Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  while according to Travis’s German counterpart,2

  The Admiral at Halifax, Nova Scotia, was a big help to us. He sent out a Daily Situation Report which reached us every evening and it always began ‘Addressees, Situation, Date’, and this repetition of opening style helped us to select very quickly the correct code in use at that time. …

  All the time, while minds and technology were being pushed to the limit at Bletchley in the attack on German signals, the most elementary blunders were being made in the defence of their own. The result was that since late 1941, the German successes had been owed not only to the growing numerical strength of the U-boat fleet, but to their knowledge of Allied convoy routes; and during 1942 the effect of the Enigma blackout was only half the story.

  Unlike the German authorities, the British were capable of recognising a mistake. The error was not that of the Admiralty alone, for GC and CS had exercised that part of its remit which called it to advise upon cipher security. But it was a part of GC and CS which had been left untouched by the revolutions elsewhere, and whose timescale still ran in terms of years. In 1941 it had devised a new system, which in 1942 the Admiralty had agreed to introduce in June 1943. Even allowing for the fact that it took six months simply to equip the Navy with new tables, this was a story of delays normal in peacetime, but bearing no connection with the new standards applied to anything considered essential for the war. If it were the decipherment of exciting messages, or airborne radar to make German cities visible for night raids, or the atomic bomb, then new industries could be conjured up in months. The less glamorous work of convoy protection called forth no such effort. Although the principle of integration had been applied so powerfully at Bletchley, it had not been extended to match up the two sides of its work.

  They had learnt, but it was a painful way to learn, and those who had suffered most were unable to benefit from the lesson. They were at the bottom of the sea. Fifty thousand Allied seamen died in the course of the war, trying to mind their own business in the most gruelling conditions of the western war; 360 in the March 1943 convoy battle alone. Nor were their trials then over; the Merchant Navy cipher system continued to be breakable for the rest of 1943, long after the Navy was protected by the introduction of its new system on 10 June. Peculiarly vulnerable, and given the lowest priority, the merchant shipping ran a danger of which few knew, and whose enormity even fewer could appreciate.

  In retrospect the failure of Allied naval communications vindicated the policy urged before the war by Mountbatten, and rejected by the Admiralty, that cipher machines should be employed. After 1943 the Navy joined the other services in an increasing use both of the Typex and of the equivalent American machine. Against these the B. Dienst made no headway. And yet the modernists such as Mountbatten might have been right for the wrong reason. Machine ciphers were not inherently secure, as the Enigma proved. The Foreign Office continued to use a hand system based on books; it remained unbroken. Bletchley deciphered the Italians’ naval machine system; but was increasingly powerless against their book ciphers. What was enciphered on a machine might all the easier be deciphered on a machine. It was not the machine, but the whole human system in which it was embodied, that mattered. Behind the mis-match of Allied cryptanalytic and cryptographic standards there lay another question: were the Typex transmissions really more secure than those of the Enigma? Perhaps the most salient fact was the negative one: that the B. Dienst made no serious effort against them, just as in 1938 no serious effort had been made against the Enigma. If an attack upon the Typex had been made with the resources mobilised at Bletchley, the story might have been very different.3 But perhaps they had no Alan Turing – nor a system in which an Alan Turing could be used.

  Such was the background against which Alan returned to base himself in Hut 8. The game had gone sour. The cryptanalysts tended to assume that their productions were being fed into a system that knew what it was doing, and it was a shock when they were told of the convoy cipher fiasco. Hut 8 itself had been taken over by Hugh Alexander during Alan’s absence. There was a story that a form had come round, asking for the name of the head of the section. Alexander had said, ‘Well, I suppose I am,’ and thereafter he remained in smooth control of the naval Enigma. There were no further crises, despite the later proliferation of German naval key-systems. The introduction of an alternative fourth wheel in July 1943 for the U-boat system caused them no problem; they were able to deduce its wiring without a capture. None of this needed Alan any more; indeed several of the high-level analysts were moved to more innovative work on Fish. Nor, indeed, did the U-boat Enigma need the British effort now. Although the British* produced the first working high-speed four-wheel Bombe in June 1943, the Americans produced more and better Bombes after August. By the end of 1943 they had taken over the U-boat work entirely, and had spare capacity for other Enigma problems.

