Alan Turing: The Enigma

(1.1) The Lay of the Turings, composed in about 1850 by the Rev. Henry Mackenzie, Bishop of Nottingham and son-in-law of the seventh Baronet. Perfect bad verse. A less romantic genealogy is detailed in Burke’s Baronetcy.

(1.2) H.D. Turing’s daughter, Penelope Turing, wrote an autobiography Lance Free (1968).

(1.3) Julius Turing’s Record of Service is in the India Office Library, London.

(1.4) The Stoney genealogy is given in Burke’s Irish Family Records.

(1.5) The Road to Wigan Pier, Part Two, (Gollancz, 1937).

(1.6) In an unpublished autobiography, The Half Was Not Told Me.

(1.7) Quoted in EST from a letter written to Mrs Turing after AMT’s death.

(1.8) The original edition was entitled A Child’s Guide to Living Things (Doubleday, Page & Co., New York, 1912).

(1.9) Mrs Turing deposited in KCC sixteen letters of AMT from Hazelhurst, six from Sherborne. The first two of these, as quoted here, did not actually bear the year ‘1923’. This, however, was what Mrs Turing guessed in her annotations, and it is consistent with Sunday being letter-writing day at Hazelhurst, as seems to have been the case.

(1.10) As note 1.6

(1.11) Mrs Turing’s own words in EST.

(1.12) A.B. Gourlay, A History of Sherborne School (Sawtells, Sherborne, 1971).

(1.13) The Western Gazette, 14 May 1926.

(1.14) Alec Waugh, The Loom of Youth (Richards Press, 1917). Alec Waugh was at Sherborne from 1911 to 1915.

(1.15) Nowell Charles Smith, Members of One Another (Chapman & Hall, 1913). A book of sermons for the years 1911-13. It may be somewhat anachronistic to quote from the pre-war period, but from all accounts, very little had changed in 1926.

(1.16) Quoting from here onwards the comments made on AMT’s school reports. These were donated by Mrs Turing to the library of Sherborne School.

(1.17) Letter to the author from Mr D.B. Neild, 23.12.78.

(1.18) A.H.T. Ross compiled an extensive book of revealing reminiscences, Their Prime of Life (Warren & Sons, Winchester, 1956). The ‘House Letter’ of 1928 is entirely typical of its style and content.

(1.19) Quoting from a letter to the author of Mr M.H. Blarney, 9.7.78.

(1.20) As note 1.12.

(1.21) Letter to the author from Canon D.B. Eperson, 16.1.78.

(1.22) The popular account was the English translation of Albert Einstein, Relativity: The Special and the General Theory (tr. R.W. Lawson, Methuen, 1920). Unfortunately it is not clear how and when the discovery of relativity fitted into AMT’s development. The Memo Book containing his notes, held in KCC, carries Mrs Turing’s assertion that the notes were written for her at Christmas 1927 – an astonishingly early date in view of the unanimous verdict of the schoolmasters that he could not express himself. The notebook contains calendars for 1928 and 1929 printed at the back, and so would presumably have been on sale at that Christmas. But this early date would not be consistent with the supposition that he got the statement of the geodesic law of motion from Eddington’s book, which appeared only in 1928. So as a working compromise I have set my account in the context of late 1928. It may be that this does an injustice to him, and understates the contrast between his intellectual development and the general Sherborne appreciation of it. There is no other piece of evidence until the reference to relativity by Christopher Morcom in his letter of 19 August 1929. This reads as though they had at least spoken together of the subject. For another point of corroboration, see note 1.27. A related question is that of how AMT found the Einstein and Eddington books – here credit must be due to the Sherborne librarian or some other helpful hand. It is a good reminder of how incomplete our knowledge must sometimes be.

(1.23) The quoted passages come from the letters and notes that AMT wrote for Mrs Morcom in 1930 and 1931 (see page 53, and note 1.26).

(1.24) This report is held together with the school reports at Sherborne. Mrs Turing has annotated it as being either 1929 or 1930, and my placing it in 1929 is only a matter of guesswork.

(1.25) A.H.T. Ross (note 1.18 makes specific mention of the danger of accepting holiday invitations from boys in other houses. Curiously enough he was writing his remarks on ‘Problems’ and ‘Tone’ in the spring and summer of 1954, with the result that they are interspersed with comments on the impact of the Montagu trials and news of AMT’s death.

(1.26) AMT kept the letters he had from Christopher Morcom, and other souvenirs (see page 47). In 1931 Mrs Morcom copied out the letters, and then the originals, which AMT kept all his life, were returned after AMT’s death. The Morcom family also kept the letters written by AMT just before and then after Christopher’s death. I am deeply indebted to Mr Rupert Morcom for making all these and other family documents available.

(1.27) There are no letters in KCC between those of May 1926 and this one. The paraphrase is of a passage on page 215 of Sir Arthur Eddington, The Nature of the Physical World (Cambridge University Press, 1928). This is good evidence that by this time he had absorbed Eddington’s account of relativity, which comes well before this discussion of the new quantum mechanical picture of matter.

The Spint of Truth

(2.1) This letter is not in KCC. Another loss is that of the letters AMT had both from his mother and his father at this time. According to EST he also kept these all his life. This deprives us in particular of a glimpse of the relationship between father and son. Mrs Turing had her say later, but in this as in so many other ways Mr Turing’s part has just been wiped out.

(2.2) Quoted in EST from a letter written to Mrs Turing by A.J.P. Andrews after AMT’s death.

(2.3) Letter to the author from Major L. Knoop, 24.1.79.

(2.4) No diary has survived from this or any other part of AMT’s life.

(2.5) Letter to the author from Mr Patrick Barnes, 12.2.79.

(2.6) This was the 1922 edition of Mathematical Recreations and Essays (Macmillan).

(2.7) A short biography of Alfred W. Beuttell (1880-1965) was commissioned and published privately by Victor Beuttell in 1971, under the title The Man Who Made Linolite.

(2.8) The Shirburnian, 36, page 113.

(2.9) Here and elsewhere I have drawn upon C. Reid, Hilbert (George Allen & Unwin; Springer Verlag, 1970), for quotations.

(2.10) As note 3.3.

(2.11) The paper was in J. Lond. Math. Soc. 8 (1933). Champernowne’s result concerned ‘normal numbers’, a fairly light-hearted application of the study of the real number’ system as it had developed since the late nineteenth century. A ‘normal’ number was defined as one whose decimal expansion contained the ten digits equally and evenly distributed in a certain precise sense. It was already known that if a real number were picked ‘at random’, then there was a probability of one hundred per cent that it would be ‘normal’. Yet no actual example of a ‘normal number’ was known until Champernowne produced one. AMT took some interest in the question later. There was a connection with his interest in randomness, but also a similarity to the concept of computability. For a ‘random’ real number has a probability of one hundred per cent of being uncomputable, but it requires some effort to produce, as he did, an example of an uncomputable number. KCC contains a letter from G.H. Hardy to AMT on ‘normal numbers’, undated but presumably of the later 1930s.

(2.12) It was undated, but written out on Clock House notepaper. This places it as composed on one of his visits. Mr Rupert Morcom writes that he believes it was written before 1933, and the handwriting style would support this belief. My guess is that 1930 is too early for the McTaggert reference, and that the style is more consistent with AMT’s wider-ranging intellectual life at Cambridge. These considerations all point to 1932. But certainly AMT could have thought in terms very like these at any time since 1929 or so, and the date of this piece of writing is not too significant.

(2.13) Quoting from the English translation of Laplace’s Essai sur les probabilités (Dover edition, 1951).

