Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Bridge Passage

  (BP 1) This is the most substantial anecdote from the wartime period in EST, and a rare example of where Mrs Turing’s deference to officials took second place to an authentic Alan Turing tone of voice. Apart from some early childhood details, this is also almost the first place in EST where Mrs Turing’s personal recollection emerges. My guess is that it was the hint of AMT making an important mission to America that made her take more notice of him.

  (BP 2) The index to Foreign Office correspondence for 1943 contains on page 428 a reference to complaints (themselves ‘weeded’) about insufficient accreditation. This might have included AMT’s – but in any case adds a few decibans to an otherwise unlikely-sounding story.

  (BP 3) Beesly, as note 4.11, pages 152, 161.

  (BP 4) The date of arrival, like subsequent dates and details of AMT’s period in New York, derives from contemporary Bell Laboratories personnel records made available to me. But with AMT’s visit making such an impression on his mother, there are a few odd details of reminiscence in EST, based presumably on his cryptic replies to her interrogation. There was ‘some hold-up about his job, which involved a useless period of idling in New York’ – very likely the two weeks or so before 19 January, and due to ‘clearance’ arrangements, just the thing to annoy him. Mrs Turing’s own assertion about the purpose of his visit to America was that ‘he probably saw something of the progress of computing machinery in the States.’ But probably AMT said Oh, seeing some of their machines, Mother’, and the word ‘computing’ was Mrs Turing’s guesswork. She also wrote ‘He seems to have taken the opportunity to visit Princeton’ – he could certainly easily have stopped off on one of his several journeys between New York and Washington. Her oddest comment was in reference to the mix-up upon his arrival: ‘Even on Ellis Island he would have found something of interest, perhaps more than he found at Washington.’ While this again reflected the way that everyone in secret work had to spin out the trivial and play down the serious, there is a hint here that while AMT could hardly say, ‘Well, Mother, I was handing over to the Americans all the work we’ve been doing for the last three years,’ he allowed something of this to come through.

  (BP 5) National Service in War and Peace (1925–1975), the second volume of A History of Engineering and Science in the Bell System, Bell Telephone Laboratories, 1978. I have taken my account of the Vocoder and the X-system directly from this source. The X-system was ‘one of the starting points of the digital transmission age that followed’, despite being until 1975 ‘an unmentionable system’.

  (BP 6) PRO file CAB 79/25. The Memorandum referred to has not been released. I am indebted to David Kahn for this reference.

  (BP 7) Minute dated 27 April 1943, in CAB 79/27.

  (BP 8) C.E. Shannon, ‘Communication in the Presence of Noise’, Proc. I.R.E. (1948) is annotated: Original manuscript received by the Institute, July 23 1940.’ His paper ‘Communication Theory of Secrecy Systems’, Bell System Technical Journal, 1949, a very rare example of cryptology treated from a post-1930 standpoint in the open literature, was originally ‘A Mathematical Theory of Cryptography’, a Bell confidential report dated 1 September 1945.

  (BP 9) C.E. Shannon, ‘A Symbolic Analysis of Relay and Switching Circuits’, Trans. Amer. I.E.E. 57 (1938). According to the Bell History, it was as a result of this that ‘the design of relay circuits changed rapidly from being a somewhat esoteric art to being a science, and it became possible to teach it as an engineering discipline.’

  (BP 10) W.S. McCulloch and W. Pitts, ‘A Logical Calculus of the Ideas Immanent in Nervous Activity’, Bull. Math. Biophys. 5, (1943). Their paper contained no reference to Computable Numbers, but in a discussion after a lecture of von Neumann (the same as in note 6.57), McCulloch mentioned that it was AMT’s paper that had inspired their ideas. See von Neumann’s Collected Works (Pergamon, 1963), volume V, page 319.

