Alan Turing: The Enigma (123 page)

(
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) Unpublished account by David Sayre, 1969.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 The proceedings contain other comments by AMT and also note his unpublished work on chess-playing machines.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.