Alan Turing: an introductory biography

by Andrew Hodges

For a guide to this website go to the Alan Turing Home Page

This article was written for the Turing Festschrift volume, published by Springer in 2004, edited by Christof Teuscher, and based on the talks given at the Turing Day at the Swiss Federal Institute of Technology, Lausanne (EPFL) on 28 June 2002. This event marked the 90th anniversary of Turing's birth. I also contributed a paper on What would Alan Turing have done after 1954. This short account of Turing's life and work was intended to be helpful in introducing the papers of the other contributors.

The Turing Day conference at the Swiss Federal Institute of Technology, Lausanne, was held to mark the ninetieth anniversary of Alan Turing's birth, which fell on 23 June 2002. Turing's life was so short that further events will soon mark the fiftieth anniversary of his death on 7 June 2004. But in that span between 1912 and 1954 Alan Turing did pioneering work, encompassing the foundations of computer science, which still continues to stimulate and inspire. As this volume illustrates, the breadth and depth of Turing's work, as well as its dramatic intensity, compensates for its chronological brevity.

Alan Turing's biography is interwoven with the course of twentieth-century history and falls naturally into pre-war, wartime and post-war periods. He was born into the British upper-middle class which had confidently run the imperial administration until the First World War, but which, under the impact of economic and political crisis, progressively lost control thereafter. In a very broad sense, Alan Turing belonged to a new, modernising, generation which reacted contemptuously against Victorian values. But Alan Turing's early life was marked by detachment from the obligatory social training, rather than rebellion against it. It was also marked from the start by his intensely individual response to science and mathematics, in particular to the relativity and quantum mechanics which had transformed the physical sciences since 1900. He became an undergraduate at King's College, Cambridge University, in 1931, reading Mathematics and graduating with distinction in 1934.

Very soon, in 1935, the lectures of M. H. A. (Max) Newman at Cambridge introduced him to the frontier of mathematical logic, which likewise had been transformed since 1900. But logic was neither Turing's immediate nor his only choice. It was his work in probability theory that won him a Fellowship of King's College in 1935, and he might easily have continued in this field, or else in the mathematical physics that had first attracted him. Thus he came to logic from a wide background in pure and applied mathematics, and it was in this eclectic spirit that he attacked the Entscheidungsproblem of David Hilbert, which at that point remained an outstanding question. Turing, working alone, and only twenty-three, attacked and settled this problem by his definition of computability. His famous paper, On Computable Numbers, with an application to the Entscheidungsproblem, was published at the turn of 1936-37. A complete outsider to the field, he won a place in the subject with a concept which after sixty years remains definitive. His definition of computability showed there could be no general method for deciding the provability of mathematical propositions, and marked the end of attempts to formalise a complete system for mathematics. But it also opened the way into new fields, which now we would recognise as computer science and the cognitive sciences.

Although Turing thereafter found himself classed as a logician, he was more a mathematician who applied himself to logic; and more than that, a scientist who behind the mathematics felt a deep concern for the fundamental questions of mind and matter. His underlying interest in the problem of mind showed up in the bold statements about human memory and states of mind which informed his arguments. His background in physics was hinted at in the 'machines' with which he made his definition of computability — the now-famous 'Turing machines', running on paper tape, an image of 1930s modernity. It was this concreteness which made Turing's definition of computability much more satisfactory than the mathematical definition offered by Alonzo Church, the Princeton logician who led the field. Mathematically, Turing's definition was equivalent to Church's. But the description of the Turing machine gave a convincing argument for why it was that this mathematical definition completely captured the concept of 'effectively calculable'.

Each Turing machine represents an algorithm; for modern readers it is hard not to see it as a computer program and to bear in mind that computers did not then exist. But Turing specifically defined a type of machine called 'universal', capable of reading the instruction table of any other machine. This is precisely the principle of the stored-program digital computer, then yet to come into being. It is possible that Turing even then entertained the possibility of constructing such a machine, for he certainly interested himself in electric and mechanical computation. But if so, he left no notes or observations on this question. Rather, he was primarily engaged in a wide variety of mathematical researches. In late 1936 Turing joined Church's group at Princeton and there embarked on more advanced logic but also on work in algebra and in developing the theory of the Riemann zeta-function, fundamental to the study of prime numbers. The mathematician John von Neumann offered him a post at Princeton to continue mathematical research, but he chose to return to England in summer 1938, conscious of the impending conflict with Germany and already prepared to make a special contribution to it.

