Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game

by Andrew Hodges

  They talked about the physiological basis of memory and of pattern recognition. Young wrote:51

  13.1.51

  Dear Turing,

  I have been thinking more about your abstractions and hope that I grasp what you want of them. Although I know so little about it I should not despair of the matching process doing the trick. You have certainly missed a point if you suppose that to name a bus it must first be matched with everything from tea-pots to clouds. The brain surely has ways of shortening this process by the process – I take it – you call abstracting. Our weakness is that we have so little idea of the clues and code it uses. My whole thesis is that the variety of objects etc. are recognised by use of comparison with a relatively limited number of models. No doubt the process is a serial one, perhaps a filtering out of recognised features at each stage and then feeding back the rest through the system.

  This probably does not make much sense in exact terms and the only evidence for it is that people do group their reactions around relatively simple models – circle, god, father, machine, state, etc.

  Can we get anywhere by determining the storage capacity given by 1010 neurons if arranged in various ways and assuming facilitation of pathways by use? Is there any finite number of sorts of arrangement that they could have? For example, each with 100 possible outputs to others arranged a) at random through the whole or b) with decreasing frequency with distance. Given any particular plan of feedback can one compare the storage capacity of these plans, assuming say a given increase of probability of re-use of a pathway with each time of use?

  This is all very vague. If you have any ideas about the next important sorts of question to ask do let me know. Would it be a great help if we could give some sort of specification of the destinations of the output (within the cortex) of each cell? I feel we ought to be able to disentangle the pattern somehow.

  Yours, John Young.

  Alan’s reply made clear the connection between his interests in the logical and the physical structure of the brain:

  8th February 1951

  Dear Young,

  I think very likely our disagreements are mainly about the use of words. I was of course fully aware that the brain would not have to do comparisons of an object with everything from teapots to clouds, and that the identification would be broken up into stages, but if the method is carried very far I should not be inclined to describe the resulting process as one of ‘matching’.

  Your problem about storage capacity achievable by means of N (1010 say) neurons with M (100 say) outlets and facilitation is capable of solution which is quite as accurate as the problem requires. If I understand it right, the idea is that by different trainings certain of the paths could be made effective and the others ineffective. How much information could be stored in the brain in this way? The answer is simply MN binary digits, for there are MN paths each capable of two states. If you allowed each path to have eight states (whatever that might mean) you would get 3MN….

  I am afraid I am very far from the stage where I feel inclined to start asking any anatomical questions. According to my notions of how to set about it that will not occur until quite a late stage when I have a fairly definite theory about how things are done.

  At present I am not working on the problem at all, but on my mathematical theory of embryology, which I think I described to you at one time. This is yielding to treatment, and it will so far as I can see, give satisfactory explanations of –

  (i) Gastrulation

  (ii) Polygonally symmetrical structures, e.g. starfish, flowers.

  (iii) Leaf arrangement, in particular the way the Fibonacci series (0,1,1,2,3,5,8,13….) comes to be involved.

  (iv) Colour patterns on animals, e.g. stripes, spots and dappling.

  v) Pattern on nearly spherical structures such as some Radiolaria, but this is more difficult and doubtful.

  I am really doing this now because it is yielding more easily to treatment. I think it is not altogether unconnected with the other problem. The brain structure has to be one which can be achieved by the genetical embryological mechanism, and I hope that this theory that I am now working on may make clearer what restrictions this really implies. What you tell me about growth of neurons under stimulation is very interesting in this connection. It suggests means by which the neurons might be made to grow so as to form a particular circuit, rather than to reach a particular place.

  Yours sincerely, A. M. Turing

  A few days later, the Ferranti Mark I computer was delivered at the Manchester department, which by now had a newly built Computing Laboratory to house it. Alan wrote to Mike Woodger back at the NPL:

  Our new machine is to start arriving on Monday [12 February 1951]. I am hoping as one of the first jobs to do something about ‘chemical embryology’. In particular I think one can account for the appearance of Fibonacci numbers in connection with fir-cones.

  It had been twenty-one years, and the computer had come of age. It was as though all that he had done, and all that the world had done to him, had been to provide him with an electronic universal machine, with which to think about the secret of life.

  Much of the computer installation that he had imagined for the ACE had now come into being; people were soon to come to it with their problems; the ‘masters’ would program it and the ‘servants’ service it. They did indeed build up a library of programs. (In fact, it was just about Alan’s last contribution to the Manchester computing system that he laid down a way of writing and filing a formal description of the programs intended for common use.) He had a room of his own in the new computer building, and was, at least in theory, the chief ‘master’. The engineers moved on to design a second, faster machine (in which he took no interest whatever), and it was up to him to take charge of the use of the first one.