(2.14) In his obituary of AMT in the Shirburnian, 1954.

(2.15) Quoted in EST from a letter written to her by Geoffrey O’Hanlon.

(2.16) A.W. Beutteil, ‘An Analytical Basis for a Lighting Code’, in The Journal of Good Lighting, January 1934.

(2.17) I am grateful to Professor W.T. Jones for bringing this passage to my attention in describing the impression AMT made on him in 1937. (See page 137). Keynes’ talk on My Early Beliefs, given in 1938, was published after his death as one of Two Memoirs (Rupert Hart-Davis, 1949).

(2.18) The Autobiography of G. Lowes Dickinson, published posthumously (Duckworth, 1973).

(2.19) New Statesman and Nation, 4 February 1933. The progressive journal here used the medical model for homosexuality.

(2.20) J.S. Mill, On Liberty (1859). I owe to Robin Gandy the identification of AMT as ‘a J.S. Mill man’. In fact I have chosen to set AMT against less business-like and competitive libertarians, but certainly this essay contains many points of contact with AMT’s outlook and convictions.

(2.21) Maurice, written in 1913, was published after E.M. Forster’s death in 1971.

(2.22) The passage quoted was actually written by Shaw in 1944, but it only condensed the comment in Shaw’s Preface to Back to Methuselah of 1920.

(2.23) Bertrand Russell’s Introduction to Mathematical Philosophy (George Allen & Unwin, 1919) did not deal with the background in geometry, but started with the problem of giving meaning to the Peano axioms. However, I have included mention of Hilbert at this point, in order to lend greater unity to the discussion.

(2.24) The minutes are held in the University Library, Cambridge.

(2.25) The Times, 10 November 1933. But if the mathematicians had delivered a politically advantageous formula, they had surrendered little in private content. The phrase ‘a mixture of logic and intuition’ was unexceptionable (compare AMT’s remarks apropos of the ordinal logics in 1938); and the work of Gödel had just recently served to delineate the limitations of deductive logic.

(2.26) The standard work for this course was Whittaker and Robinson, The Calculus of Observations, 1924.

(2.27) Lindeberg, Math. Zeitschrift 15 (1922).

(2.28) AMT would have offered about six advanced courses for the Schedule B examination. Unfortunately the records of the Faculty of Mathematics do not seem to show what these were.

(2.29) AMT’s fellowship dissertation, On the Gaussian Error Function, remained unpublished. The original typescript is held in KCC.

(2.30) As note 2.9.

(2.31) An English translation of Gödel’s paper is in The Undecidable, ed. Martin Davis (Raven Press, New York, 1965).

(2.32) This was Hardy’s Rouse Ball Lecture for 1928, published in Mind, 1929, as ‘Mathematical Proof’.

(2.33) AMT’s paper was ‘Equivalence of Left and Right Almost Periodicity’, J. Land. Math. Soc. 10 (1935).

(2.34) J. von Neumann, Trans. Amer. Math. Soc. 36 (1934).

(2.35) For a modern biographical study, with many points of contact with this book, see Steve J. Heims, John von Neumann and Norbert Wiener (MIT Press, 1980).

(2.36) AMT also corresponded with von Neumann. In KCC there is an isolated letter from von Neumann to ‘My dear Mr Turing’, dated ‘December 6’ without year. It concerns a theorem about topological groups proposed to him by AMT. The year is most likely 1935; von Neumann’s letter contains a reference to the mailboat, so this could not be 1936 or 1937. By 1938 AMT’s research interests had moved away from this field. My search through the von Neumann papers in the Library of Congress did not reveal any more of this correspondence.

(2.37) AMT’s great paper, quoted here, was ‘On Computable Numbers, with an Application to the Entscheidungs problem’, Proc. Land. Math. Soc. (2), 42 (1937). It is reprinted in The Undecidable (as note 2.31).

(2.38) Did AMT think in terms of constructing a universal machine at this stage? There is not a shred of direct evidence, nor was the design as described in his paper in any way influenced by practical considerations. Yet in his obituary of AMT in The Times, Newman wrote: ‘The description that he then gave of a “universal” computing machine was entirely theoretical in purpose, but Turing’s strong interest in all kinds of practical experiment made him even then interested in the possibility of actually constructing a machine on these lines.’ (My italics.) Newman did not repeat this claim in his Royal Society memoir, in which the practical side was so much played down, although there he commented on how bold an innovation it had been to bring ‘paper tape’ into symbolic logic. Both comments reflected the impact made by AMT’s concreteness upon a classical pure mathematician, but like the other obituary writers, Newman was concerned to delineate AMT’s mental unorthodoxy, rather than to document anything in the history of technology. We have nothing more to go on. My own belief is that the ‘interest’ must have been at the back of his mind all the time after 1936, and quite possibly motivated some of his eagerness to learn about engineering techniques. But as he never said or wrote anything to this effect, the question must be left to tantalise the imagination.

(3.1) A. Church, ‘A Note on the Entscheidungs problem’, in J. Symbolic Logic, 1 (1936), reprinted in The Undecidable (note 2.31). The paper of a year earlier was ‘An Unsolvable Problem of Elementary Number Theory’, Amer. J. Math. 58 (1936), presented 19 April 1935.

(3.2) The first letter in what was to be a more copious flow of correspondence during the Princeton period, in which AMT managed while away to think of something to say every three weeks or so. There are only eighteen letters in KCC for the five academic years 1931 to 1936, but twenty-eight for the two Princeton years. This frequency was never resumed, a total of nine letters home representing the remaining sixteen years of his life.

(3.3) G.H. Hardy, AMathematician ‘s Apology (Cambridge University Press, 1940).

(3.4) When Mrs Turing came to write her biography, she found herself better informed about AMT’s environment at Princeton than anywhere else, thanks to his letters. Though largely transcribing the information in these, she added one story which does not derive from a KCC letter: ‘Though prepared to find democracy in full flower, the familiarity of the tradespeople surprised him; he cited as an extreme case the laundry vanman who, while explaining what he would do in response to some request of Alan’s, put his arm along Alan’s shoulder. “It would be just incredible in England.’” Perhaps there was something of an ‘alas!’ in AMT’s remark, which would not have fitted in with Mrs Turing’s ideas about tradesmen.

(3.5) Two postcards from Scholz, dated 11 February and 15 March 1937, are in KCC.

(3.6) A remark quoted in the review of von Neumann’s contributions to the ‘Theory of Games and Mathematical Economics’, by H.W. Kuhn and A.W. Tucker, Bull. Amer. Math. Soc. 64 (1958).

(3.7) Published posthumously in The Undecidable (note 2.31).

(3.8) Post’s paper is reprinted in The Undecidable.

(3.9) Letter to the author from Dr A.V. Martin, 26.1.78.

(3.10) See note 8.67.

(3.11) The brief logic paper was in J. Symbolic Logic, 2 (1937). The work related to that of Baer was in Compositio Math. 5 (1938). The other group theory paper was in Ann. Math. (Princeton) 39 (1938).

(3.12) A copy of von Neumann’s letter is held in AMT’s file at the Department of Mathematics, Princeton University. Formal recommendation of AMT came from the Vice-Chancellor of Cambridge University on 25 June.

(3.13) One letter from Bernays to AMT, dated 24 September 1937, is in KCC. AMT’s correction note appeared in Proc. Lond. Math. Soc. (2) 43 (1937). There were other mistakes and inconsistencies in the specification of the universal machine, some of them detailed by Post in a 1947 paper (reprinted in The Undecidable, as note 2.31).

