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For each possible setting of the rotors, which had of the order of 10 19 states, or 10 22 for the four-rotor U-boat variant, the bombe performed a chain of logical deductions based on the crib, implemented electrically. rotor order, rotor settings and plugboard settings), using a suitable crib: a fragment of probable plaintext. The bombe searched for possible correct settings used for an Enigma message (i.e. At Bletchley Park, Turing built an electromechanical machine, the bombe, that could help break Enigma more effectively than the Polish bomba kryptologiczna, from which its name was derived. IG spends a lot of telling the story of Turing’s role in decrypting messages sent by the Enigma machine. Not a bad result for an undergraduate at King’s College.
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The movie doesn’t go on to mention that Turing showed that the halting problem for Turing machines was undecidable, but that’s OK since Von Neumann acknowledged that the central concept of the modern computer was due to this paper. As many of you know, he proved that such a machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. The movie even shows a copy of the 1928 article by David Hilbert’s paper “On Computable Numbers, with an Application to the Entscheidungsproblem (Decision Problem).” It goes into some detail describing what a Turing machine is. A couple of the revelations might spoil your enjoyment but you have been warned.ĬB spends a fair amount of time on Turing’s work on computability.
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I guess at this point I should give a SPOILER ALERT that I am about to describe some pivotal events in his life, which are revealed in the movie. Remarkably these two films give almost disjoint accounts of his life. The Imitation Game (IG) is a great movie which has brought a lot of attention to Alan Turing but if you like it, you should also watch the 2013 film Codebreaker (CB), which can be streamed on Netflix.