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# Untangling the Threads of a Heroic and Complicated Life

BOOK REVIEW: Alan Turing: The Enigma. By Andrew Hodges, Princeton University Press, Princeton, New Jersey, 2014, 768 pages, \$16.95.

The Imitation Game opened to solid reviews on Christmas Day and, as announced on January 15, received several 2015 Oscar nominations (including for Best Picture). Loosely based on Andrew Hodges’s 1983 book Alan Turing: The Enigma, the film stars Benedict Cumberbatch as Turing and Keira Knightley as his wartime co-worker (and one-time fiancée) Joan Clarke. To coincide with the release of the movie, Princeton University Press has reissued Hodges’s book, with a new preface by the author.

Among the finest scientific biographies known to this reviewer, the book chronicles Turing’s career in pure and applied mathematics, along with his many related interests, to his death, apparently by suicide, in 1954. Hodges devotes several chapters to Turing’s early life, in an effort to identify the roots of his adult behavior. His task is facilitated by the numerous letters Turing wrote throughout his life.

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Mere months after his birth, in London, in 1912, Turing’s mother and father––the latter a career officer in the Indian Civil Service––returned to the subcontinent, leaving Alan and his elder brother in the care of an English couple, Colonel and Mrs. Ward. From then until they entered university, the boys’ time was divided between stays with the Wards, a succession of boarding schools, and occasional family vacations when the parents were on leave in England.

Permanent influences on Alan included a book titled Natural Wonders Every Child Should Know. Meant to explain biological growth in a way that young children could understand, the book opened Alan’s eyes to the nature and allure of scientific knowledge, while stressing that the human body and mind are machines adapted to certain basic tasks, but capable of untold others.

Also influential were the story of Snow White and the poisoned apple, and the death of his school friend and first romantic (though apparently Platonic) love Christopher Morcom, in February 1930. Already friends, the two had bonded while rooming together for a week at Trinity College, Cambridge, where they had gone to compete for university scholarships. Morcom was immediately successful, but Turing had to return the following year to secure a scholarship to King’s, his second choice among the Cambridge colleges.

Turing’s performance on the scholarship exams was commendable, but by no means without precedent. Others had won more lucrative scholarships, at earlier ages. Not until the summer of 1931, when he actually entered King’s––a bastion of free-thinkers heavily influenced by John Maynard Keynes and the ageing Bloomsbury set––did he truly begin to blossom. In April 1935, at the age of 22, he was elected to a fellowship in King’s. His first mathematical paper, on group theory, was published a month later. The fellowship carried a stipend of £300 a year, ordinarily renewable for an additional three years, with no specific duties. Beyond the stipend, it entitled him to room, board, and a seat at High Table whenever he chose to reside in Cambridge. The boys at Sherborne School––where he had prepped for university––were inspired by his success to intone that

 Turing Must have been alluring To get made a don So early on.

The terms of the fellowship left him free to travel, and he elected to spend time in Princeton, then replacing Göttingen as the center of the mathematical universe. Turing arrived in Princeton in September 1936, having just completed his magnum opus “On Computable Numbers, with an Application to the Entscheidungsproblem.” Page proofs reached him in October, and the paper was published the following spring.

Formulated by Hilbert, the entscheidungsproblem had already been solved by Alonso Church, Turing’s host in Princeton, using his powerful $$\lambda$$-calculus. But the “Turing machine” proof, suggesting the feasibility of a universal computer capable of performing any possible computation, was far more memorable and portentous.

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Alan Turing with two colleagues and the Ferranti Mark I computer, January 1951. Photo courtesy of the University of Manchester.
Hodges identifies five key events in Turing’s professional career, spaced roughly five years apart. The first two were Christopher Morcom’s death in 1930 and the conception of the Turing machine in 1935. The others were Turing’s conquest of the German navy’s version of the Enigma device in 1940, his design for the ACE (Automatic Computing Engine) in 1945, and his formulation of the morphogenetic principle in 1950. Hodges further insists that Turing was still at the top of his game at the time of his death, having been able at last to gain hands-on experience with the Manchester computer.

