Alan Turing: The Enigma (30 page)

There
was one person, one of those few who were professionally interested in mathematical logic, who read the paper with a very considerable personal interest. This was Emil Post, a Polish-American mathematician teaching at the City College of New York, who since the early 1920s had anticipated some of Gödel and Turing ideas in unpublished form.
⁷
In October 1936 he had submitted to Church’s
Journal of Symbolic Logic
a paper
⁸
which proposed a way of making precise what was meant by ‘solving a general problem’. It referred specifically to Church’s paper, the one which solved the Hilbert decision problem but required an assertion that any definite method could be expressed as a formula in his lambda-calculus. Post proposed that a definite method would be one which could be written in the form of instructions to a mindless ‘worker’ operating on an infinite line of ‘boxes’, who would be capable only of reading the instructions and

(a) Marking the box he is in (assumed empty),

(b) Erasing the mark in the box he is in (assumed marked),

(c) Moving to the box on his right,

(d) Moving to the box on his left,

(e) Determining whether the box he is in, is or is not marked.

It was a very remarkable fact that Post’s ‘worker’ was to perform exactly the same range of tasks as those of the Turing ‘machine’. And the language coincided with the ‘instruction note’ interpretation that Alan had given. The imagery was perhaps that much more obviously based upon the assembly line. Post’s paper was much less ambitious than
Computable Numbers
; he did not develop a ‘universal worker’ nor himself deal with the Hilbert decision problem. Nor was there any argument about ‘states of mind’. But he guessed correctly that his formulation would close the conceptual gap that Church had left. In this it was only by a few months that
he
had been pre-empted by the Turing machine, and Church had to certify that the work had been completely independent. So even if Alan Turing had never been, his idea would soon have come to light in one form or another. It had to. It was the necessary bridge between the world of logic and the world in which people did things.

In another sense, it was that very bridge between the world of logic, and the world of human action, that Alan Turing found so difficult. It was one thing to have ideas, but quite another to impress them upon the world. The processes involved were entirely different. Whether Alan liked it or not, his brain was embodied in a specific academic system, which like any human organization, responded best to those who pulled the strings and made connections. But as his contemporaries observed him, he was in this respect the least ‘political’ person. He rather expected truth to prevail by magic, and found the business of advancing himself, by putting his goods in the shop window, too sordid and trivial to bother with. One of his favourite words was ‘phoney’, which he applied to anyone who had gained some position or rank on what Alan considered an inadequate basis of intellectual authority. It was a word that he applied to the referee of one of the group-theory papers he submitted in the spring, who had made a mistaken criticism of it.

He
knew that he ought to make more effort on his own behalf, and he could not help noticing that his friend Maurice Pryce was someone who both had the intellectual ability, and made sure that it was used to its best advantage.

Both of them had come a long way since that week in Trinity in December 1929. Alan had been the first to be elected a Fellow (thanks to King’s looking generously at his dissertation subject). But Maurice had just now been elected a Fellow of Trinity, which was that bit more impressive. And everyone could see that it was he who was the rising star. Their interests had developed in a complementary way, for Maurice had taken up quantum electrodynamics, while keeping up an interest in pure mathematics. But both alike were interested in fundamental problems. They had quite often met at Cambridge lectures, sometimes exchanging notes over tea; it had transpired that the Pryces also lived at Guildford, and Maurice had once been invited to tea at 8 Ennismore Avenue, where Mrs Turing had welcomed him as one of the deserving poor from the grammar school. Alan had visited and admired the laboratory that Maurice had fixed up in the Pryce garage.

At Princeton, Maurice had been supervised in his first year by Pauli, the Austrian quantum physicist, but this year was loosely under the wing of von Neumann. And Maurice knew everyone; everyone knew him. He would be seen at the von Neumanns’ luxuriant parties, spectacles ‘like eighteenth-century operas’, although there were less of these this year, because the von Neumann marriage was in difficulties. And if any of the English graduate students came to know John von Neumann, to find him sociable, exuberant, and a pretended playboy with an encyclopaedic knowledge, then it was Maurice Pryce – and certainly not Alan Turing. But at the other end of the scale, it was also Maurice who knew how to engage the reclusive Hardy in conversation. He could get on with everyone, and indeed it was he who made Alan himself feel welcome in the New World.

