Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game

by Andrew Hodges

  Yet it is not easy to separate transcendence from emergency: it is striking how leading scientific intellects were recruited to meet the existential threat Britain faced in 1939. The struggle with Nazi Germany called not just for scientific knowledge but the cutting edge of abstract thought, and so Turing’s quiet logical preparations in 1936–38 for the war of codes and ciphers made him the most effective anti-Fascist amongst his many anti-Fascist contemporaries. The historical parallel with physics, with Turing as a figure roughly analogous to Robert Oppenheimer, is striking. This legacy of 1939 is still unresolved, in the way that secret state purposes are seamlessly woven into intellectual and scientific establishments today, a fact that is seldom remarked upon.

  The same timelessness lies behind the central element of Alan Turing’s story: the universal machine of 1936, which became the general-purpose digital computer in 1945. The universal machine is the focal, revolutionary idea of Turing’s life, but it did not stand alone; it flowed from his having given a new and precise formulation of the old concept of algorithm, or mechanical process. He could then say with confidence that all algorithms, all possible mechanical processes, could be implemented on a universal machine. His formulation became known immediately as ‘the Turing machine’ but now it is impossible not to see Turing machines as computer programs, or software.

  Nowadays it is perhaps taken rather for granted that computers can replace other machines, whether for record-keeping, photography, graphic design, printing, mail, telephony, or music, by virtue of appropriate software being written and executed. No one seems surprised that industrialised China can use just the same computers as does America. Yet that such universality is possible is far from obvious, and it was obvious to no one in the 1930s. That the technology is digital is not enough: to be all-purpose computers must allow for the storage and decoding of a program. That needs a certain irreducible degree of logical complexity, which can only be made to be of practical value if implemented in very fast and reliable electronics. That logic, first worked out by Alan Turing in 1936, implemented electronically in the 1940s, and nowadays embodied in microchips, is the mathematical idea of the universal machine.

  In the 1930s only a very small club of mathematical logicians could appreciate Turing’s ideas. But amongst these, only Turing himself had the practical urge as well, capable of turning his hand from the 1936 purity of definition to the software engineering of 1946: ‘every known process has got to be translated into instruction table form …’ (p. 409). Donald Davies, one of Turing’s 1946 colleagues, later developed such instruction tables (as Turing called programs) for ‘packet switching’ and these grew into the Internet protocols. Giants of the computer industry did not see the Internet coming, but they were saved by Turing’s universality: the computers of the 1980s did not need to be reinvented to handle these new tasks. They needed new software and peripheral devices, they needed greater speed and storage, but the fundamental principle remained. That principle might be described as the law of information technology: all mechanical processes, however ridiculous, evil, petty, wasteful or pointless, can be put on a computer. As such, it goes back to Alan Turing in 1936.

  That Alan Turing’s name has not from the start been consistently associated with praise or blame for this technological revolution is due partly to his lack of effective publication in the 1940s. Science absorbs and overtakes individuals, especially in mathematics, and Alan Turing swam in this anonymising culture, never trying to make his name, although frustrated at not being taken seriously. In fact, his competitive spirit went instead into marathon running at near-Olympic level. He omitted to write that monograph on ‘the theory and practice of computing’, which would have stamped his name on the emergent post-war computer world. In 2000 the leading mathematical logician Martin Davis, whose work since 1949 had greatly developed Turing’s theory of computability, published a book1 which was in essence just what Turing could have written in 1948, explaining the origin of the universal machine of 1936, showing how it became the stored-program computer of 1945, and making it clear that John von Neumann must have learnt from Turing’s 1936 work in formulating his better-known plan. Turing’s very last publication, the Science News article of 1954 on computability, demonstrates how ably he could have written such an analysis. But even there, on terrain that was incontestably his own discovery, he omitted to mention his own leading part.

  Online search engines, which work with such astonishing speed and power, are algorithms, and so equivalent to Turing machines. They are also descendants of the particular algorithms, using sophisticated logic, statistics and parallel processing, that Turing expertly pioneered for Enigma-breaking. These were search engines for the keys to the Reich. But he asked for, and received, very little public credit for what has subsequently proved an all-conquering discovery: that all algorithms can be programmed systematically, and implemented on a universal machine. Instead, he nailed his colours to the mast of what he called ‘intelligent machinery’, but which came to be called Artificial Intelligence after 1956. This far more ambitious and contentious research programme has not developed as Turing hoped, at least as yet. Why did Turing go so public on AI, and make so little of himself as an established maestro of algorithms and the founder of programming? Partly because AI was for him the really fundamental scientific question. The puzzle of mind and matter was the question that drove him most deeply. But to some extent he must have been a victim of his own suppressed success. The fact that he knew so much of the algorithms of the secret war, and that the war had made the vital link between logic and electronics, cramped his style and constrained his communication. In his 1946 report his guarded allusion to the importance of cryptographic algorithms (p. 418) reflects an inhibition that must have infected all that came later.

