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just the last question - Hilbert's
Entscheidungsproblem
(the decision problem).
Enter Alan Turing and his amazing machines.
Turing machines
At the age of nineteen, Turing (
B.6.5
) went to King's College, Cambridge in
1931 to study mathematics. He passed his final mathematics examinations at
Cambridge in 1934 with a distinction and was awarded the title of “Wrangler,”
a title still used at Cambridge to denote the top mathematics students each
year. In the spring of 1935, Turing attended a lecture course given by Max
Newman on “The Foundations of Mathematics.” Unusual for mathematicians at
Cambridge at that time, Newman was an expert in the emerging field of topol-
ogy and had also followed the progress of mathematical logic and set theory
since the efforts of Frege and Russell. In particular, Newman had attended the
1928 international congress at which Hilbert had announced his challenge to
B.6.5. Computer-generated image of Alan Turing. Alan Mathison Turing (1912-54) was one
of the founders of computer science. His name is mainly associated with Turing machines,
universality, the Church-Turing thesis, and artificial intelligence and the Turing Test. After
attending Sherbourne “public school” - in England this means a private school - Turing
went to King's College, Cambridge in 1931 to study mathematics. He was twenty-four when
he wrote his groundbreaking paper, “On Computable Numbers, with an Application to the
Entscheidungsproblem.” Turing was a good long-distance runner - his best time for the marathon
was only eleven minutes slower than the winning time at the 1948 Olympics - and, for recreation,
he liked to go running in the countryside around Cambridge. He said later that he conceived
the idea of how to answer Hilbert's third question while lying in the meadow at Grantchester, a
village near Cambridge, at a break in one of his runs. It is no exaggeration to say that this paper is
one of the cornerstones of computer science.
During the war he worked on code breaking at Bletchley Park, for which he was honored as an
Officer of the British Empire. After the war, Turing returned to his ideas of building a physical real-
ization of his abstract machine. At the U.K. National Physical laboratory (NPL) in 1945 he designed
the Automatic Computing Engine (ACE) which could have been the first stored-program computer.
Because of bureaucratic delays for the ACE project, Turing became frustrated and left NPL. In 1949
he started to work at the computing laboratory in Manchester where he developed programs for
the Manchester Mark I computer.
The following year Turing published the paper “Computing Machinery and Intelligence” in
which he speculated about whether computers can think. In this paper he described what has
become known as the Turing test. This is a purely operational definition of intelligence. A human
interrogator poses questions to a closed room containing either a computer or a person. If the
interrogator is unable to tell which is the computer and which is the person from the responses
the computer is deemed to have Turing's test for intelligence.
In 1952 homosexuality was still illegal in Britain and Turing was charged with committing
a homosexual act by Manchester police. As an alternative to prison Turing opted for hormone
therapy which had some unpleasant side effects. Turing died in 1954 after eating an apple contain-
ing cyanide; an inquest ruled his death to be suicide. Details of his school days, his foundational
research on computability, his work on the German Enigma machine at Bletchley Park, and the
tensions caused by his homosexuality are contained in a wonderful biography by Andrew Hodges,
Alan Turing: The Enigma of Intelligence.
In September 2009, after an Internet campaign, the then
British prime minister Gordon Brown issued an official public apology “for the appalling way he
[Turing] was treated.” Finally on the 24 December 2013, Turing was given a posthumous pardon by
the Queen.
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