The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries)

by David Leavitt

  Another German error of which Turing took full advantage was the fact that in choosing three-letter message keys, German operators often took the path of least resistance. An operator might, for instance, repeatedly choose the first three letters of his girlfriend’s name; or he might resort to the use of three-letter sequences that cut diagonals across the typewriter keyboard: RFV and TGB, say. The cryptanalysts knew to look for such repetitions, which they called cillis, or sometimes sillies, and when they found them (which was often), their work was made that much simpler.

  Lastly, the mathematicians at Bletchley got considerable help from the British navy, which periodically managed to confiscate Enigma equipment, codebooks, logbooks, and instruction manuals from sunken U-boats and intercepted German trawlers. On one occasion, the gunner on an English ship managed to salvage a waterlogged canvas bag containing two days worth of Enigma settings as well as an operator’s log including full plaintext and ciphertext for all messages sent on those days. On another, sailors boarding a U-boat located two intact Enigma rotors: this was a particularly helpful catch, because it came just after the Germans had increased the number of rotors from five to eight for naval Enigma traffic. The two rotors were, in fact, two of the three that had just been added.

  But for every piece of good luck, there was a setback. Occasionally the Germans would make unexpected changes in their method of transmitting messages (usually for the purpose of increasing internal security and protecting against spies), thus wiping out weeks of intense cryptanalytic labor and forcing the team at Bletchley to go back to the drawing board. While certain Enigma networks operated according to principles that rendered their traffic easier to read, moreover, one system—the naval Enigma—employed a host of extra security measures that made it maddeningly resistant to interception. For instance, the naval Enigma not only had a provision for the use of three out of eight rotors (increasing the number of possible rotor orders by a factor of almost six); it also employed an adjustable reflector that could be fixed in any of twenty-six positions. (Later the German navy started using a four-rotor Enigma machine.) To make matters even more complicated, operators in the naval Enigma system dispensed altogether with the old system of beginning each message with a ciphered version of the key necessary for the message’s decipherment; instead, they coded the key using an entirely different system based on bigram substitution tables; two three-letter groups selected by the operator would each be padded with a fourth random letter, then aligned:

  The letters in the group would then be arranged as vertical “bigrams,” or groupings of two letters:

  The bigrams, in turn, would be replaced with those indicated on a daily bigram substitution table. The apparent impenetrability of the naval Enigma was particularly problematic because its traffic contained the information that the British admiralty needed most urgently in order to secure the waters of the Atlantic and the Pacific against U-boat attacks.

  On occasion a seemingly inconsequential change in the method of transmitting Enigma traffic—such as an alteration to the bigram substitution tables—was enough to stop the cryptanalysts at Bletchley in their tracks for weeks at a time. Fortunately they soldiered on; indeed, their eventual victory over the Enigma owed as much to the hours of drudge work put in by the many very dedicated (and very patient) men and women who worked at Bletchley as it did to the theoretical and engineering breakthroughs for which Turing himself was chiefly responsible. Through tireless analysis of the mathematical foundation of polyalphabetic ciphers, relentless exploitation of even the tiniest chinks that appeared in the machine’s armor, and the clever use of electrical equipment to mechanize and thus dramatically speed up the testing and elimination of thousands upon thousands of possible key combinations, Turing managed to render the Enigma, if not a powerless antagonist, at least a manageable one. Eventually he even cracked the naval Enigma code, thus bringing about a sharp decrease in the sinking of Allied ships by U-boats. It was a bravura, even heroic performance, which contributed significantly to Hitler’s defeat.

  It was also a performance of which Turing was the undisputed organizer. True, the original conception of the bombe had to be credited to the Poles. Yet, as Budiansky points out, “the fundamental mathematical insight behind the British bombe was wholly Turing’s,” as was “the discovery that matching strings of plain and cipher text defined a characteristc geometric relationship” and “the idea of feeding a contradiction back into an interconnected loop of Enigma machines.” As Hodges notes, Turing got the last laugh on Wittgenstein, since “these contradictions would make something go very wrong for Germany, and lead to bridges falling down.”

  5.

