# Turing , Alan Mathison

Turing , Alan Mathison
(1912–1954) British mathematician
Turing, who was born in London, saw little of his parents in his early years. His father served in the Indian Civil Service before retiring in 1926; thereafter they lived in France to eke out a small pension. Turing was educated at Cambridge University, where he gained a fellowship at King's College in 1935. He spent the period from 1936 to 1938 at Princeton. During this time he published one of the most significant mathematical papers of the century, On Computable Numbers (1937).
He began by describing a hypothetical universal computer, since known as a Turing machine. It consists of an infinite length of tape divided into cells, a movable scanner/printer capable of reading the tape, printing, erasing, moving to the left and right, and halting. In each cell the tape has a symbol taken from a finite set of symbols (in a simple case 0 and 1). The control unit of the machine can be in one of a finite set of internal states (states S1, S2, S3, etc.). The machine has a ‘program’, which is a set of groups of five symbols. For example, one set of five symbols might be S101XS2, where X is R, L, or N. This is interpreted as meaning that the machine is in state S1 (the first symbol of the five) and reading 0 (the second symbol). In this state it replaces the 0 by 1 (third symbol). If X = R it moves to the next cell on the right, if X = L it moves to the next on the left, and if X = N it does not move (it halts). Finally it goes into state S2. The program, which can be used to do calculations, consists of a set of such quintuples (e.g., S100RS1, S110RS2, S201RS3, etc.).
Turing went on to define a set of integers N as computable if there was a Turing machine which, given any number m as input, will halt on 1 if m is a member of N, and halt on 0 otherwise. Using a variant of Cantor's diagonal argument Turing proved, echoing earlier work by Kurt Godel and Alonzo Church, that some sets of integers are not computable.
Soon after the outbreak of war in 1939 Turing joined the government Code and Cypher School at Bletchley Park, Buckinghamshire. The Germans were known to be using a coding device called ‘Enigma’. The basic model looked like an electric typewriter; the keyboard (input) was connected to the typed output by three rotors which changed position after each letter. This was equivalent to a polyalphabetic system with a periodicity of 263 = 17,576. The military version of Enigma added a number of complications. The positions of the rotors could be changed, increasing the periodicity to 105,456. Further improvements increased the periodicity to over a trillion. The Germans felt that the military Enigma was ‘very close to practical insolvability’.
Turing, along with a motley collection of mathematicians, linguists, and chess grandmasters, worked initially on the naval version of Enigma. The key innovation was the development of a computer, known as a ‘Bombe’, to handle the vast amounts of traffic. The name derived from the fact that early models designed by Polish analysts ticked very loudly. The Bombe allowed numerous possible solutions to be quickly checked against traffic and eliminated. By March 1940 they were reading some of the traffic and finding that it consisted of nursery rhymes sent as practice transmissions. By June 1941 they were reading operational naval traffic. This, however, was not the end of Turing's work. In early 1942 the German navy adopted a new Enigma system and added a fourth rotor to its design. The sinking of Allied shipping rapidly increased. The breakthrough came in December 1942. The Germans were transmitting weather reports daily by Enigma machines using only the first three rotors. Cribs of the weather reports were provided rapidly from other sources. It was therefore only necessary for the Bombes to work through the 26 possibilities of the fourth rotor to decipher fully encrypted traffic. By the new year Allied shipping could once more be diverted away from known U-boat positions. Shortly after this Turing left Bletchley Park for nearby Hanslope Park where he worked for the rest of the war on speech encipherment. Few individuals can have contributed so much to the war effort, or have saved so many lives, as Turing. In 1946 he was awarded an OBE for his services.
Turing was reluctant to return to Cambridge and a career in pure mathematics. Consequently he accepted a position at the National Physical Laboratory working on the design of a new computer, ACE (Automatic Computing Engine). He moved to Manchester University in 1948 to undertake similar work on the development of MADAM (Manchester Automatic Digital Machine).
During this period Turing produced two influential papers. In hisComputing Machinery and Intelligence (1950) he challenged his critics to specify how computers could be distinguished from intelligent human beings. In the imitation game the interrogator posed questions to two ‘individuals’ A and B; he was asked to determine from their written replies which answer came from a computer. Both can of course lie. The Turing test, as the procedure is now called, has been cited as a way of testing machine intelligence and still causes debate and experiment. Turing himself was in no doubt that one day computers would be able to think.
Turing's other paper, The Chemical Basis of Morphogenesis(1952), concerned the generation of form. How can an assemblage of cells develop, as with the case of a starfish, a five-fold symmetry? Or how does a sphere of cells, in the process of gastrulation, form a groove at a specific point? He argued that it was possible for differences in chemical concentration to develop, even though the original situation had a uniform concentration. Turing's original model was mathematical. Chemists have, however, since found that there are systems, namely reaction–diffusion models, which mimic Turing's ‘morphogens’.
Before he could develop his ideas further Turing committed suicide. He was homosexual and, for the times, fairly open about his life. A friend of a casual pick-up had stolen a few items of no great value from Turing's house and Turing reported the theft to the police. The culprit was arrested and in the course of investigations it was revealed that Turing had been sexually involved with a 19-year-old man. He was charged with gross indecency. Reluctantly he allowed himself to be persuaded to plead guilty and the court placed him on probation on the condition that he undergo hormone treatment. Although he seemed to find the process no more than irritating, and although his job remained secure, to the surprise of his family and friends he took his own life in 1954 by eating an apple dosed with cyanide.

Scientists. . 2011.

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