Alan Turing: The Enigma (104 page)

Yet, wrote Tolstoy, however nonsensical the idea of free will, ‘without this conception of freedom not only would he be unable to understand life
but he would be unable to live for a single moment. Life would be intolerable because all man’s aspirations, all the interest that life holds for him, are so many aspirations and strivings after greater freedom. …To imagine a man wholly destitute of freedom is the same thing as to imagine a man destitute of life.’

For Alan Turing there remained one freedom, not perhaps one that Tolstoy would have had in mind. It was that of exiled pleasure. The head master having taken action to prevent associations within the house, he had to fall back upon the possibilities offered by the boys in the other houses.
^*
For Alan would not let the system defeat him. On May Day 1952 there was a meeting of the Ratio Club at Cambridge, which he attended, and it was probably then that he saw Norman Routledge at King’s. Alan explained about the trial and the hormone treatment (‘I’m growing
breasts
I’) and Norman told him that he had heard that in Norway (of all places) there were dances ‘for men only’.

In the summer of 1952 Alan went for a holiday in Norway, one which turned out to be a disappointment regarding the rumoured dances. But he met a number of Scandinavians, enough to have the addresses of five or six,
²¹
and he was particularly struck by one young man called Kjell, whose photograph he showed to Robin on his return. Kjell had been somewhat coquettish, and little had transpired, but Alan had thereby demonstrated his unbroken will, which was perhaps the most important thing.

As for what the endocrinologists called intellectual ‘performance’, Alan’s work on the biological theory did continue, despite everything, to develop in range and scale. He was tackling the problems which he had outlined in the first paper. In particular, he was trying out on the computer the solution of the very difficult differential equations that arose when it was attempted to follow the chemical theory of morphogenesis beyond the moment of budding, taking into account the essential non-linearity. This was experimental work, in which he would be trying out many different initial conditions to see what happened. But it also required some rather sophisticated applied mathematics, which involved the use of ‘operators’ rather as in quantum mechanics. Numerical analysis was also important, in deciding how to approximate the equations for the purpose of the calculation. In this it was like a private atomic bomb, the computer in both cases following the development of interacting fluid waves.

As a rather separate line of attack, he also developed a purely descriptive theory of leaf-arrangement, or ‘phyllotaxis’ as it was called in biological
Greek, in which he found ways of using matrices to represent the winding of spirals of leaves or seeds round a stem or flower-head. He brought into this theory a concept of ‘inverse lattices’ somewhat like that used by crystallographers. It was also accompanied by a good deal of measurement-making of his own. The intention was that ultimately these two approaches would join up when he found a system of equations that would generate the Fibonacci patterns expressed by his matrices.

Although there was some correspondence with a number of biologists, this work was essentially done on his own. The Manchester botanist, C. W. Wardlaw, was particularly interested and wrote a paper
²²
describing, in biologists’ terms, the significance of the first Turing paper. This finally appeared in August 1952, and soon Alan had a letter
²³
from C. H. Waddington expressing interest but scepticism as to the correctness of the essential chemical hypothesis. But on the whole, Alan would tend to speak-to Lighthill, in particular – as though rather disappointed with the slow speed with which his ideas diffused, and the lack of reaction to them. There was, perhaps, an analogy with
Computable Numbers
in this respect, for the ‘confirmed solitary’ whom Max Newman had diagnosed in 1936 still lacked the talent for patient, persistent pushing. Neither had his abilities as a lecturer improved. One side-line that developed was an interest in irreversible thermodynamics, and after giving his seminar in the chemistry department Alan had a meeting with W. Byers Brown to discuss the subject; but this soon faded out, Alan possibly being more interested in young Byers Brown than in this branch of physical chemistry. But one difference from the reaction to his earlier achievements was that this time no one had pre-empted his ideas. He was quite alone.

Robin had persuaded Alan to come with him to the 1952 British Mathematical Colloquium in the spring; it was held at the Royal Naval College, Greenwich, which meant that they had the excuse to take a jaunt on the Thames steamer. Alan found some interesting wild flowers on the Greenwich bombsites, and there was a nice moment at the lunchtime bar, when Alan suddenly disappeared through one doorway on spotting a particularly dull logician bear down upon him from another. By this time he was becoming quite famous as the author of
Computable Numbers
. He liked to hear references to Turing machines (‘Pryce’s buoy’ in his story) but he did not like paying the price, that of being pinned down for shop-talk by those trying to make connections.

