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Are the Androids Dreaming Yet?

simply translated as 'the Decision Problem' – could you decide the truth
of a mathematical statement using some sort of automatic computation
– an 'algorithm' as we now call it?

It is difficult to imagine, but Turing worked on 'computing' before
the invention of the computer. When he talked of computing, he
meant the abstract idea of doing something mechanically. The nearest
thing he had to a 'computer' at the time was a human mindlessly but
methodically calculating something with pencil and paper! The scientific
paper he submitted to the London Mathematical Society described both
the theoretical basis of computing, and the design of a general-purpose
computing machine: the forerunner of all modern computers.

At the time, only a handful people in the world could assess
Turing's paper. One of them, Alonzo Church, was based at the Institute
of Advanced Mathematics in the USA on the Princeton University
campus, next door to the Institute for Advanced Study that housed
Einstein. Turing travelled to America in 1937 and completed his doctoral
thesis at Princeton. He might have stayed, but Europe was heating up
and war seemed inevitable, so Turing returned to England to take up
a part-time job in the government code-breaking branch. Here he was
able to indulge his passion for hands-on engineering, experimenting
with the newly invented valve technologies. When war finally broke out
Turing was ordered to report to Bletchley Park, just north of London.
This was to be the home of the top-secret British code-breaking group
tasked with cracking Enigma. Turing's first task was to debrief the
Polish mathematicians and see what they had discovered. The Polish
mathematicians had seen there were flaws in Enigma that made it repeat
itself. They had made a copy of the machine to test different coding
configurations and had been routinely cracking Enigma for 6 years,
but the Germans had been getting smarter and it was taking longer and
longer to crack the codes. Turing realized he could apply the Polish ideas
in a more general way and break the codes on an industrial scale. He was
installed at Bletchley Park to lead the project.

Initially he was successful but as the war continued, Enigma
developed subtleties making it harder to break. At one point, it was
taking a whole month to break a single day's messages. Turing realized
the only solution was to use computer technology to fully automate the
decryption. He built a computing machine that could simulate thousands
of Enigma machines and try out all the possible settings in a short space
of time. The machine acquired the nickname 'a bombe', perhaps because
of the ominous ticking sound it made as it calculated (or maybe as a
reference to the smaller Polish machines).

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