Alan Turing: The Enigma (95 page)

Mrs Webb was just the latest person
to be given a talk on the Fibonacci spiral pattern of the fir cone, the pattern which showed itself also in the seeds in sunflower heads, and the leaf arrangements of the common plants. It was the problem of explaining its occurrence in nature that he set himself as a serious challenge. But this required the analysis of a two-dimensional
surface
, and he chose to leave it while he first considered in detail some rather simpler cases.

In a chapter called ‘Nature’s Repair Shop’, Brewster had dwelt upon the regeneration of the
Hydra
, the small fresh water worm, which could grow a new head or new tail from any chopped-off section. Alan took the hydra, with its simple tubular form, and simplified it yet again, by neglecting its length, and concentrating upon the idea of a
ring
of cells. Then, he found, taking a model of just two interacting chemicals reacting and diffusing around this ring, that he was able to give a theoretical analysis of all the different possibilities for the moment of budding. And the idea, although admittedly in a grossly oversimplified and hypothetical way, actually worked. It appeared that under certain conditions the chemicals would gather into stationary waves of concentration, defining a number of lobes on the ring. These, it could be imagined, would form the basis for the pattern of tentacles. The analysis also showed the possibility of waves gathering into asymmetrical lumps of concentration, which reminded him of the irregular blotches and stripes on animal hides. With this last idea he did some experimental numerical work. By the end of 1950 the prototype computer had been closed down, and the scientists at the university were waiting for the new one to arrive from Ferranti, so this work was done on a desk calculator. It produced a dappling pattern rather resembling that of a Jersey cow. He was beginning to
do something
once more.

At Christmas 1950 Alan met J.Z. Young again, to follow up the discussion about brain-cells that they had had in October 1949. Young had just given the Reith Lectures for 1950,
⁴⁹
presenting a rather aggressive statement of the claims of neuro-physiology to explain behaviour. Young later recalled
⁵⁰
Alan’s

… kindly teddy-bear quality as he tried to make understandable to others, ideas that were still only forming in his own mind. To me, as a non-mathematician, his exposition was often difficult to follow, accompanied as it was by funny little diagrams on the blackboard and frequently by generalizations, which seemed as if they were his attempt to press his ideas on me. Also, of course, there was his rather frightening attention to everything one said. He would puzzle out its implications often for many hours or days afterwards. It made me wonder whether one was right to tell him anything at all because he took it all so seriously.

They talked about the physiological basis of memory and of pattern recognition. Young wrote:
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 10
¹⁰
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 (10
¹⁰
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 to 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.)