Continued from Part 1
Sleeping DeathIn the wake of Turing's dramatic suicide in 1954, the task of interpretation fell first to Newman, writing the Royal Society Biographical Memoir. This document is about Turing; but also about Newman and his Cambridge-mindedness. Newman had no interest in convention or pleasing worldly people. Yet integrity and truth are highly divisible in social practice, and the 1952 trial was no more mentionable in British obituaries than it would have been in Russia. It is perhaps impossible now to recover how shocking Turing was, blasting through public and private truth in a world where no-one was ever supposed to question bishops, judges, or police. 'The poor sweeties,' Turing called the police watching him in 1953. I found in 1977 that this traumatic story was undiscussed memory in all who knew him, like some frozen mammoth from the cold war crisis years. After completing the ghastly task of this Memoir, Newman rarely spoke of Turing, and the world largely followed his example.
In that Memoir, Newman tried to express an overall unity in Turing's thought which subverted the conventional separation of 'pure' and 'applied'. But Newman was apparently embarrassed by Turing's work in the trivial mathematics of computing. He misrepresented Turing, referring to designers of computers not knowing of Turing's universal machine concept, apparently forgetting that Turing was one such designer himself. (This omission did lasting damage to Turing's reputation.) The now-popular Turing Test was perhaps what Newman meant by disparaging the 'gimcrack' quality in Turing's thought. (I wonder what Newman would have thought of today's exaggerations and promotion stunts in name of 'public understanding of science'; its science exhibitionism at the expense of science research.) Newman also gave a misleading picture of Turing's work at Bletchley. He was of course bound by intense secrecy but even so it is strange that he rendered the invention of the Bombe, the fight with the Service mentality, the night shifts breaking daily Enigma settings and hair-raising voyages, as a happy time of 'congenial colleagues' and 'a mild routine to shape the day'.
Newman lamented that the trivial demands of war took Turing away from serious problems, and gave far more attention to the ordinal logics of 1939 than to mere computers. Turing's real mathematics, he suggested, had been eclipsed by mundanely useful chess-playing. In so saying, Newman's survey evoked Turing's fertile thought-world of 1938, the would-have-been problems he could have taken on instead of breaking the Enigma and inventing the computer: perhaps pursuing the Riemann zeta-function, perhaps the extension of ordinal logics. The justification for Newman's unpopularisation is that to understand mathematicians, you must understand this priority and scale in time. Their unworldliness may turn out in time to be the most realistic.
Roger Penrose has recently expressed this theme: though holding Turing the leading pioneer of the dominant technology of the late twentieth century, he has stressed that Turing's own work showed the limitations of computability. He has also pointed to a real question here. What would Turing have made of the physics of the brain in 1938, if he had taken seriously the idea expressed in his ordinal logics that the mind does something uncomputable in seeing 'intuitively' the truth of a Gödel statement? We are entitled to ask because of Turing's earlier fascination, stimulated by Eddington, with the quantum mechanical physics of the brain and the 'nature of spirit.' There is now more than one fictional Turing set in 1939, but a more interesting story lies in this unpursued investigation. What if Wittgenstein in 1939 — but this remains a contrafactual enigma.
The child in timeWhen Turing was elected a Fellow of the Royal Society in 1951, the citation referring to the work he had done fifteen years earlier, he commented that they could hardly have elected him at twenty-four. It was Hardy's comment that maths is a young man's game, though the point of this observation is often overdone, given that Hardy said he was at his best at just after forty. Newman wrote of Turing as being at the height of his powers in 1954, when he was forty-one.
Turing proudly acted the enfant terrible. Nowadays, postmodern critics pick over the Turing Test for its alleged agenda of gender identity, but if Alan Turing had an identity crisis it was not over gender but over innocence and experience: the roles of boy and man. He demanded freshness, and one reason why he never gave definitive completions of his work was that he always wanted to start on something new. Excluded from the real men's computer engineering world, his late morphogenetic theory, which seems to have gone back to childhood wonder, gave him a way to make fresh discovery on the computer he had invented. The origin of that work lay in D'Arcy Thompson, back at the beginning of the century; and in other ways too Turing's work sprung from the crises of 1900. The germs of Turing's work were to be seen in Hilbert's 1900 problems, Russell's 1901 paradox, and Planck's 1900 quantum. What Turing led was not so much a linear advance in any one of these fields as allowing their synthesis, and connection with the practice of computation and communication. Turing's work has spanned much of the century, and in 2000, quantum cryptography is the first practical advance outside the scope of Turing's conceptions.
