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Edward Simpson CB ceased being an active statistician in 1947, when he joined the Civil Service. But statistics owes him much. He is the Simpson of Simpson's index of diversity1 and of Simpson's paradox2, the bizarre apparent contradiction which he published in 1951 and which has puzzled students of statistics ever since. Perhaps more importantly, for the world as well as for statistics, from 1942 to 1945 he was a code breaker at Bletchley Park, where Alan Turing and others broke enemy ciphers and the world's first modern computer was developed. Here Edward Simpson tells the hitherto unpublished story of the part that Bayesian statistics played in breaking two of the enemy ciphers.