The actual size of the ACE as originally contemplated was the outcome of long consideration by Mr Womersley and Professor von Neumann during Mr Womersley’s visit to the United States.
Already by 1950, Alan Turing was an unperson, the Trotsky of the computer revolution.
But he was never one to complain, once he had made his decision. In many ways his position at Manchester was parallel to that at Hanslope, in terms of status and class and struggles over equipment. One difference was the harshness of the Manchester environment, which surely exacerbated his rudeness. Another was that in 1943 his move sideways and downwards had gained for him practical experience with electronics. In 1948 it gained for him the use of a computer. And this remained a paramount consideration. He had conceived of a universal machine, and now he could work or play with one of the two that existed in the world of 1949. There was a method in his madness.
For the time being he contented himself with paying off some scores to old days that would vindicate the power of the universal machine. The first thing he did was to revive the zeta-function calculation. The gear wheels that had been cutting when the phoney war broke in could now be replaced by instructions on the tape of a universal machine, in the phoney peace of 1950. It did not go quite according to plan, this being partly the machine’s fault and partly his own:19
In June 1950 the Manchester University [prototype] Electronic Computer was used to do some calculations concerned with the distribution of the zeros of the Reimann zeta-function. It was intended in fact to determine whether there are any zeros not on the critical line in certain particular intervals. The calculations had been planned some time in advance, but had in fact to be carried out in great haste. If it had not been for the fact that the computer remained in serviceable condition for an unusually long period from 3p.m. one afternoon to 8a.m. the following morning it is probable that the calculations would never have been done at all. As it was, the interval 2π.632
… The interval 1414
This was an unusual joint exercise, on which Kilburn stood by all night. Alan would hold up the output teleprinter tape to the light to read:
The content of a tape may afterwards automatically be printed out if desired [sic] … the output consisted mainly of numbers in the scale of 32 … writing the most significant digit on the right. More conventionally the scale of 10 can be used, but this would require the storage of a conversion routine, and the writer was entirely content to see the results in the scale of 32, with which he is sufficiently familiar.
Another old score, that of the Enigma, was also paid off at about this time:20
I have set up on the Manchester computer a small programme using only 1000 units of storage, whereby the machine supplied with one sixteen figure number replies with another within two seconds. I would defy anyone to learn from these replies sufficient about the programme to be able to predict any replies to untried values.
He had, in other words, devised a cipher system which he reckoned impregnable even with the help of known plain-text. The lumbering wheels of the Second World War were already heading towards the same obsolescence as that of his zeta-function machine.
There were some other hints of a continued interest in cryptology. Another item that he demanded from the engineers as a hardware function of the Mark I Ferranti machine was what they called a ‘sideways adder’. It would count the number of ‘1’ pulses in a 40-bit sequence. This would have no application in a numerical program, but would be very useful in one where the digits coded ‘yes’ or ‘no’ answers to some Boolean question, and it was required to count the ‘yes’ answers – just what the Colossus had done. Such applications might possibly have been spare-time interests of his own. However, it was during this period, as the international situation hardened, that he found himself consulted by GCHQ. It would indeed have been remarkable had they not consulted the person who knew more about cryptology and the potential of electronic computers than did anyone else. And had he not described cryptanalysis as the most ‘rewarding’ field for the application of programming? Few, however, were in a position to perceive this fact, the subject being more secret than ever.
A hark-back to cryptology also featured in his discussions with a young American, David Sayre, in this period. A graduate of the wartime MIT Radiation Laboratory, Sayre was now at Oxford studying molecular biology with Dorothy Hodgkin. Having worked with F. C. Williams during the war, he made a visit to Manchester to see the computer, explaining that it might help in X-ray crystallography. Williams passed him on to Alan, who showed an unusual kindness and geniality, making Sayre21 ‘perfectly at ease with him’. They talked for two and a half days, interrupted only when ‘the telephone would ring to say that the machine was free for a few minutes in case he wanted to use it, and he would gather up sheaves of paper and ribbons of punched paper tapes … and disappear for a bit.’
David Sayre was able to guess that Alan had worked on cryptological problems during the war. The point was that X-ray crystallography, which was now being applied to the problem of determining the structure of proteins, was remarkably similar in nature to cryptanalysis. The X-rays would leave a diffraction pattern, which could be regarded as the encipherment of the molecular structure. Performing the decipherment process was closely analogous to the problem of finding both plain-text and key, given the cipher-text alone.* The result of this analogy was that
… Before we finished he had re-invented by himself most of the methods which crystallographers, up to that time, had worked out. He had, for this purpose, a breadth of knowledge greatly surpassing that of any crystallographer I have known, and I am confident that he would have advanced the crystallographic situation very decidedly if he had worked in it seriously for a time. As it was, he may have had hold of one line which in 1949 had not yet appeared in crystallography, concerned with establishing quantitatively how much information it is necessary to have on hand at the outset of a search for a solution to ensure that a solution can be found.