  If they did not need Alan Turing on what had become a routine task, his help might well have been of use in the cryptographic context, where 1943 saw a slightly greater degree of cooperation and coordination prevail. He had already been introduced to the job of inspecting speech cipher systems, and to the delicate work of Anglo-American liaison. The Allies now had the problem of recovering from the delays and narrow vision of 1942, at a time when communications were expanding enormously and growing towards their great climax. The times had been out of joint, something they could not afford to allow in the intricate plans for 1944. For Alan Turing this would be dull and dispiriting work compared with the excitement of the relay race; but it was the job crying out for expert attention.4

  After June 1943 the Atlantic war turned dramatically in favour of the Allies, with ship sinkings reduced to tolerable levels. In retrospect, March 1943 had seen ‘the crisis’ of the battle of the Atlantic, and thereafter it could be claimed that ‘the U-boat was defeated’. But more truly, 1943 saw a continuing state of crisis, one in which it was not the boat but the system that was beaten from day to day by a superior system. At last they introduced long-range air patrols to cover the mid-Atlantic gap. And the logical advantage held by the U-boats in 1940 had been reversed. They were now visible from afar through the Enigma (by the end of 1943 the British had a clearer idea of where they were than did their own command), and at close range through the airborne radar work of TRE. Meanwhile the convoy communications became secure. The combination was a winning one, and the Atlantic poker game appeared as a quiet front, only noticed when occasionally the cheating failed to work. But from the German point of view it was not a quiet front at all. For them, 1943 saw a tremendous stepping up of the attack. At the end of the year they would have over 400 U-boats to deploy, equipped with elaborate measures to counter the radar detection they believed responsible for all their failure to find convoys. The fleet was still alive and aggressive, even if individual U-boats were increasingly short-lived. It was a game of perfect information – or Sigint, as it became in the new language of 1943 – for one player. But the other did not admit defeat. The Second World War was not a game.

  The introduction of the fourth rotor in February 1942 thus had effects unknown in Germany. That it was employed half-heartedly and foolishly, allowing it to be mastered after December 1942, meant the loss of the battle of the Atlantic. But that it had been employed at all meant that it had introduced electronic engineers to Bletchley and hence to the Fish problem. And while 1943 saw a general resolution of Anglo-American friction over Intelligence, by means of an agreement to divide the world between them – Britain taking Europe and America taking Asia – the US Navy retained its more aggressive stance. Their rapid development of Bombes reflected the fact that the Atlantic was now an American sea. Alan Turing’s work had denied the ocean lanes to Germany, and secured them for the United States.

  Alan had written to Joan while away in America, asking her what she would like as a present, but in her reply she had not been able to answer this question because of the censorship. In the event he brought back a good q
uality fountain pen for her – and others too had presents. There were Hershey bars among the sweets he left for general consumption in Hut 8, and he also brought an electric shaver for Bob, making a transformer to convert it from the American to the British voltage. He told Joan how seeing Mary Crawford in January, just after Jack had died, had affected him with a sense of how much they had meant to each other. He hinted that they should ‘try again’, but Joan did not take up the hint; she knew that it was over.

  He showed her a book on Go, and lay on the floor in his room at the Crown Inn demonstrating some of the situations in the game. And he also lent her a remarkable new novel. It was by his friend Fred Clayton, though under a pseudonym,5 and had been published in January 1943. The Cloven Pine, as it was called, in a cryptic reference to Ariel’s imprisonment by Sycorax in The Tempest, vented groans about politics and sex which were closer to Fred’s experiences and problems than to Alan’s, Fred having set his plot in the Germany of 1937 and 1938, and drawing upon his complex and conflicting reactions to the Vienna and Dresden of a little earlier.