(3.14) J. Symbolic Logic, 2 (1937).

(3.15) As described in The Undecidable, page 71.

(3.16) J.B. Rosser, J. Symbolic Logic 2 (1937).

(3.17) Letter from A.E. Ingham dated 1 June 1937 in KCC.

(3.18) The following account draws heavily on H.H. Edwards, Riemann’s Zeta Function (Academic Press, New York, 1974), which also discusses AMT’s contributions.

(3.19) S. Skewes, J. Lond. Math. Soc. 8 (1933). There is a letter in KCC from Skewes, dated 9 December 1937, with a brief expression of interest in AMT’s ideas.

(3.20) A.G.D. Watson, ‘Mathematics and its Foundations’, in Mind 47 (1937).

(3.21) AMT was right. During the war Gerard Beuttell made important contributions to the design of instruments to estimate the visual range by measuring the scattering of light within a small enclosed space. (J. Scientific Instruments, 26 (1949)). He died on a meteorological reconnaissance flight over the north Atlantic in early 1945.

(3.22) Letter to the author from Dr M. MacPhail, 17.12.77.

(3.23) It was in service until 1960, then being supplanted by a digital computer, and may now be seen in the Liverpool City Museum.

(3.24) Letter from E.C. Titchmarsh in KCC.

(3.25) The original PhD thesis is held in the mathematics library at Princeton University; it was published as ‘Systems of Logic based on Ordinals’ in Proc. Lond. Math. Soc. (2) 45 (1939), and reprinted in The Undecidable.

(3.26) Letter to the author from Professor S. Ulam, 16.4.79.

(3.27) C. Andrew, ‘The British Secret Service and Anglo-Soviet Relations in the 1920s, Part I’ in the Historical Journal, 20 (1977).

(3.28) Hinsley I (see note 3.31), page 10.

(3.29) Hinsley I, page 20.

(3.30) Administrative files relating to GC and CS are held at the Public Record Office in FO 366.

(3.31) F.H. Hinsley et al., British Intelligence in the Second World War. Volume I (1979), Volume II (1981). Published by HMSO as an official war history.

(3.32) FO 366/978.

(3.33) Hinsley I, page 54.

(3.34) As note 3.27.

(3.35) Hinsley I, page 53.

(3.36) Hinsley I, page 54.

(3.37) From records of the Faculty of Mathematics, Cambridge University.

(3.38) Parts of the revised Encyklopädie appeared in December 1939, but Scholz’s section on the foundations of mathematics, including the reference to AMT’s work, had to wait until August 1952.

(3.39) A transcript compiled from notes taken by others attending the lectures has been published as Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939, ed. Cora Diamond (Harvester Press, 1976). The quoted dialogue comes from lectures 21 and 22. It is perhaps a pity that the most extensive verbatim record of AMT should be concerned with a discussion which was not central to his concerns, and where he was not in his element. AMT sometimes liked to give the impression that he had scored off Wittgenstein at some point, but if so the evidence is not to be found in this transcript. In fact he showed a curious diffidence, one feature being that despite long discussions about the nature of a ‘rule’ in mathematics, AMT never offered a definition in terms of Turing machines.

(3.40) This is in KCC. It was corrected and completed by A.M. Cohen and M.J.E. Mayhew, Proc. Lond. Math. Soc. (3) 18 (1968). Using AMT’s approach they reduced the ‘Skewes number’ to . But in 1966 R.S. Lehman had by another method reduced the bound to the comparatively miniscule value of 1.65 X 10¹¹⁶⁵.

(3.41) His paper ‘A Method for the Calculation of the Zeta-function’ appeared only in 1943, in Proc. Lond. Math. Soc. (2) 48.

(3.42) Quoting from a copy of part of the letter made by Mrs Turing and deposited in KCC. My guess is that she omitted some reference to the function of the proposed machine as a cipher generator, not knowing whether this would be a transgression of secrecy.

(3.43) Minutes of the Council of the Royal Society.

(3.44) The blueprint, initialled ‘D.C.M.’, is in KCC.

(3.45) Hinsley I, page 51.

The Relay Race

(4.1) Letter and list of names in FO/366/1059, which contains no further reference to AMT.

(4.2) M. Muggeridge, The Infernal Grove (Collins, 1973).

(4.3) Pre-eminently H.F. Gaines, Elementary Cryptanalysis, 1939. Only at the end of the 1970s did a serious technical discussion of specific modern cipher systems begin to appear.

(4.4) I am grateful to the staff of the National Archives, Washington, for bringing this material to my attention. In late 1940 the German raider Komet made several captures of British merchant ships and took this code and cipher material. This then found its way into German archives captured after the war.

(4.5) There is an account of Polish Enigma work in the appendix to J. Garlinski, Intercept (Dent, 1979). A fuller and better version is given by M. Rejewski, ‘How Polish Mathematicians Deciphered the Enigma’, in Annals of the History of Computing 3 (1981). This would seem to be the definitive account, ending much confusion and speculation in earlier discussions.

(4.6) Hinsley I, page 490, itself quoting from the Polish claim at the time.

(4.7) Hinsley I, page 492.

(4.8) Letter to the author from Professor R.V. Jones, 7.2.78, expanding upon a passage of his Most Secret War (Hamish Hamilton, 1978).

(4.9) The following account of the Bombe is a simplified version of Gordon Welchman, The Hut Six Story (McGraw Hill, New York; Allen Lane, London, 1982). It is worth noting Welchman’s comment: ‘We thought very little, in these hectic days, of who should take credit for what.’ AMT would have thought least of all, though he did say that he thought Welchman’s idea had been the important one. Establishing priority and originality is hard enough in open work, let alone when considering ideas kept secret for over forty years. I hope that the departure from truth, in this and other passages suffering from the same difficulty, is not too great. The more important point lies in the fact that pre-war cryptology, fossilised and isolated by secrecy, was transformed as soon as any contemporary mathematical mind was brought to bear on the subject.

(4.10) Hinsley I, page 493. The account in B. Johnson, The Secret War (BBC, London, 1978), identifies AMT as the ‘emissary’, following a statement made to BBC researchers by General Bertrand before his death. This seems rather unlikely as he was working on the Bombe, not the sheets, and as this was not really a job for a ‘man of the Professor type’. But it might be so – I have found no further evidence one way or the other. EST has a story concerning AMT being sent abroad, a mix-up over papers, and managing for a day with ‘a few francs’, but this could be taken to fit the 1945 mission (page 311).

(4.11) P. Beesly, Very Special Intelligence (Hamish Hamilton, 1977), which gives the Admiralty side of the story.

(4.12) Hinsley I, page 103.

(4.13) Hinsley I, page 336.

(4.14) Hinsley I, page 163.

(4.15) F.W. Winterbotham, The Ultra Secret, (Weidenfeld & Nicolson, 1974), which gives a secret service view.

(4.16) P. Beesly, as note 4.11.

(4.17) Hinsley I, page 109.

(4.18) Hinsley I, page 144.

(4.19) Hinsley I, page 336.

(4.20) I.J. Good, ‘Studies in the History of Probability and Statistics XXXVII. A.M. Turing’s Statistical Work in World War II’, in Biometnka 66 (1979), which this description of AMT’s ideas follows closely. Further details are given in a note by Good appended to the article by M. Rejewski (note 4.5).

(4.21) Quoting from I.J. Good’s lecture at the National Physical Laboratory, 1976; this has since been published in slightly revised forms in several places, the most accessible being as a paper ‘Pioneering Work on Computers at Bletchley’ in the misleadingly entitled volume A History of Computing in the Twentieth Century, eds. N. Metropolis, J. Howlett and G.-C. Rota (Academic Press, New York, 1980).

