Alan Turing presumably thought that eventually a machine would be capable of writing a book such as this. In his 1951 radio talk, set against the opening of the Festival of Britain, he commented that ‘It is customary … to offer a grain of comfort, in the form of a statement that some peculiarly human characteristic could never be imitated by a machine. I cannot offer any such comfort, for I believe that no such bounds can be set.’ There was an element here of épater les bourgeois, especially when he gave as example of a peculiarly human quality, that of being ‘influenced by sex appeal’. Yet he was quite serious in describing the ‘almost certain’ advent of intelligent machines as a development ‘which can give us anxiety’ of a kind much more urgent than that of the Darwinian fright of a century before ‘that we might be superseded by the pig or the rat.’
In actual fact I should gladly have surrendered my technical problems to a machine – and a word processor would have saved weeks of chopping and gluing – but these have not been the real difficulties in the composition of this book. More pressing, to give just one very pertinent example, has been the need to overcome the twentieth-century chasm between scientific thought and human life – moreover to resist the strong view held in certain quarters that my book should actually reinforce that separation. I have had to live, and even to struggle a little, for my vision; to put this point of view I have had to act this point of view.
One event of particular interest for me while working on these ideas was the appearance of Douglas Hofstadter’s Gödel, Escher, Bach in 1979. It put my work in a Tangled Loop, for central to his book is its exploration of a topic I have brushed aside – the significance of Gödel incompleteness and Turing undecidability for the concept of Mind. I do not myself believe that these results, concerning as they do infinite, static, undisturbed logical systems, have any direct consequence for our finite, dynamic, interacting brains. Far more significant, in my view, is the limitation of human intelligence by virtue of its social embodiment – and this is a problem relegated to a marginal place in Hofstadter’s work as in so many other accounts, though I have placed it at the centre of my own. The study of Alan Turing’s life does not show us whether human intelligence is limited, or not limited, by Gödelian paradoxes. It does show intelligence thwarted and destroyed by its environment. But why, as Alan Turing might have put it, should machine intelligence be any less constrained by worldly reality? Indeed, there seems every reason to suppose that the clever machine will accommodate itself to the crazy demands of the political system in which it is embodied. In the academic sanctuary it is too easy to concentrate on infinitely more theoretical considerations.
For this reason my anxieties are rather different from those Alan Turing referred to: what worries me most is not whether we say machines are ‘thinking’ or not, but the place of such ‘thought’ in the body politic. Given the state of our modern Heartbreak House, I fear a victory not of anyone’s intelligence, but of the pig and the rat.
* * *
* For mathematicians he has immortality through the expression Turing machine. Many people must have used his name without any conception of his historical existence – the nearest thing to the life as a disembodied spirit that he once pondered on. Going even further, modern papers sometimes employ the usage of turing machine. Sinking without a capital letter into the collective mathematical consciousness (as with the abelian group, or the riemannian manifold) is probably the best that science can offer in the way of canonisation.
* But she did this very carefully, and only when trying to draw connections did the facade of intelligence fail. Even so, the jigsaw puzzling had more the effect of omitting and diminishing much of what he had done, rather than suggesting that he had done something more than was in fact the case. There was just one point where a definitely misleading statement resulted: cribbing a phrase by Philip Hall which in fact referred to the zeta-function machine, and setting it in a different context, she led readers to deduce that Alan had set about constructing a universal machine before the war. This no doubt encouraged A. Cave Brown in Bodyguard of Lies to suggest that he had done so in order to decode the Enigma. This suggestion then appeared as fact in J. Rohwer, The Critical Convoy Battles of 1943. Thus one sees a myth being made. The trouble is that truth does not reside in strings of symbols on the page; the business of interpreting them correctly requires experience.
* Though Geoffrey O’Hanlon had spilt the beans in 1954, writing in his obituary of Alan in The Shirburnian that ‘During the war he was engaged in breaking down enemy codes…. His work was hush-hush, not to be divulged even to his mother.’