More to his taste was talking with Christopher Strachey, who had brought a fresh breeze from King’s into the technical atmosphere of the Manchester computer laboratory. He had much the same attitudes as Alan, and the same sense of humour. His draughts program was much developed
²⁴
and played throughout the summer of 1952, this being the first time that the kind of automatic game-playing that Alan had so long talked about was seriously tried. But he and Alan also used the random number facility in a program to compose ‘love letters’. One of these ran:

Darling Sweetheart,

You are my avid fellow feeling. My affection curiously clings to your passionate wish. My liking yearns to your heart. You are my wistful sympathy: my tender liking.

Yours beautifully, MUC

Those doing real men’s jobs on the computer, concerned
with optics or aerodynamics, thought this silly, but it was as good a way as any of investigating the nature of syntax, and it greatly amused Alan and Christopher Strachey – whose love lives, as it happened, were rather similar too.

Tony Brooker, meanwhile, had written a program system called FLOATCODE, which did the work of interpreting floating-point arithmetic, rather as Alan had envisaged in 1945, but had never bothered to do for Manchester. It was based on similar work he had done at Cambridge on the EDSAC. And Alick Glennie went further in 1952 with something called AUTOCODE which was, in effect, the first working high-level computer language in the world. Christopher Strachey was enthusiastic about it – AUTOCODE was in line with the ideas he had written about in 1951, of translating mathematical formulae into machine instructions. But Alan took little interest. Alick Glennie talked to him about it, but found that he was bored by mere translation, something that he had described as obvious in 1947 and had never chosen to take any further himself. He would have been interested in something that would actually
do
the algebra, rather than translate it.

The computer industry was now in a position to expand beyond the confines of a small trained élite, programming languages opening the universal machine to a much wider clientele. AUTOCODE did not in fact play this role, and was little known away from Manchester. But the American FORTRAN was not far behind, one of a chain of developments with which Alan Turing had quite parted company.

By 1952 the Manchester engineers not only had a Mark II machine in hand, but had begun the design of a small transistor-based prototype. No one could have guessed from his total lack of participation in these developments that Alan Turing had once been avid to keep abreast of the latest technological advances, and had broken unwritten rules in order to get his hands on them himself. All this had been dropped in 1949 when it finally became clear that the world saw such an interest only as a nuisance. There was no reflection of his attempts to make a practical contribution to computer development in a book called
Faster than Thought
,
²⁵
the definitive account of British computers as they stood in 1951–2. Here he appeared principally as the writer of part of a chapter on ‘Digital Computers applied to Games’; he wrote up his chess game with Alick Glennie, helped with some comments on the play by Hugh Alexander; Besides a one-line
mention as the author of
Computable Numbers
and as one of Womersley’s assistants, there was one telling entry in the glossary:

Türing Machine
. In 1936 Dr Turing wrote a paper on the design and limitations of computing machines. For this reason they are sometimes known by his name. The umlaut is an unearned and undesirable addition, due, presumably, to an impression that anything so incomprehensible must be Teutonic.

The world of 1945 was now as remote, and effectively as secret, as that of 1942; a fact to which Alan seemed entirely resigned.

Robin kept him interested in the theory of types, and some work he had done stimulated Alan to dig out the paper he had written during the war, but had left unpublished, as his attempt to persuade mathematicians into a more careful use of ‘nouns’ and ‘adjectives’. Here again, the suggestions for ‘The Reform of Mathematical Notation’, as his essay was entitled, were at a tangent to the development of post-war mathematics, in which the muddles to which Alan objected were being cured by other means.