(4.22) Quotation is from Beesly, as note 4.11, although I follow Hinsley in stating the capture to have been planned and not an accident.

(4.23) Messages as translated into English at the time, and taken from the first few pages of the gigantic PRO file DEFE 3/1.

(4.24) Hinsley I, page 337.

(4.25) Beesly, as note 4.11, pages 57, 97.

(4.26) Hinsley I, pages 273-4.

(4.27) Quoted in EST. There he appeared anonymously (presumably because working for GCHQ) as a colleague who later proved a ‘staunch friend’ – Mrs Turing’s only concession to the events of 1952.

(4.28) Hinsley I, page 296.

(4.29) R. Lewin, Ultra Goes to War (Hutchinson, 1978), page 183.

(4.30) Obituary of A.C. Pigou by D.G. Champernowne in Roy. Stats. J. A122 (1959).

(4.31) As note 4.2.

(4.32) Dorothy Sayers, The Mind of the Maker (Methuen, 1941). AMT referred to reading it in the first wartime letter to his mother, in August 1941 (see note 5.8), saying ‘You should read it when you come.’ The quoted passage is the one he himself quoted in 1948 (see page 377).

(4.33) Princeton records show that von Neumann gave a popular lecture on the game of poker on 19 March 1937. It would be very surprising if AMT had not attended it. He did not, in his discussions with Jack Good, draw a connection between his chess programs and game theory – nor indeed with the machines of Computable Numbers. But I have assumed that he had a general acquaintance with game theory, just as he could hardly have forgotten his own ‘machines’. I have also given space to game theory for another reason: AMT certainly showed an interest in it later, and often pointed out examples of strategies in everyday life.

(4.34) AMT’s letters to Newman are in KCC. They are undated but can mostly be placed by passing references to events.

(4.35) This essay, ‘The Reform of Mathematical Notation and Phraseology’, remained unpublished. The typescript is in KCC with other unpublished work on type theory. Excerpts are included in a historical paper by R.O. Gandy, ‘The Simple Theory of Types’, in Logic Colloquium 1976, eds. R.O. Gandy and J.M.E. Hyland (1977).

(4.36) AMT’s joint paper with M.H.A. Newman was ‘A Formal Theorem in Church’s Theory of Types’, in J. Symbolic Logic 7 (1942).

(4.37) AMT’s paper appeared in the same 1942 volume of the Journal of Symbolic Logic. The two ‘forthcoming’ papers, ‘Some Theorems about Church’s System’ and ‘The Theory of Virtual Types’, never appeared. But in 1947 (see page 355 and note 6.34) he submitted a further paper on type theory which represented a revision of work done at this period.

(4.38) Hinsley I, page 338.

(4.39) Beesly, as note 4.11, page 164. I have inserted ‘September’ for Beesly’s ‘November’ to make it consistent with the Hinsley account.

(4.40) Letter quoted from Hinsley II, page 655.

(4.41) Hinsley II, page 657.

(4.42) Quoting from B. Randell, The Colossus, an account written from the engineering side. First published as a University of Newcastle-upon-Tyne report in 1976 this is now available in the Metropolis volume (see note 4.21).

(4.43) Peter Hilton was speaking informally during a conference session of Reminiscences of Logicians, published as a section of Algebra and Logic, Springer Mathematical Notes 450, ed. J. Crossley, 1975.

(4.44) As note 4.21.

(4.45) Hinsley II follows earlier writers in calling the German enciphering machine a Geheimschreiber. But my understanding is that there was more than one type of machine covered by this generic term, and that the photograph of a Siemens machine in B. Johnson, The Secret War (as note 4.10) is not actually of the one that was deciphered as Fish.

(4.46) As note 4.43.

(4.47) Stories taken from EST. With mind-boggling sang froid she added: ‘The idea of “Prof.” being nearly arrested caused much amusement in his department.’

(4.48) As note 4.43.

(4.49) Hinsley II, page 56.

(4.50) I am grateful to the State Department for supplying copies of documents relating to AMT’s entry to the US in 1942. They are of a purely routine administrative nature. They account for all the references to AMT in the general index to State Department files held in the National Archives, Washington. In contrast, there are no corresponding British documents. There is a reference in the index to Foreign Office correspondence for 1942 to ‘Turing: sea travel facilities to Washington: finances.’ But the relevant file has been ‘weeded’: destroyed.

(4.51) FO/371/32346.

(4.52) As note 4.2.

(4.53) I owe this reference to Dr G. DiVita. It was on 14 February 1941. Of course the report gave no indication of the scale and modernity of operations, but it is curious to see any mention whatever of ‘Nazi codes’ being broken, when comprehensive secrecy on the subject lasted for a quarter of a century after Nazi Germany’s demise.

(4.54) For AMT’s pre-war voyages I was able to draw upon the Board of Trade passenger lists. But none exist for the wartime period, so the evidence here is indirect. The State Department information (see note 4.50) shows that he was admitted at New York on 13 November 1942. Information from the Naval Historical Center, Department of the Navy, Washington D.C. shows that this was the day that the Queen Elizabeth arrived.

The fast passenger liners converted to troop transporters being the normal means of ferrying high-level personnel, I have assumed this to settle the question. But it is confused by the statement of Mrs Turing that his passage west was very overcrowded, and that he was the only civilian on board apart from a couple of children. Here, surely, she was mistaken. It was the eastbound passages which were desperately crowded. The Queen Elizabeth carried a mere 557 passengers west, most of them civilians, to return in March with 10,261 troops. See also note BP 11, for evidence regarding AMT’s eastbound voyage.

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 technology. … 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).

(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.

(6.5) Mike Woodger has told me of a reference in NPL files, since destroyed, to the ACE report being in existence by the end of 1945. But in any case it was ready in time for Womersley to compose his own report by 13 February 1946; this was essentially 1945 work.

(6.6) In the papers of Mike Woodger.

(6.7) Paper E.881 in the NPL Executive Committee records.

(6.8) Both letters are in DSIR 10/385.

(6.9) J.H. Wilkinson has described his association with AMT and the ACE project in an article in The Radio and Electronic Engineer, July 1975, in the Pioneers of Computing oral history, ed. C. Evans, Science Museum, London, 1975, and in a paper ‘Turing’s work at the National Physical Laboratory …’ in the Metropolis volume (see note 4.21).

(6.10) DSIR 10/385.

(6.11) Letter in the von Neumann archive, Library of Congress.

(6.12) Minutes of the Council of the Royal Society, 1946.

(6.13) S.S. Snyder, Influence of US Cryptologie Organisation on the Digital Computer Industry. Declassified NSA report SRH 003, 1977, available at the National Archives, Washington DC.

(6.14) H.H. Goldstine, The Computer from Pascal to von Neumann (Princeton University Press, 1972), mentions this visit and the ‘third version’ in passing on page 218. My study of the Goldstine archive at Hampshire College, Amherst, Mass., failed to locate the ‘third version’.

(6.15) Letter in the von Neumann archive, Library of Congress. My search revealed only one reference to AMT in von Neumann’s letters beside this glancing comment on the thesis of finitely many mental states’. It was in a letter to Wiener of 26 November 1946: ‘I did think a good deal about self-reproductive mechanisms. I can formulate the problem rigourously [sic], in about the style in which Turing did it for his mechanism. I can show that they exist in this system of concepts …’

(6.16) H. Hotelling, Ann. Math. Stat. 14 (1943).