The stone that the builders reject may turn out to be the cornerstone. Russell thought his paradox a blow, not a discovery. But mathematics works a slow miracle, not the science-magazine hype which demands a revolution every week: it took centuries of logic to see what Gödel saw, and as Turing wrote, one man can do so little in a lifetime. Turing never foresaw quantum computing; did not see the advent of complexity theory. All this was left to others, Feynman amongst them, but also Roger Penrose, who has sought to repair Turing's lack of investigation into the physics of computability, which goes to the heart of Turing's connection between the logical and physical. At the very least, Penrose has clarified the assumption implicit in Turing's 1950 argument, that the physics of the brain is computable.
Turing made a young man's game of his assumption of the computability of the mind, by framing his famous Test — rather as he had made a game of the Second World War. It is nonetheless the deadly serious question, central to science as that war to history. It is the question of Frankenstein, the creation of real life: a question so great as to be unbearable for an individual to carry, unbearable perhaps as being critical to the war. It will take the new century, perhaps more, to see whether Turing is right, or whether Penrose has located that awkward detail, rejected by the builders of Artificial Intelligence, which becomes cornerstone of an entire new world of thought.
Both Turing and Penrose learnt about quantum-mechanical reality from the lectures of Dirac, another mind hard to classify as Cambridge's. There are mysteries to Turing's last year; we do not know what the secret state demanded; we can only guess whether Turing may have been trying to regain the lost freshness of Cambridge youth in 1935. There is a clue to Turing's motivation: in 1951 Turing gave a radio talk which referred to Eddington and in two sentences said that quantum mechanics might mean that the behaviour of the brain was not computable. So Turing was alive to this question — Penrose's question — and it may well be that this is why he thereafter concerned himself with wave-function reduction, though not coming to any conclusion before his death.
Hyperboloids of wondrous light, wrote Alan Turing to his friend and student Robin Gandy in a strange last postcard of March 1954 'from the unseen world' — an allusion to Eddington, but uncanny in foreshadowing the wondrous light of Penrose's relativity, uneconomic as Hardy, unworldly as Newman, unpopular as Turing himself.
Alan Turing killed himself on 7 June 1954, but for many people his death has brought hateful mathematics to life. What was for decades an unspeakable truth, has become the small change of Internet newsgroup banter. Now, talk of memorials to him reinforce the fact that the most awkward and unpopular can become the cornerstone; I myself would say fit for a cornerstone in Trafalgar Square, a non-violent Nelson on patient service for a new century. He took away the sins of the 1940s world, then found himself the sinner. But was it really his sexuality that demanded the public stoning? Or the transgression of demarcation lines, lines of class and trade? Or did it lie in being so necessary in 1940 when the British state was humiliatingly dependent on individual wits, wits that the literature-educated could not fathom? Or did his sin lie in the unbearable duty of genius to speak the truth? His theory denied the Self; yet he made a self-sacrifice of the wild scientific mind.
References:The Collected Works of A. M. Turing, eds. J. Britton, P. T. Saunders. D. C. Ince, R. O. Gandy and C. E. M. Yates (Elsevier, three volumes 1992; one volume 2001)
A. M. Turing, Computing Machinery and Intelligence, Mind 49, pp 433-460. Reprinted many times, e.g. in Margaret Boden (ed.)The Philosophy of Artificial Intelligence (Oxford University Press, 1990)
F. L. Bauer, Decrypted Secrets, Second edition (Springer-Verlag, 2000)
Arthur S. Eddington, The Nature of the Physical World (Cambridge University Press, 1928)
G. H. Hardy, A Mathematician's Apology (Cambridge University Press, 1940)
F. H. Hinsley and Alan Stripp (eds.) Codebreakers (Oxford University Press, 1993)
Andrew Hodges, Alan Turing: the Enigma (Burnett, London and Simon & Schuster, New York, 1983; new editions Vintage, London, 1992, Walker, New York, 2000)
Andrew Hodges, Turing: a natural philosopher (Phoenix, London 1997 and Routledge, New York, 1999. Also in The Great Philosophers, eds. Ray Monk and Frederic Raphael, Weidenfeld and Nicolson, London, 2000)
Andrew Hodges: Alan Turing Website at http://www.turing.org.uk
M. H. A. Newman, Alan Mathison Turing, Biographical Memoirs of the Royal Society, 1955
Roger Penrose, The Emperor's New Mind (Oxford University Press, 1989)
Roger Penrose, Shadows of the Mind (Oxford University Press, 1994)