Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Given a complicated electrical circuit and the characteristics of its components, the response to given input signals could be calculated. A standard code for the description of the components could easily be devised for this purpose, and also a code for describing connections.

  It would mean the automatic solution of circuit problems such as he had spent weeks over at Hanslope. The second was a more mundane example of the world’s work:

  To count the number of butchers due to be demobilised in June 1946 from cards prepared from the army records.

  The machine, he wrote, ‘would be quite capable of doing this, but it would not be a suitable job for it. The speed at which it could be done would be limited by the rate at which cards can be read, and the high speed and other valuable characteristics of the calculator would never be brought into play. Such a job can and should be done with standard Hollerith equipment.’ The third non-numerical problem* was described thus:

  A jig-saw puzzle is made up by cutting up a halma-board into pieces each – consisting of a number of whole squares. The calculator could be made to find a solution of the jig-saw, and, if they were not too numerous, to list all solutions.

  This was the nearest he came to a mention of cryptanalysis, although it was latent in a number of his ideas, such as including the logical operations of AND and OR from the start, and regarding them as on an equal footing with arithmetical operations. Alan wrote that this particular problem was ‘of no great importance, but it is typical of a very large class of non-numerical problems that can be treated by the calculator. Some of these have great military importance, and others are of immense interest to mathematicians.’ But at the end came the suggestion that he was most interested in himself, although he could hardly expect it to motivate the government:

  Given a position in chess the machine could be made to list all the ‘winning combinations’ to a depth of about three moves on either side. This is not unlike the previous problem, but raises the question, ‘Can the machine play chess?’ It could fairly easily be made to play a rather bad game. It would be bad because chess requires intelligence. We stated at the beginning of this section that the machine should be treated as entirely without intelligence. There are indications however that it is possible to make the machine display intelligence at the risk of its making occasional serious mistakes. By following up this aspect the machine could probably be made to play very good chess.

  This was not so much a report, as a plan of campaign in which tactical and strategic were jostling as close on paper as they did in his own mind. The promise of an electronic ‘brain’ was as fanciful as space travel, and this report was like explaining the advantages of colonising Mars, while in next breath describing the design of a fuel pump. The naive, colloquial style was not calculated to appeal to the authorities, and its detailed considerations went far beyond their absorptive capacities. No one was going to work through the example programs or the circuit diagrams, nor resolve the baldly stated paradox of a machine ‘entirely without intelligence’ nevertheless ‘displaying intelligence’. Even Hartree found it very hard going.

  Although undated, the ACE report was completed by the end of 1945,5representing an amazing burst of energy. It then went to Womersley, who wrote both a memorandum6 for Darwin and an introductory report7 for the Executive Committee meeting of 19 February 1946. Womersley was quick to perceive the opportunities offered by a universal machine, and whatever the intellectual limitations noted by Alan and the other mathematicians, he certainly wrote an able defence of what he claimed as ‘one of the best bargains the DSIR* has ever made.’ ‘The possibilities inherent in this equipment are so tremendous that it is difficult to state a practical case …without it sounding completely fantastic …’ Optics, hydraulics, and aerodynamics could be ‘revolutionised’; the plastics industry could be ‘advanced in a way that is impossible with present computing resources.’ Besides the range table problem already noted by Alan, a problem expected to require three years of work by the existing Mathematics Division, Womersley claimed that ‘The machine will also grapple successfully with problems of heat-flow in non-uniform substances, or substances in which heat is being continuously generated’ – of explosives old and new, in fact. Womersley also claimed that ‘the promised support of Commander Sir Edward Travis, † of the Foreign Office, will be invaluable.’

  On the more theoretical side, Womersley stressed that ‘this device is not a calculating machine in the ordinary sense of the word. One does not need to limit its functions to arithmetic. It is just as much at home in algebra And on the more political side he drew attention to the large sums already expended in America on machines whose capacities would be far outstripped by the ACE. More subtly, Womersley pointed to the advantage to be gained from having such a machine installed in the NPL:

  …we in this country, and particularly in this Division, have a unique contribution to make to world progress. I can say quite definitely that in the use of such equipment we shall be far more resourceful and cunning than the Americans. …All the USA machines are in Electrical Engineering Departments. In this Division the machine will be in the hands of the user, rather than the producer …

  Discussion of this visionary cooperation of British brain and hand was postponed until the meeting of the Executive Committee on 19 March. This time Alan was invited to attend, and after being dauntingly introduced by Womersley as ‘an expert in the field of mathematical logic’, he did his best to explain the ACE as simply as possible. It was a particularly clear account, in which he began by saying

  that if a high overall computing speed was to be obtained it was necessary to do all operations automatically. It was not sufficient to do the arithmetical operations at electronic speeds: provision must also be made for the transfer of data (numbers, etc.) from place to place. This led to two further requirements – ‘storage’ or ‘memory’ for the numbers not immediately in use, and means for instructing the machine to do the right operations in the right order. There were then four problems, two of which were engineering problems and two mathematical or combinatory.