(6.17) I.J. Good’s book was not published until 1950. In the meantime Shannon’s theory of communication had emerged from wartime secrecy in 1948, and Good was able to add a few comments to his text remarking upon the similarity of Shannon’s concepts to those of ‘weight of evidence’.

(6.18) A. Wald, Sequential Analysis, 1947. In KCC there is a manuscript by AMT headed ‘Sequential Analysis’ and outlining the ideas: as with the algebraic work (note 5.14) he might well have felt there should be something in his papers to reflect the mathematical substance of his work. (But Wald’s theory was used in R.B. Braithwaite’s discussion of scientific method, and AMT later found it coming into Robin Gandy’s work on the logic of science; so war work was not his only point of contact.)

(6.19) D. Gabor, J. Inst. Elect. Eng. 93 (1946).

(6.20) The Times, 1 November 1946.

(6.21) Nature, 20 April 1946 and 12 October 1946.

(6.22) Hartree on 7 November, Darwin on 13 November 1946.

(6.23) The Electrician, 8 November 1946.

(6.24) Surrey Comet, 9 November 1946.

(6.25) The Listener, 14 November 1946 (page 663). A photograph (page 672) claimed to show an earnest engineer ‘wiring one of the sections of the automatic computer’ at the NPL; but it was later revealed (page 755) to be nothing of the kind.

(6.26) TRE documents (see note 6.27) show that F.C. Williams was supplied with the ACE report only in October 1946, and so could not have read of the ‘regeneration’ principle there. It was not, apparently, an obvious idea: Williams’ account in the Pioneers of Computing oral history (note 6.9) explains that it was some time before ‘the penny dropped’. No one at the time, nor since, seems to have noticed that AMT thought of it earlier; just one example of the refusal of people to believe he could do anything practical.

(6.27) These are not NPL minutes but TRE documents, quoted and discussed by S.H. Lavington in Electronics and Power, November 1978, and then in his Early British Computers (Manchester University Press, 1980).

(6.28) The ensuing correspondence between M.V. Wilkes and Womersley, and AMT’s reaction to it, has been taken from a copy held in the papers of Mike Woodger.

(6.29) As note 6.6.

(6.30) The lectures described Versions V, VI and VII of the ACE design. Only the first two and part of the last were actually given by AMT. Hartree’s notes of the last two lectures are held in the Hartree archive, Christ’s College, Cambridge; and photocopies of these are in KCC. The whole lecture course, however, was written up by T.H. Marshall for a report The Automatic Computing Engine, for the Mechanical and Optical Instruments Branch, Military College of Science, Shrivenham. This was dated February 1947.

(6.31) Remarks by Professor M.V. Wilkes in a covering note to the Wilkes-Womersley correspondence (see note 6.28), dated 7 February 1977.

(6.32) Daily Telegraph, 27 December 1946; Evening News, 23 December 1946.

(6.33) Proceedings of a Symposium on Large-Scale Digital Calculating Machinery, published as volume XVI of the Annals of the Computation Laboratory, Harvard, 1948.

(6.34) AMT’s paper was ‘Practical Forms of Type Theory’, in J. Symbolic Logic, 13 (1948). There are extensive drafts in KCC (see also note 4.37).

(6.35) H.H. Goldstine (note 6.14) refers to this visit on pages 191, 219, 291. AMT’s results on .matrix inversion were more general than those of von Neumann and Goldstine, though the latter appeared first (Bull. Amer. Math. Soc. 53, 1947). AMT’s paper (note 6.47), when it appeared in 1948, described the relation thus: ‘In the meantime another theoretical investigation was being carried out by J.v. Neumann, who reached conclusions similar to those of this paper for the case of positive definite matrices, and communicated them to the writer at Princeton in January 1947 before the proofs given here were complete’.

(6.36) The MCS report (see note 6.30) contains a reference to this reflection problem, suggesting that this was what was on his mind at the time. The patent (number 694,679) was filed only in 1952. Another patent (718,895), in the joint names of Turing, Woodger and Davies, and covering aspects of the ACE design, was filed in 1951. These were the only patents bearing AMT’s name. Both were taken out by the National Research Development Corporation and at the NPL were regarded light-heartedly. No benefit accrued to the individuals named.

(6.37) Note dated 14 August 1946 in DSIR 10/275.

(6.38) As note 5.21.

(6.39) I have assumed that he was clear on this point all along – after all, it was what he himself had proved in 1936! He must very early have faced the question as to how it was that his universal machine, without using program modification, could be set up to simulate the progress of a ‘learning machine’. I have here quoted his best-expressed answer to this question from the 1950 Mind article (note 7.34), although he also discussed it, not quite so clearly, in the 1948 report (note 6.53). Not everyone was clear on this point; thus Goldstine (as note 6.14, page 266) supposed that program modification would extend the range of possible operations.

(6.40) As note 6.6.

(6.41) Letter undated. Mermagen had asked him to give a talk at Radley and AMT replied characteristically that he would do so when he had ‘lantern slides and possibly even an instructional film, which would make it more fun.’

(6.42) C.G. Darwin, The Next Million Years (Rupert Hart-Davis, 1952).

(6.43) Diagrams of this work, dated 2 March 1947, survive in Mike Woodger’s notebook, as do details of Huskey’s ‘Test Assembly’.

(6.44) As note 6.6.

(6.45) The Times, 28 August 1947.

(6.46) Indulging my Carpenter parallel again: words he used just before his own move from Cambridge to the North in the 1870s. From S. Rowbotham and J. Weeks, Socialism and the New Life (Pluto Press, 1977), page 35.

(6.47) AMT’s paper was ‘Rounding-off Errors in Matrix Processes’, in Quart. J. Mech. App. Math. 1 (1948), appearing in Russian translation in Uspek. Matern. Nauk. (NS) 6 (1951). It required NPL permission for him to publish. KCC contains a letter from Sir Charles Darwin to AMT, dated 11 November 1947, acknowledging the copy submitted to him for approval. ‘… I must say that I read it through with some attention and interest, but spent most of the time cursing you for giving me such a perfectly smudgy copy to read. Next time I hope somebody else and not myself [will] be the sufferer, but I think the best plan would be to get some better carbon paper’.

(6.48) Progress Report on the Automatic Computing Engine, Mathematics Division, National Physical Laboratory, April 1948. This internal report, classified as ‘confidential’, contained extensive examples of programming for the ACE design as it then stood. Progress on each of the current British projects, was also summarised by H.D. Huskey on his return to the United States in Math. Tables and Other Aids to Computation, 23, page 213 (1948); this included a brief critique of AMT’s plans for the ACE. For a recent account of the programming techniques developed at the NPL, see M. Campbell-Kelly, ‘Programming the Pilot ACE …’, in Annals of the History of Computing, 3 (1981).

(6.49) Minutes of the Senate Committee, Manchester University, 22 March 1948.

(6.50) The minutes of the Moral Science Club give no more than the title of the talk, which was presented in S. Toulmin’s rooms.

(6.51) The discussion in J. von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour, 1944, had approximated the game of poker by treating the cards as having a continuous range of values. AMT’s work differed only in that it considered the cards as a discrete set. This manuscript, and that of his analysis of the game of Psychology, are in KCC. He used the reverse sides of papers used in the King’s College Choir School examinations.

(6.52) As note 6.6.

(6.53) The original typescript is in KCC. It was published in Machine intelligence 5, eds. B. Meitzer and D. Michie (Edinburgh University Press, 1969). Unfortunately this edition is marred by misprints, in particular the date 8/7/48 appearing as ‘8 August 1947’.

