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

by Andrew Hodges

  Smith explained that this was very difficult. ‘Apart from the small number of staff now working for Dr F. C. Williams most of the able circuit technicians had been transferred to the Department of Atomic Energy’ – a statement reflecting another post-war story. So ‘the only way in which TRE could continue to contribute would be to second a small number of staff … to work under Dr Williams’ direction at Manchester University.’ This was not at all what Sir Charles Darwin wanted to hear, but he did not give up. The meeting was enlarged to include Williams and Uttley from TRE, and Womersley for the NPL, while Alan was allowed in as well. In the discussion of the ACE

  … It appeared that although an elaborate paper design had been laid down, the fundamental problem of storage of information had not been solved and that, as had been suspected, the experimental work of Dr Williams at TRE on storing information on a cathode ray tube was considerably in advance of the work which the Post Office were doing on the use of delay lines for storage purposes ….

  Williams had, in fact, already succeeded in storing a spot on a cathode ray tube for an indefinite period. A compromise formula was agreed, according to which Williams’ work ‘should continue with as little disruption as possible’. The NPL drafted a contract for Williams to sign, according to which he would develop both electronic storage and components for the arithmetical hardware.

  There was, however, a triple misunderstanding. For one thing, there was still the strong possibility of Manchester funding allowing Williams to develop his storage independently of NPL requirements. For another, the ACE design and programming had been done for a delay line store, and would have to be completely reworked if policy changed to the use of cathode ray tubes. Very probably Darwin and Womersley did not appreciate that the storage medium effectively dictated many aspects of the design of the machine and its programming. Alan might not have minded rewriting everything if it meant that progress could be achieved, but there was a deeper difficulty. While Darwin spoke as though he had had a ‘mathematician’ to lay down a design, and now was finding a practical man to build it, Williams’ attitude was that he was negotiating for funds wherewith to construct his computer. They were talking at cross-purposes. Success would depend upon bridging that gap, so closely tied in with social class, between ‘mathematics’ and ‘engineering’. But the crossing of demarcation lines was very difficult now. No longer was Germany enforcing cooperation upon its enemy.

  Hartree, wanting to see more cooperation, took the next step. On 19 November he explained to Darwin that ‘Mr Wilkes was prepared to give as much help as he could on the ACE as he had facilities at Cambridge; he had experience of making up [delay] lines and would exchange information with Dr Turing.’ Next day Wilkes wrote28 to Womersley:

  I believe Professor Hartree has told you that I am beginning to do a little work on electronic calculating machines and that I am anxious to co-operate with you. As you know I recently paid a visit to the United States and saw what they are doing over there. Professor Hartree said he had discussed the matter with you and thought perhaps we might be able to make some mutually advantageous arrangement.

  Wilkes visited the NPL a week later, on 27 November, to discuss his plans. On 2 December he wrote again:

  I have been thinking over in more detail the subject we were discussing last Wednesday and what I have now in mind is that I should build up a group here containing about eight people of varying grades in addition to the mechanic and boy who are at present in the workshop. This would involve an annual wage bill of something like £2,500. In addition there will be cost of materials and getting things made outside.

  I am quite convinced that the construction of a pilot model of some sort is an essential step in designing ACE.* I do not see how else one can test out such things as control circuits. I am attaching a note I have written on the design of the pilot model and I think it would be a good thing if you decide to place a contract with us to call for this specifically. It does not follow that no part of ACE may be ordered until the pilot model is finished but there will be many matters which it will be hard to settle, without experience at least of trying to get a pilot model working.

  But the attached note outlined the specification of a computer on the EDVAC model, and thus entirely different from the ACE. Not only did it employ a central accumulator, but it ran counter to the Turing philosophy of keeping the hardware as simple as possible, and putting the work into the programming. Instead, it made the programming as easy as possible, at the cost of requiring electronic circuits to do the work of recognising and executing the various arithmetical instructions. Wilkes wrote apparently in ignorance of the fact that at the NPL they already had Version VII of a detailed design, for which six months’ hard work had been put into writing programs. Even to contemplate Wilkes’ proposal, as Womersley apparently did, was to undermine his own division’s work. On 10 December he passed the proposal to Alan, whose reaction was understandably brusque:

  Mr Womersley:

  I have read Wilkes’ proposals for a pilot machine, and agree with him as regards the desirability of some such machine somewhere. I also agree with him as regards the suitability of the number of delay lines he suggests. The ‘code’ which he suggests is however very contrary to the line of development here, and much more in the American tradition of solving one’s difficulties by means of much equipment rather than by thought. I should imagine that to put his code (which is advertised as ‘reduced to the simplest possible form’) into effect would require a very much more complex control circuit than is proposed in our full-size machine. Furthermore certain operations which we regard as more fundamental than addition and multiplication have been omitted.

  It might be argued that if one is to have so little memory then it is necessary to have a complex control to make up. In so far as this is true I would say that it is an argument for either having no pilot model, or for not using it for serious problems. It is clearly rank folly to develop a complex control merely for the sake of the pilot model. I favour a model with a control of negligible size which can later be expanded if desired. Only test problems would be worked on the minimal machine.

