidables

Stuart Hampshire

  • Alan Turing: The Enigma by Andrew Hodges
    Burnett, 587 pp, £18.00, October 1983, ISBN 0 09 152130 0

This is a very long biography, and before it appeared Alan Turing was not very well-known; his genius was of a kind that is not likely to be spread abroad. An immense amount of work has gone into this book, which expresses profound, and sometimes almost obsessional, admiration. It is not hagiography, but rather a study of a hero, an intellectual hero. I found it continuously readable and interesting, and it will, I think, be found moving and unforgettable by those who are ready to enter into the cryptographical and mathematical technicalities. The author quite often steps forward and gives the reader a piece of his mind on public issues, and his manner of presentation and style are as unlike those of an assured professional biographer as they could possibly be. But the style matches the subject. Alan Turing evidently was proud to be an odd-man-out: he insisted on informality in all circumstances, and even among his mathematical colleagues he seems to have cultivated an air of amateurishness. Mr Hodges gives a most convincing picture of this side of his character.

The story of an intellectually adventurous life begins with an immensely normal, typically English, middle-class family and an ordinary public school education: no disturbing precocity as a schoolboy, no outward brilliance marking him out, as Russell and F.P. Ramsey were marked out in their earlier years. Mr Hodges includes photographs of seaside family holidays, redolent of their period and typical of a social class. He includes letters between Turing and a school friend to whom Turing was passionately attached, who died prematurely and who was always to be remembered with emotion. At Sherborne, and before Cambridge, Turing showed his independence and the gift for solitary thinking which he never lost: but he did not display any overwhelming mastery as a mathematician. Mr Hodges remarks that Turing did not at any time revolt against his school and family background in the supposedly traditional manner of intellectuals. A ‘dowdy, Spartan amateurism, in which possessions and consumption played a small role’, was a not unusual feature of middle-class public schools at that time. At Cambridge he rowed in the boat and played bridge with his contemporaries at King’s. Throughout his life he enjoyed communal games and simple amusements. But while he was still an undergraduate, he was invited to read a paper to the Moral Sciences Club, an unusual honour, and his subject was ‘Mathematics and Logic’. In 1935, at the age of 22, he was elected to a research fellowship at King’s, also an unusual recognition of his potentialities. His early achievements in logic and mathematics became known to the British mathematician Max Newman, and to the great John von Neumann in Princeton. He already speculated simultaneously on the foundations of mathematics, in Hilbert’s and Gödel’s sense, and on the conceivable capacities and limits of computing machines, and this combination of interests was his genius. He liked to think like an engineer, and at the same time to think in the broadest logical abstractions. Mr Hodges describes very well this two-faced talent, which set him apart from the more single-minded mathematicians and logicians of his time.

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