  Problem (1) (Engineering) To provide a suitable storage system.

  Problem (2) (Engineering) To provide high speed electronic switching units.

  Problem (3) (Mathematical) To design circuits for the ace, building these circuits up from the storage and switching units described under Problems 1 and 2.

  Problem (4) (Mathematical) To break down the computing jobs which are to be done on the ace into the elementary processes which the ace is designed to carry out. …To devise tables of instructions which translate the jobs into a form which is understood by the machine.

  Taking these four problems in order, Dr Turing said that a storage system must be both economical and accessible. Teleprinter tape provided an example of a highly economical but inaccessible system. It was possible to store about ten million binary digits at a cost of £1, but one might spend minutes in unrolling tape to find a single figure. Trigger circuits incorporating radio valves on the other hand provided an example of a highly accessible but highly uneconomical form of storage; the value of any desired figure could be obtained within a microsecond or less, but only one or two digits could be stored for £1. A compromise was required; one suitable system was the ‘acoustic delay line’ which provided storage for 1000 binary digits at a cost of a few pounds, and any required information could be made available within a millisecond.

  But explaining excitedly to the committee how the delay line was to work, he rapidly became too technical and was cut off before even touching upon the question of devising ‘tables of instructions’. Darwin was therefore sceptical, reasonably enough.

  The Director asked what would happen, in cases where the machine was instructed to solve an equation with several roots. Dr Turing replied that the controller would have to take all the possibilities into account, so that the construction of instruction tabies might be a somewhat ‘finicky’ business.

  Hartree
came to the rescue with an argument which appealed less to science than to post-war patriotism:

  …It requires only 2000 valves as against 18000 in the eniac, and gives a ‘memory’ capacity of 6000 numbers compared with the 20 numbers of the eniac …if the ace is not developed in this country the USA will sweep the field. …this country has shown much greater flexibility than the Americans in the use of mathematical hardware. He urged that the machine should have every priority over the existing proposal for the construction of a large differential analyser.

  This was a genuinely far-sighted and generous recommendation, coming as it did from a person who had spent much of his own time and energy on the differential analyser. It was a remarkably smooth victory for the digital over the analogue approach. Hartree had, of course, seen the ENIAC when near to completion, and might also have seen the Colossus after the war had ended. He was also a particularly cooperative and helpful person.

  Darwin was still not convinced and

  enquired whether the machine could be used for other purposes if it did not fulfil completely Dr Turing’s hopes. Dr Turing replied that this would depend largely on what part of the machine failed to operate, but that in general he felt that many purposes could be served by it.

  He was probably gritting his teeth at Darwin’s failure to grasp the principle of universality. Now Womersley infiltrated a new concept into the discussion, one which had played no role in the Turing report. It was that of a pilot machine.

  There was next some discussion as to the possible cost of the machine and Mr Womersley said that a pilot set-up could possibly be built for approximately £10000, and it was generally agreed that no close estimate of the overall cost of the full machine could be made at this stage.

  Not much notice was taken of Alan’s estimate of capital cost. Womersley had said it should be multiplied by a factor of four or five. In fact they were probably annoyed that he had trespassed across the demarcation line into the administrative province; the more so as he wrote as though he could shop around for the equipment himself. Recommendations were passed on, notably that of the Ministry of Supply which handled all military contracts.*

  Then the

  Committee resolved unanimously to support with enthusiasm the proposal that Mathematics Division should undertake the development and construction of an automatic computing engine of the type proposed by Dr A.M. Turing, and Director agreed to discuss the financial and other aspects of the matter with Headquarters.

  Alan Turing held a great and burning dislike for committee meetings such as this, resenting the fact that the decisions were made not because of a clear understanding of his ideas, but for political and administrative reasons. The report he had submitted was, in fact, largely irrelevant, and played the role of pleasing Humpty Dumpty by having something down on paper, no matter what it was. But Sir Charles Darwin did take swift action. Indeed already, on 22 February, he had written8 to the Post Office about this ‘electronic mathematical machine of a novel type, which should be immensely superior in every way to anything hitherto constructed anywhere’.

  Very broadly it works using principles developed by your staff during the war for a certain Foreign Office project, and we want to be able to take advantage of this, enlisting the help …in particular of Mr Flowers who has had much experience in working out the electronic side of it.

  The initial response from the Post Office was encouraging, and on 17 April Darwin was able to present to the Advisory Council of the DSIR a cogent plan of action, which showed that he had by this time marshalled the essential ideas:

  …The possibility of the new machine started from a paper by Dr A.M. Turing some years ago, when he showed what a wide range of mathematical problems could be solved, in idea at any rate, by laying down the rules and leaving a machine to do the rest. Dr Turing is now on the staff of the NPL and is responsible for the theoretical side of the present project, and also for the design of many of the more practical details.