King’s had sheltered Alan from the more pushy aspects of academic life, which in America were more noticeable. He fitted no better into the American Dream, of winning through the competition, than into the conservative British idea of life, of playing a programmed part in the system.

But
King’s also sheltered him from hard realities in another way. At Cambridge he could joke about it. When Victor visited in May 1936 there had been a small scandal, a certain old Shirburnian being caught with ‘a lady’ in his room and sent down. Alan commented wryly that it was not a sin of which
he
was guilty. Alan was not a moaner, and tried always to show a sense of humour, but there was nothing particularly funny about the problem that he faced in coming out into the world.

In
Back to Methuselah
, Bernard Shaw imagined super-intelligent beings of 31,920 A.D. growing out of the concerns of art, science and sex (‘these childish games – this dancing and singing and mating’) and turning away to think about mathematics. (‘They are fascinating, just fascinating. I want to get away from our eternal dancing and music, and just sit down by myself and think about numbers.’) This was all very well for Shaw, for whom mathematics could symbolise intellectual enquiry beyond his reach. But Alan had to think about mathematics at twenty-four, when he had by no means tired of the ‘childish games’. He did not divide his mind into rigidly separate compartments, once saying that he derived a sexual pleasure from mathematics. Then with his new friend Venable Martin, he went to H.P. Robertson’s lectures on relativity in the new year of 1937, and also went canoeing, perhaps in the stream that fed Carnegie Lake. At one point he
⁹
‘indirectly indicated’ an ‘interest in having a homosexual relation’, but his friend made it clear that he was not interested. Alan never broached the matter again and it did not affect their relationship in other ways.

The New Jersey poet would have understood. But Alan did not see the America of Walt Whitman, only the land of sexual prohibition. The country of Daddy and Mama had adopted homosexuality as a deeply Un-American activity, especially since the twentieth century clean-up had got under way. At Princeton there was no one talking about a ‘pretty normal bisexual male’. Alan was lucky to be rebuffed by so tolerant a person as Venable Martin.

He faced the difficulty that confronted any homosexual person who had successfully resolved the internal psychological conflicts attendant on waking up in a Looking-Glass world. The individual mind was not the whole story; there was also a social reality which was not at all the mirror image of heterosexual institutions. The late 1930s offered him no help in coping with it. Except for those with eyes to see through the stylised heterosexuality of Fred Astaire and Busby Berkeley, the times favoured ever more rigid models of ‘masculine’ and ‘feminine’. There was, all the time, quite another America of cruising blocks and steam baths and late-night bars, but to an Alan Turing this might as well have been on another planet. He was not ready to make the social adaptation that his sexuality, at least outside Cambridge, demanded.

He could reasonably have felt that there was
no
acceptable adaptation; that this particular mind-body problem had no solution. For the time being his shyness kept him from confronting the harshness of this social reality, and he continued to try to cope at an individual level, making gentle approaches to some of those he met through his work. It was not a great success.

Alan
did spend some time in New York at Thanksgiving, but this was because duty called him to accept the invitation of a right-wing cleric who was a friend of Father Underhill,
^*
Mrs Turing’s favourite priest. (‘He is a kind of American Anglo-Catholic. I liked him but found him a bit diehard. He didn’t seem to have much use for President Roosevelt.’) Alan spent his time ‘pottering about Manhattan getting used to their traffic and subways (underground)’ and went to the Planetarium. More relevant, perhaps, to Alan’s emotional state, perhaps, was the holiday at Christmas when Maurice Pryce took him on a skiing trip in New Hampshire for two weeks:

He suggested going on the 16th and on the 18th we left. A man called Wannier attached himself to the party at the last moment. Probably just as well; I always quarrel if I go on holiday with one companion. It was charming of Maurice to ask me to join him. He has been very kind to me whilst I have been here. We spent the first few days at a cottage where we were the only guests. Afterwards we moved to a place where there were several Commonwealth Fellows and others of various nationalities. Why we moved I don’t know, but I imagine Maurice wanted more company.