(6.54) AMT’s attitudes contrast particularly sharply with the male competitiveness described so acutely, if unconsciously, in J. Watson, The Double Helix, 1968.

(6.55) AMT’s letters have not survived, but his programs were copied into G.C. Tootill’s notebook. The long division routine is dated 8 July 1948.

(6.56) Described in more detail in an article on computer chess in Personal Computing, January 1980.

(6.57) A lecture ‘The General and Logical Theory of Automata’, rendered as a paper in 1951, and included in volume V of von Neumann’s Collected Works (Pergamon, 1963).

The Greenwood Tree

(7.1) F.C. Williams in the Pioneers of Computing oral history (see note 6.9).

(7.2) Letter in the von Neumann archive, Library of Congress.

(7.3) In his Programmers’ Handbook (note 7.7), page 4.

(7.4) F.C. Williams, ‘Early Computers at Manchester University’, in The Radio and Electronic Engineer, 1975.

(7.5) Quoting from a progress report made by M.H.A Newman, considered by a Manchester University committee (which ‘Mr Turing attended by invitation’) on 15 October 1948.

(7.6) Lyn Newman’s introduction to EST.

(7.7) His Programmers’ Handbook was a duplicated document of over 100 pages, dated March 1951. It was rapidly superseded by new versions thereafter.

(7.8) A slightly revised version of an account written by her in 1969, and quoted by M. Campbell-Kelly, ‘Early Programming Activity at the University of Manchester,’ in Annals of the History of Computing, 2 (1980). This paper gives detailed examples of the programming work.

(7.9) In an appendix to the Programmers’ Handbook, giving an account of the prototype machine and the work done on it.

(7.10) The design survives as an appendix dated 21 November 1949 to an ‘Informal Report on the Design of the Ferranti Mark I Computing Machine’, in the papers of G.C. Tootill.

(7.11) There might well have been other popular articles on this theme, but I have simply taken the one noted by Mrs Turing. My research in the Wiener archive at MIT did not bring to light any correspondence with AMT or comment on the 1947 visit; most likely it had no great significance for either of them. For a more serious and much more sympathetic account of Wiener’s ideas see the study by Steve Heims (as note 2.35).

(7.12) In Faster than Thought, page 323 (see note 8.25).

(7.13) British Medical Journal, 25 June 1949.

(7.14) The Times, 11 June 1949.

(7.15) This letter, Newman’s letter, and photographs of the prototype computer, all appeared in The Times on 14 June 1949.

(7.16) Proceedings published in duplicated form by the Mathematical Laboratory, Cambridge, 1950. From a technical point of view AMT’s paper was a first ‘program proof’, anticipating ideas of the 1960s. It has recently been reproduced, annotated and reviewed by F.L. Morris and C.B. Jones Annals of the History of Computing 6 (1984).

(7.17) M.V. Wilkes, Computers Then and Now, the 1967 Turing Lecture of the [American] Association for Computing Machinery.

(7.18) Instead of following the policy adopted in 1946, the Pilot ACE was used as a working computer, and duplicated as a commercial version, DEUCE, by English Electric. It may now be seen in the Science Museum, London. It went there in 1958 when superseded at the NPL by a larger machine called ‘ACE’. At the opening day the then Superintendent of the appropriate NPL Division declared ‘Today, Turing’s dream has come true.’ But the 1958 ACE was a tardy anachronism: it had retained mercury delay lines in the age of magnetic core store, and even vacuum tubes in the era of the transistor. This was not his dream.

(7.19) AMT described the computer work in his paper ‘Some Calculations of the Riemann Zeta function’, in Proc. Lond. Math. Soc. (3) 3 (1953). Giving as much detail as he did about the base-32 coding and the running of the machine was itself a highly characteristic Turing touch, one not at all to be expected in a pure mathematical paper by a more conventional person. I have inserted the word ‘prototype’ to avoid a tiresome confusion caused by the fact that he called the prototype the ‘Mark I’, and then the 1951 ‘Mark I’, the ‘Mark II’. The names used in my text are those that prevailed. Although AMT did not get very far himself with the computations, his method was sound and was applied by D.H. Lehmer in 1955-6 to check that the first 25,000 zeroes of the zeta function all lie on the critical line.

(7.20) Quoted from the article in Mind (note 7.34). There it formed part of his argument that a determinate system need not necessarily be predictable in practice; a machine need not behave in a recognisably ‘mechanical’ way.

(7.21) Unpublished account by David Sayre, 1969. He adds ‘One does not expect to find in one man both the most admirable intellect one had met and a person of the rarest human quality, but Turing was such a man, at least for me’.

(7.22) D. Sayre, ‘Some Implications of a Theorem Due to Shannon’, Acta Cryst. 5 (1952). But Dr Sayre writes: ‘a more important paper by the Japanese crystallographers S. Hesoya and M. Tokonami in 1967 comes, I think, much closer to what Turing had in mind’.

(7.23) Symposium on Information Theory, London Papers. Report of proceedings published by Ministry of Supply, 1950; re-issued by the Institute of Radio Engineers, 1953. The proceedings contain other comments by AMT and also note his unpublished work on chess-playing machines.

(7.24) C.E. Shannon, ‘Programming a Computer for Playing Chess’, Phil. Mag. Ser. 7, 41 (1950).

(7.25) Correspondence and notes relating to the Ratio Club are held by Dr J. A. V. Bates, at the National Hospital for Nervous Diseases, London.

(7.26) W. Ross Ashby, Design for a Brain (1952), and W. Grey Walter, The Living Brain (1953).

(7.27) As note 4.43.

(7.28) AMT’s paper was ‘The Word Problem in Semi-groups with Cancellation’, Ann. Math. (Princeton) 52 (1950). This was reviewed, clarified, and careless misprints corrected, by W.W. Boone, J. Symbolic Logic 17 (1952).

(7.29) The letter from von Neumann is in KCC. My search in the von Neumann archive did not uncover any reply from AMT.

(7.30) Quoting from M. Polanyi, Personal Knowledge (Routledge & Kegan Paul, 1958), pages 397, 403. Polanyi’s weighty volume was based on his Gifford Lectures for 1951–2.

(7.31) K. Popper, ‘Indeterminism in Quantum Physics and in Classical Physics’, Brit. J. Phil. Sci., 1950.

(7.32) Quoted by Polanyi, as note 7.30, page 20.

(7.33) Professor W. Mays, Department of Philosophy, Manchester University, has made available to me rough notes of this Discussion.

(7.34) The 1950 Mind article has been reprinted in several anthologies, most recently The Mind’s I, eds. D. Hofstadter and Daniel C. Dennett (Basic Books, New York; Harvester, Brighton, 1981).

(7.35) Letter in KCC. The index to the Russell papers has no mention of AMT except for the receipt in 1937 of Computable Numbers.

(7.36) See note 7.58.

(7.37) Edward Carpenter, Civilisation its Cause and Cure, first published 1889, quoted here from 1921 edition (George Allen & Unwin); the chapter ‘Modern Science: a Criticism’.

(7.38) In the January 1952 radio discussion (page 450 and note 7.61).

(7.39) In the May 1951 radio talk (note 7.56).

(7.40) R.V. Jones, Most Secret War (as note 4.8), page 522.

(7.41) He had a place in Who’s Who after the 1951 election to the Royal Society.

(7.42) As discussed by N. Bohr, Nature 131 (1933), page 457.

(7.43) C.H. Waddington, Organisers and Genes, 1940.

(7.44) P. Weiss, Quart, Rev. Biol., 1950.

