How Turing - and Bayes - cracked Enigma

Written by Brian Tarran on . Posted in History of Stats & Science

Tomorrow sees the release of The Imitation Game, a film chronicling the work of mathematician Alan Turing (played by Benedict Cumberbatch, both pictured), who led efforts to unravel the German Enigma code - a development that helped the Allies win the Second World War. Turing employed several technologies and techniques in his work, including Banburismus, a process he invented which used sequential conditional probability to infer information about the likely settings of the Enigma machine.

In the book The Theory That Would Not Die, science writer Sharon Bertsch McGrayne describes Banburismus as 'a highly intensive, Bayesian system' that allowed Turing and colleagues to guess a stretch of letters in an Enigma message, measure their belief in the validity of these guesses - using Bayesian methods to assess the probabilities - and add more clues as they arrived.

'If it worked, it would identify the setting for two of Enigma's three wheels and reduce the number of wheel settings to be tested,' wrote Bertsch McGrayne. 'At a time when every hour counted, the difference could save lives.'

And it did. However, Turing wasn't the only code breaker at the top secret Bletchley Park to use Bayesian statistics in his work. In the June 2010 issue of Significance, Edward Simpson recounted his work in Block B to break the Japanese Naval cipher JN 25.

To mark the release of The Imitation Game, we have made Simpson's article open access. Follow the link below to read and download your copy.

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