Alan told him about the Shannon theorem which he had exploited for the Delilah, and Sayre made use of it in a paper22 which much advanced the theory of the subject. But Alan did not decide to work seriously in this area, although he encouraged young Sayre to return and use the Manchester machine for computations; this was a branch of science where exciting progress was being made, and yet for him it would perhaps have been too much a research into things past, like all these other 1949 encounters. Or perhaps it would have been too crowded and competitive a field. He always wanted something that would be self-contained.
Claude Shannon was himself another visitor. Since 1943, their discussions on machines and minds, information and communication, had been opened up to all. In September 1950 there was a London symposium23 on ‘information theory’, at which Shannon was the star guest. His paper24 on chess-playing, which explained the principles of minimax play and tree searching, had just appeared. Someone reviewed it and made a remark that Alan thought had confused cause and effect, or in typical Turing language, it was
… like taking a statistical analysis of the laundry of men in various positions and deciding, from the data collected, that an infallible method of getting ahead in life was to send a large number of shirts to the wash each week.
Afterwards, Shannon went to Manchester to see the prototype machine, then in its last days, and Alan told him all about the zeta-function calculation.*
The conference which gave occasion to this visit was a manifestation of the ‘cybernetics’ movement. Another was that in July 1949, following a talk by K. Loren
z at Cambridge on animal behaviour, an informal cybernetics discussion group had been started, meeting in London about once a month over a dinner. It was called the Ratio Club. McCulloch who with Wiener was one of the original high priests of cybernetics, addressed the first meeting. (He also travelled to Manchester to see Alan, who thought him ‘a charlatan’.) Alan was not in the Ratio Club’s founding group, but at the first meeting, his name was put forward25 by Gold and the biologist John Pringle, who had been Alan’s undergraduate contemporary at King’s.
Thereafter Alan used to go to meetings every few months, and found them good entertainment. Robin Gandy went to some meetings later, and Jack Good joined after attending Alan’s talk on ‘Educating a Digital Computer’ in December 1950. Uttley from TRE and the philosophical physicist D. Mackay, were also very interested in machine intelligence, while W. Grey Walter and W. Ross Ashby, neurologists who both brought out early and influential books26 on cybernetic ideas, were keen members. (Grey Walter made some motorised ‘tortoises’ which could recharge themselves when their batteries were low.) The meetings were held at the National Hospital for Nervous Diseases, whose John Bates acted as secretary and galvaniser. There was a lot of enthusiasm, though it fell off over the next few years, as it was found that cybernetics offered no immediate solutions to the problems posed by human beings.
In some ways it was an attempt to revive the democratic association of young scientists which had characterised the war years. They excluded those of professorial rank, and Alan’s light touch went down well. Many of the Ratio Club had worked at TRE, where they had held what were called Sunday Soviets, according to the illusions of the day – much the same way as each section worked at Bletchley. It was just a faint ghost of the ‘creative anarchy’.
As it happened, Peter Hilton from Bletchley days had left Oxford to join the Manchester mathematics department in 1948, and Alan took him to see the machine which in some ways had grown out of their experiences. Peter Hilton was also present at a discussion in the department in 1949 which also touched upon subjects in Alan’s remoter past, the two fields of group theory and mathematical logic which had set his professional career in motion.
The discussion concerned the ‘word problem’ for groups. This was like the Hilbert Entscheidungsproblem that Computable Numbers had settled, but instead of asking for a ‘definite method’ for deciding whether or not a given theorem was provable, it asked for a definite method for determining whether or not some given product of group elements was equal to some other given product; that is, whether some given sequence of operations would have the same effect as some other sequence.* Emil Post had given the first new result in this direction in 1943, by showing that the word problem for ‘semi-groups’ was insoluble.† The question for groups still remained open. Peter Hilton was amazed because27
Turing claimed he had never heard of this problem, and found it a very interesting problem, and so, though at that time his principal work was in machines, he went away and about ten days later announced that he had proved that the word problem was unsolvable. And so a seminar was arranged at which Turing would give his proof. And a few days before the seminar he said: ‘No, there was something a little wrong in the argument, but the argument would work for cancellation semi-groups.’ And so he in fact gave his proof for cancellation semi-groups.‡
The proof required quite new methods, technically more difficult than those of Computable Numbers, in order to relate the ideas of doing and undoing operations to the action of a Turing machine. It showed that at any time, even though he was so out of touch, he could revert to being ‘a logician’. It was a great comeback, and yet for him it would not have been coming back, but going back. He spent some more time on the original problem for groups, but did not dedicate himself to it. It offered the innocence of the work of his twenties, before he had got mixed up with the world’s affairs. But it did not offer the direction in which to move onward.
Alan submitted his results28 to von Neumann’s journal, where it was received on 13 August 1949, and elicited a reply29 from the big man himself:
September 13 1949
Dear Alan,
… Our machine project is moving along quite satisfactorily, but we aren’t yet at the point where you are. I think that the machine will be physically complete early next year. What are the problems on which you are working now, and what is your program for the immediate future?
