# Turing, Alan Mathison

- Andrew Hodges

#### Alan Mathison Turing (1912–1954)

Turing, Alan Mathison (1912–1954), mathematician and computer scientist, was born on 23 June 1912 at Warrington Lodge, Warrington Avenue, London, the younger child (after his brother, John) of Julius Mathison Turing, of the Indian Civil Service, and Ethel Sara Stoney (1881–1976), daughter of Edward Waller Stoney, chief engineer of the Madras Railways. The unusual name of Turing was best known for the work of H. D. Turing on fly-fishing; more scientific connections could be found in the Stoneys (notably in a remote relative, the Irish physicist G. J. Stoney).

### Education and early scientific interests

Until his father's retirement in 1926 the sons were fostered in various English homes, and Turing attended Hazelhurst preparatory school in 1922–6; during those years he found his extra-curricular passion for chemistry experiments. At twelve he expressed conscious fascination with using 'the thing that is commonest in nature and with the least waste of energy' (letter from Turing to his mother, 1925, cited in Hodges, *Enigma*, 19), presentiment of a life seeking fresh answers to fundamental questions. Despite this, he was successfully entered for Sherborne School. The headmaster soon reported, almost correctly: 'If he is to be solely a scientific specialist, he is wasting his time at a Public School' (Hodges, 26).

Turing's private notes on the theory of relativity showed a degree-level appreciation, yet he was almost prevented from taking the school certificate lest he shame the school. The stimulus for communication and competition came only from another very able pupil at Sherborne, Christopher Morcom, to whom he found himself powerfully attracted. Morcom gave Turing a vital period of intellectual companionship, which ended with the former's sudden death in 1930.

Turing's conviction that he must now do what Morcom could not apparently sustained him through a long crisis. His thoughts turned to the question of how the human mind was embodied in matter, and whether, accordingly, it could be released from matter by death. This led him to wonder whether quantum mechanical theory affected the traditional questions of mind and matter. As an undergraduate at King's College, Cambridge, from 1931, he entered a world more encouraging to free-ranging thought. His reading of J. von Neumann's new work on the logical foundations of quantum mechanics helped a transition from emotion to intellectual enquiry.

Turing's homosexuality became a definitive part of his identity, and the special ambience of King's College gave him a first real home. His association with the anti-war movement of 1933 did not develop into Marxism, nor into the pacifism of his occasional lover James Atkins, a fellow mathematician. He was closer in thought to the liberal-left economists J. M. Keynes and A. C. Pigou. His relaxations were not found in the literary circles generally associated with the King's College homosexual milieu, but in rowing, running, and later in sailing a small boat.

### The universal Turing machine

Turing's progress seemed assured: a distinguished degree in 1934 was followed by a fellowship of King's in 1935 and a Smith's prize in 1936 for work on probability theory, and he might then have seemed on course for a successful career as a mildly eccentric King's don engaged in pure mathematics; but his uniqueness of mind drove him in a direction none could have foreseen. By 1933 he had introduced himself to Russell and Whitehead's *Principia mathematica* and so to the arcane area of mathematical logic. However, many questions had by then been raised about how truth could be captured by formalism. K. Gödel had shattered Russell's picture by showing the existence of true statements about numbers which could not be proved by the formal application of rules of deduction. In 1935 the topologist M. H. A. Newman introduced Turing to a question which still lay open: the question of decidability, the *Entscheidungsproblem*. Did there exist a definite method or process by which all mathematical questions could be decided?

To answer such a question needed a definition of ‘method’ both precise and compelling, and this Turing supplied. He analysed what could be achieved by a person performing a methodical process, and, seizing on the idea of something done ‘mechanically’, expressed the analysis in terms of a theoretical machine able to perform certain precisely defined elementary operations on symbols. He presented convincing arguments that the scope of such a machine was sufficient to encompass everything that would count as a ‘definite method’. Daringly he included an argument based on ‘states of mind’ of a human being performing a mental process. Having made this novel definition of what should count as a ‘definite method’ it was possible to answer this question in the negative: no such method exists.

In April 1936 Turing showed his result to Newman, but at the same moment the parallel conclusion of the American logician A. Church became known, and Turing was robbed of his full reward. His paper, 'On computable numbers with an application to the *Entscheidungsproblem*' (*Proceedings of the London Mathematical Society*, 42, 1936, 230–65; 43, 1937, 544–6) was delayed. However the originality of his concept—the ‘Turing machine’—was recognized and has become the foundation of the theory of computation.