  It gave three examples of large calculations that it would be able to perform, and explained:

  The complete machine will naturally be costly; it is estimated that it may call for over £50,000, but probably not twice as much. A smaller one, containing the essential characteristics, could be constructed first, perhaps for a cost of £10,000, but its chief function would be to reveal some of the details of design that cannot be planned without trial, and its scope would be too limited to be worth constructing for its own sake. This would involve development work on delay lines and trigger circuits, and this part of the work would be undertaken by the Post Office, where facilities and specially trained staff exist, with the collaboration of Dr Turing and his assistants. …

  The small machine would not be a miniature substitute for the large machine but would later constitute a part of the full scale machine in due course. It is hoped that the complete machine can be constructed in three years. …It is proposed to proceed immediately, and with high priority, in the design and construction of this preliminary machine, but in doing so it is important to know that if it fulfils its promise there will be full backing for the greater sums required for the real operating machine. In view of its rapidity of action, and of the ease with which it can be switched over from one type of problem to another it is very possible that the one machine would suffice to solve all the problems that are demanded of it from the whole country …

  Darwin requested up to £10,000 to be allocated to the ‘small machine’ in the current financial year. On 8 May 1946 the DSIR agreed to support his application, and also that if the ‘small machine’ fulfilled expectations then they would recommend the expenditure of up to £100,000 on a full-scale machine. On 15 August the Treasury sanctioned the £10,000, although according to standard procedure refused further commitment. Meanwhile by 18 June the NPL had committed itself by sending a letter to the Post Office asking for development work on delay lines. The ACE was under way. It might now be couched in terms more like those of a Five Year Plan than those getting on with it in a hut, but it still promised a machine that would solve all the problems demanded of it from the whole country. The legacy of a total war, and of the capture of a total communication system, could now be turned to the construction of a total machine.

  After submitting the report, Alan continued to improve the design and to write ‘instruction tables’ for the paper machine. In this he gained some assistance, Darwin having decided that ‘high priority’ meant the allocation of two Scientific Officers to the project. First came J.H. Wilkinson, one of the pure-mathematical Part III class of 1939, by now experienced through six years of work in the numerical analysis of explosives problems. It was Charles Goodwin who had sought to bring him to the NPL, to work in numerical analysis; but when Wilkinson made a visit he found himself being told by Alan about the exciting ACE plans.9 It was the ACE that made him decide to remain in government service, rather than to return to Cambridge mathematics. It was agreed that he should work half-time for Goodwin on desk machines and half-time on the ACE. It was a position fraught with possible inter-departmental frictions, but fortunately Jim Wilkinson was the most equable and diplomatic person. He joined on 1 May 1946. A second assistant joined a little later: this was the young Mike Woodger, son of the theoretical biologist and philosopher of science J.H. Woodger. He was immediately attracted by the Turing vision of a universal machine. Unfortunately, after training on desk machines in June, he caught glandular fever and was away until September.

  Mike Woodger was there when Alan’s official honour was announced in June. For his war service he was appointed to the Order of the British Empire — standard for civil servants of the rank that he had officially held. The letters OBE were added to his office door, which made him furious, perhaps because he did not want to be asked what it was for, perhaps at the absurdity of advertising a token recognition. The King was ill, so the OBE medal, bearing the inscription Tor God and the Empire’, arrived by post. It was lodged in his tool-box.

 
Already by May, when Jim Wilkinson joined in work on the ACE design, it had reached a Version V. One difference was that this incorporated a hardware facility for conditional branching. It was quickly replaced by a transitional Version VI and then a Version VII. By this time Alan was devoting more attention to speed of operation than he had done in the original report, at the cost of more hardware. In Version VII enough equipment was added to make it possible for an instruction to have the effect of a complete arithmetical operation, taking two numbers from store, adding them, and putting the result back into store. Again in the interest of speed, it was necessary to program the instructions so that as far as possible each instruction would be leaving its delay line just as the previous one had been executed. Since different operations would take different lengths of time to complete, this made the construction of tables into a crossword-puzzle operation. It also led to a decision that every instruction should specify which instruction the ‘head’ was to take next, abandoning the idea of a natural stream of consecutive orders, flowing with only occasional interruptions. It also increased the length of the instruction words from thirty-two to forty pulses, again requiring more equipment. In Version VII each such operation would take forty microseconds, but it would then take another forty microseconds to assemble the next instruction in the control circuits. Again in the interest of speed, Alan wished to eliminate this period by duplicating part of the equipment so that each instruction could be assembled while the last was being performed.

  It was entirely in line with his original report that as experience was gained with writing instruction tables, he should modify aspects of the hardware design. It was consistent, too, that he should sacrifice a certain amount of simplicity for the sake of greater speed. All the same, the assembling of actual components could not begin too soon for him; the paper ‘tables’ were intended for a real machine, not as theoretical exercises.