With best regards, Yours sincerely, John
Von Neumann’s machine at the IAS was lagging years behind because the Iconoscope, upon which such hopes had been placed, could not be made to work. The first American computers to be completed were Eckert and Mauchly’s BINAC, used for aircraft engineering, in August 1950, and then the CSAW’s cryptanalytic ATLAS in December 1950. But by late September 1949 the Soviet Union had tested its atomic bomb, and this encouraged the American decision in early 1950 to construct a thermonuclear weapon. The IAS machine and its copy MANIAC at Los Alamos were then pushed ahead, although even so it was 1952 before they were completed. The 1950–52 calculation for H-bomb feasibility was performed by 1930s methods, with slide rules and desk calculators, absorbing years of human work. In the end they had to scrap the special Iconoscope and use Williams’ ordinary cathode ray tubes. With two assistants, he had beaten American industry. It was still possible for British ingenuity to ‘jump in ahead of the Americans’.
But where did this leave Alan? What was his programme for the immediate future? It was a very pertinent question that the Wizard posed to Dorothy – not least because the facilities of the Manchester computer, when completed, would not match the ambitions spelt out by Alan in 1948 for ‘learning’ and ‘teaching’ and ‘searching’. He had to reconcile himself to the fact that those ideas were dreams on the edge of reality, and find some new way in which to continue.
Meanwhile the claims of cybernetics had attracted the attentions of philosophers more weighty than Jefferson, and Alan was drawn into a more professional defence of his views. The motive force was supplied by Michael Polanyi, the Hungarian emigré who had held the Chair of Physical Chemistry at Manchester from 1933 to 1948, since when he had occupied a new Chair of ‘social studies’, specially created to facilitate his philosophical ambitions.
Polanyi had long led an opposition to the notions of Planned Science. Even during the war he had founded a ‘Society for Freedom in Science’, and after the war attempted to combine political and scientific philosophy, marshalling a variety of arguments against various kinds of determinism. In particular, he seized on Gödel’s theorem as a proof that mind would do something that was beyond any mechanical system. It was this subject that most engaged Alan and Polanyi in discussion. Alan would run over to the Polanyi home, which was not far from his lodgings at Hale. (Once Polanyi visited Alan, only to find him practising the violin in freezing cold, not bothering or not daring to ask the landlady for proper heat.) But Polanyi had many other suggestions up his sleeve. He rejected Eddington’s argument for free will from the Uncertainty Principle. But, unlike Eddington, he thought that the mind could interfere with the motions of molecules, writing that30 ‘some enlarged laws of nature may make possible the realization of operational principles acting by consciousness’, and that the mind might ‘exercise power over the body merely by sorting out the random impulses of the ambient thermal agitation.’
Polanyi also favoured an extension of the ‘Jabberwocky’ argument, that science was all in the mind anyway, and had no meaning apart from the ‘semantic function’ which the human mind alone could supply. Karl Popper, who held similar views, said in 195031 that ‘It is only our human brain which may lend significance to the calculators’ senseless powers of producing truths.’ Popper and Polanyi both held that people had an inalienable ‘responsibility’, and that science only existed by virtue of conscious, responsible decisions. Polanyi held that science should rest on a moral basis. ‘My opposition to a universal mechanical interpretation of things,’ he wrote, ‘… also imp
lies some measure of dissent from the absolute moral neutrality of science.’ There was a schoolmasterish tone to this ‘responsibility’ that was rather different from gentle Eddington’s vision of Mind-stuff perceiving the spiritual world. There was also a powerful Cold War thread to it. Polanyi attacked the Laplacian picture on the grounds that it ‘induces the teaching that material welfare … is the supreme good’ and that ‘political action is necessarily shaped by force.’ These unpalatable doctrines he associated with the Soviet government rather than with that of the other Great Power, complaining at the suggestion that ‘all cultural activities should subserve the power of the State in transforming society for the achievement of welfare.’ Alan liked the point that all measurements ultimately involved an element of decision, and produced for Polanyi a photograph of a horse-race finish, in which of two neck-and-neck horses one could be said to have won if a jet of spittle were counted as part of its body, and not otherwise – a contingency not allowed for in the rules.32 But the thrust of the Christian philosopher’s arguments lay in a very different direction from his own.
This was the background to a formal discussion on ‘The Mind and the Computing Machine’33 held in the philosophy department at Manchester on 27 October 1949. Just about everyone in British academic life with a view to express had been assembled. It began with Max Newman and Polanyi arguing about the significance of Gödel’s theorem, and ended with Alan discussing brain cells with J. Z. Young, the physiologist of the nervous system. In between, the discussion raged through every other current argument, the philosopher Dorothy Emmet chairing. ‘The vital difference,’ she said during a lull, ‘seems to be that a machine is not conscious.’
But such a use of words would satisfy Alan no more than would Polanyi’s assertion that the function of the mind was ‘unspecifiable’ by any formal system. He wrote up his own view, which appeared as a paper, ‘Computing Machinery and Intelligence’,34 in the philosophical journal Mind in October 1950. It was typical of him that the style he employed in this august journal was very little different from that of his conversation with friends. Thus he introduced the idea of an operational definition of ‘thinking’ or ‘intelligence’ or ‘consciousness’ by means of a sexual guessing game.
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 65