  There was plenty that could be done in the way of seminars and publications and demonstrations, for this was the world’s first commercially available electronic computer, beating by a few months the UNIVAC made by Eckert and Mauchly’s firm. It also enjoyed the firm support of the British government, whose National Research Development Corporation, chaired by the administrator Lord Halsbury, managed the investment, sales and patent protection after 1949. In fact they went on to sell eight copies of the Mark I, the first to the University of Toronto, for the design of the St Lawrence Seaway, then others* more discreetly to the Atomic Weapons Research Establishment and to GCHQ. With Alan fulfilling a consultant role for GCHQ, it may be reasonably supposed that he played a part in suggesting how they should use the universal machine he had promised to Travis six years or so before. But this was not where his heart lay now. As electronic computers began to impinge upon the world economy, Alan Turing continued to back away, and remained engrossed in the otherwise forgotten ‘fundamental research’.

  A big inaugural conference was planned for July, but this work was done entirely by the engineers and Ferranti Ltd. It was not that Alan got in the way; he simply avoided participation. No one could have guessed that officially he was paid to ‘direct’ the laboratory. In the spring of 1951 he found a way to off-load his remaining responsibilities when R. A. Brooker, a young man from the Cambridge EDSAC team, called in to have a look at the new machine on his way back from a climbing weekend in west Wales. For reasons of his own he liked the idea of moving to the North, and asked Alan if he had a job to offer. Alan said he did, and in fact Tony Brooker joined later in the year.

  Alan’s detachment was annoying to the engineers, who felt that their achievement was hardly getting the recognition it deserved within the mathematical and scientific world. In many ways the Computing Laboratory remained as secret as Hut 8, just as computation remained the lowest form of mathematical life. Recognition did, however, come to Alan Turing. In the 1951 elections, which took place on 15 March, he became a Fellow of the Royal Society. The citation referred to his work on computable numbers which had, of course, been done fifteen years earlier. Alan was rather amused by this and wrote t
o Don Bayley (who had sent his congratulations) that they could not really have made him an FRS when he was twenty-four. The sponsors were Max Newman and Bertrand Russell. Newman had lost all interest in computers and was only grateful that Alan had regenerated his pulse with the morphogenetic theory.

  Jefferson, himself a Fellow since 1947, also sent a letter of congratulation,52 saying ‘I am so glad; and I sincerely trust that all your valves are glowing with satisfaction, and signalling messages that seem to you to mean pleasure and pride! (but don’t be deceived!).’ He managed to confuse the logical and the physical levels of description even within one sentence. Alan would refer to Jefferson as an ‘old bumbler’ because he never grasped the machine model of the mind, but Jefferson certainly found an apt description of Alan,53 as ‘a sort of scientific Shelley’. Apart from the more obvious similarities, Shelley also lived in a mess,54 ‘chaos on chaos heaped of chemical apparatus, books, electrical machines, unfinished manuscripts, and furniture worn into holes by acids,’ and Shelley’s voice too was ‘excruciating; it was intolerably shrill, harsh and discordant.’ Alike they were at the centre of life; alike at the margins of respectable society. But Shelley stormed out, while Alan continued to push his way through the treacly banality of middle-class Britain, his Shelley-like qualities muted by the grin-and-bear-it English sense of humour, and filtered through the prosaic conventions of institutional science.

  Mrs Turing was very proud of the Fellowship, a title which raised Alan to the eminence of George Johnstone Stoney, and laid on a party at Guildford where her friends could meet him – hardly the function to appeal to Alan, who once walked wordlessly out of a sherry party to which his brother had invited him, after a bare ten minutes. His mother found it hard to overcome her amazement that important personages could speak well of her Alan, but in this respect she was making progress, and had come a long way since the 1920s. Although Alan complained to his friends of her patronising fussiness and religiosity, there remained the fact that she was one of the few people who took an interest in his doings. Mostly this came out in her efforts to improve Alan’s domestic life, with instructions on the right and wrong ways to perform each little routine. (‘Mother says …’, Alan would explain to Robin, with a half-amused, half-exasparated twinkle.)

  Nor was their contact very frequent; Alan would visit Guildford about twice a year, annoying both mother and brother by announcing his imminent arrival with a telegram or postcard and no more. His mother made the journey to Wilmslow once in the summer each year. Besides the postcards there might be a few telephone calls; Alan finding for instance that they both liked the stories on Children’s Hour and telling her when a good one was coming. But Mrs Turing did like to have the feeling of involvement in Alan’s work, and felt happier with the biology than with the computers. Although she really had no clue as to what he was doing at Manchester, she would help with the wild flowers and the big maps. With her nineteenth-century optimism she construed it in terms of usefulness to humanity, bringing him closer to the Pasteur of whom she had long ago dreamed. Perhaps, she speculated, it might lead to a cure for cancer! It was not a foolish connection to draw, but it was not his motive. Nor was there any way of knowing where his Faustian dabblings might lead this time; they were just as relevant to the state-controlled embryology of Brave New World. Even if his practical methods had something in common with the naive natural history of the past century, and even if it meant a return to childhood fascinations, his work lay firmly within the great modernisation of biology, in which the technical advances of the 1930s were being followed by the application of the quantitative analysis so triumphant in physics and chemistry. The problem of life could no longer be allowed to lag behind; they had to know how its machinery worked.