  But Womersley wrote back to Wilkes on 19 December:

  Thanks for your suggestions regarding the pilot model for the ACE. They don’t quite agree with Turing’s ideas of what a minimal machine should be. In his opinion the control part of it is too elaborate though he agrees about the amount of memory. I have therefore asked him to prepare a note giving his ideas of what the minimal machine should contain, and this I propose to send to you (without commitment on either side) so that we can meet and discuss further the question of a formal contract.

  Meanwhile the publicity given to the ACE had engendered a couple of enquiries from British industry regarding the potential of the new machine. On 7 November the editor of the Industrial Chemist had requested an article from Alan, who replied that while the ACE ‘would be well adapted to deal with heat transfer problems, at any rate in solids or in fluids without turbulent motion,’ he thought that an article would be appropriate only ‘when a few similar problems have actually been solved with the ACE and more practical details can be given.’ On 11 November, Alan had been invited to give a paper to the Institution of Radio Engineers, to which Mountbatten had vouchsafed his revelations a few days earlier. In this case, however, Alan had to write:29

  I am sorry that I cannot give such a paper without permission from our Director. I suggest you write to him about it.

  The administrators, by this time, were concerned to reduce to a minimum the exposure of Alan Turing to the outside world. There had already been enough embarrassment in the newspapers. Thus Womersley suggested to Darwin that ‘Dr Turing, rather than explaining his machine to a number of isolated people on many different occasions, should conserve his time by giving a course of lectures intended primarily for those who will be concerned with the technical development of the machine….’ Such a course was indeed arranged to take place on Thursday
afternoons during December and January at the Adelphi, headquarters of the Ministry of Supply.30 The invitations, less than twenty-five in all, went to the relevant electronic engineers, component manufacturers, military departments, and to a few others already in the know. The scene was set for a British equivalent of the Moore School lectures, although the setting was subtly different. According to an NPL memorandum, there was to be ample time after Alan’s exposition for ‘Discussion – in particular, criticism of Dr Turing’s technical proposals.’ They did not trust him to know what he was talking about. Criticism was, in any case, inevitable; for by this time several of those who attended had ideas of their own, and no inclination to be fitted into the Turing plans. Wilkes wrote31 later that he

  found Turing very opinionated and considered that his ideas were widely at variance with what the main stream of computer development was going to be. I may have gone to his second lecture but I certainly went to no more. Hartree continued to go and insisted on giving me his notes, but I found them of little interest.

  On the other hand, lectures on elementary electronics did not go down well with those from TRE, who could also see for themselves how the ACE design was built round the delay line storage. It had been intended that ‘from these discussions would emerge more clearly what contribution TRE should make’ to the ACE. This was indeed to happen, but not in the way that Darwin had hoped.

  As it happened, the scheme of lectures was suddenly disrupted, thanks to the arrival of a letter from America. On 13 December Womersley found himself invited to a grand Symposium on Large Scale Digital Calculating Machinery to be held at Harvard from 7 to 10 January, in connection with the inauguration of Aiken’s Mark II relay calculator. But Darwin quickly decided that it would be better for Alan to drink at the fount of American wisdom, making arrangements for him to attend the conference, and then to visit the ENIAC and the von Neumann group. Jim Wilkinson took over the Adelphi lectures. Alan spent Christmas at David Champernowne’s parents’ house at Dorking, and in a Boxing Day athletics meeting lost the three-mile race by one foot,32 with a time of 15 minutes, 51 seconds. The sports reporter of the Evening News obtained a unique statement from him regarding the authorship of the digital computer:

  ‘ELECTRONIC’ ATHLETE

  Antithesis of the popular notion of a scientist is tall, modest, 34-year-old bachelor Alan M. Turing, scratch man in the Walton Athletics Club’s three-mile open event on Boxing Day.

  Turing is the club’s star distance runner, although this is his first season in competitive events. At the National Physical Laboratory, at Molesey [sic], he is known as Dr Turing, [and] is also credited with the original idea for the Automatic Computing Engine, popularly known as the Electronic Brain.

  He is diffident about his prowess in science and athletics, gives credit for the donkey work on the ACE to Americans, says he runs only to keep fit, but admits he rowed in his college eight at Cambridge.

  After trying and failing to find a post office so that he could mail his sweater and pullover to his mother, who took in his non-shrink washing, he boarded the Queen Elizabeth that evening. This visit to the land of Oz was a very pale reflection of the liaison of just four years before. But taking the laundry parcel with him, to be ‘lugged round America’ in a characteristically awkward Turing style, he went to see the donkey workers.

  The conference had brought together almost every conceivable interested American party,* but Alan was the only British participant. He played a large part in the discussions. For example, he discussed the cathode ray tube storage proposals made by J. W. Forrester and J. A. Rajchman, the latter being responsible for development of the Iconoscope at RCA. His discussion33 was in characteristic style, taking an engineering problem and locating a point of abstract principle that lay behind it:

  Dr Turing: I do not know whether I should really ask my question of Dr Rajchman or Dr Forrester, because this difficulty arises in both papers. Dr Forrester mentioned that there was a possibility of reconstituting the charge by use of low velocity electrons and said that Dr Rajchman would explain it in his paper. I understand from Dr Forrester that the method should be applicable to his type of storage. But there seems to me to be a fundamental difficulty which in principle amounts to this: unless the storage medium has some kind of association with the granular structure, such a method cannot be applicable because if any one such pattern is stable, then by a symmetry argument, by a slight shift one way or the other, as it were, a slightly different configuration is also stable. Thus you do not get a finite number of stable configurations, but an infinite number.