The ‘universal Turing machine’ was an idea of immense practical significance: there is an infinity of possible Turing machines, each corresponding to a different ‘definite method’ or algorithm. But imagine, as Turing did, each particular algorithm written as a set of instructions. Then the work of interpreting and obeying these instructions is itself a mechanical process, and so can itself be embodied in a particular Turing machine, namely the universal Turing machine.

The Turing machine can now be thought of as a computer program, and the mechanical task of interpreting and obeying the program as what the computer itself does. So the universal Turing machine is now seen to embody the principle of the modern computer: a single machine which can be turned to any task by an appropriate program. The universal Turing machine also exploits the fact that symbols representing instructions are no different in kind from symbols representing data—the ‘stored program’ concept of the digital computer. However, no such computer existed in 1936, except in Turing's imagination.

Turing spent two years at Princeton University enrolled as a graduate student. He did not shoot to fame, but worked on showing that his definition of computability coincided with that of Church, and on an extension of these logical ideas for a PhD. This, his deepest and most difficult work, investigated the structure of uncomputable functions, with a suggestion that these were related to human intuition. He also published new theorems in algebra and number theory. Yet he found time to make an electromagnetic cipher machine, a link from 'useless' logic to what Turing saw as the prospect of war with Germany.

### Code-breaking, 1938–1945

In 1938 Turing was offered a temporary post at Princeton by von Neumann, who was by then acquainted with his ideas, but he preferred to return to Cambridge, even though without a lectureship. Unusually for a mathematician, he joined in Wittgenstein's classes; unusually again, he engineered a cogwheel machine to calculate the Riemann Zeta-function. Publicly he sponsored the entry of a young German refugee. Secretly, he worked part-time for the government cryptanalytic department. Pre-scientific methods had failed to penetrate the mechanical Enigma cipher used by Germany. No significant progress was made, however, until the gift of information and ideas from Poland, where mathematicians had long been employed on the problem.

When war was declared Turing moved to the Government Code and Cypher School at Bletchley Park. One Polish idea, embodied in a machine called a Bombe, was developed by Turing into a far more powerful device. Another Cambridge mathematician, W. G. Welchman, made an important contribution, but the critical factor was Turing's brilliant mechanization of subtle logical deductions. From late 1940, the Turing–Welchman Bombe made reading of Luftwaffe signals routine. In contrast, the more complex Enigma methods used in German naval communications were generally regarded as unbreakable. Happy to work alone on a problem that defeated others, Turing cracked the system at the end of 1939, but it required the capture of further material by the navy, and the development of sophisticated statistical processes, before regular decryption could begin in mid-1941. Turing's section, Hut 8, which deciphered naval and in particular U-boat messages, then became a key unit at Bletchley Park. The battle of the Atlantic turned towards allied advantage, but in February 1942 the Atlantic U-boat Enigma was changed and this advantage annihilated.

Electronics then made its first appearance at Bletchley as telephone engineers were pressed into an effort to enable the machines to work at ever higher speeds, and thus Turing was introduced to the potential of this new and untried technology. As it turned out, however, the electronic engineers found themselves called upon to mechanize the breaking of the ‘Fish’ material: messages enciphered on the quite different system used for Hitler's strategic communications. Here again Turing's statistical ideas underlay the methods employed, though it was M. H. A. Newman who played the organizing role.

By this time Turing was the *genius loci* at Bletchley Park, famous as ‘Prof’, shabby, nail-bitten, tieless, sometimes halting in speech and awkward of manner, the source of many hilarious anecdotes about bicycles, gas masks, and the Home Guard, the foe of charlatans and status-seekers, relentless in long shift work with his colleagues, mostly of student age. To one of these, Joan Clarke, he proposed marriage and was gladly accepted, but he then retracted, telling her of his homosexuality.

Turing crossed the Atlantic in November 1942, for liaison not only on the U-boat Enigma crisis, but on the electronic encipherment of top-level speech signals. Before his return in March 1943 logical weaknesses in the changed U-boat system had been brilliantly detected, and U-boat Enigma decryption restored. With the battle of the Atlantic regained for the allies, chess champion C. H. O'D. Alexander took charge of Hut 8, and Turing became the chief consultant to the vast cryptanalytic operation. As such he saw the Fish material cracked by the Colossus machines in June 1944, demonstrating the feasibility of large-scale digital electronic technology. He himself devoted much time to learning electronics, ostensibly for his own, elegant, speech secrecy system, effected with one assistant, Donald Bayley, at nearby Hanslope Park. However, he had a more ambitious end in view: in the last stage of the war (for his part in which he was appointed OBE), he planned the embodiment of the universal Turing machine in electronic form, or, in effect, invented the digital computer.

