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

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Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 33

by Andrew Hodges


  Looking at the cipher traffic, an experienced hand might say that such and such a thing ‘seemed likely’, but now that mass production was the objective, it was necessary to make vague, intuitive judgments into something explicit and mechanical. Much of the mental apparatus required for this had already been constructed in the eighteenth century, although it was new to GC and CS. The English mathematician Thomas Bayes had seen how to formalise the concept of ‘inverse probability’ – this being the technical term for the likely cause of an effect, rather than the probable effect of a cause.

  The basic idea was nothing but the common sense calculation of ‘likeliness’ of a cause, such as people would use all the time without thinking. The classical presentation of it was like this: suppose there to be two identical boxes, one containing two white balls and one black ball, the other containing one white ball and two black balls. Someone then has to guess which box is which, and is allowed to make an experiment, that of taking just one ball out of either box (without, of course, looking inside). If it turns out to be white, the common-sense judgment would be that it is twice as likely that it has come from the box containing two white balls, as from the other. Bayes’s theory gave an exact account of this idea.

  One feature of such a theory was that it referred not to the happening of events, but to the changes in a state of mind. In fact, it was very important to bear in mind that experiments could only produce relative changes in ‘likeliness’, and never an absolute value. The conclusion drawn would always depend upon the a priori likeliness which the experimenter had had in mind at the beginning.

  To give a concrete feel to the theory, Alan liked to think in terms of a perfectly rational person obliged to make bets upon hypotheses. He liked the idea of betting, and put the theory into the form of odds. So in the example, the effect of the experiment would be to double the odds, one way or the other. If further experiments were allowed, the odds would eventually increase to very large numbers although, in principle, certainty would never be attained. Alternatively, the process could be thought of as one of accumulating more and more evidence. From this point of view, it would be more natural to think of adding something each time an experiment was made, rather than of multiplying the current odds. This could be achieved by using logarithms. The American philosopher C. S. Peirce had described a related idea in 1878, giving it the name ‘weight of evidence’. The principle was that a scientific experiment would give a numerical ‘weight of evidence’ to be added to, or subtracted from, the likeliness of a hypothesis. In the example, the discovery of a white ball would add a weight of log 2 to the hypothesis that the box it came from was the one with two white balls. It was not a new idea, but20

  Turing was the first to recognise one value of naming the units in terms of which weight of evidence is measured. When the base of logarithms was e he called the unit a natural ban, and simply a ban when the base was 10…. Turing introduced the name deciban in the self-explanatory sense of one-tenth of a ban, by analogy with the decibel. The reason for the name ban was that tens of thousands of sheets were printed in the town of Banbury on which weights of evidence were entered in decibans for carrying out an important process called Banburismus.

  So a ‘ban’ of evidence was something that would make a hypothesis ten times as likely as it had been before. Rather like a decibel, a deciban would be ‘about the smallest change in weight of evidence that is directly perceptible to human intuition’. He had mechanised guessing, and was ready to put it on machines which would add up decibans to arrive at a rational decision.

  Alan developed the theory in several ways. The crucially important application lay in a new procedure for making experiments, later to be called ‘sequential analysis’. His idea was to set a target for the weight of evidence required one way or the other, and to continue making observations until that target was attained. This would be a far more efficient method than deciding in advance how many experiments to make.

  But he also introduced the principle of judging the value of an experiment by the amount of weight of evidence that it would, on average, produce; and he even went on to consider the ‘variance’ of the weight of evidence produced by an experiment, a measure of how erratic it was likely to be. In bringing these ideas together, he brought the art of guessing, as employed in cryptanalysis, into the 1940s. Typically, he had worked it all out for himself, either not knowing of earlier developments (as in the case of ‘weight of evidence’ defined by Peirce) or preferring his own theory to the statistical methods pioneered by R. A. Fisher in the 1930s.

  Now, therefore, when they thought that a crib was ‘probably’ right, or that one message had ‘probably’ been transmitted twice, or that the same setting had ‘probably’ been used twice, or that one particular rotor was ‘probably’ the outermost one, there lay the possibility of adding up the weight of evidence from faint clues in a systematic, rational way, and of designing their procedures so as to make the most of what they had. To save an hour thereby was to gain an hour in which a U-boat gained six miles upon a convoy.

  Just after the end of 1940, the theory began to turn into practice. In about December Alan wrote to Shaun Wylie, then teaching at Wellington College, and invited him to join. He arrived in about February 1941. Later Hugh Alexander, the British chess champion, was transferred to Hut 8 from elsewhere in Bletchley. Alexander was also a Kingsman, one who had graduated in 1931 and attributed his failure to become a mathematical Fellow to his having played too much chess. Instead, he had taught at Winchester and then became Director of Research for the John Lewis Partnership, the leading group of department stores. At the outbreak of war he and the other British chess masters had been caught in Argentina at the 1939 Chess Olympiad. It was a matter of some satisfaction that the British team had managed to return while the Germans could not. The next increase in strength in Hut 8 would come when the young mathematician I. J. Good was detached from his Cambridge research work with Hardy to join in May 1941. But by that time everything would have changed.21

  When I arrived at Bletchley I was met at the station by Hugh Alexander the British chess champion. On the walk to the office Hugh revealed to me a number of secrets about Enigma. Of course we were not really supposed to talk about such things outside the precincts of the office. I shall never forget that sensational conversation.

