When Turing returned to Cambridge, he attended lectures given in 1939 by
Ludwig Wittgenstein about the
foundations of mathematics. The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes. Turing and Wittgenstein argued and disagreed, with Turing defending
formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths, but rather invents them.
Cryptanalysis During the Second World War, Turing was a leading participant in the breaking of German ciphers at
Bletchley Park. The historian and wartime codebreaker
Asa Briggs has said, "You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius." From September 1938, Turing worked part-time with the
Government Code and Cypher School (GC&CS), the British codebreaking organisation. He concentrated on
cryptanalysis of the Enigma cipher machine used by
Nazi Germany, together with
Dilly Knox, a senior GC&CS codebreaker. Soon after the July 1939 meeting near
Warsaw at which the
Polish Cipher Bureau gave the British and French details of the wiring of
Enigma machine's rotors and their method of decrypting
Enigma machine's messages, Turing and Knox developed a broader solution. The Polish method relied on an insecure
indicator procedure that the Germans were likely to change, which they in fact did in May 1940. Turing's approach was more general, using
crib-based decryption for which he produced the functional specification of the
bombe (an improvement on the Polish
Bomba). . Turing worked here in 1939 and 1940, before moving to
Hut 8. On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS. Like all others who came to Bletchley, he was required to sign the
Official Secrets Act, in which he agreed not to disclose anything about his work at Bletchley, with severe legal penalties for violating the Act. Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war. The others were: deducing the indicator procedure used by the German navy; developing a statistical procedure dubbed
Banburismus for making much more efficient use of the bombes; developing a procedure dubbed
Turingery for working out the cam settings of the wheels of the
Lorenz SZ 40/42 (
Tunny) cipher machine and, towards the end of the war, the development of a portable
secure voice scrambler at
Hanslope Park that was codenamed Delilah. By using statistical techniques to optimise the trial of different possibilities in the code breaking process, Turing made an innovative contribution to the subject. He wrote two papers discussing mathematical approaches, titled
The Applications of Probability to Cryptography and
Paper on Statistics of Repetitions, which were of such value to GC&CS and its successor
GCHQ that they were not released to the
UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician, "who identified himself only as Richard," said at the time that the fact that the contents had been restricted under the Official Secrets Act for some 70 years demonstrated their importance, and their relevance to post-war cryptanalysis: Turing had a reputation for eccentricity at Bletchley Park. He was known to his colleagues as "Prof" and his treatise on Enigma was known as the "Prof's Book". According to historian
Ronald Lewin,
Jack Good, a cryptanalyst who worked with Turing, said of his colleague:
Peter Hilton recounted his experience working with Turing in
Hut 8 in his "Reminiscences of Bletchley Park" from
A Century of Mathematics in America: While working at Bletchley, Turing, who was a talented
long-distance runner, occasionally ran the to London when he was needed for meetings, and he was capable of world-class marathon standards. Turing tried out for the
1948 British Olympic team, but he was hampered by an injury. His tryout time for the marathon was only 11 minutes slower than British silver medallist
Thomas Richards' Olympic race time of 2 hours 35 minutes. He was Walton Athletic Club's best runner, a fact discovered when he passed the group while running alone. When asked why he ran so hard in training he replied: Due to the challenges answering questions concerning what an outcome would have been if a historical event did or did not occur (the realm of
counterfactual history), it is hard to estimate the precise effect Ultra intelligence had on the war. However, official war historian
Harry Hinsley estimated that this work shortened the war in Europe by more than two years. He added the caveat that this did not account for the use of the atomic bomb and other eventualities. At the end of the war, a memo was sent to all those who had worked at Bletchley Park, reminding them that the code of silence dictated by the Official Secrets Act did not end with the war but would continue indefinitely.
Bombe Within weeks of arriving at Bletchley Park, now at
The National Museum of Computing on Bletchley ParkThe bombe searched for possible correct settings used for an Enigma message (i.e., rotor order, rotor settings and plugboard settings) using a suitable
crib: a fragment of probable
plaintext. For each possible setting of the rotors (which had on the order of 1019 states, or 1022 states for the four-rotor U-boat variant), the bombe performed a chain of logical deductions based on the crib, implemented
electromechanically. The bombe detected when a contradiction had occurred and ruled out that setting, moving on to the next. Most of the possible settings would cause contradictions and be discarded, leaving only a few to be investigated in detail. A contradiction would occur when an enciphered letter would be turned back into the same plaintext letter, which was impossible with the Enigma. The first bombe was installed on 18 March 1940.