  Appreciation in the Computing Laboratory was on a more down-to-earth level. There history began in 1951, and no one connected with the computer knew about Computable Numbers. At the NPL there had been strong connections with Cambridge mathematics and with the Royal Society; the new masters of the Mark I were quite a different crew, and had no sense of his past. Nor did Alan try to explain. An applied mathematics research student, N. E. Hoskin, had just become involved in using the new computer, and when he said over coffee ‘I never thought of you as an FRS,’ Alan just laughed – with that wince-inducing, mechanised laugh.

  He did look young for an FRS, although at thirty-eight he was by no means the youngest to be elected. Hardy had been elected at thirty-three, and the self-taught Indian mathematician Ramanujan at thirty. Maurice Pryce was also elected in 1951, so in this respect Alan had caught up a year on the mathematical physicist, whom he did not meet again after the war. Writing to Philip Hall at King’s, who also had congratulated him, he said it was ‘very gratifying to be about to join the Olympians’. After a mathematical description of his ‘waves on cows’ and ‘waves on leopards’, he added ‘I am delighted to hear Maurice Pryce is also in the list. I met him first when up for scholarship exam in 1929, but knew him best in Princeton. He was quite my chief flame at one time.’ In what was more of a mathematician’s joke he wrote, ‘I hope I am not described as “distinguished for work on unsolvable problems”.’

  In his retirement from the organisation of the laboratory, it barely impinged on Alan that the new computer was used to perform calculations for the British atomic bomb. A young scientist, A. E. Glennie, spent time at Manchester on this work. He would sometimes chat with Alan about mathematical methods, though it went no further than talk in general terms. Once, however, Alick Glennie found himself collared by Alan, when he wanted a ‘mediocre player’ on whom to try out his current chess-playing program. They went back to Alan’s room for three hours in the afternoon. Alan had all the rules written out on bits of paper, and found himself very torn between executing the moves that his algorithm demanded, and doing what was obviously a better move. There were long silences while he totted up the scores and chose the best minimax ploy, hoots and growls when he could see it missing chances. It was ironic that, despite all the developments of the past ten years, he was little closer to actually trying out serious chess-playing on a machine – the existing computers had neither speed nor space for the problem.*

  Alick Glennie sometimes thought of Alan as Caliban, with his dark moods, sometimes gleeful, sometimes sulky, appearing in the laboratory on a somewhat random basis. He could be absurdly naive, as when bursting with laughter at a punning name that Glennie made up for an output routine: RITE. To Cicely Popplewell he was a terrible boss, but on the other hand, there was no question of having to be polite or deferent to him – it was impossible. He was regarded as a local authority on mathematical methods; those who wanted a suggestion would just have to ask him straight out, and if they could keep his interest and patience, they might get a valuable hint. Alick Glennie was rather surprised by his knowledge of hydrodynamics. All the same, he was no world-standard mathematician, and it was often more amazing to the professional mathematician what he did not know, than what he did. He never approached the von Neumann status or breadth of knowledge; indeed he had read very little mathematics since 1938.

  In April 1951 he had another look at the word problem for groups, and came up with a result which J. H. C. Whitehead at Oxford found ‘sensational’ – but it was never published.55 Max Newman kept him interested in topology, and he went to seminars. But the trend of postwar pure mathematics was moving away from his interests. Mathematics was flowering through a greater and greater abstraction for its own sake, while Caliban on his island remained somewhere in between the abstract and the physical. Nor was he a keen conference-goer, loathing the academic chit-chat, but he went to the British Mathematical Colloquia that Max Newman helped to get started. In spring 1951 he went with Robin to one at Bristol, which got him interested in discussing topology with the mathematician Victor Guggenheim. But these were only diversions.

  Another diversion was offered by the BBC, whose new highbrow Third Programme was offering a series of five talks on
computers. One was by Alan, the others by Newman, Wilkes, Williams and Hartree. Alan’s went out on 15 May 1951 and was entitled ‘Can Digital Computers Think?’. Largely it ran over the ground of the universal machine and the imitation principle.56 There were some references to the ‘age-old controversy’ of ‘free will and determinism’, which harked back twenty years with a mention of Eddington’s views on the indeterminacy of quantum mechanics, and back ten years with some suggestions on how to incorporate a ‘free will’ element in the machine. It could be done either by ‘something like a roulette wheel or a supply of radium’ – that is, by the kind of random number generator that worked like the Rockex tape generator, off random noise – or else by machines ‘whose behaviour appears quite random to anyone who does not know the details of their construction.’ His listeners could scarcely have imagined the secrets which lay behind that bland suggestion! He ended with his justification for investigating machine intelligence:

  The whole thinking process is still rather mysterious to us, but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves.

  This short talk did not include any details of how he proposed to program a machine to think, beyond the remark that it ‘should bear a close relation to that of teaching.’ This comment sparked off an immediate reaction in a listener: Christopher Strachey, the son of Ray and Oliver Strachey.