# Alan Turing: The Enigma

In his foreword, Douglas Hofstadter writes: "Atheist, homosexual, eccentric, marathon-running English mathematician, A.M. Turing was in large part responsible not only for the concept of computers, incisive theorems about their powers, and a clear vision of the possibility of computer minds, but also for the cracking of German ciphers during the Second World War". This one sentence says who Turing was. The biographer Hodges, has an obvious empathy for his subject, being a mathematician himself, working in fundamental physics in Oxford and activist in the gay liberation movement of the seventies. He compiled a well researched biography, and his background allowed him to sketch not only the war history, but also the social situation of English academic life of Turing's lifespan, and to give a clear exposition of Turing's philosophical and scientific ideas concerning mathematics and computer science. He continues promoting Turing and his work in the media and he is maintaining the website www.turing.uk.org.

The essentials of the biography have been widespread since the centennial year 2012 (Turing was born 23 June 1912). His father worked for the Indian Civil Service and the parents hopped between England and India, leaving Alan and his elder brother John with a retired couple. During his school days at Sherborne Alan read Einstein's work at the age of 16 and he has been interested in quantum physics ever since. He lost his faith and became a fervent atheist when his fellow student and dear friend Christopher Morcom died in 1930. During his university studies at King's College, he started his first major work about Turing machines. These theoretical devices were a formal mechanization for solving Gödel's *Entscheidungsproblem*. His paper was published shortly after the results of Church who obtained the same result via lambda calculus. Turing showed later that both approaches were equivalent. He visited Church in Princeton where he got his PhD in 1936. The *Institute of Advanced Studies* (IAS) there was a point of attraction for the most prominent mathematicians and physicists of that time like Einstein, Weyl, Von Neumann, Gödel, and Pauli. Several of these were fleeing Europe for the impending Nazi threat. During his US stay, Turing also designed an electro-mechanical binary multiplier and studied cryptanalysis. Back in Cambridge in 1938, Wittgenstein, teaching there on the foundations of mathematics, disagreed with Turing's formalistic approach.

Turing's knowledge of cryptanalysis was very useful when he was recruited for the *Government Code and Cypher School* (GC&CS). The primary goal was to decode the German messages during the war that were encoded via the *Enigma* typewriters by varying the position of rotors and the dashboard wirings. The Poles brought some elementary knowledge of this machine to the British GC&CS at *Bletchley Park* and Turing, joining an army of code breakers, could automate the process which resulted in *the bombe* an electro-mechanical machine simulating the different settings of the rotors and wirings. Turing was essential for the design of this machine and improvements in subsequent devices like the *Colossus*. The Colossus was designed by Tommy Fowles to analyze the Lorentz cipher. It used a statistical analysis that went well beyond the bombe that could only make yes or no decisions. It was basically the first programmable digital computer. Turing's reports on code breaking were only released by the British secret service in 2012.

During this period he developed a passion for long distance running. His mother didn't know about his secret work and considered him eccentric. For his coworkers he was the "Prof", non-conformist and on his own. Although homosexual, he was for a short period engaged to Joan Clarke, one of the code breakers. In 1942 he traveled to Princeton for a year to collaborate with the US Navy on cryptanalysis, and he also visited the people building the first computing machines. At *Bell Labs* he met Nyquist and Shannon who were working on speech processing. After his return he exchanged Bletchley Park for *Hanslope Park* where he designed a device to scramble voice communication (code name *Delilah*).

After the war, he joined the *National Physical Laboratory* (NPL) in Teddington where he worked on the *Automatic Computing Engine* (ACE) project and he produced a report in 1946 for a computer, which contained not only the data but also the instructions to process it, a blueprint for the modern computer. To some extent it was a realization of ideas already present in his abstract Turing machine. His report was well superior to the report of Von Neumann on the EDVAC project. But the pressure and priorities imposed by the war removed, the project resulted in a working test run only in 1950. In 1948 he was appointed reader at the *University of Manchester* where he continued working on abstract mathematics trying to simulate the human mind. It was then that he proposed the Turing test in an attempt to identify intelligence in a man or a machine. While trying to understand the brain, he started research on the chemical basis of morphogenesis.

When he and the much younger Arnold Murray, engaged in a sexual relationship, things went terribly wrong. This "gross indecency" was accidentally detected when the police was investigating a burglary at Turing's home. He was condemned in 1952 to hormonal treatment which made him impotent. Two years later, on 7 June 1954, totally unexpected, he was found dead in his home, an apple half eaten nearby and cyanide in the room. The police investigation concluded it was suicide.

Turing was always interested in the theoretical aspects and the possible (abstract) generalizations. For example, these computers could break a code, but he was also thinking of using them for computing the zeros of the zeta function to verify the Riemann hypothesis, an aborted project from his student years at King's College. The practical applications were almost fortunate side effects. He also never considered himself as the leading figure on top of the ladder. He was uncomfortable when people depended on him. Somewhat unorganized, a clumsy negotiator, and politically eccentric, he preferred to work on his own most of the time. With many quotations from letters, reports, and testimonies by people who have known Turing, Hodges could give a very clear picture of Turing's character, his mind, and how he arrived at his results. Although his contributions seem quite diverse, in the end they are all rather closely related and very logically connected. It is indeed *the* ultimate biography of Alan Turing. It will bring you as close as possible to his enigmatic personality.

**Submitted by Adhemar Bultheel |

**2 / Jan / 2015