Sandy Zabell on Alan Turing & the Power of Probability in Cryptography 🧩

In the years before World War II Bayesian statistics went into eclipse, a casualty of the combined attacks of statisticians such as R. A. Fisher and Jerzy Neyman. During the war itself, however, the brilliant but statistical naif Alan Turing developed de novo a Bayesian approach to cryptananalysis which he then applied to good effect against a number of German encryption systems. The year 2012 was the centenary of the birth of Alan Turing, and as part of the celebrations the British authorities released materials casting light on Turing's Bayesian approach. In this talk I discuss how Turing's Bayesian view of inductive inference was reflected in his approach to cryptanalysis, and give an example where his Bayesian methods proved more effective than the orthodox ones more commonly used. I will conclude by discussing the curious career of I. J. Good, initially one of Turing's assistants at Bletchley Park. Good became one of the most influential advocates for Bayesian statistics after the war, although he hid the reasons for his belief in their efficacy for many decades due to their classified origins.