### The electronic digital computer

In 1944 Turing knew his own concept of the universal machine; the speed and reliability of electronics; and the inefficiency of building new machines for new logical processes. These provided the principle, the means, and the motivation for the modern computer, a single machine capable of any programmed task. He was spurred by a fourth idea that the universal machine should be able to acquire the faculties of the brain. Turing was captivated by the potential of the computer he had conceived. His earlier work had shown the absolute limitations on what any Turing machine could do, but his fascination now lay in seeing how much such machines could do, rather than in what they could not, and in the power of the concept of the universal machine. Indeed from now on he argued that uncomputable functions were irrelevant to the problem of understanding the action of the mind. His thought became strongly determinist and atheistic in character, holding that the computer would offer unlimited scope for practical progress towards embodying intelligence in an artificial form.

For a second time Turing was pre-empted by an American publication, in this case the 1945 EDVAC plan for an electronic computer, written in von Neumann's name, but this competition stimulated the National Physical Laboratory (NPL) to appoint him to plan a rival project. He despised his nominal superior J. Womersley, but this applied mathematician showed an appreciation of Turing's ideas, and steered his completely original design to approval in early 1946 as the Automatic Computing Engine, or ACE. The details of the design were short-term, but Turing's prospectus for the use of the computer was visionary. He projected a computer able to switch at will from numerical work to algebra, code-breaking, file handling, or chess-playing. Methods for handling subroutines included a suggestion that the machine could expand its own programs from an abbreviated form, an idea well ahead of contemporary American plans. He depicted a computer centre with remote terminals, and the prospect of the machine progressively taking over more advanced levels of programming work. However, nothing of the ACE was assembled, and Turing remained without influence in its engineering. The lack of co-operation, so unlike the wartime spirit, he found deeply frustrating.

From October 1947 the NPL allowed, or preferred, that Turing should spend a year at Cambridge. After study in neurology and physiology, he wrote a paper exploring the properties of what would now be called neural nets, amplifying his earlier suggestions that a mechanical system could exhibit learning ability. This was submitted to the NPL but never published in his lifetime. No advance was made with the construction of the ACE, and other computer projects took the lead. Indeed it was Newman, who had been the first reader of 'On computable numbers', and in charge of the electronic breaking of the ‘Fish’ ciphers, who was partly responsible for this. On his 1945 appointment to the chair of pure mathematics at Manchester University, he had negotiated a large Royal Society grant for the construction of a computer. Newman strongly promoted Turing's principle of the stored-program computer, but unlike Turing, intended no personal involvement with engineering. He conveyed the basic ideas to the leading radar engineer F. C. Williams, who had been attracted to Manchester, and the latter's brilliant innovation made possible a rapid success: Manchester in June 1948 had the world's first demonstration of Turing's computer principle in working electronics.

Although losing in this race, Turing ran very competitively in a literal sense. He developed his strength with frequent long-distance training, and top-rank competition in amateur athletics. Return to Cambridge gave him a circle of lasting friendships, particularly with Robin Gandy, who later inherited Turing's mantle as a leading mathematical logician. Although never secretive about his sexuality, he now became more outspoken and exuberant, and all conformity was abandoned. A mathematics student at King's College, Neville Johnson, became a lover.

Newman offered Turing the post of deputy director of the Manchester Computing Laboratory. Turing accepted, resigned from the NPL, and moved in October 1948. The meaningless title reflected an uncertain status. He had no control over the project, whose government funding was determined by its sudden necessity for the British atomic bomb, but he had a clear role as the organizer of programming for the engineers' electronics. Having lost the chance to put his name to the first working computer hardware, he now had the opportunity to shape the nascent world of programming, but although exploring advanced ideas, such as the use of mathematical logic for program checking, he largely missed this opportunity. His work on programming at Manchester, produced only as a working manual on machine-code writing, was limited in scope.