  Only after thirty years did the scale and depth of wartime cryptanalysis at Bletchley Park begin to leak out, allowing a serious assessment of Alan Turing’s life to be attempted. This point coincided with the break-out of cryptology theory into an expanding computer science, with a reassessment of the Second World War in general, and with the impact of 1970s sexual liberation. The 1968 social revolution, which Turing anticipated, had to happen before his story could be liberated. (Even so, the change in UK vetting and military law came only in the 1990s, and a legal principle of equality was not established until 2000. ‘Don’t ask don’t tell’ ended only in 2011, showing how the issues of chapter 8 have remained literally unspeakable in the US military.) Alan Turing’s story shows the first elements of this liberating process in the Norway of 1952, since the men-only dances he heard about (p. 599) were probably organised by the fledgling Scandinavian gay organisation. In addition to the gay-themed novels mentioned on p. 613, Norman Routledge recalled in 1992 how Turing expected him to read André Gide in French. One regret, voiced in note 8.31, is that his letters to Lyn Newman did not survive. Their content can be guessed from what in 1957 she wrote to a friend: ‘Dear Alan, I remember his saying to me so simply & sadly “I just can’t believe it’s as nice to go to bed with a girl as with a boy” and all I could say was “I entirely agree with you – I also much prefer boys.”’ This interchange, then confined to a discreet privileged circle, could now be a TV chat show joke, with a happy resonance of the repartee of his famous imitation game. But Alan Turing’s simple openness came decades too early.

  It is not difficult to imagine the hostility and stigma of those days, for such hatred and fear is still, whether in Africa, the Middle East or the United States, a major cultural and political force. It is harder now to imagine a world where persecution was not just asserted but taken as an unquestionable axiom. Alan Turing faced the impossible irony that his demand for honesty ran up against the two things, state security and homosexuality, which were the most fraught questions of the 1950s. It is not surprising that it proved impossible to contain them in a single brain. His death left a jagged edge in history, something no one (with the extraordinary exception of his mother) wanted to
talk about. My fusion of these elements into a single narrative certainly encountered criticism in 1983. But nous avons changé tout cela: since then, his life and death have been as celebrated as those of any scientific figure. Hugh Whitemore’s play Breaking the Code, based on this book and featuring leading performers, pushed at the envelope of public acceptability. It made Alan Turing’s life a popular story in 1986, reinforced by a television version in 1997. By that time the Internet had transformed personal openness. In a curious way, Turing had anticipated this use of his technology, already hinted at in the risqué text-messaging of his imitation game. The love letters created by the Manchester computer (p. 601), and his message about the Norwegian youth, rendered as a nerdy computer printout (p. 608), suggest a Turing who would have relished the opportunity for electronic communication with like-minded people.

  In 2009 the British prime minister, Gordon Brown, made a statement of apology for Turing’s trial and punishment in 1952–54, framed by a wider vision of how the values of post-war European civil society had been won with his secret help. This statement was enlisted through a popular web-based petition, something impossible in 1983, but already then being mooted as the sort of thing the ‘mighty micro’ could bring about. My own comments (p. 608) in the concluding Author’s Note about future revision of printed text reflected this mood. And indeed from 1995 onwards my website has supplied updating material. In this light it is surprising that such a long volume has remained continuously in print since 1983. But perhaps one thing that a traditional stack of paper still makes possible is an immersion in storytelling, and this time-consuming experience was one I certainly supplied.

  As narrator I adopted a standpoint of a periscope looking just a little ahead of Alan Turing’s submerged voyage, punctuated by just a few isolated moments of prophecy. The book bears in mind that what is now the past, the 1940s and 1950s, was once the completely unknown future. This policy required an unwarranted confidence that readers would wade through the pettier details of Alan Turing’s family origins and early life, before being offered any reason for supposing this life had any significance. But it has had the happy outcome that the text has not dated as do texts resting on assertions about ‘what we know now’. So although so much has changed, the story that follows can be read without having to subtract 1983-era comment. (Of course, this is not true of the Notes, which now show what sources were available in 1983, but do not indicate a guide to ‘further reading’.)

  After a further thirty years, how would I reassess Alan Turing’s pure scientific work and its significance? My book made no attempt to trace the legacy of Turing’s work after 1954; that would be far too large a task. But naturally, the expansion of scientific discovery continually forces fresh appraisals of Turing’s achievement. His morphogenesis theory, since 2000 more actively pursued as a physico-chemical mechanism, would now require more material on the various different approaches and models. As another example, Turing’s strategy of combining top-down and bottom-up approaches to AI, and the neural nets he sketched in 1948, have acquired new significance. There has been a parallel explosion in quality and quantity of the history of science and technology since the 1970s, with many detailed studies of Turing’s papers. The centenary year of 2012 saw a climax of new analysis from leading scientific figures. Alan Turing’s work is accessible as never before, and topics that attracted scant attention in 1983 are now the subject of lively debate.