  He had tried to understand the collapse of the ideals of 1933. On one level, he showed German individuals, no less and no more lovable than English individuals. On another, he showed the system, the Nazi system. And while he portrayed himself as the Englishman, asking how Germans could believe such things, he tried to see himself and English attitudes through German eyes. In an internationalist gesture, The Cloven Pine was dedicated jointly to George, his younger brother, and to Wolf, one of the boys in Dresden that he had known. ‘Freedom and consistency of mind’, he had the German boy of his story think to himself, analysing English liberalism, ‘They were illusions! What freedom or consistency was there in this Self, a thing of moods that did not understand one another. …’ It was the conclusion of a King’s liberal, trying hard to comprehend the absolute denial of Self.

  There was a second thread to his story, that of the English schoolmaster’s friendship with the German boy which remained ‘suspended in an atmosphere of semi-Platonic sentimentality’. This for Joan represented a quality of self-restraint that deserved admiration, but Alan, who had often teased Fred in terms rather like these, would probably have taken a different view. The book was saved from the obvious danger, one that Evelyn Waugh had mocked in Put Out More Flags, by the stringency and sophistication with which it examined the contradictions. The personal realities were ever questioning, and questioned by, a political background which included the late-1930s Nazi propaganda about boy-corrupting Jews and Catholic clergy. On this level it served Alan as a way of saying that of his ‘tendencies’ could not be separated from his place in society, nor regarded as peripheral to his own freedom and consistency of mind.

  Although he had dropped away from the direct cryptanalytic work, Alan remained within the Bletchley fold, and was to be seen in the cafeteria off duty. Conversation at these times often revolved round mathematical and logical puzzles, and Alan was particularly good at taking some quite elementary problem and showing how some point of principle lay behind it – or conversely, illustrating some mathematical argument with an everyday application. It was part of his special concern for connecting the abstract and the concrete, as well as a pleasure in demystifying the higher mathematician’s preserve. It might be wallpaper patterns for an argument about symmetries. His ‘paper tape’ in Computable Numbers had the same flavour, bringing an ‘abstruse branch of logic’ down to earth with a bump.

  One person who appreciated this approach was Donald Michie, to whom as a classicist it all came as fresh and new. He became very friendly with Alan, and in 1943 they began to meet every Friday evening in a pub at Stony Stratford, just north of Bletchley itself, to play chess and talk – or more often, for Donald to listen. The Prof’s chess had always been something of a joke at Bletchley, being all the more exposed to invidious comparison when the chess masters arrived. Harry Golombek had been able to give him queen odds, and still win; or when Alan resigned he was able to turn the board round and win from the position given up as hopeless. He complained that Alan had no idea how to make the pieces work together, and it might well be that as in his social behaviour, he was too conscious of what he was trying to do, to play with fluency. As Jack Good saw it, he was too intelligent to accept as obvious the moves that others might make without thinking. He always had to work it out from the beginning. There had been an amusing moment when Alan had come off a night shift (this would have been in late 1941) and then played a game with Harry Golombek in the early morning. Travis had looked in and was embarrassed to find, as he thought, his senior cryptanalyst playing while on duty. ‘Er … er … want to see you about something, Turing,’ he said awkwardly, like the housemaster catching a sixth-former with a cigarette in the toilet. ‘Hope you can beat him,’ he added to Golombek as they left the room, assuming quite wrongly that the master cryptanalyst was the champion player. But young Donald Michie was a player of Alan’s standard.