Whilst the Second World War took many of his scientific contemporaries into the physics of radar and the atomic bomb, it took Alan Turing into cryptology. After 1938, his grappling with the infinitudes of mathematical logic was complemented by the finite but still highly challenging logical problem of the German Enigma enciphering machine. In 1939, partly thanks to a brilliant Polish contribution, Turing was able to propose a highly ingenious method of testing a 'probable word' for Enigma-enciphered messages. His logical scheme was rapidly materialised in very large electromechanical devices called Bombes, which from 1940 onwards worked as the central engines of decipherment throughout the war. For this work, Turing was based at the now famous centre at Bletchley Park, Buckinghamshire, which recruited increasingly large sectors of the British intelligentsia. Amongst these, Alan Turing remained the chief scientific figure. His central contribution, after the logic of the Bombe, lay in Bayesian statistics for measuring 'weight of evidence', a development close to Shannon's theory of information measure. Turing led what was in effect a scientific revolution, and because he took personal charge of the crucial U-boat message problem, was able to see his approach triumph in the battle of the Atlantic. Alan Turing's role mirrored the developing course of the war: at first a lone British figure against all the odds, and later, as the work developed on a major industrial and transnational scale, handing over the British contribution to the power by which it was eclipsed: the United States.

Turing's personality traits became more striking when outside the Cambridge environment; shy but outspoken, nervous but lacking deference, he was not well adapted to military manners or to the diplomacy of the embryonic Anglo-American relationship. But his commanding scientific authority made him the top-level technical liaison between the wartime Allies, demanding a voyage to America in the winter of 1942-43 at the height of the Atlantic battle. None of this experience, however, gave him a taste for power or detracted from his primary vocation as a pure scientist. The undiminished tenacity of his scientific calling was well illustrated by the use he made of his wartime experience. For after 1943 Turing knew from Bletchley Park work that large-scale digital electronic machinery had the speed and reliability to make possible a practical version of his 'universal machine.' From that point onwards he made the construction of such a machine his principal ambition, and he arranged his work so as to gain personal experience of electronic components — designing and building an advanced speech scrambler. And so, at the end of the Second World War, he had a plan for an electronic computer, but it was motivated not by military or economic needs. It was for the exploration of the scope of the computable and in particular for comparing machine processes with human mental processes. He called it 'building a brain'.

For his war work, which some would judge critical to the Atlantic war, Turing was honoured with the modest British formality of an OBE. But his work remained completely secret until the mid-1970s, and he derived no advantage from it in his subsequent scientific career. Nevertheless, the post-war period began with great promise, for he was invited to take up an appointment at the National Physical Laboratory, near London, in October 1945, and his electronic computer plan, the proposal for the Automatic Computing Engine (ACE), was swiftly adopted in March 1946.

At that time, which was before the word 'computer' had its modern meaning, Turing used the term Practical Universal Computing Machine. But although fond of the word 'practical', Turing did not have the human gift of getting his practical way with people and institutions who did not share his vision. From the outset, it became clear that the NPL had no clear idea on how it was to build the machine he had designed, and it failed to adopt a policy speedy enough to satisfy Alan Turing. Turing's plans for software, exploiting the universality of the machine, were the strongest feature of his proposal, but they were little developed or publicised because of the dominating problem of hardware engineering. Impatient for progress, Turing took up marathon running to near-Olympic standard, but this did not relieve the stress. In the autumn of 1947 he returned to Cambridge for a sabbatical year, and while there was approached by Max Newman, since 1945 professor of mathematics at Manchester University, to take an appointment there instead. Newman had played a most important part at Bletchley Park after 1942 and had organised a section using the most sophisticated electronic machinery; he was also fully acquainted with Turing's logical ideas. At Manchester he had rapidly recruited both Royal Society funding and top-rank engineers, and by June 1948 a tiny version of the universal machine principle was working there — in marked contrast to the lack of progress at the NPL. Turing accepted the appointment as Deputy Director of the Computing Laboratory. But already in 1948 it became clear that the engineering would dominate the Manchester environment, and before long both Newman and Turing were sidelined and did not direct anything at all.

