Part 5 of Turing: a natural philosopher  (1997)

Triumph of the Computer

You have often asked me about possible applications of various branches of mathematics. I have just discovered a possible application of the kind of thing I am working on at present. It answers the question 'What is the most general kind of code or cipher possible', and at the same time (rather naturally) enables me to construct a lot of particular and interesting codes. One of them is pretty well impossible to decode without the key, and very quick to encode. I expect I could sell them to H.M. Government for quite a substantial sum, but am rather doubtful about the morality of such things. What do you think?

Nothing more is known about Turing's theoretical investigation, but at Princeton he spent time on building a machine out of electromagnetic relays which effected binary multiplication as an encoding device, with some theory of immunity to cryptanalysis. This Turing machine has not survived, nor has its theory, nor do we know the course of his moral decisions regarding its application. Incidentally, to give the flavour of Turing's personality, he was at this point highly indignant at Baldwin and the British establishment for opposing Edward VIII's marriage. ('As for the Archbishop of Canterbury, I consider his behaviour disgraceful'.) However he lost sympathy with the ex-king on learning that he had behaved improperly with state papers. Meanwhile he was an astute judge of the prospect of war with Germany.

When back at Cambridge, Turing also designed and partially built another machine, which approximated by gear-wheel motion a Fourier series for the Riemann zeta-function. It was intended to shorten the hard labour of finding the possible locations of zeros — the subject of the Riemann hypothesis, which remains today perhaps the most important unsolved problem in mathematics. But Turing meanwhile had indicated his interest in cryptography, probably through King's College channels. Whatever the moral and practical means, a rational miracle came about, in which an unworldly person found a perfect application at the heart of the world crisis. In September 1938 he began part-time work on the outstanding problem facing British intelligence: the German Enigma cipher. Progress, however, depended on the Polish mathematicians' work, donated to Britain after the British guarantee to Poland in July 1939. After Hitler called this bluff, Turing began full-time work at Bletchley Park, wartime home of the cryptanalytic establishment.

Turing had substantial influence on the course of the war. In summary: (1) He took on the naval version of Enigma in 1939, when it was thought beyond hope, and found a solution. He said himself that he took up the challenge because [8] 'no-one else was doing anything about it and I could have it to myself.' The reading of U-boat communications, achieved under Turing's direction, was arguably the most vital aspect of Bletchley Park work. (2) Turing crowned the design of the machine (the 'Bombe') which was central to the analysis of all Enigma traffic, with a logical idea which had a curious echo of the discussion with Wittgenstein, as it depended on the flow of logical implications from a false hypothesis. (3) Turing created a theory of information and statistics which made cryptanalysis a scientific subject; he was chief consultant and liaison at the highest level with American work.

Practical work brought with it demands of cooperation and organisation to which Turing was unsuited, and in the early part of the war he had to fight a difficult corner on questions of strategy and resources, at one point joining with other leading analysts to appeal to Churchill over the heads of the adminstration. But there was another side to this uncongenial coin: war broke peacetime boundaries and gave him practical experience of technology at its leading secret edge. In peace his ideas had flowed into small-scale engineering; in war they led to the electronic digital computer of 1945.

Electronic speeds made a first impact on the Enigma problem in 1942, and thereafter in the engineering of very advanced large-scale Colossus electronic machines for breaking the other high-level German machine cipher, the Lorenz. Note, incidentally, that the Colossus was nothing to do with the Enigma, as is often lazily stated; also that Turing had no part in designing the Colossi, but had input into their purpose and saw at first-hand their triumph. Turing did, however, have an electronic design of his own: in 1944, he with one engineer assistant built a speech scrambler of elegant and advanced principle. It appears that in proposing the speech scrambler, not an urgent requirement, he had his own hidden agenda: to acquire electronic experience. The scrambler worked in 1945, and at the same time, Turing combined logic and engineering, pure and applied mathematics, to invent the computer.

Care with words and claims is required: the word 'computer' has changed its meaning. In 1936 and indeed in 1946 it meant a person doing computing, and a machine would be called an 'automatic computer.' Until the 1960s people would distinguish digital computers from analogue computers; only since then, as digital computers have swept the field, has the word come to mean a machine such as Turing envisaged. Even now, the word is sometimes applied to any calculating machine. In speaking of 'the computer', I take the salient feature to be that programs and data are alike regarded as symbols which may be alike be stored and manipulated — the 'modifiable stored program' — and this is the feature implied by Turing in speaking of a 'practical universal machine,' which is how he described his own idea.

Even here, however, care is required. Although the universal machine was presented in 1936 with instructions and working space all in the common form of the 'tape', the instructions only required reading, not manipulation or modification, so it would not matter if they were stored in some unalterable physical form. Turing recognised this and counted Babbage's Analytical Engine, on which instructions were fixed cards, as a universal machine. In practice, however, the recognition that programs and data could be stored alike in a symbolic form and could alike be manipulated, was immensely liberating. It made a clean break from the Babbage-like machines which culminated in the electronic ENIAC of 1946. In enunciating the power of the universal machine concept, Turing was far ahead of contemporary wisdom; his idea that a single type of machine could be used for all tasks was stoutly resisted well into the 1950s.

[7] Letter to Turing's mother, Mrs E. Sara Turing, now in the Turing Archive at King's College, Cambridge.
[8]A. P. Mahon, History of Hut 8 (1945), released from secrecy by the National Archives, Washington DC, April 1996.

© 1997, Andrew Hodges.

CONTINUE to part 6

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