Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  (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.