Turing’s work on the naval Enigma machine was truly heroic. Great Britain relied on 35 million tons of imports a year; from July 1940, when German U-boats began operating from French ports, through October 1, they sank a million tons of British shipping. By the early months of 1941, the flow of imports had been reduced to an annualized rate of only 28 million tons. Churchill acknowledged to Roosevelt that, unless the war in the Atlantic took an abrupt turn for the better, Britain would be forced to sue for peace within the year. Only by reading the German navy’s Enigma communications could British codebreakers hope to inform convoys at sea of the whereabouts of German submarines in time to avoid contact.

During the 1920s, Polish intelligence had obtained an early version of the Enigma machine and constructed a device (“Bombe”) to decode its messages. By November 1939 Turing––who had volunteered for code-breaking duties the previous year––could refer in internal documents to “the machine [‘superbombe’] now being made at Letchworth, resembling, but far larger than, the Bombe of the Poles. . . .” Hodges offers a detailed description of the improvements made by Turing and his Bletchley colleague Gordon Welchman to the superbombe. In time, those improvements enabled Bletchley to read virtually every message sent to and from the U-boat fleet between June 1941 and February 1942, when Germany added an additional rotor to the naval Enigma.

The resulting decryption blackout enabled the U-boats to reassert control of the sea lanes. Only the capture of U-559 off Port Said in October 1942 provided the clue that––some months later––enabled Bletchley to resume its “same day” decryption of most U-boat messages. In the meantime, Allied shipping suffered losses that, if continued, would surely have prevented the buildup of men and materiel needed to undertake the Normandy landings of June 1944.

Turing, in fact, had relatively little to do with the final decipherment of U-boat communications, having been dispatched to the U.S. in November 1942 with authority to disclose anything and everything known to the British about Enigma decryption. After several months spent conferring with U.S. codebreakers, he returned to England in March 1943. Thereafter, he devoted most of his time to the development of a secure telephone communication system, first at Bletchley and later at a satellite location. That project, which he completed almost single-handedly, was not finished in time to impact the war effort.

In October 1945, he joined a group at the National Physical Laboratory tasked with the construction of a working stored-program computer. Later he moved to the University of Manchester, where a group led by engineer F.C. Williams had taken the lead in hardware development. On June 21, 1948, by finding the largest factor of a given integer, the group’s prototype became the first “electronic computing machine” to successfully execute a stored program. The milestone had taken longer to reach than expected because, in the absence of wartime urgency, progress in all directions had slowed considerably. Perhaps to alleviate his frustrations, Turing increased his involvement in long-distance running during these years. As a marathoner, he nearly qualified for the London Olympics of 1948.

In 1949, a contract was signed with Ferranti Ltd. to produce a commercial version of the Manchester machine, which owed more to von Neumann’s design than to Turing’s. Known as the Mark I, it was delivered in May 1951, well before NPL produced either its “Pilot ACE,” a drastically scaled-down version of the machine proposed by Turing, or the less than full-scale version that eventually followed. Both were obsolete by the time they were completed. It was on the Manchester Mark I that Turing was finally able to launch experiments that he had long been planning. Among them were early versions of the Turing test of a machine’s ability to think, and several trials related to his theory of morphogenesis.

It was at about this time that he was convicted of gross indecency––the legal euphemism for homosexuality––and given a choice between jail time and chemical castration. Choosing the latter, he endured a series of hormonal treatments that clearly affected his work and personality. The treatments were discontinued after a year, and he seemed rather quickly to resume his former lifestyle.

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Unlike the book, the film makes no attempt either to convey the substance of Turing’s mathematical activities, or to depict his life as a homosexual. Beginning with his arrest on suspicion of espionage, rather than gross indecency, The Imitation Game reduces Turing’s prior history to a series of flashbacks depicting the hazing he endured at boarding school, his relationship with Morcom, his lifelong attraction to long-distance running, his arrival at Bletchley, his romance with Joan Clarke, and his many battles with the military brass.

Turing’s wartime discovery process is boiled down to a single “Aha!”  moment sited, like its counterpart in the movie version of A Beautiful Mind, in a bar. A chance remark made there by one of Bletchley’s many Morse code-reading girls sends the entire Bombe crew on the run to Hut #8, where, fed the input she describes, “Alan’s machine” succeeds for the first time in determining the Enigma machine’s current rotor setting, thereby sealing the fate of “Fortress Europe.” It is an entertaining film, with an excellent cast, which succeeds by ignoring the threads that Hodges so deftly unravels!

James Case writes from Baltimore, Maryland.