  These meetings were an opportunity for Alan to develop the ideas for chess-playing machines that had begun in his 1941 discussion with Jack Good. They often talked about the mechanisation of thought processes, bringing in the theory of probability and weight of evidence, with which Donald Michie was by now familiar. The development of machines for cryptanalytic work had in any case stimulated discussion as to mathematical problems that could be solved with the mechanical aid – that of finding large prime numbers, for instance, was a topic that came up in lunchtime conversations, rather to the amazement of Flowers, the electronic engineer, who could see no point in it. But Alan’s talk went in rather a different direction. He was not so much concerned with the building of machines designed to carry out this or that complicated task. He was now fascinated with the idea of a machine that could learn. It was a development of his suggestion in Computable Numbers that the states of a machine could be regarded as analogous to ‘states of mind’. If this were so, if a machine could simulate a brain in the way he had discussed with Claude Shannon, then it would have to enjoy the faculty of brains, that of learning new tricks. He was concerned to counter the objection that a machine, however intricate its task, would only be doing what a person had explicitly designed it to do. In these off-duty discussions they spent a good deal of time on what would be said to count as ‘learning’.

  Implicit in these discussions was the materialist view that there was no autonomous ‘mind’ or ‘soul’ which used the mechanism of the brain. (He had perhaps hardened his stance as an atheist, and his conversation was more free with anti-God and anti-church jokes than it would have been before the war.) To avoid philosophical discussions about what ‘mind’ or ‘thought’ or ‘free will’ were supposed to be, he favoured the idea of judging a machine’s mental capacity simply by comparing its performance with that of a human being. It was an operational definition of ‘thinking’, rather as Einstein had insisted on operational definitions of time and space in order to liberate his theory from a priori assumptions. This was nothing new – it was an entirely standard line of rationalist thought. Indeed in 1933 he had seen it on the stage, for in Back to Methuselah Shaw had a future scientist produce an artificial ‘automaton’ which could show, or at least imitate, the thought and emotions of twentieth century people. Shaw had the ‘man of science’ assert that he had no way of drawing a line between ‘an automaton and a living organism’. Far from it being a novelty, Shaw was trying to make this argument appear a dated piece of Victoriana. Again, his Natural Wonders book had accepted the rationalist view, with a chapter called ‘Where some of the Animals do their Thinking’ which treated thought, intelligence and learning as differing only in degree as between monocellular animals and human beings. It was no new idea, therefore, when Alan talked in terms of an imitation principle: that if a machine appeared to be doing as well as a human being, then it was doing as well as a human being. But it gave a sharp, constructive edge to their discussions.

  Meanwhile Donald Michie had been plucked from the Testery
, and Jack Good from Hut 8, to work as Newman’s first staff on a very exciting development of the Fish analysis. Donald Michie had continued to work on refinements of the Turingismus method, reporting informally to Alan on their progress – advances reflected in the fact that at the beginning of 1943 a proportion of the Fish signals were being read regularly and with little delay. The Turing theory of statistics, with its formalisation of ‘likeliness’ and ‘weight of evidence’, and with its ‘sequential analysis’ idea, were also playing a general part in the Fish work, in which it found greater application than in the Enigma methods. But by the spring of 1943, Newman’s ideas for mechanisation had begun to bear fruit. Here the new developments with electronic technology, in which the crucial steps had been taken while Alan was in America, were in themselves very significant.

  The Post Office engineers had been able to install a first electronic counting machine in Hut F, where Newman and his two assistants worked, in about April 1943. This and its successors were called the ‘Robinsons’.* Although they had overcome some of the engineering problems associated with passing paper tape very rapidly through an electronic counter, these ‘Robinsons’ still suffered from many defects. They were prone to catch fire; the paper tapes were always breaking; and the counts were unreliable. This was because the slower parts of the counting process were performed by the old relays, and these produced an electrical interference effect upon the electronic components. But the fundamental technological problem was that of synchronising the ingestion of the two separate paper tapes demanded by the method. For all these reasons, the Robinsons proved too unreliable and too slow for effective cryptanalytic use. They were employed only for research purposes. There was also another fundamental difficulty, not so much physical as logical, which made the machine method too slow. In using it for the cryptanalytic process, the operator would constantly have to produce fresh tapes, resorting for this purpose to an6 ‘auxiliary machine that was used to produce the tapes which formed one of the two inputs to the Heath Robinson.’