Banburismus

The bombes were the bottleneck at Bletchley Park: too few machines and too many possible rotor orders in the naval Enigma. Banburismus was the preparatory work that made bombe time worth spending. Two ciphertexts were punched as holes into long paper sheets, printed in Banbury and therefore called banburies, and laid over each other on a light table. The sheets were slid past one another a position at a time, and at each offset the coincidences were counted — how often the same letter stood in the same place in both.

The point is that natural language is not uniformly distributed. Two texts that happen to have been enciphered at the same rotor position produce more coincidences than chance would: about one in seventeen rather than one in twenty-six. An excess was therefore evidence that the texts lay in depth, and so evidence about the rotors' relative starting positions. Any single observation was weak, so Turing added them up.

To add up evidence he needed a unit, and invented the ban — the base-ten logarithm of the odds ratio, so one ban is a factor of ten. In practice the working unit was the deciban, a tenth of a ban being roughly the smallest change in weight of evidence a human notices. This is sequential Bayesian analysis, some years ahead of Abraham Wald's independent version, and classified so long that Turing never got to publish it. The method was dropped in 1943, when American bombes made brute force cheaper than cunning.