Alan Turing: The Enigma

By on June 29th, 2017 in Book Reviews, Magazine Articles, Societal Impact

The Book That Inspired the Film The Imitation Game. By Andrew Hodges.
Updated Edition. Princeton Univ. Press, 2014.

Reviewed by Sandy Zabell


In 1970, Alan Turing was best known for his work in two areas: mathematical logic and computer science. In the years immediately prior to World War II, Turing had solved Hilbert’s Entscheidungsproblem, that is, the “decision problem,” whether there exists a mechanical procedure for determining if a mathematical statement expressed in a formal language has a proof. In order to do this Turing introduced the concept of what is now termed a “Turing machine,” a mathematical abstraction of an algorithm. After World War II, Turing then turned to the foundations of computer science, including his famous popular paper on whether a machine can think, which introduced the “Turing test,” the original imitation game.

But for the period of the war itself, almost nothing was known of Turing’s activities. In her 1959 biography of her son, Sarah Turing devoted just a short chapter to the war, noting:

Immediately on the declaration of war he was taken on as a temporary Civil Servant in the Foreign Office, in the Department of Communications …. At first even his whereabouts were kept secret, but later it was divulged that he was working at Bletchley Park, Bletchley. No hint was ever given of the nature of his secret work, nor has it ever been revealed.

It was only decades later that the scope and importance of Turing’s work at Bletchley Park – breaking German codes and ciphers – first became known. The success of the initial English embargo on any mention of their remarkable wartime cryptanalytic successes may be judged by the total absence of any mention of them in David Kahn’s encyclopedic 1967 book The Code-breakers which in contrast devoted an entire chapter to the US exploitation of Japanese codes and ciphers.

All this changed after the publication in 1973 of General Gustav Bertrand’s book Enigma. It emerged that in 1932 the Polish military had hired three mathematicians, Marian Rejewski, Jerzy Różycki. and Henryk Zygalski, to work on the decryption of the Enigma, a mechanical device for enciphering messages that the German military had begun using just a few years before. For the better part of a decade (from 1933 to 1939), thanks in part to information provided by a German spy working in the Cipher Bureau of the German Ministry of Defense and passed on by Bertrand, the Poles were able to read a substantial majority of the German Enigma messages, ultimately only defeated towards the end of the decade by a succession of German communications security upgrades. In July of 1939, in a famous conference near Warsaw (no doubt sensing the impending outbreak of war), the Poles revealed all this to their French and English counterparts, describing their methods and providing replicas of the device itself.

Now that Bertrand had let that the secret was out, the English lifted their embargo on any discussion of “Ultra,” the codename for intelligence deriving from this source. Frederick Winterbotham’s The Ultra Secret (1974) revealed the scope and success of the Allied wartime efforts; followed several years later by F. H. Hinsley’s multivolume British Intelligence in the Second World War (1979–1990). But these early books focused almost entirely on the use of the intelligence generated rather than the technical methods used to acquire it, nor did they say much about the new role played by the “boffins” (the technical and scientific experts). This was a significant omission, because signals intelligence in the 1939–1945 war was a very different affair than it had been earlier. In the years leading up to the war, the major military powers had turned to sophisticated machine encryption of their messages, and these were largely impervious to the linguistic methods of attack used successfully in earlier periods. Instead, mathematics and machines came to the forefront, and with them, the need for “men of the Professor type.”

So some of Turing’s wartime colleagues began to discuss his vital role. One of these was I. J. (“Jack”) Good, who served as Turing’s primary statistical assistant for a year. But it was only in the 1980s that the technical veil itself was first lifted. In 1981 Rejewski wrote a paper describing the use the Poles had made of the mathematics of permutations to break Enigma messages. This was followed in 1982 by Gordon Welchman’s most informative book, The Hut Six Story. Indeed, Welchman was regarded by the British authorities as being too informative, and lost his security clearance. Welchman had reported to Bletchley at the outbreak of war, made key contributions to the cryptanalysis of the Enigma, and ultimately became the head of Hut 6 (Army and Luftwaffe cryptanalysis). Turing, as Welchman revealed, had played a key part in developing the attack on the Enigma, helping, among other things, to develop the “Bombe,” a mechanical device used to determine the daily settings of the machine.

So by 1982 a modest amount was known. Turing and Bletchley, it turned out, were the perfect combination. Turing liked to attack from scratch hard problems that had stymied others. It was precisely this mindset that emboldened him to attack the Entscheidungsproblem. The time was therefore ripe for a full account of his life: Andrew Hodges’s 1983 biography, Alan Turing: The Enigma. Hodges’s book described in extensive and sympathetic detail the whole of Turing’s life, from his boyhood in the 1920s to his tragic suicide in 1954. It became an instant classic. One detail, from many that could be cited, illustrates the meticulous care that Hodges took. In the autumn of 1928 Turing had been a student at Sherborne, an English public school. His mathematics master at the time, D. B. Eperson, later wrote:

All that I can claim is that my deliberate policy of leaving him largely to his own devices and standing by to assist when necessary, allowed his natural mathematical genius to progress uninhibited. (Hodges, p. 43)

In a footnote, Hodges gives as his source for this statement a “letter to the author from D. B. Eperson, 16.1.78” (i.e., 50 years after the events in question)!