  But I would not take a radically different point of view. My division of the book into Logical and Physical was already radical, reflecting a rejection of conventional description of him as a pure logician, and portraying him as always, and increasingly, involved in the nature of the physical world. This fundamental perception could now be asserted with even greater confidence. He came to the ideas of 1936 with an unusual knowledge of quantum mechanics, and this is now a more interesting connection, for since the mid-1980s quantum computing and quantum cryptography have become important extensions of Turing’s ideas. Likewise, the renewed interest in quantum mechanics in Turing’s last year, whose significance was correctly signalled with a supersized footnote (p. 645) could now be linked more closely with his 1950 and 1951 arguments about computers and minds. These issues have arisen sharply since 1989, when Roger Penrose2 discussed the significance for minds of the uncomputable numbers Turing had discovered. Penrose himself suggested an answer which related Turing machines to a radical new view of quantum mechanics. Writing now, I would draw more attention to what is now called the physical Church–Turing thesis. Did Turing consider that the scope of the computable includes everything that can be done by any physical object? And what would this mean for his philosophy of the mind? In this light, Church’s 1937 review (p. 157) of Turing’s work has more importance than I noted. Turing’s decisive shift of focus to what could be done by algorithms, as stated on p. 138, I would now move from 1936 to 1941 (at p. 266). Turing’s argument about infallibility (p. 454) would deserve more analysis, as also his use of ‘random’ elements, and a number of general statements about thinking and doing in my text. But sharper sensitivity to these questions would bring out few if any new answers; it would only make more acute the questions about what Turing really thought.

  Much more positive detail could now be given regarding his secret wartime work. Even in the 1992 preface to the Vintage edition, new material could be given from the third volume of F. H. Hinsley’s official history of British Intelligence. But since the mid-1990s, raw American and British documents on Second World War cryptanalysis have been officially released, and it has been possible to elucidate the internal story with far more details than Hinsley allowed. What has emerged has only enhanced the quality and significance of Bletchley Park work, and of Turing as its chief scientific figure. The park itself is now a famous visitor attraction, though its lesson, that reason and scientific methods were the heroes of the hour, has not really caught on.

  These documents show how on 1 November 1939 Turing could announce ‘the machine now being made at Letchworth, resembling, but far larger than the Bombe of the Poles (superbombe machine)’. That prefix ‘super’ dramatised the advance that my explanation (p. 229) was unable, for lack of supporting narrative detail, to highlight as the crucial breakthrough. Turing’s own 1940 report on the Enigma-breaking methods clarified how he made this advance, called ‘parallel scanning’. All of this is now working physically in the rebuilt Bombe at the Bletchley Park Museum. In addition to the document release, members of the original cryptanalytic team have written fully about the technical work, such as the details of the bigram tables which made the Naval Enigma so much more challenging, and the statistical Banburismus method. The super-fast bombes, the break into the Lorenz cipher, and the now-famous Colossus are all open to study, a great deal being due to the inspiring work of the late Tony Sale. The description in this book is now unnecessarily hazy. On the other hand, there was no room for any more codebreaking technicalities in the book, and the reader will not be seriously misled by its summary.

  In particular, these revelations have only reinforced the significance of the ‘Bridge Passage’ between the logical and the physical, Turing’s top-level liaison visit to the United States in the winter of 1942–43. His report of 28 November 1942 from Washington, now released, documents the difficult and anomalous position he faced, including an initial confinement to Ellis Island (p. 305). He was not overawed by the US Navy: ‘I am persuaded that one cannot very well trust these people where a matter of judgment in cryptography is concerned.’ Something that I had heard only as rumour in 1983 has been confirmed: on 21 December a train brought Turing to Dayton, Ohio, where the US Bombes were under construction. There is also more revealed on his initiation into the most secret US speech encipherment technology. There is more on his response to it, the Delilah speech scrambler – an interim report dated 6 June 1944, and a later complete description. As a precursor of the mobile phone, this belongs to the future, whilst the Enigma was a mediocre adaptation o
f 1920s mechanical engineering. This new material only underlines that in the post-war period, Turing had a unique knowledge of the most advanced American technology, as it emerged from victory in 1945.

  This fact draws further attention to the question of what he did for GCHQ after 1948. In the 1992 preface I floated the suggestion that this might have been connected with the now famous Venona problem of Soviet messages. But there has been no comparable release of GCHQ or other secret documents on 1948–54, which might indicate the nature of his work. Richard Aldrich’s recent history of GCHQ3 opened by saying that ‘Today it is more important than ever – yet we know almost nothing about it.’ We know more now, from Edward Snowden, about the work whose foundation stone was laid by Alan Turing. No one could miss seeing how much it has to do with the power of the universal machine. And it is hard to believe that Turing played no part in giving secret advice about the potential of computing in the early days of the Cold War. As I wrote in the 1992 preface, who else could have done this?

  Answers to such questions were strikingly absent from the British government statement of 24 December 2013 when, in response to a demand from illustrious figures, a posthumous Royal Pardon was granted to Turing in respect of the conviction for ‘gross indecency’ of 31 March 1952. There must have been memoranda within government detailing the prospect of their top scientific consultant going on public trial for a crime which rang all the alarm bells of Security. Hugh Alexander must have reported on his participation in the trial. As observed in note 8.17 the question arises as to whether the Foreign Office had an influence on Turing being treated with hormones (then seen as a soft option) instead of going to prison. But no such papers appeared; nor indeed were they asked for.