Perhaps Alan wanted Maurice more to himself, for his friend was something of a grown-up Christopher Morcom. They drove back through Boston, where the car broke down, and on their return,

Maurice and Francis Price arranged a party with a Treasure Hunt last Sunday. There were 13 clues of various kinds, cryptograms, anagrams, and others completely obscure to me. It was all very ingenious, but I am not much use at them.

One clue was ‘Role of wily Franciscan’, which wittily attracted the party into the bathroom that Francis Price and Shaun Wylie shared, to locate the next clue in the toilet paper. Shaun Wylie himself was amazingly good at anagrams. The treasure hunt bemused the more earnest Americans with its ‘undergraduate humour’, and ‘typical English whimsy’, There were charades and play-readings, in which Alan joined. At lunchtimes they would play chess and Go and another game called Psychology. Tennis began as the snow melted, and the hockey was energetically continued.
‘Virago Delenda Est’
, wrote Francis Price on the notice board as they set off for an away match, and some bolder spirit crossed out the first ‘a’. On the playing-fields of Princeton, from which in May 1937 they watched the flames of the
Hindenburg
illuminate the horizon, the new men rehearsed an Anglo-American alliance.

Alan
enjoyed all this, but his social life was a charade. Like any homosexual man, he was living an imitation game, not in the sense of conscious play-acting, but by being accepted as a person that he was not. The others thought they knew him well, as in conventional terms they did; but they did not perceive the difficulty that faced him as an individualist jarring with the reality of the world. He had to find himself as a homosexual in a society doing its best to crush homosexuality out of existence; and less acute, though equally persistent as a problem in his life, he had to fit into an academic system that did not suit his particular line of thought. In both cases, his autonomous self-hood had to be compromised and infringed. These were not problems that could be solved by reason alone, for they arose by virtue of his physical embodiment in the social world. Indeed, there were no solutions, only muddles and accidents.

At the beginning of February 1937 the offprints of
Computable Numbers
arrived and some he sent out to personal friends. One went to Eperson (who had now left Sherborne for the more suitable Church of England), and one to James Atkins, who had now taken up a career as a schoolmaster, and was teaching mathematics at Walsall Grammar School. James also had a letter
¹⁰
from Alan which described, in a rather detached way, that he had been feeling depressed and mentioned that he had even thought of a scheme for ending his life. It involved an apple and electrical wiring.

Perhaps this was a case of depression after the triumph; the writing of
Computable Numbers
would have been like a love affair, now over but for mopping-up operations. Now he had the problem of
continuing
. Had he killed off the spirit? Was his work a ‘dead end’? He had done something, but what was it for? It was all very well for Bernard Shaw’s Ancients to live on truth alone, but it was asking a great deal of him. Indeed, it was not his ideal. ‘As regards the question of why we have bodies at all, why we do not or cannot live free as spirits and communicate as such, we probably could do so but there would be nothing whatever to do. The body provides something for the spirit to look after and use.’ But what was his body to
do
, without the loss of innocence, or the compromise of truth?

The months from January to April 1937 were absorbed in writing up a paper on the lambda-calculus, and two on group theory.
¹¹
Of these, the logic paper represented a small development of Kleene’s ideas. The first group theory paper was work related to that of Reinhold Baer, the German algebraist now attached to the IAS, which had mostly been done in 1935. But the second was a new departure, which arose through contact with von Neumann. It was a problem suggested by the emigré Polish mathematician S. Ulam, that of asking whether continuous groups could be approximated by finite groups, rather like approximating a sphere by polyhedra. Von Neumann had passed the problem on to Alan, who successfully dealt with it by April, when it was submitted. This was fast work, although as he had shown that continuous groups could
not
in general be approximated in this way, it was a rather negative result. Nor, he wrote, was he ‘taking these things so seriously as the logic.’