  He also identified the guiding principle which distinguished his plans for the ACE from those of the von Neumann group and of Wilkes:

  We are trying to make greater use of the facilities available in the machine to do all kinds of different things simply by programming rather than by the addition of extra apparatus….

  This is an application of the general principle that any particular operation of physical apparatus can be reproduced within the EDVAC-type machine.* Thus, we eliminate additional apparatus simply by putting in more programming.

  The conference brought Alan into contact with Claude Shannon and Andrew Gleason again. He also took the opportunity to brush up and submit to Alonzo Church’s journal some wartime work on type theory.34

  Afterwards, Alan spent about two weeks at Princeton. The Americans were no further ahead in constructing an electronic computer than was the NPL, and had run into parallel problems. The line between ‘mathematics’ and ‘engineering’ was one of these, Eckert and Mauchly having split off to found their own company, and a patent suit over aspects of the EDVAC design being in progress. Von Neumann and Goldstine had been thinking, like Alan, about the problem to do with the numerical analysis of matrix inversion, and also about the physics of mercury delay lines.35 Goldstine got the false impression that Alan thought delay lines could not work. This might have been because Alan talked about some of the more subtle difficulties. He had, for instance, already devised a grid36 (later patented) to be inserted in the short ‘temporary storage’ lines to prevent reflected pulses from travelling backwards.

  He did not bring anything back from America which changed his ideas about the ACE. This was the one kind of liaison which at the present time he did not need at all, and it had been irrelevant to his plans. But he brought back some presents – some nylons and dried fruit for his mother, and a food parcel for Robin Gandy which included a much-valued tin of cream. Britain was now even more severely rationed than during the war, the balance of payments proving a sterner constraint than the U-boats. And as he returned across the Atlantic, the bitter winter of early 1947 had set in.

  The talk of cooperation was still going on, but it was only talk. On 21 January E. S. Hiscocks, the NPL Secretary, had reported that ‘the Post Office had succeeded in keeping a number circulating for half an hour through their delay line set-up. This news was very encouraging. Professor F. C. Williams’s work on electronic storage will, of course, continue.’ But two days later Williams had declined the NPL contract and the illusion that he was doing work for the ACE finally crumbled away. Wilkes had written to Womersley on 2 January, expecting a contract, the incompatibility in design notwithstanding. (‘I shall be glad to hear of Turing’s ideas on the subject of a pilot model.’) This letter remained embarrassingly in Womersley’s in-tray. Another of Hartree’s ideas had proved to be more realistic. He had invited H. D. Huskey, one of the ENIAC team, to spend 1947 as a sabbatical year at the NPL, and he was already installed when Alan arrived back in a shivering Britain to give the last of the talks at the Ministry of Supply. The rationale37 was that he would bring with him American expertise especially on ‘the apparatus side’. But otherwise, the twelve months of 1946, a period within which the Colossus had been designed and built from scratch, had passed and nothing had happened. Alan took advantage of his American tour to summarise the state of affairs at the NPL:

  My visit to the USA has n
ot brought any very important new technical information to light, largely, I think, because the Americans have kept us so well informed during the last year. I was able, however, to get a useful impression of the values of the various projects, and the scale of their organisation. The number of different computing projects is now so great that it is no longer possible to have a complete list. I think this is a mistake, and that they are dissipating their energies over too wide a range. We ought to be able to do much better if we concentrate all our effort on the one machine, thereby providing a greater drive than they can afford on any single one. At the present, however, our effort is puny compared with any one of the larger American projects. To give an idea of the numbers of people involved in this work in the USA I may mention that there were between 200 and 300 present at the Symposium at Harvard, and that about 40 technical lectures were given. We are quite unable to match this.

  One point concerning the form of organisation struck me very strongly. The engineering work was in every case being done in the same building with the more mathematical work. I am convinced that this is the right approach. It is not possible for the two parts of the organisation to keep in sufficiently close touch otherwise. They are too deeply interdependent. We are frequently finding that we are held up due to ignorance of some point which could be cleared up by the engineers, and the Post Office find similar difficulty; a telephone conversation is seldom effective because we cannot use diagrams. Probably more important are the points which are misunderstood, but which would be cleared up if closer contact were maintained, because they would come to light in casual discussion. It is clear that we must have an engineering section at the ACE site eventually, the sooner the better, I would say.

  Looking on the bright side my visit confirmed that our work so far has been on the right lines. It is probable that the Princeton machine, based on the Selectron, will have some advantage over the ACE in speed, but our proposed machine has some compensating advantages, and I think that, other things being equal, it is better that the two different types should both be tried. The Princeton group seem to me much the most clear headed and far sighted of these American organisations, and I shall try to keep in touch with them.