(7.45) As note 7.30, pages 339, 356, 400.

(7.46) Here quoting from AMT’s paper ‘The Chemical Basis of Morphogenesis’, Phil. Trans. Roy. Soc. B 237 (1952).

(7.47) Ibid.

(7.48) Actually two books: G. Bentham, Handbook of the British Flora, revised by Sir J.D. Hooker and A.B. Rendle, 1947, and A.R. Clapham, T.G. Tutin, E.F. Warburg, Flora of the British Isles, 1952.

(7.49) Published as J.Z. Young, Doubt and Certainty in Science, 1951.

(7.50) Writing after AMT’s death to Mrs Turing, and as quoted in EST.

(7.51) Letters in KCC.

(7.52) Not in KCC, but quoted in EST.

(7.53) Writing after AMT’s death to Mrs Turing, and as quoted in EST.

(7.54) Quoting from J. A. Symonds, Shelley (Macmillan, 1887).

(7.55) A manuscript of the result, and of Whitehead’s letters, are in KCC.

(7.56) Transcript in KCC. The BBC has not preserved the recording of this, nor of the January 1952 broadcast. Nor does any other tape-recording seem to have survived, so that AMT’s unusual voice is lost to posterity.

(7.57) Letter in KCC.

(7.58) This talk, ‘Intelligent Machinery, a Heretical Theory’ was given to the ‘51 Society’ at Manchester, presumably in or after 1951. The typescript is in KCC. It was reprinted in EST.

(7.59) The proceedings were printed by Ferranti Ltd. They also record AMT’s comments on other talks during the course of the conference.

(7.60) Manuscript in KCC. Only three pages survive, of which the section quoted here is from the first, and that quoted on page 519 is from the third. In between his story diverges from what actually happened in December 1951, bringing in different characters and locations. I have taken this to confirm my impression from other sources that AMT ‘knew the score’ in Manchester already; this was not his first Manchester pick-up, although it might well have been the first time that he invited someone home as a boyfriend. For this reason I have included a transitional passage on page 428. AMT’s story is also concerned to give equal space to ‘Alec’, i.e. himself, and ‘Ron’, and so contains phrases in which he imagines himself as seen by a hard-up youth: ‘… Didn’t seem to be very well dressed. What an overcoat! … No, he was having a furtive look. Just a bit shy. … Seemed to be quite a toff after all. You could tell by the way he talked ..’.

(7.61) Transcript in KCC.

(7.62) Lecture 30 of the 1939 course (see note 3.39).

On the Beach

(8.1) Documents relating to the case are held at Chester Record Office. They include the statements made by AMT and Arnold Murray, and the police account of what was said on the evening of 7 February 1952. See also note 8.17.

(8.2) Sunday Pictorial, 25 May, 1 June, 8 June 1952. The series reflected the fact that there had been correspondence on homosexuality in the British Medical Journal since a conference in September 1947; this in turn took off from more theoretical agitation of the 1930s and a government Report on the Psychological Treatment of Crime of 1939.

(8.3) Page 166 of G. Westwood (actually a pseudonym, for Michael Schofield), Society and the Homosexual (Gollancz, 1952).

(8.4) A.C. Kinsey et al., Sexual Behaviour in the Human Male (W. B. Saunders, Philadelphia & London, 1948) page 261.

(8.5) Alderley Edge and Wilmslow Advertiser, 29 February 1952.

(8.6) J.W.S. Pringle, ‘The Origin of Life’, in no. VII of the Symposia of the Society for Experimental Biology, 1953.

(8.7) I am grateful to Professor W. Byers Brown for diary entries which give these details. Curiously, Prigogine later forgot about the discussions of AMT’s ideas at Manchester. In his paper (with G. Nicolis and A. Babloyantz), in Physics Today, November 1972, Prigogine included a historical passage (which can also stand here to indicate a Nobel prize winner’s assessment of the significance of AMT’s work): ‘The development of irreversible thermodynamics of open systems by the Brussels school had, by the 1950s, led to the investigation of non-linear processes. … It was only then that we noticed a remarkable paper by A.M. Turing (1952) who had actually constructed a chemical model showing instabilities. His work had previously escaped our attention because it dealt with the more specific subject of formation of morphogenetic patterns. The work we have undertaken since then has demonstrated the relation of this type of behaviour to thermodynamics as well as its wide applicability to biology’.

(8.8). The discussions were fully minuted in an internal Nuffield Foundation report, kindly made available to me.

(8.9) Blair Niles, Strange Brother (Liveright, New York, 1931).

(8.10) S.J. Glass, H.J. Duel and C.A. Wright, ‘Sex Hormone studies in Male Homosexuality’, Endocrinology 26 (1940).

(8.11) S.J. Glass and R.H. Johnson, ‘Limitations and Complications of Organotherapy in Male Homosexuality’, J. Clin. Endoain., 1944.

(8.12) C.W. Dunn, J. Amer. Med. Ass. 115, 2263 (1940).

(8.13) A. Karlen, Sexuality and Homosexuality (Macdonald, London, 1971), page 334.

(8.14) F.L. Golla and R. Sessions Hodge, ‘Hormone Treatment of the Sexual Offender’, The Lancet, 11 June 1949.

(8.15) D.E. Sands, ‘Further Studies on Endocrine Treatment in Adolescence and Early Adult Life’, J. Mental Science, January 1954.

(8.16) As note 8.3, pages 69, 70.

(8.17) In contrast to the committal proceedings, which are fully documented (note 8.1), the Quarter Sessions trial records are limited to bare statements of the charges and judgments, and the report in the Alderley Edge and Wilmslow Advertiser, 4 April 1952. Many questions thus remain unanswered. Was there a psychiatric report? Who suggested the hormone treatment, and what claims were made of it; at what point did AMT learn of it and agree to it? Did the Home or the Foreign Office intervene, and if so how? Unfortunately it is not even possible to discover how unusual the probation condition was: there are no statistics available for the administration of ‘organotherapy’.

(8.18) As note 8.15. The cited paper by S. Zuckerman was in Ciba. Found. Coll. Endocrin. 3 (1952).

(8.19) Writing in her introduction to EST.

(8.20) Quotation from Part Two of the Epilogue to War and Peace, tr. Rosemary Edmonds (Penguin, 1957).

(8.21) On 24 April 1978, the author was shown a list including a number of Scandinavian and Greek addresses, which happened to be among AMT’s unpublished work on morphogenesis. This address list (in AMT’s handwriting), has since been ‘lost’. This ‘loss’ occurred at the Atomic Weapons Research Establishment, Aldermaston.

(8.22) C.W. Wardlaw, ‘A Commentary on Turing’s Diffusion-Reaction Theory of Morphogenesis’, The New Phytologist 52 (1953). An article by the mathematician H.S.M. Coxeter, in Scripta Math. 19 (1953), referred briefly to the Fibonacci numbers in phyllotaxis, and to the expected appearance of a paper by AMT on how the numbers arise in the course of plant growth.

(8.23) Held in KCC.

(8.24) Much material on the draughts and love-letter programs are held in the Christopher Strachey archive, Bodleian Library, Oxford. But the quoted love-letter is one that the public knew about: according to S. Lavington, A History of Manchester Computers (National Computer Centre, Manchester, 1975) it appeared in the 1955 edition of Pears Cyclopaedia.

(8.25) Faster than Thought, ed. B. V. Bowden (Pitman, 1953). The glossary entry, even if hard on AMT in a tongue-in-cheek way, was in fact typical of the felicitous editing and commentary by Vivian Bowden, relieving the otherwise mundanely technical descriptions. It also reprinted the whole of Lady Lovelace’s memoir on the Analytic Engine.