  It was during his years at Bletchley that Turing earned his reputation for eccentricity, social awkwardness, and slovenliness. The episode of his aborted enrollment in the home guard dates from this period. So do certain legends that, true or not, still circulate: that he wore a gas mask when he bicycled to work each morning (supposedly to keep from breathing in pollen); that when he rode his bicycle he counted the revolutions of the wheels, stopping one revolution before he knew the chain was going to come off; that at the end of each day he chained his tea mug to a radiator pipe. At Bletchley, rumor had Turing keeping his trousers held up with string, wearing his pajamas under his sports coat, rarely shaving or cutting his nails. All of which might have been true: he had never been very tidy. Such atypical conduct as he displayed, moreover, could be easily written off as actually characteristic of a certain “type”: the “absent-minded professor” of which Sidney Stratton was another exemplar. And yet simply to laugh off Turing’s idiosyncratic behavior during his years at Bletchley is to miss both its more disturbing and less comic implications. Yes, tea mugs were in short supply during the war, but didn’t chaining one to a radiator suggest a slight degree of paranoia? Likewise the obsessive counting of tire revolutions on a bicycle he never had repaired, since if he had, as Hodges observes, it would have meant that someone else would have been able to ride it. Turing might have no use for the conventions (bucking clichés of masculinity, he learned to knit while at Bletchley), nor any patience for “pompousness or officialdom. . . . [H]e wouldn’t suffer fools or humbugs as gladly as one sometimes has to.” Still, he himself had acknowledged the necessity of subscribing, at least to some degree, to the social niceties, when he had written to his mother at Princeton that his friend Maurice Pryce was “much more conscious of what are the right things to do to help his career.” Sworn to secrecy regarding his work, bereft of pretty much all sexual possibility, and sidetracked by necessity from the work on the universal machine for which he had been preparing before the war, Turing seems to have gone beyond the pale at Bletchley, gradually losing whatever capacity he possessed for playing by the rules.

  As the war drew to a close, the work Turing had at first orchestrated was able to move forward more or less by itself. In deciphering Enigma traffic, Bletchley was meeting with a degree of success of which even the most overconfident of cryptanalysts would scarcely have dreamed. The running of the bombes became an industrial matter; “Job up! Strip machines,” the operators would cry once the Enigma cipher for the day had been broken. Yet as the well-oiled machine of code breaking began, as it were, to run itself, its architect was left with increasingly little to do. Bletchley sent him to the United States, to consult on the construction of an electronic bombe intended to deal with the threat of a four-rotor naval Enigma. He also contributed to the construction of a machine intended to decipher an entirely different type of traffic, enciphered on a teleprinter and known as Fish. In a more immediate sense, however, his work as a code breaker was finished.

  The extent of his contribution to the war effort—of which he never spoke during his lifetime—should not be underestimated, and though it would probably be an exaggeration to say that without Turing the Allies would not have won the war, it is reasonable to suppose that without him it would have taken them several more years to do it. At the same time, had
the British authorities known that Turing was homosexual, they might have refused to let him anywhere near Bletchley, in which case, as his friend Jack Good observed, “we might have lost the war.”

  Turing’s years at Bletchley constitute the best-documented period in his life, yet in the end his work as a code breaker amounted to a very long diversion from his dream of building a universal machine. For the bombes were about as far from universal as you could get. Their very design guaranteed their obsolescence, since it depended on the quirks and particularities of another, much smaller machine, the Enigma, of which the bombe was the huge, distorted shadow. Nor did the high stakes of the venture, the pressure to decipher as much Enigma traffic as swiftly as possible, allow Turing any latitude or free time to experiment with the possibility of setting a universal machine to the specific task of code breaking. Speed was too much of the essence. Because, in “Computable Numbers,” the machine of which Turing wrote was intended for use only in the landscape of the theoretical, its fastness or slowness was inconsequential. But during the war there was no time to waste. Lives depended—literally—on how well the bombe was able to do its job.

  Today Bletchley Park continues on, as a sort of museum and memorial to the men and women who gave so many years to breaking the Enigma code. There’s a terrific gift shop at which you can buy Enigma key chains, T-shirts, and wall magnets. Former Wrens, now in their eighties, take you on a tour through the mansion, the outbuildings, and the various huts, including Hut 8, which now contains a huge replica of one of the bombes. Presumably, the originals were destroyed after the war ended, both for the sake of security and because they no longer served any purpose. They were as onetime as the onetime pads used in sending a cipher.

  Turing’s presence is everywhere. The guides, as they lead you through, talk warmly about “the Prof.” They show you with pride the ornamental oars from a 1935 “bumps” race at King’s College, displayed in the main house and engraved with the news that Turing replaced W. M. “Bill” Colles on the number two boat.

  During a lull in my tour of Bletchley, as we were approaching a monument to the Polish code breakers, I told my guide that I was writing a book about Turing. She shook her head and said, “What a tragedy. People didn’t really understand about homosexuality in those days.”

  The implication, of course, was that today people understood better.

  “Did you know him?” I asked.

  “Oh yes,” she said. “Sometimes he tied string around his waist to keep his trousers up.”

  But then, before I could ask more, the crowd of visitors stilled. My guide cleared her throat and began to tell us the amazing story of Marian Rejewski.

  * * *

  *Hardy, though not a participant in the seminar, was often cited as a sort of avatar of traditional mathematical thinking; Wittgenstein took particular interest in the distinction that Hardy drew between “knowing” and “believing in” a mathematical theorem or hypothesis, such as Goldbach’s conjecture. He liked to turn Hardy’s ideas about proof upside down, as in this passage from the fourteenth lecture: “Professor Hardy says, ‘Goldbach’s theorem is either true or false.’—We simply say the road hasn’t been built yet. At present you have the right to say either; you have a right to postulate that it’s true or that it’s false.—If you look at it this way, the whole idea of mathematics as the physics of the mathematical entities breaks down. For which road you build is not determined by the physics of mathematical entities but by totally different considerations.”