* Perhaps, however, the magic of the 1940s could never be recaptured amidst the dull white heat of the 1960s technological revolution. And perhaps the closest evocation of the Turing spirit in this period was not in science, but in science fiction – a cinematic Back to Methuselah. The date of 2001: A Space Odyssey was presumably taken from the fifty-year prophecy in the Mind paper, which was specifically cited in Arthur C. Clarke and Stanley Kubrick’s book. Their picture of hal was essentially based on Turing ideas; and, quite uncannily, their plot had hal destroyed by ‘the logic of the planners’, whose ‘twin gods of Security and National Interest meant nothing to hal. He was only aware of the conflict that was slowly destroying his integrity – the conflict between truth, and concealment of truth.’
* This is not always appreciated. Thus a typical view emerges in The Mighty Micro by Christopher Evans (Gollancz, 1979), which was perhaps the first widely disseminated mention of the trial:
… he came to a tragic end. A solitary individual who confided little in other people, he was also a practising homosexual at a time when homosexuality was viewed as a criminal offence. Somehow he brushed with the law – the sad, sorry details are hard, and perhaps unnecessary to come by – and one evening, depressed and disillusioned, he retired to his room and bit into an apple laced with potassium cyanide.
But in 1977 Lord Halsbury had led the defeat of an attempt to reduce the ‘age of consent’ to eighteen – and any kind of street encounter, whether or not involving money, is still illegal. Prosecutions for homosexual offences, furthermore, have roughly trebled since 1967, and currently run at twice the 1952 level. State control of sexuality has changed since the 1950s, but the elements of youth and of street life are ‘viewed as’ crimes as much now as then. More directly pertinent to the theme of The Mighty Micro is that the computer has facilitated a far more comprehensive process of ‘brushing with the law’, with ‘sad, sorry details’ filed away for the police, employers and security officials quite regardless of whether crimes have been committed. The process of positive vetting, in particular, is supposed to prevent a homosexual ever again having access to anything of state importance. Whatever the arguments, these are not issues of the past. Nor is the ‘detail’ of chemical castration a dead question. But even prophets of the ‘information explosion’ can exhibit a wish not to know.
* Twistors, as geometric objects which allow the formulation of a different description of space and time from the usual one, are not quite ‘Hyperboloids of wondrous Light’. But they are based on light rays and an objective of twistor theory is the unification of general relativity and quantum mechanics. So the last Turing messages have a special resonance for me. And the privilege of working in so dramatically original a theory, and studying under such a person, has been a vital ingredient in my approach to Alan Turing.
* Some have not been preserved; thus conspicuously absent is any announcement of his engagement in 1941. Mrs Turing also performed some half-hearted censorship on the letters, which like all incomplete suppression merely draws attention to the anxieties of the censor. Only one sentence, probably a reference to the engagement, is actually rendered illegible. I also feel a distinct debt to Lyn Newman for a subtle moral encouragement: in her introduction to Mrs Turing’s book she called it ‘a source-book for a future biographer’, which is exactly how I have used it.
Notes
&nb
sp; These notes are not intended to supply a complete catalogue of sources for every statement. They cover only (1) the sources of direct quotations (2) the specification of documents and publications mentioned in the text (3) a fairly complete list of known documents with first-hand information about AMT, and (4) some source-critical comments and other points that require a discussion outside the time-frame of the text. I have not annotated sources which are fully specified within the text itself, and I have not regarded AMT’s letters home (as held in the King’s College archive) as all requiring explicit identification. I have not employed the academic formula of ‘Private Communication’ to indicate material gained from interviews: this seems to add nothing useful, and the reader will have in any case to trust me as the historical journalist with what I offer in the way of new biographical material. These notes must also serve as an inadequate bibliography; a full discussion of the literature surrounding AMT’s work would go far beyond the scope of the present book. The same applies to ‘further reading’, although here I make one exception: Mathematics Today (ed. L. A. Steen, Springer Verlag, 1978).
I have used the following abbreviations throughout:
EST: The biography Alan M. Turing, by Sara Turing (Heffers, Cambridge, 1959).
KCC: The archive of letters and other documents relating to AMT held in the library of King’s College, Cambridge.
Esprit de Corps
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 60, 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 53). 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 Spirit 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’, an 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 ev
enly 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 McTaggart 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.
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 85