  For Alan Turing’s ideas had been embodied in a working system. The Bombe was at the centre, but there was punched-card machinery, and the ‘big room girls’ working in a production line, to make the guessing-game as effective and rapid as the improvised conditions allowed. They were beginning to do something for the war.

  The first planned capture took place on 23 February 1941, during a raid on the Lofoten Islands on the Norwegian coast. It meant that someone died for the Enigma instructions that Alan needed:22 ‘the German armed trawler Krebs was disabled, her commanding officer killed before he could complete the destruction of his secret papers, and the ship abandoned by the survivors.’ Enough was taken for it to be possible for Hut 8 to read the whole of the naval traffic for February 1941 at various dates from 10 March onwards.

  The time lag, for those interpreting the messages, was profoundly frustrating. The naval messages, unlike the bulk of those emanating from the other services, had to carry pieces of first-rate information. One of the first to be decrypted read:23

  Naval Attache Washington reports convoy rendezvous 25th February 200 sea miles east of Sable Island. 13 cargo boats, 4 tankers 100,000 tons. Cargo: aeroplane parts, machine parts, motor lorries, munitions, chemicals. Probably the number of the convoy is HX 114.

  But on 12 March, when its decipherment was achieved, it was three weeks too late to do anything but wonder how the Naval Attaché had found out so much. Two days later they read a message from Dönitz:

  From: Admiral commanding U boats

  Escort for U69 and U107 will be at point 2 on March 1st at 0800 hours.

  which two weeks earlier would have been exactly wha
t the Tracking Room wanted – if only it could be known where Point 2 was. It was necessary to amass the traffic in order to attack such problems of interpretation. Thus:

  English ship Anchises lies in AM 4538, damaged from the air.

  would, provided it were not slung into the waste-paper basket as in Room 40 days, reveal the location of grid reference AM 4538.

  No break was made into the March 1941 traffic. But then came a triumph for Hut 8: the decryption of the April traffic without the benefit of any further captures. Both April and May messages were read ‘by cryptanalytic methods’. At last they were beginning to beat the system. Hut 4 was now able to look right into the eye of the enemy, with messages such as:

  [24 April; deciphered 18 May]

  From: NOIC Stavanger

  To: Admiral West Coast

  Enemy Report Offizier G and W

  Supreme Naval Command (First operations division) wires no. 8231/41 re captured Swedish fishing vessels:

  1) Operations division believes that it was the task of the Swedish fishing vessels to obtain information about mines in the interests of Britain.

  2) Make certain that neither Sweden nor the enemy hears about their capture. The impression should for the time being be allowed to arise that the vessels were sunk by mines.

  3) Crews are to be kept under arrest until further notice. You are to forward a detailed report of their interrogation.

  Some were even more ironic:

  [22 April; deciphered 19 May]

  From: C in C Navy

  The U boat campaign makes it necessary to restrict severely the reading of signals by unauthorised persons. Once again I forbid all authorities who have not express orders from the operations division or the Admiral commanding U boats to tune in on the operational U boat wave. I shall in future consider all transgressions of this order as a criminal act endangering national security.

  Weeks-old material still had value in building up a knowledge of the system, but of course it was of desperate importance that the time-lag be reduced. By the end of May 1941 they were able to bring down the time to as little as a day. One message that was deciphered within a week read:

  [19 May; deciphered 25 May]

  From: Admiral commanding U boats

  To: U 94 and U 556

  The Fuehrer has decorated both captains with the Ritterkreuz to the Iron Cross. I wish to convey to you, on the occasion of this recognition of the services and successes of the boats and their crews, my sincere congratulations. Good luck and success in future too. Defeat England.

  That defeat would now be more difficult than they imagined. For even old messages imperilled German plans. When the Bismarck sailed from Kiel on 19 May, the delay of three days or more in decipherment rendered Hut 8 powerless to reveal the secrets of her course. But on the morning of 21 May, some April messages emerged to put it beyond doubt she was making for the trade routes. Thereafter it was left to the Admiralty to derive intelligence in its more traditional way, which included plotting a radio direction on the wrong kind of map projection, though its eventual good guessing was confirmed by a Luftwaffe Enigma message on 25 May. The sequence of events was extremely complicated, and naval Enigma played only a minor role in it. But had the Bismarck sailed just a week later, the story would have been very different. New developments in Hut 8 were transforming the picture.

  This was because the older material was discovered to have powerful implications:24

  After studying the decyphered traffic of February and April, GC and CS was able to show conclusively that the Germans were keeping weather-ships on station in two areas, one north of Iceland and the other in mid-Atlantic, and that, though their routine reports were transmitted in weather cypher and were different in outward appearance from Enigma signals, the ships carried the naval Enigma.

  This clever analysis of essentially dull material represented a victory for the new men and the new methods, in which Alan had a personal share. The Admiralty would never have had the time or wit to make the amazing discovery that these vulnerable little weather-ships were supplied with the keys to the Reich. But they were now prepared to act on the prompting of a civilian department, and plotted a series of captures.