Given such meticulous attention to detail, it is no surprise Hodges’s book was then and remains today the single most important source of information about Turing’s life before and after the war. But for the war itself – and in particular Turing’s work during it – the sources available to Hodges were quite limited. Some of these have been noted above. Much more has become available since, such as the “internal” history of Hut 8, the section of Bletchley Park devoted to the cryptanalysis of the Naval Enigma, the most secure of the different German military versions of the Enigma. The release of this document in 1996 (but written in 1945) provided a great deal of information about the operations of Hut 8 as a whole, as well as the vital role Turing played in developing the attack on the Naval Enigma. Before Turing, Naval ciphers “had received scant attention” (p. 12) and the “Naval Enigma was generally considered in 1939 to be unbreakable” (p, 14). So why did Turing turn to so unpromising a nut to crack?

When Turing joined the organization in 1939 no work was being done on Naval Enigma and he himself became interested in it “because no one else was doing anything about it and I could have it to myself”. Machine cryptographers were on the whole working on the Army and Air Force cyphers with which considerable success had been obtained. …

Turing’s successful attack, which came online in 1941, involved a method called “Banburismus”; it became “the fundamental process which Hut 8 performed for the next 2 or 3 years.” The ability of the Allies to read German U-boat traffic played a vital role in the battle of the Atlantic, and saved thousands of lives.

Since 1983 a tsunami of information has become available about almost every aspect of the operations of Bletchley Park and its parent organization GCCS (the predecessor of GCHQ, the present-day U.K. signals intelligence and information security organization). This includes the release of the 500+ page “General Report on Tunny” in 2000 (“Tunny” was the code name for an important online German teleprinter encryption device), as well as wartime manuals and technical papers of Turing, Alexander, and others, other archival materials, and memoirs of many people who worked in the different units at Bletchley.

The book under review is a reissue of Hodges’s original 1983 biography. One can certainly sympathize with his decision not to write a new edition. The book is a unified whole, and any attempt to incorporate the flood of information about Turing’s wartime activities and the cryptologic war would have been a daunting task. Instead, Hodges has limited himself to writing a brief preface touching on a few topics in light of the new information now available (although even here the discussion of the period of the war is minimal). It would have been appropriate to use the preface to mention at least a few of the most important books and papers that have since appeared. Not to do so is a curious omission. Instead, Hodges points us to a website, saying “further additional and corrective material may be found on”

And what or the film The limitation Game, whose appearance was the impetus for this reissue? Alas, despite Benedict Cumberbach’s masterful performance, no actor can surmount the limitations of his script, and The Imitation Game is a Hollywood biopic, inaccurate on many fronts. One can of course appreciate the challenges in producing a successful movie centered on cryptanalysis, and the reasons for simplifying complex ideas, merging events or characters, and so on. But the main frustration of The Imitation Game is that it often takes liberties where the underlying reality is every bit as romantic or gripping.

Here is one particularly egregious example. In the movie Hugh Alexander, a Bletchley Park cryptanalyst, is portrayed as obstructing Turing, and Turing responds by writing a letter of protest to Prime Minister Winston Churchill. Now a letter was indeed written to Churchill on October 21, 1941, six weeks after he visited Bletchley Park on September 6, 1941. It noted with frustration impediments to the cryptanalysts’s work, such as the absurdity that some messages were not being decrypted due solely to a “shortage of trained typists.” The letter was hand-delivered to Churchill’s private secretary at 10 Downing, who promised it would be given directly to Churchill. This was done and Churchill promptly wrote a memo (headed “Action This Day”) directing his principal staff officer: “Make sure they have all they want on extreme priority and report to me that this has been done.” Not surprisingly, there were no problems after that!

But the letter had been signed by four people, not just Turing. These were the head and deputy head of Hut 6, namely Gordon Welchman (who drafted the letter) and P.S. Milner-Barry (who delivered it), and the head and deputy head of Hut 8, Alan Turing and Hugh Alexander. Thus Alexander, far from being the subject of the letter’s complaint, was one of its signatories! The baseless canard in the movie is particularly annoying because Alexander was in fact one of the best cryptanalysts working on the Naval Enigma (Jack Good once wrote, “I was quite good at this game (Banburismus). but Alexander was the champion”), and had a long and distinguished career at GCHQ after the war. Why distort history when the reality itself is so compelling?

In sum: Hodges’s book was – and remains – the definitive overall biography of Turing. It is an exemplary work of scholarship to which Hodges brought dedication, enthusiasm, and passion. It is hard to imagine its discussion of Turing’s life before or after the war being substantially improved on for a very long time. But for the period of the war itself, Hodges labored under the disadvantage that at the time he wrote, only a very limited amount of information was available about Turing’s wartime activities. Today various detailed accounts of the cryptologic war have appeared, such as Stephen Budiansky’s Battle of Wits, but the definitive discussion and assessment of Turing’s part in all this remains to be written.


Sandy Zabell is Professor of Mathematics and Statistics at Northwestern University. He has written a commentary for Cryptologia on two wartime papers of Turing first released in 2012, and an essay on “Statistics at Bletchley Park,” for the scholarly edition of the “General Report on Tunny” currently in press. His email address is: