First, a Turing Machine, just for fun:
Nearby Rich says:
Just to start with an aside, for me, Alan Turing is a huge figure in several fields: mathematics, computer science, programming, computer systems engineering, artificial intelligence… but also probability and cryptanalysis. He managed to get a lot done even in his short life. I thoroughly recommend Andrew Hodge’s biography Alan Turing: The Enigma.
But here Rich challenges us with two or three related questions: the role of Turing in cracking Enigma; the roles of the Polish mathematicians; and the public perception of those respective roles. I would never be surprised to find Hollywood presenting a story which is written to sell and to entertain rather more than it is written to inform. To the extent that Hollywood steers the public perception, we shouldn’t be surprised to find misattribution and distortion in the public mind.
The fundamental flaw in Enigma, as I understand it, is that a letter will never be mapped to itself. That feels like a tiny flaw indeed. And yes, I think the Poles saw a way in, and the technique was smuggled out and found its way to Bletchley Park. But, I believe, it was also necessary for the Axis powers to make design errors in their procedures and operational mistakes in their usage. Enigma as deployed over the course of the war became ever more difficult to crack, and it was a race between the cryptographers and the cryptanalysts. Had Enigma been used from the start as it was at the end, it might well never have been cracked.
(Among the great innovations brought to bear in decryption was the diagonal board - if you’re so inclined, it’s well worth trying to understand that. It enormously reduced the search space that the Bombes explored.)
Anyway, enough of my vague statements - here are some links. First, GCHQ on Turing:
He met Polish counterparts in Paris in January 1940, a meeting at which they gave him the insights he needed to build on their foundations by designing the Bombe. This was the first special-purpose cryptanalytic machine, and made major contributions to the exploitation of German Naval Enigma, before moving on to work on secure speech systems.
Here’s Tony Sale’s take: Alan Turing, the Enigma and the Bombe.
Graham Ellsbury’s site is very technical: The Enigma and the Bombe
Andrew Hodges again: The Military Use of Alan Turing which is part of his extensive website on Turing, a companion to his biography mentioned above.
This article will review Alan Turing’s mathematical work in the Second World War, discuss how this relates to the history and philosophy of computing, and then raise the wider question of his place in mathematics and war.