Turing hovered in 1949 between many other topics new and old. Out of this confused era arose, however, the most lucid and far-reaching expression of his philosophy in the paper 'Computing machinery and intelligence' (*Mind*, 59, 1950, 433–60). This, besides summarizing his view that the operation of the brain could be captured by a Turing machine and hence by a computer, also absorbed his first-hand experience with machinery. The wit and drama of the 'Turing test' has proved a lasting stimulus to later thinkers, and a classic contribution to the philosophy and practice of artificial intelligence. At the same time, in 1950, there emerged a clear direction for new thought: as Turing settled in Manchester, with a house at outlying Wilmslow, he had a fresh field in view—the mathematical theory of morphogenesis, the theory of growth and form in biology.

Outwardly an extraordinary change of direction, for Turing this was a return to a fundamental problem; even in childhood he had been observed 'watching the daisies grow' (caption, by Turing's mother, to a pencil sketch of him playing hockey, 1923, cited in Hodges, *Enigma*, 28). He fixed on the emergence of asymmetry out of initially symmetric conditions as the first thing requiring explanation, and answered that it could arise from the non-linearity of reaction and diffusion. He modelled hypothetical chemical reactions, and became the pioneer user of a computer in testing them numerically. He was elected to a fellowship of the Royal Society in 1951 for the work done fifteen years before, but equal originality was soon to appear: his paper 'The chemical basis of morphogenesis' (*PTRS*, 237, 1952, 37–72) was submitted that November. Long overlooked, it was a founding paper of modern non-linear dynamical theory.

### Trial and death

Turing was brought to trial on 31 March 1952 for his sexual relationship with a young Manchester man. He made no serious denial or defence, instead telling everyone that he saw no wrong in his actions. He was concerned to be open about his sexuality even in the hard atmosphere of Manchester engineering. To avoid prison he accepted, for a year, injections of oestrogen. His work on the morphogenetic theory continued. He developed his theory of pattern formation into the realm of spherical micro-organisms and plant stems, setting as a particular goal the explanation for the appearance of the Fibonacci numbers in the leaf patterns of plants. He also refreshed his early interest in quantum physics and relativity, with a hint of considering a non-linear mechanism for wave-function reduction.

Turing had also continued to be consulted by GCHQ, the successor to Bletchley Park, but homosexuals had become ineligible for security clearance, and he was now excluded. His personal life was now subject to intense surveillance by the authorities, who regarded his sexuality as a security risk. State security personnel also seem to have been responsible for what he described as another intense crisis, as police searched for a visiting Norwegian youth, and a holiday in Greece taken by Turing was unlikely to calm the nerves of intelligence officers. Though silent with his friends on questions of official secrecy, in other ways he sought greater intimacy with them and with a Jungian analyst. Eccentric, solitary, gloomy, vivacious, resigned, angry, eager—these were Turing's ever-mercurial characteristics, and despite his strength in defying outrageous fortune, no one could safely have predicted his future course.

Turing was found dead by his cleaner, at his home, Hollymeade, Adlington Road, Wilmslow, on the morning of 8 June 1954. He had died the day before of cyanide poisoning, a half-eaten apple beside his bed. His mother held that he had accidentally ingested cyanide from his fingers after an amateur chemistry experiment, but it is more credible that he had successfully contrived the manner of his death to allow her to believe this. At his inquest the verdict was suicide. His remains were cremated at Woking crematorium on 12 June 1954.

### Sources

A. Hodges,

*Alan Turing**: the enigma*(1983)Find it in your libraryGoogle PreviewWorldCat; repr.(1992)Find it in your libraryGoogle PreviewWorldCat

- E. S. Turing,
*Alan M. Turing*(1959) - R. Herken, ed.,
*The universal Turing machine*(1988) *Collected works of A. M. Turing*, ed. J. L. Britton, D. C. Ince, and P. T. Saunders (1992)- M. H. A. Newman,
*Memoirs FRS*, 1 (1955), 253–63 - A. Hodges,
*Turing**: a natural philosopher*(1997) - inquest documents, King's Cam.
- records of Woking crematorium

### Archives

- King's AC Cam., corresp. and papers
- University of Manchester, National Archive for the History of Computing, working papers

- Trinity Cam., corresp. with A. E. Ingham

### Likenesses

- Elliott & Fry, photograph, 1951, NPG [see illus.]
- Elliott & Fry, photograph, RS; repro. in Newman,
*Memoirs FRS* - W. Stoneman, photograph, RS
- photographs, King's Cam.

### Wealth at Death

£4603 5*s*. 4*d*.: probate, 20 Sept 1954, *CGPLA Eng. & Wales*