  (BP 11) The evidence regarding AMT’s eastbound voyage is less clear than for that of November 1942. According to EST ‘he returned in a destroyer or similar naval vessel and experienced a good tossing on the Atlantic.’ But I think that she was mistaken here; it is hard to believe that the ‘top cryptanalyst’ would have been entrusted to a destroyer when a fast independent troop transporter was available. Instead, I think her recollection of him being the only civilian on board a crowded ship (see note 4.54) must in fact refer to this voyage. Then it fits (apart from the ‘couple of children’) with the information (from the Naval Historical Center, Washington) about the Empress of Scotland. This sailing, furthermore, was the only independent eastbound sailing in the rest of March. The week’s delay may be accounted for by the fact that this was when the convoy battle was at its height. Since Mrs Turing was certainly fallible – an example being in her annotations to KCC, which incorrectly stated Jack Crawford’s death to have occurred before AMT’s visit in 1938 – I have based the narrative on this not quite conclusive evidence.

  (BP 12) I am grateful to Richard Plant for pointing out this reference in H. Heiber, Reichsführer! (Deutsche Verlags-Anstalt, Stuttgart, 1968).

  (BP 13) E.M. Forster, Post-Munich, 1939, reprinted in Two Cheers for Democracy (Edward Arnold & Co., 1951).

  Running Up

  (5.1) Volume I of Allied Communications Intelligence and the Battles of the Atlantic, report SRH 009 declassified by the National Security Agency, available at the National Archives, Washington.

  (5.2) Kapitän H. Bonatz, head of the B. Dienst, quoted in M. Middlebrook, Convoy (Allen Lane, 1976).

  (5.3) PRO file FO 850/171 contains a memorandum of May 1945, from the Cypher Policy Board to the Foreign Office, with instructions for use of the Typex. It explains that ‘When encyphering on the Typex machine, the encyphered version of a letter can never be the letter itself. This sometimes makes it possible to assign with absolute accuracy even a small number of words known or estimated to be in a message to the actual letters of the cypher version …’, and gives procedures for burying addresses and other stereotyped beginnings and endings amidst nonsense, inserting extra letters between and within words, and so forth. These were just the procedures which, if correctly applied, would render Enigma transmissions immune to decipherment. One cannot tell whether the existence of such a memorandum means that the lesson had, or had not, been learnt by British operators within the six years of war.

  (5.4) The year between March 1943 and March 1944 is the least well documented of AMT’s life. Certainly there is clear evidence that both before and after this period he was engaged as a cryptographic consultant, and it is reasonable to suppose that this was also true during this year of catching-up. There are surely some interesting facts yet to emerge concerning his interaction with this phase of the war, although my impression is that there was nothing engaging him with the intensity that characterised the earlier period. The other dark year of his life was, of course, his last. There might in fact be some connection between them, since if he continued to do top level work in examining Anglo-American communication systems in preparation for D-Day, he would have had access to new American machine systems and much else still important in years after the Second World War. And who would have known how much he knew? As one apparently given access to American establishments on Churchill’s personal authority, he was quite outside the usual service systems.

  (5.5) Frank Clare, The Cloven Pine (Seeker & Warburg, 1943).

  (5.6) B. Randell, The Colossus, as note 4.42.

  (5.7) The Explanatory Caption attached to the photographs of the Colossus in PRO file FO 850/234 claims a direct link with Babbage and Computable Numbers:

  Babbage’s work in 1837 first established the logical principle of digital computers. His ideas were developed further in Turing’s classical paper in 1936. The COLOSSUS machine produced by the Department of Communications of the British Foreign Office, and put into operation in December 1943, was probably the first system to implement these principles successfully in terms of contemporary electronic te
chnology. … The requirement for the machine was formulated by Professor M.H.A. Newman, and the development was undertaken by a small team led by T.H. Flowers. A. Turing was working in the same department at that time, and his earlier work had its full influence on the design concept.

  I assume that ‘the logical principle …’ means ‘conditional branching’. Although this makes sense as retrospective comment, it is not my impression that this analysis was formulated at the time, and still less that there is some document in GCHQ dating from 1943 with references to Babbage or to Computable Numbers. The first two sentences have rather the function of giving a suitably imposing rationale for ‘declassification’. The reference to AMT in the last sentence also seems to me to be misleading, except in the extremely general sense that he had done so much for the mechanisation of processes before Newman arrived. The essential part that AMT played in this development was in providing a statistical theory: not the machine, but the purposes for which it would be used.