Turing's programming never exploited the advanced possibilities he had mapped out in 1946, and he failed also to write the papers that could have established his claim to the theory and practice of modern computing. Instead, the the main theme of his work became the more futuristic prospect of Artificial Intelligence, or 'intelligent machinery' as he called it. Already prefigured in 1946, this was expounded in papers of 1947, 1948, and 1950, arguing strongly that computable operations could encompass far more than those things considered 'merely mechanical' in common parlance, and indeed could emulate human intelligence. The last of these papers, the only one to be published in his lifetime, appearing in the philosophical journal Mind, has become famous for the Turing Test and its fifty-year prophecy, and stands still as a flagship for confidence in the ultimate mechanizability of Mind. But Turing's constructive arguments for how Artificial Intelligence might be achieved are perhaps as significant as the long-term vision. Notably, his ideas encompassed both the 'top-down' and the 'bottom-up' ideas that were to become bitter rivals in later AI research. But it is also notable that he did very little to follow up these ideas with active research, even when he had the resources of the Manchester computer.

In 1951, Turing was elected to a Fellowship of the Royal Society, the citation referring to his 1936 work. This was a watershed year for Turing: although he had largely failed in the immediate post-war period to capitalise on his wartime achievement, he now started a quite fresh development, demonstrating the part he could still have in the great expansion of science and mathematics that began in the 1950s. His new ambition was that of giving a mathematical explanation for morphogenetic phenomena, thus showing an interest in biology that went back to childhood, but which was now expressed in advanced methods for studying non-linear partial differential equations with the computer simulations which had just become possible on the Manchester computer.

At the end of 1951 Turing submitted a first paper on this work, which for mathematical biology was to be as important as his 1936 work had been for logic. But at just this point, Alan Turing was arrested. As a homosexual, he was always in danger from the law which at that time criminalised all homosexual activity: an injudicious liaison turned that potential into fact. The trial, in March 1952, resulted in his being forced to accept injections of oestrogen. He fought hard to prevent this from arresting his work. Unrepentant, open and unashamed, Alan Turing found himself a very isolated figure at Manchester. In 1953 there was another 'crisis' with the police, which may well have been related to the fact that as a known homosexual he fell into the new category of 'security risk', one who could no longer continue the secret work he had previously been doing. His holidays abroad to less hostile climes would not have calmed the nerves of security officers. Amidst this Cold War story, however, Turing also found time not only for substantial developments in his morphogenetic theory, but for a stab at a new field: the interpretation of the quantum mechanics that had first absorbed him in youth. All this was, however, cut off by his death by cyanide poisoning at his home at Wilmslow, Cheshire, in 1954, by means most likely contrived by him to allow those who wished to do so to believe it an accident.

An awkward figure, who delighted yet often infuriated his friends, Alan Turing was wrapped up in world events and yet most concerned with an intense personal integrity. Writing as plainly as he spoke, he was an Orwell of science; but his large capacity for frivolity, as illustrated in his discussion of the Turing Test setting, gave him an honourable place in the lighter and cheekier side of English culture. His life was full of paradox, not least that he, of all people original and socially nonconforming, should be the foremost advocate of the view that the mind was purely mechanical. The most purely scientific in spirit, his application to war work was of greater effect than perhaps any other individual scientist. Committed to honesty and truth, he found his life enveloped by secrecy and silence.

The strange drama of Alan Turing's death in 1954 has in its way given him a lasting life in public consciousness. His state of mind at death remains an enigma, but so too does the true inner story of his life. Prickly and proud, yet self-effacing, Turing wrote little about the development of his ideas. There is the unknown background to his fascination with the problem of Mind, where only juvenile fragments survive. There is the question raised by Newman, of whether he might have done greater things in mathematics, but for the war; and the question of the real motivations for Turing's abandonment of deep mathematical work for the sake of the war. The vexed question of the emergence of the digital computer in 1945, and of Turing's relationship with von Neumann, remains a gap at the heart of twentieth-century technology. The true genesis of his Artificial Intelligence programme during the war, and the question of whether his concern for the significance of Gödel's theorem was really resolved — all this remains unknown, spur to twenty-first century thought and our fascination with the theory and practice of intelligent life.

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