Alan mentioned his ‘reform’ proposals to Don Bayley when he paid a visit to him and his wife at Woburn Sands, near Bletchley, that summer. He gave Don some mathematical help, but the main point of the weekend was to make one last serious attempt to retrieve the silver bars. This time Don had got hold of a commercial metal detector, and they went out to the bridge near Shenley in his car. Alan said, ‘It looks a bit different’, as he took off his socks and shoes and paddled in the mud. ‘Christ, do you know what’s happened? They’ve rebuilt the bridge and concreted over the bed!’ They tried for the other bar in the woods, finding that the pram in which he had wheeled the ingots in 1940 was still there, but without any more luck than before in locating the spot. They found nails and oddments, just as Alan had done on the earlier attempt with Donald Michie. Giving up both bars as lost for ever, they made their way to the Crown Inn at Shenley Brook End for some bread and cheese. The disappointment was not too great, and largely dissipated by the warm welcome accorded to him by Mrs Ramshaw, his wartime landlady.

When Don Bayley had met him at Bletchley station, he noticed Alan was carrying a Norwegian grammar. Alan explained that he had just had a holiday in Norway, and that the language interested him. Although at this point his knowledge was rudimentary, he made sufficient progress with Norwegian and Danish to read Hans Christian Andersen stories to his mother a year later. It did not occur to Don that the Norwegian holiday might have had a particular motive, even though Alan explained that now he would have to go abroad for pleasure. He had written to Don about the charge and the trial, as to his other friends, and on the visit spoke with his usual light-hearted bravado of the outcome. He also referred to a letter he had written to a titled lady politician, calling for a change in the law. This was no pleading, as Oscar Wilde had done, that it was no crime but
sickness. He had drawn attention to the homosexuality of the politician’s son. All he had received in reply was a brusque disclaimer from her secretary.

In October 1952, both Don Bayley and Robin went up to Wilmslow for a weekend, a re-creation of Hanslope. Don was there first and they waited together for Robin on the station, Alan showing Don the diffraction pattern that appeared when looking at the station lights through his handkerchief. On the summer visit Alan had taken his usual pleasure in being looked after for a weekend within the more conventional domesticity of the Bayley household, and Don was struck by the contrasting spartan, untidy arrangements of the Prof’s home. Alan pointed to a stack of filing trays overflowing with letters from all over the world about logic, but said that he was not bothering to appear at the university now, and worked at home. He explained that he had an assistant who had taken over the organisation of the computer. Don advised him to watch out, or his assistant would take over. ‘Pooh!’, said Alan, as if to say ‘see if I care!’

But if his computer days were over, this did not mean the end of his underlying interest in the human mind. October 1952 also saw Polanyi and the philosophy department at Manchester score something of a
coup
over the psychology department, by having the Swiss psychologist Jean Piaget to give a course of lectures,
²⁶
which Alan attended. They concerned the child’s learning of logical ideas, and connected symbolic logic with actual psychological observations. So perhaps for the first time, Alan found himself listening to arguments about learning and teaching that did not just come from his own experience, and which were touched by modern theories of education that no one at Sherborne would have known to exist. At about the same time he breached his self-sufficiency in another way. He began seeing a Jungian psychoanalyst, Franz Greenbaum.

There was an element of resistance in his attitude towards this step, because of the implication that there was something wrong with him, and in particular, that his homosexuality was something that should be changed. The 1950s were, indeed, witnessing a powerful come-back of psychoanalysis, and increasingly vocal claims to the effect that its techniques could eradicate homosexual desire. But Greenbaum did not take such a view; homosexuality was not ‘a problem’ to him. He accepted Alan as a ‘natural homosexual’, and as a Jungian, he did not consider human activities in terms of displaced or unconscious sexuality. Rather, as a German refugee of 1939 with a Jewish father and Catholic mother, it was the psychology of religion that interested him most. As with Jung himself, there was no devaluation of the intellect in Greenbaum’s approach, and he was proud to know Alan as the inventor of the computer and as one who was working on the nature of life. His emphasis, as with Jung, was on the
integration
of ‘thinking’ and ‘feeling’. To apply intelligence to himself; to look at his own system from outside like Gödel, and break his own code – these were
natural extensions of Alan’s long-growing interest in psychology. A turning-point was indicated on 23 November 1952, when he wrote to Robin in connection with his now completed PhD thesis, and added:
²⁷