  *In fact, when Michael Apted made the film Enigma (a film, incidentally, conspicuous for the absence of any character resembling Turing), he chose to use a different country estate for location shooting.

  *The principal sources for the account that follows are Singh’s The Code Book and Budiansky’s Battle of Wits.

  *Simon Singh notes that none of these machines was very successful, the most spectacular failure being the American version, Edward Hebern’s “Sphinx of the Wireless.”

  *As Hodges observes, this practice of incorporating the indicator code into the body of the message paralleled Turing’s idea of expressing instructions in the same mathematical language as processes in the universal machine.

  *In the fall of 1941, however, administrative problems, overcrowding, and the poor quality of the Bletchley plumbing, among other concerns, prompted Turing to write, in conjunction with Welchman and two other colleagues, a letter to Winston Churchill asking for help. Churchill’s response was swift and emphatic: “Make sure they have all they want on extreme priority and report to me that this had been done.”

  6

  The Electronic Athlete

  1.

  In the summer of 1942, Max Newman, Alan Turing’s mentor at Cambridge, arrived at Bletchley, where he was assigned to the analysis of the Fish traffic. Turing’s contribution to the project had been the development of a statistical process known as Turingismus. (The mathematicians at Bletchley were fond of monikers of this sort; a procedure developed by Turing as part of the attack on the naval Enigma was nicknamed Banburismus, since the sheets on which he and his colleagues entered their data were printed in the town of Banbury.) Efforts to break the Fish traffic by hand took place in a section of Bletchley called the Testery, but with Newman’s arrival, the focus shifted. Like the Enigma code, Fish was generated by a German machine, the Lorenz. Now Newman concluded, as Turing had before him, that the only way to break this machine-generated cipher was with a machine built specifically for that purpose. So he settled down to work in Hut 11, which came to be known as the Newmanry. In his research, he got assistance from the engineers at the recently established Telecommunications Research Establish-ment, or TRE, in Malvern, as well as the Post Office Research Station at Dollis Hill, in the London suburbs.

  The first of the machines designed to take on the Lorenz was delivered by the Post Office to Bletchley in June 1943. It was called the Heath Robinson, in honor of the Edwardian cartoonist whose drawings featured immensely complex industrial contraptions that performed absurdly simple or simply absurd tasks. (Subsequent Robinsons included a Peter Robinson and a Robinson and Cleaver, named after a London department store.) Unfortunately, the name Heath Robinson turned out to be prescient: the machine was notoriously bad-tempered, prone to breaking down and catching on fire. Worse, the teleprinter tapes that were central to its design tended to tear. Luckily, Newman soon found an ally in the electronic engineer Tommy Flowers, who was based at Dollis Hill, and with Flowers’s help he was able to overcome the technical difficulties that plagued the Robinsons. The result was the much more efficient Colossus, which employed 1,500 electronic valves and with which Newman successfully tackled the Fish traffic.

  Given that its architect was his former mentor, one would think that Turing would have played a central role in the development of the Colossus. As the war neared its end, however, Turing had begun to move away from cryptanalysis and into other areas of research. In addition to his stay in Washington, his trip to the United States had included a visit to Bell Labs in New Jersey, where he had spent two months studying the relatively new science of speech encipherment: essentially, the manipulation and deliberate distortion of sound waves by a signal that would function as a key or indicator and that could be applied both by the sender and by the receiver of the message, scrambling or unscrambling as the case might be. The theory behind speech encipherment was not dissimilar to the one according to which the Enigma had been designed, the difference being that, instead of writing, it was speech itself that was being rendered unintelligible. It was an idea that fascinated Turing; especially after so many years spent searching out and exploiting the vulnerabilities in someone else’s cipher, he relished the opportunity to apply all that he had learned to the design of a truly impregnable system of his own.

  His exposure to the activities at Bell Labs was not the only source of the liberation that Turing experienced during his months in the States. He also met with Claude Shannon, an America
n pioneer of computer science based at MIT, with whom he discussed at length the question of whether a machine could be built that imitated the behavior of the brain; Shannon, who believed that one could, went so far as to imagine a day when humans might read poetry to machines or play music for them. Turing also spent a considerable amount of time in New York City, where he professed astonishment at the casual ease with which a stranger propositioned him at a hotel—a different sort of liberation.

  Having acquired a good working knowledge of both the electronic equipment and the mathematical theory required to design a speech encipherment system, he returned to Bletchley in the spring of 1943, where he found that Hut 8 had hardly missed him. The chess champion Hugh Alexander, a more able and ambitious manager, had more or less taken over work on the naval Enigma. Watching the bombes tick away as busy Wrens reset and reshuffled the rotors, Turing must have felt like a parent whose child had passed into adolescence and no longer needed him. In addition, he was not particularly keen to join the team at the Newmanry, given that most of the work on the Colossus had been done in his absence. Although Turingismus provided the theoretical and statistical basis for the design of the Colossus, the machine was not his “baby” in the way that the bombe had been. Besides, his imagination was taking him in a new direction.