**ALAN TURING**

Alan Turing was born on 23 June, 1912, in London. His father was in the Indian Civil Service and Turing’s parents lived in India until his father’s retirement in 1926. Turing studied mathematics at Cambridge University, and subsequently taught there, working in the burgeoning world of quantum mechanics. It was at Cambridge that he developed the proof which states that automatic computation cannot solve all mathematical problems. This concept, also known as the Turing machine, is considered the basis for the modern theory of computation.

In 1936, Turing went to Princeton University in America, returning to England in 1938. He began to work secretly part-time for the British cryptanalytic department, the Government Code and Cypher School. On the outbreak of war he took up full-time work at its headquarters,Bletchley Park.

Here he played a vital role in deciphering the messages encrypted by the German **Enigma machine**, which provided vital intelligence for the Allies. He took the lead in a team that designed a machine known as a bombe that successfully decoded German messages. He became a well-known and rather eccentric figure at Bletchley.

After the war, Turing turned his thoughts to the development of a machine that would logically process information. He worked first for the National Physical Laboratory (1945-1948). His plans were dismissed by his colleagues and the lab lost out on being the first to design a digital computer. It is thought that Turing’s blueprint would have secured them the honour, as his machine was capable of computation speeds higher than the others. In 1949, he went to Manchester University where he directed the computing laboratory and developed a body of work that helped to form the basis for the field of artificial intelligence. In 1951 he was elected a fellow of the Royal Society.

The son of a British member of the Indian civil service, Turing entered King’s College, University of Cambridge, to study mathematics in 1931. After graduating in 1934, Turing was elected to a fellowship at King’s College in recognition of his research in probability theory. In 1936 Turing’s seminal paper “On Computable Numbers, with an Application to the *Entscheidungsproblem* [Decision Problem]” was recommended for publication by American mathematician-logician Alonzo Church,who had himself just published a paper that reached the same conclusion as Turing’s.

In 1936 Turing and Church independently showed that in general this problem has no solution, proving that no consistent formal system of arithmetic is decidable. This result and others—notably the mathematician-logician Kurt Gödel’s incompleteness theorems—ended the dream of a system that could banish ignorance from mathematics forever. (In fact, Turing and Church showed that even some purely logical systems, considerably weaker than arithmetic, are undecidable.)

An important argument of Turing’s and Church’s was that the class of lambda-definable functions (functions on the positive integers whose values can be calculated by a process of repeated substitution) coincides with the class of all functions that are effectively calculable—or computable. This claim is now known as Church’s thesis—or as the Church-Turing thesis when stated in the form that any effectively calculable function can be calculated by a universal **Turing machine**, a type of abstract computer that Turing had introduced in the course of his proof. (Turing showed in 1936 that the two formulations of the thesis are equivalent by proving that the lambda-definable functions and the functions that can be calculated by a universal Turing machine are identical.) In a review of Turing’s work, Church acknowledged the superiority of Turing’s formulation of the thesis over his own, saying that the concept of computability by a Turing machine “has the advantage of making the identification with effectiveness…evident immediately.”

The machine can be described as a finite state control device (meaning that it has a finite number of states that control its operations), with a tape of unlimited length, divided into squares, upon which symbols may be written or stored. A sequence of actions can take place when a symbol is scanned by a read/write head and the machine is in a certain state. The sequence of actions is the “program.”

At any point in time, the finite state control will be in one state and the tape head will be scanning a single symbol, or square, on the tape. On the basis of this symbol and the current state, it will write a symbol on the square, or choose to leave the symbol alone, move the tape one square to the left or the right, and change to a “new” (possibly the same) state. All this constitutes a “move” of the basic machine.

The purpose of the machine was to provide a method for deciding mathematical questions. Turing had become interested in the foundations of logic, and one of the unsolved or open questions was the “decideability” problem.

**Code breaker**

In the summer of 1938 Turing returned from the United States to his fellowship at King’s College. At the outbreak of hostilities with Germany in September 1939, he joined the wartime headquarters of the Government Code and Cypher School at Bletchley Park, Buckinghamshire. The British government had just been given the details of efforts by the Poles, assisted by the French, to break the Enigma code, used by the German military for their radio communications. As early as 1932, a small team of Polish mathematician-cryptanalysts, led by Marian Rejewski, had succeeded in reconstructing the internal wiring of the type of Enigma machine used by the Germans, and by 1938 they had devised a code-breaking machine, code-named *Bomba* (the Polish word for a type of ice cream).. At the end of the war, Turing was made an officer of the Order of the British Empire for his code-breaking work.

**Computer designer**

In 1945, the war being over, Turing was recruited to the National Physical Laboratory (NPL) in London to design and develop an electronic computer. His design for the Automatic Computing Engine (ACE) was the first relatively complete specification of an electronic stored-program general-purpose digital computer. Had Turing’s ACE been built as planned, it would have had considerably more memory than any of the other early computers, as well as being faster. However, his colleagues at NPL thought the engineering too difficult to attempt, and a much simpler machine was built, the Pilot Model ACE.

* Automatic Computing Engine*

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