  (5.8) The third of only three wartime letters in KCC. The first, written in August 1941 while at Portmadoc, gave a few details of the holiday and a reference to the Dorothy Sayers book; the second, later in 1941, mentioned a week in Cambridge and meeting David Champernowne (‘Didn’t find any others I know except the old fogies’), slight bombing at Shenley, and a possible visit to Rossall to see to Bob’s future. I am grateful to Canon H.C.A. Gaunt for finding the dates of the Lake District holiday in A.C. Pigou’s diaries. These, incidentally, show that this was the only visit AMT made there except that in 1948.

  (5.9) CAB 80/41. I found no further references to AMT in these or the corresponding American files.

  (5.10) FO/850/256.

  (5.11) Shannon had included it in the paper submitted in 1940 (see note BP 8). Professor I.J. Good has written to the author: ‘The “sampling theorem” … is not due to Shannon although it is often attributed to him. It dates back at least to E.T. Whittaker, Proc. Roy. Soc. Edin. 35 (1915).’

  (5.12) As note 4.21.

  (5.13) J. Ramsbottom, Edible Fungi, 1943.

  (5.14) These pages are in KCC. They begin in mid-sentence, and are bereft of the necessary definitions, so do not make much sense. But the underlying problem addressed by AMT was clearly that of finding ‘exceptional’ rotor wirings permutations with some symmetrical feature, leaving a non-randomness that the cryptanalyst could exploit. Such wirings would have to be avoided when constructing an Enigma-type machine. The pages also give a strong impression of the high-powered algebraic and statistical work he had done on rotor machines.

  (5.15) Quoting from The War Speeches of the Rt. Hon. Winston S. Churchill (Cassell, 1951-2).

  (5.16) According to EST he was actually ‘offered a lectureship’ at Cambridge in 1945, and M.H.A. Newman’s Biographical Memoir also states this. But the records of the Faculty Board lend no support to this claim. Most likely he was speaking to his mother of continuing as a Part III lecturer, just as he would have been in 1940 but for the war.

  (5.17) In Mind, 1950 (see page 415 and note 7.34).

  (5.18) In the ACE report (note 6.1).

  (5.19) In Intelligent Machinery (note 6.53). These three quotations express ideas so fundamental, and so characteristic of his thought, that I believe the anachronism of setting them in summer 1945 is justified.

  (5.20) Quoting from Mrs Turing’s words in EST. This is explicitly given as a nugget of recollection, even if given a maternal gloss of ‘service’. ( I have inserted ‘machine’ for her word ‘computer’, since in this context there is no distinction whatever in meaning, and I do not wish to introduce the word prematurely.)

  (5.21) Reprinted fully in Faster than Thought (note 8.25).

  (5.22) Quoting from letters in the von Neumann archive, Library of Congress, Washington DC.

  (5.23) The relevant passage is in the extract included in The Origins of Digital Computers, ed. B. Randell (Springer Verlag, Berlin, 1973).

  (5.24) This letter was to Col. L.B. Simon at the Ballistics Research Laboratory.

  (5.25) Frankel’s letter was written to B. Randell in 1972, in connection with the latter’s detective work ‘On Alan Turing and the Origins of Digital Computers’. This paper, quoting Frankel’s letter, appeared in Machine Intelligence 7 (Edinburgh University Press, 1972). See also note 5.26.

  (5.26) Randell’s 1972 work (note 5.25), arose from the fact that the EDVAC report was supposed by everyone to be the fons et origo of the digital computer. In trying to see how the ACE ‘fitted in’, he came across an assertion by Lord Halsbury, writing in 1959 as managing director of the NRDC, that one of the most important events in the evolution of the modern computer was ‘of course the meeting of the late Doctors Turing and von Neumann during the war.’ (Computer Journal, 7, 1959).

  Randell continued to stress this question of a meeting, but my own conclusion is that whether or not they happened to meet (and I have found no more evidence of a meeting than Randell did), Halsbury was mistaken in thinking it important. The story of AMT and von Neumann is that of two utterly different personalities, in different social environments, but drawn to parallel problems within the movement of mid-century science. Either figure was perfectly capable of assembling the necessary ideas for the digital computer out of the conjunction of Hilbertian rationalism and Second World War technology. Both did, responding in slightly different ways according to their circumstances. There is no gap on either side that needs to be explained by a meeting, or some other conspiracy theory of history. Much the same applies to the question of when and how AMT discovered Babbage’s work: it would have fascinated and encouraged him, but was ultimately irrelevant.

