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‘Prof ’s Book’ is a very personal document. It was evidently typed by him, with many mis-types,
and the corrections and diagrams are in his hand. Joan Clarke wrote of it:^13
I was the guinea pig, to test whether his explanation and worked example were understandable,
and my task included using this method on [that] half of the material [which Turing had] not used
in the example.
Amid the complex and not particularly mathematical reasoning of ‘Prof ’s Book’, and among
the details of the electrical installation required, we find:^14
In order to avoid bogus confirmations we cover up the constatations with shirt buttons as they
are used.
This is a splendid example of the way Turing would go straight to a creatively simple solution to
a problem—a trait that led the more conventional to brand him as eccentric.
Twiddling
As Chapter 12 explained, the bombes’ hypotheses went back to Hut 8 to be examined and
sometimes tested by hand. Cipher text was typed on a replica Enigma and plain German was
looked for in the output. Christine Ogilvie-Forbes was there too:^15
The bombes stopped every time they got a possible answer. Wrens would send these results to
us via the ‘spit and suck’ tube. There were two or three machines and we would set up each stop
and Twiddle, hoping for German: it didn’t take many letters.
But it was not always straightforward. As Eileen Plowman recalled:^16
As a linguist I enjoyed my later work, on machines and decoding messages into German, much
more. I was in charge of ‘twiddling’: adjusting settings to get out correctly the messages that had
not come out when decoded by other girls. I remember working on a message with Alexander
and Turing breathing down my neck and standing at my shoulder, waiting for the message to
come out correctly. The message was then taken straight off to High Command, and I later
heard that the U-boat had been sunk.
Conclusion: the factor method
This compressed account necessarily omits many features, some helpful to understanding,
some not. The Germans applied some rules which, though intended to enhance security, sim-
plified the task of the Banburists. For example, that there always had to be at least one naval
wheel among the three in use reduced what would have been 8 × 7 × 6 = 336 possible combina-
tions to 276. A further rule, that the same wheel should never be used in the same position in
consecutive two-day periods, could reduce it further (depending on the particular combination
of wheels) to as few as 105.
Neither Alexander’s nor Mahon’s history mentioned the word ‘Bayes’, and Turing himself
generally referred to ‘the factor’. However, a still-withheld history by Alexander entitled ‘The
factor method’^17 showed that the term ‘factor’ was widely used, and that Bayes’ theorem was