Action This Day By late 1941, Turing and his fellow cryptanalysts Welchman,
Hugh Alexander and
Stuart Milner-Barry were frustrated. Building on the
work of the Poles, they had set up a good working system for decrypting Enigma signals, but their limited staff and bombes meant they could not translate all the signals. In the summer, they had considerable success, and shipping losses had fallen to under 100,000 tons a month; however, they badly needed more resources to keep abreast of German adjustments. They had tried to get more people and fund more bombes through the proper channels, but had failed. On 28 October they wrote directly to
Winston Churchill explaining their difficulties, with Turing as the first named. They emphasised how small their need was compared with the vast expenditure of men and money by the forces and compared with the level of assistance they could offer to the forces. As
Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect." Churchill wrote a memo to
General Ismay, which read: "ACTION THIS DAY. Make sure they have all they want on extreme priority and report to me that this has been done." On 18 November, the chief of the secret service reported that every possible measure was being taken. The cryptographers at Bletchley Park did not know of the Prime Minister's response, but as Milner-Barry recalled, "All that we did notice was that almost from that day the rough ways began miraculously to be made smooth." More than two hundred bombes were in operation by the end of the war.
Hut 8 and the naval Enigma at Bletchley Park, commissioned by
Sidney Frank, built from half a million pieces of Welsh slate Turing decided to tackle the particularly difficult problem of cracking the
German naval use of Enigma "because no one else was doing anything about it and I could have it to myself". In December 1939, Turing solved the essential part of the naval
indicator system, which was more complex than the indicator systems used by the other services. That same night, he also conceived of the idea of
Banburismus, a sequential statistical technique (what
Abraham Wald later called
sequential analysis) to assist in breaking the naval Enigma, "though I was not sure that it would work in practice, and was not, in fact, sure until some days had actually broken". For this, he invented a measure of weight of evidence that he called the
ban.
Banburismus could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes. Later this sequential process of accumulating sufficient weight of evidence using decibans (one tenth of a ban) was used in
cryptanalysis of the Lorenz cipher. Turing travelled to the United States in November 1942 and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington. He also visited their
Computing Machine Laboratory in
Dayton, Ohio. Turing's reaction to the American bombe design was far from enthusiastic: During this trip, he also assisted at
Bell Labs with the development of
secure speech devices. He returned to Bletchley Park in March 1943. During his absence,
Hugh Alexander had officially assumed the position of head of Hut 8, although Alexander had been
de facto head for some time (Turing having little interest in the day-to-day running of the section). Turing became a general consultant for cryptanalysis at Bletchley Park. Alexander wrote of Turing's contribution:
Turingery In July 1942, Turing devised a technique termed
Turingery (or jokingly
Turingismus) for use against the
Lorenz cipher messages produced by the Germans' new
Geheimschreiber (secret writer) machine. This was a
teleprinter rotor cipher attachment codenamed
Tunny at Bletchley Park. Turingery was a method of
wheel-breaking, i.e., a procedure for working out the cam settings of Tunny's wheels. He also introduced the Tunny team to
Tommy Flowers who, under the guidance of
Max Newman, went on to build the
Colossus computer, the world's first programmable digital electronic computer, which replaced a simpler prior machine (the
Heath Robinson), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages. Some have mistakenly said that Turing was a key figure in the design of the Colossus computer. Turingery and the statistical approach of Banburismus undoubtedly fed into the thinking about
cryptanalysis of the Lorenz cipher, but he was not directly involved in the Colossus development.
Delilah Following his work at
Bell Labs in the US, Turing pursued the idea of electronic enciphering of speech in the telephone system. In the latter part of the war, he moved to work for the Secret Service's Radio Security Service (later
HMGCC) at
Hanslope Park. At the park, he further developed his knowledge of electronics with the assistance of
REME officer Donald Bayley. Together they undertook the design and construction of a portable
secure voice communications machine codenamed
Delilah. The machine was intended for different applications, but it lacked the capability for use with long-distance radio transmissions. In any case, Delilah was completed too late to be used during the war. Though the system worked fully, with Turing demonstrating it to officials by encrypting and decrypting a recording of a
Winston Churchill speech, Delilah was not adopted for use. Turing also consulted with Bell Labs on the development of
SIGSALY, a secure voice system that was used in the later years of the war.
Early computers and the Turing test Between 1945 and 1947, Turing lived in
Hampton, London, while he worked on the design of the
ACE (Automatic Computing Engine) at the
National Physical Laboratory (NPL). He presented a paper on 19 February 1946, which was the first detailed design of a
stored-program computer.