  Mrs Turing got the picture exactly right when she wrote that his aim was ‘to see his logical theory of a universal machine, previously set out in Computable Numbers, take concrete form in an actual machine.’ Since she knew nothing of Computable Numbers but that a German professor had commended it, this was certainly not her own analysis; Newman could have guided her (see note 2.38) but her statement was more definite than anything that Newman had written. Most likely it was simply what AMT himself had told her again and again, trying to explain that all the logic she had thought so useless in the 1930s had come to something practical after all. The connection between 1936 and 1945 was also perfectly clear during AMT’s time at the NPL. It was only later that this simple and direct truth was forgotten, to the extent that in 1972 Randell, writing his historical paper, could see ‘no obvious connection’ between the Universal Turing Machine and the ACE; and mentioned the ACE report only in terms of its relationship to the EDVAC report. It is astonishing how difficult people have found it, both in AMT’s own time and since, to accept that he could both think of something abstract, and set out, without making any particular fuss, to make it concrete. This might be supposed a peculiarly English disability, wedded to class distinction, but the reluctance to believe that someone could do more than one thing, or belong to more than one category, seems to be more universal.

  (5.27) Sir George Thomson, describing Sir Charles Darwin in a Biographical Memoir of the Royal Society, 1963.

  (5.28) Here and frequently in the following narrative I draw on the collected minutes and reports of the Executive Committee of the NPL.

  (5.29) Nature, 7 April 1945.

  (5.30) Memorandum by J.R. Womersley, ‘ACE Project – Origin and Early History’, dated 26 November 1946, in DSIR 10/385. According to EST: ‘On submission to the Government of the outline of his design for such a [universal] machine he was taken on to the staff … in October, 1945.’ While AMT might have given some kind of verbal description to Womersley, no formal ‘submission’ appears in the records and most likely Mrs Turing was going on the memory of AMT’s ACE report being formally accepted a few months later.

  (5.31) Lyn Newman, in her introduction to EST.

  (5.32) Edward Carpenter s autobiography, My Days and Dreams (George Allen & Unwin, 1916).

  (5.33) Forster’s article in Tribune was reprinted in Two
Cheers for Democracy (as BP. 13), where it followed a 1942 essay on Tolstoy voicing similar thoughts: ‘Do you yourself believe in simplicity as a cure for our present troubles? And, if so, how do you think simplicity can be worked in a world that has become industrialised? Tolstoy’s outlook was agricultural: he never realised the implications of the machine’.

  (5.34) Quoting from Angus Calder, The People’s War (Jonathan Cape, 1969).

  Mercury Delayed

  (6.1) AMT’s report was headed only ‘Proposed Electronic Calculator’, and did not use the name ‘ACE’. But he used the name as soon as the report was discussed, and so to simplify matters I have called it ‘the ACE report’. A copy of the report, though without the pages of diagrams, is in DSIR 10/385, the main file covering the ACE development from 1946 to 1948. A complete version was issued in a limited edition by the Division of Computer Science, National Physical Laboratory, in April 1972 as report Com. Sci. 57. A first analysis of it was made in 1975 by B.E. Carpenter and R.W. Doran, later appearing in Computer Journal 20 (1977).

  (6.2) The fragments consist of just four typescript pages. They survive only because he used the reverse sides as scrap paper on which to explain some circuit theory to Mike Woodger in 1947.

  (6.3) This was his lecture to the London Mathematical Society, 20 February 1947 (see page 356). The typescript (until now unpublished and unquoted) is in KCC. I have employed it here at the cost of jumping out of sequence, as I could hardly improve upon his own exposition of the ideas announced more starkly in the original ACE report.

  (6.4) In January 1947 J.V. Mauchly pointed out the idea that ‘one set of instructions’ could ‘modify another set’. Paper reprinted in The Origins of Digital Computers (as note 5.23), page 366.