(8.26) Translated from French and published as J. Piaget, Logic and Psychology (Manchester University Press, 1953).

(8.27) Photocopies of this and the subsequent letters from AMT to Robin Gandy are in KCC.

(8.28) C.G. Jung, ‘Approaching the Unconscious’, in the collection edited by him, Man and his Symbols (Aldus Books with W.H. Allen, 1964).

(8.29) This was a Symposium on Automatic Digital Computation, held at the NPL from 25 to 28 March 1953. AMT gave no talk. Notes made by Mike Woodger show that he commented on applications of computers to pure mathematics after a talk by J.C.P. Miller of Cambridge – mainly on the zeta function but also mentioning problems in algebraic topology.

(8.30) The Shirburnian, 1953.

(8.31) The attribution to 1953 may here be wrong. This fragment of a letter in KCC was headed only ‘May’; it might have been May 1954. It was a note of apology for not visiting the Newmans (who retained their house in a village outside Cambridge) when on a visit to Cambridge two weeks or so earlier. ‘I found such a round of gaieties had been arranged for me that it was quite impossible to get out to see you.’ Nothing else of this correspondence has survived; my suspicion is that it probably held the most revealing and sophisticated psychological comment that he ever put into letters. But also, of course, an area where AMT’s life could not be separated from the privacy of others. Mrs Newman died in 1973.

(8.32) Letter to the author from Professor J. Polanyi, 6.10.78.

(8.33) Minutes of the University Council show that this had been decided by January or February 1953.

(8.34) As note 8.21.

(8.35) Fritz Peters, Finistère (Gollancz, 1951).

(8.36) Rodney Garland, The Heart in Exile (W.H. Allen, 1953).

(8.37) Depositions and post-mortem report are in KCC. The coroner’s remarks were reported in the local newspaper on 18 June 1954, in the Daily Telegraph on 11 June.

(8.38) Mrs Turing left the golden teaspoon in KCC.

(8.39) The last, at least, in the series in KCC.

(8.40) Letter in KCC.

(8.41) Unpublished work in KCC. The second paper, as drafted, fell into three parts: I. Geometrical and descriptive phyllotaxis. II. Chemical theory of morphogenesis. III. A solution of morphogenetical equations for the case of spherical symmetry. This last part was the work of Bernard Richards. The passage quoted, the ‘Outline of Development of the Daisy’, did not fall within any of these; it was in a mass of less coherent ancillary material which worked out in more detail some specific examples of the ‘chemical theory’.

(8.42) P.S. Novikov, Doklady Akad. Nauk. SSSR (N.S.) 85 (1952).

(8.43) A few pages of this work survive in KCC; not enough to see where it might have led. He seems to have been interested in reformulating the connection between spinors and vectors, ideas probably inspired by Dirac.

(8.44) P.A.M. Dirac, Nature 139, 323 (1937).

(8.45) Robin Gandy wrote to Newman very shortly after the death, and described these ideas. The letter is in KCC. The problem to do with quantum-mechanical ‘observation’, that ‘a watched pot never boils’, is still a live question. I owe Philip Pearle for a recent reference: Ahanarov et al., Phys. Rev. D 21, 2235 (1980).

(8.46) One negative point deserves mention: rumours floated about after AMT’s death that a second charge had been brought, but these had absolutely no foundation. One other curiosity reflects ambiguously upon his relationship with the state at the end of 1952, which was rather before the real crackdown began. On 28 November 1952 AMT wrote to Sir John Stopford, the Vice-Chancellor, saying that he had been ‘invited by the Foreign Office to give a number of lectures at five German universities’ in the spring, and that he would ‘very much like to go’ for the two weeks required. Perhaps this was a form of compensation for the loss of his consultancy work – but it is surprising that he should actually have been encouraged into the treacherous fields of post-war Germany. In the event he did not go after all. Permission was, of course, granted by the university, but on 22 January AMT wrote: ‘I have however now cancelled my tour, as I found myself unable to undertake the work that would be involved.’ Was this the real reason? There is obviously much more as yet unknown, and it can only be noted that British official silence regarding ‘security’ is total.

(8.47) Interim Report submitted to the Committee on Expenditures in the Executive Departments by its Subcommittee on Investigations pursuant to S. Res. 280 (81st Congress). Reprinted in D.W. Cory, The Homosexual in America, (Greenberg, New York, 1951).

(8.48) Alan Moorehead, The Traitors (Hamish Hamilton, 1952).

(8.49) In contrast, British policy only emerged ten years later, on account of a case where in late 1953 the vetters had not made a very searching investigation, and where a press campaign forced the government to admit that it had employed a homosexual in the diplomatic service. The quotations are from the Report of the Tribunal appointed to Inquire into the Vassall Case and Related Matters, 1963. There is a very interesting contemporary account in fictional form of these issues in Rodney Garland, The Troubled Midnight (W.H. Allen, 1954).

(8.50) Here and elsewhere in this passage I draw on Peter Wildeblood, Against the Law (Weidenfeld & Nicolson, 1955).

(8.51) Hansard, Parliamentary Debates (Commons) 521, pages 526 and 1297.

(8.52) Hansard, Parliamentary Debates (Lords), 187, pages 737-767.

(8.53) Published in the Journal of Mental Science, April 1954.

(8.54) K. Sand and H. Okkels, in Endokrinologie 19 (1938).

(8.55) Hansard, Parliamentary Debates (Commons) 526, page 1866

(8.56) Quoting this report from Peter Wildeblood’s book.

(8.57) R.S. Cline, Secrets Spies and Scholars (Acropolis Books, Washington DC, 1976). Cline wrote as a retired deputy director of the CIA.

(8.58) This was certainly just the kind of thing that the CIA was supposed to know about, but apparently it did not. According to a letter of 29.11.79 to the author, the CIA has no records concerning AMT.

(8.59) As note 8.39.

(8.60) As note 8.49.

(8.61) In What I Believe, 1938, reprinted in the anthology Two Cheers for Democracy, as note BP 13.

(8.62) As note 8.28.

(8.63) An appreciation written by Robin Gandy and submitted to The Times to follow the more formal obituary by Max Newman, but not published. It is in KCC.

(8.64) Her introduction to EST.

(8.65) As note 8.61.

(8.66) See note 7.60

(8.67) The letter itself did not survive, although the fact that AMT did write to James Atkins in early 1937 is established by AMT’s reference in a letter home to his having sent an offprint of Computable Numbers to his friend. I have drawn on James Atkins’ recollection of the ‘apple’ and ‘electrical wiring’ mentioned in the letter, a recollection as clear and distinct and unsolicited as any that have come my way. The sceptical reader may wonder whether this was not a projection of the news of 1954 into a memory of 1937. Here again it is as clear as anything I have been told that James Atkins never knew that an apple had actually featured in AMT’s death, until he heard of it from me. It had not been mentioned in the Daily Telegraph, where he had read the report in 1954, and he had no knowledge that Mrs Turing or anyone else had written about it.

(8.68) As note 2.18.

(8.69) In The Challenge of our Time, a 1946 radio broadcast, published in Two Cheers for Democracy, as note BP 13. A rather more polemical critique of Forster was given by the author and David Hutter in With Downcast Gays (Pomegranate Press, London, 1974; Pink Triangle Press, Toronto, 1977).

Notes

Esprit de Corps

The Spint of Truth

New Men

The Relay Race

Bridge Passage

Running Up

Mercury Delayed

The Greenwood Tree

On the Beach