Von Neumann's incomplete
First Draft of a Report on the EDVAC had predated Turing's paper, but it was much less detailed and, according to
John R. Womersley, Superintendent of the NPL Mathematics Division, it "contains a number of ideas which are Dr. Turing's own". Although ACE was a feasible design, the effect of the
Official Secrets Act surrounding the wartime work at Bletchley Park made it impossible for Turing to explain the basis of his analysis of how a computer installation involving human operators would work. This led to delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a sabbatical year during which he produced a seminal work on
Intelligent Machinery that was not published in his lifetime. While he was at Cambridge, the
Pilot ACE was being built in his absence. It executed its first program on 10 May 1950, and a number of later computers around the world owe much to it, including the
English Electric DEUCE and the American
Bendix G-15. The full version of Turing's ACE was not built until after his death. According to the memoirs of the German computer pioneer
Heinz Billing from the
Max Planck Institute for Physics, published by Genscher, Düsseldorf, there was a meeting between Turing and
Konrad Zuse. It took place in
Göttingen in 1947. The interrogation had the form of a colloquium. Participants were Womersley, Turing, Porter from England and a few German researchers like Zuse, Walther, and Billing (for more details see Herbert Bruderer,
Konrad Zuse und die Schweiz). commemorating Alan Turing's work at the
University of Manchester where he was a
Reader from 1948 to 1954 In 1948, Turing was appointed
reader in the
Mathematics Department at the
University of Manchester. He lived at "Copper Folly", 43 Adlington Road, in
Wilmslow. A year later, he became deputy director of the Computing Machine Laboratory, where he worked on software for one of the earliest
stored-program computers—the
Manchester Mark 1. Turing wrote the first version of the Programmer's Manual for this machine, was elected to membership of the
Manchester Literary and Philosophical Society, and was recruited by Ferranti as a consultant in the development of their commercialised machine, the Ferranti Mark 1. He continued to be paid consultancy fees by Ferranti until his death. During this time, he continued to do more abstract work in mathematics, and in "
Computing Machinery and Intelligence", Turing addressed the problem of
artificial intelligence, and proposed an experiment that became known as the
Turing test, an attempt to define a standard for a machine to be called "intelligent". The idea was that a computer could be said to "think" if a human interrogator could not tell it apart, through conversation, from a human being. In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better to produce a simpler one to simulate a child's mind and then to subject it to a course of education. A
reversed form of the Turing test is widely used on the Internet; the
CAPTCHA test is intended to determine whether the user is a human or a computer. In 1948, Turing, working with his former undergraduate colleague,
D.G. Champernowne, began writing a
chess program for a computer that did not yet exist. By 1950, the program was completed and dubbed the
Turochamp. In 1952, he tried to implement it on a
Ferranti Mark 1, but lacking enough power, the computer was unable to execute the program. Instead, Turing "ran" the program by flipping through the pages of the algorithm and carrying out its instructions on a chessboard, taking about half an hour per move. The game was recorded. According to
Garry Kasparov, Turing's program "played a recognizable game of chess". The program lost to Turing's colleague
Alick Glennie, although it is said that it won a game against Champernowne's wife, Isabel. His Turing test was a significant, characteristically provocative, and lasting contribution to the debate regarding artificial intelligence, which continues after more than half a century.
Pattern formation and mathematical biology When Turing was 39 years old in 1951, he turned to
mathematical biology, finally publishing his masterpiece "
The Chemical Basis of Morphogenesis" in January 1952. He was interested in
morphogenesis, the development of patterns and shapes in biological organisms. He suggested that a system of chemicals reacting with each other and diffusing across space, termed a
reaction–diffusion system, could account for "the main phenomena of morphogenesis". He used systems of
partial differential equations to model catalytic chemical reactions. For example, if a catalyst A is required for a certain chemical reaction to take place, and if the reaction produced more of the catalyst A, then we say that the reaction is
autocatalytic, and there is positive feedback that can be modelled by nonlinear differential equations. Turing discovered that patterns could be created if the chemical reaction not only produced catalyst A, but also produced an inhibitor B that slowed down the production of A. If A and B then diffused through the container at different rates, then you could have some regions where A dominated and some where B did. To calculate the extent of this, Turing would have needed a powerful computer, but these were not so freely available in 1951, so he had to use linear approximations to solve the equations by hand. These calculations gave the right qualitative results, and produced, for example, a uniform mixture that oddly enough had regularly spaced fixed red spots. The Russian biochemist
Boris Belousov had performed experiments with similar results, but could not get his papers published because of the contemporary prejudice that any such thing violated the
second law of thermodynamics. Belousov was not aware of Turing's paper in the
Philosophical Transactions of the Royal Society. Although published before the structure and role of
DNA was understood, Turing's work on morphogenesis remains relevant today and is considered a seminal piece of work in mathematical biology. Some of this work aimed to understand plant
phyllotaxy, specifically how plant
primordia form in a ring around the apical
meristem during plant growth and development, forming Fibonacci series. One of the early applications of Turing's paper was the work by James Murray explaining spots and stripes on the fur of cats, large and small. Further research in the area suggests that Turing's work can partially explain the growth of "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest". In 2012, Sheth, et al. found that in mice, removal of
Hox genes causes an increase in the number of digits without an increase in the overall size of the limb, suggesting that Hox genes control digit formation by tuning the wavelength of a Turing-type mechanism. Later papers were not available until
Collected Works of A. M. Turing was published in 1992. A study conducted in 2023 confirmed Turing's mathematical model hypothesis. Presented by the
American Physical Society, the experiment involved growing
chia seeds in even layers within trays, later adjusting the available moisture. Researchers experimentally tweaked the factors which appear in the Turing equations, and, as a result, patterns resembling those seen in natural environments emerged. This is believed to be the first time that experiments with living vegetation have verified Turing's mathematical insight. ==Personal life==