  The München was found and taken on 7 May 1941 and it was with the settings thus obtained that they became able to read the June traffic ‘practically currently’. At last, they had a command of the day-to-day tactics. The July settings were captured from another of the weather-reporting trawlers, the Lauenburg, on 28 June. Meanwhile on 9 May, an accidental, but brilliantly conducted operation had taken place. A convoy escort detected and disabled the U-110 which had attacked the convoy. In a split-second manoeuvre on the high seas, they boarded the U-boat and took intact its cipher material. The lessons of 1940 had been learnt. The material filled some outstanding gaps, for it included ‘the code-book used by the U-boats when making short-signal sighting reports’, and ‘the special settings used in the Navy for “officer-only” signals’. These Offizierte signals were doubly enciphered for extra security within the U-boat itself. From the Hut 8 point of view, these were signals which, even after the day’s settings had been found and the decryption process applied, remained gibberish while the other messages became German. It required a second stage of attack to recover these, the innermost secrets of the U-boat operations. Now they had what they needed to do it.

  The growing body of knowledge was rapidly put to use by the Admiralty. As June 1941 opened, and the naval traffic was read currently, it was able to make an almost clean sweep of the supply ships sent into the Atlantic in advance of the Bismarck, disposing of seven out of the eight. This bulldog action, however, provoked a disturbing question. In Hut 8, as they read messages about U-boat rendezvous points and so forth, they assumed quite naively that with the aid of this wonderful information, the U-boats could readily be despatched. In June 1941 this simple view was presumably also taken by the Admiralty, for only afterwards did anyone voice concern that the succession of sinkings, following the loss of the Bismarck, might alert the German authorities to the possibility of cipher compromise.

  In fact, the operation had betrayed Alan’s success, for the German authorities decided that the positions of the supply vessels had somehow been disclosed, and set up an investigation. Their experts, however, ruled out the possibility that the Enigma cipher had been broken. Instead, they pinned the blame upon the British secret service, which enjoyed a high reputation in German ruling circles. It was a diagnosis remote from the truth. They had assigned an a priori probability of zero to Enigma decryption, and no weight of evidence sufficed to increase it.

  It was a blunder, but one easy to make when the implications were so shattering. At Bletchley, where it was explained to Hut 8 that decrypts could not in future be exploited so easily, there was nothing to do but to cross their fingers. The Bombe method, which was central to the system, hung upon a single thread. If, to be on the safe side, the Germans had gone over to a double encipherment of every message, then there would have been no more cribs, and all would have been lost. At any time, the mere suspicion that something had gone wrong might stimulate such a change. They walked on a knife-edge.

  From mid-June 1941, the Admiralty caught on to the idea that messages which contained information derived exclusively from Enigma decryption (normally until then, from Luftwaffe Enigma) should go out as ULTRA SECRET on special one-time pads. The other services also began to adapt, setting up Special Liaison Units, attached to headquarters in the field and around the Empire, charged with the reception and control of Bletchley information.

  But there was still far to go in the integration of brain and brawn. The Admiralty was the most flexible in this regard, but they laboured under the difficulty that while a year before there had been too little information, in mid-1941 they were swamped by its abundance. The OIC could not cope with the new era, in which a vast German system had to be mirrored by a British one.

  It had been a revolutionary innovation to pl
ace a civilian, a barrister called Rodger Winn, in charge of the OIC Tracking Room at the end of 1940, replacing an ancient naval Paymaster. It was through the mind of Winn that the output of Hut 8 had to be translated into action. Fortunately it was an imaginative mind, one which suggested forecasting where the U-boats were going to be, in time for the convoys to dodge them. Despite great initial resistance, towards the spring of 1941 this entirely novel idea was ‘beginning to gain acceptance’. Winn considered25 that

  it was worth while to ‘have a go’. If, as he subsequently said, one beat the law of average [sic] and was right only fifty-one per cent of the time, that one per cent, in terms of lives and ships saved, or U-boats sunk, was surely worth the effort.

  However new to the Navy, this was hardly an idea which matched the finesse of ‘sequential analysis’. And as the translated decrypts passed down the teleprinter line to the OIC, they travelled back fifty years in time. Even after great improvements,

  … Winn still had fewer than half a dozen assistants. They had to maintain an Atlantic plot on which were shown not only the latest estimated positions of all U-boats but also the positions and routes of British warships, convoys and independently routed vessels. This of course was on top of their task of dealing with the minute to minute and hour to hour flow of incoming signals concerning attacks, sightings, D/F fixes, and the queries from the Operations, Plans and Trade Divisions in the Admiralty, from Coastal Command and from headquarters in Ottawa, Newfoundland, Iceland, Freetown, Gibraltar and Cape Town. The situation was beginning to resemble that in Room 40 in 1916 when only the most urgent matters could receive attention. When the flow of decrypts began, Winn, partly for security reasons and partly because of shortage of staff, had to handle and file them all himself. He had no shorthand typist, not even a confidential filing clerk.

 

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