140 | 13 INTRODUCING BANBURISmUS
Alexander’s history stated that a four-letter repeat was 100 times as likely to occur in German
naval language as in a random series of letters. With a six-letter repeat the likelihood was 15,000
times greater.
Experience showed that with these much more numerous pairs of messages, those to be
examined had to be confined to pairs with tetragram repeats or better, in order to keep the task
manageable. The ‘traffic’, the colloquial term for the totality of enciphered messages received,
was sent in batches to Freeborn’s Hollerith section, where this input was searched for tetragram
or better repeats between pairs of messages.
Enigma’s day generally ended, and the new one began, at midnight (the German Naval
Enigma in the Mediterranean was an exception) and the Freebornery’s punching was done
around the clock. Each day’s ‘Tetra catalogue’, listing all the tetragram or better repeats found, was
delivered to Hut 8 by instalments throughout the day. Iris Brown joined Hut 7 in February 1942,
at age 17; later the assistant to Freeborn’s secretary, she was initially a ‘message girl’. She recalls:^15
In that winter I was taking original Tetra messages back to Hut 8 many times a day.
Alexander acknowledged the importance of the Freebornery’s search for repeated groups:^16
Without this work we should have been helpless and we owe much to the efficient and speedy
service we received.
weighing the evidence
So from the two parallel operations of sliding Banburies and finding tetragram repeats, both
following Basile Bouchon in exploiting holes punched in cards, Hut 8 had an array of pairs of
messages which might, from the evidence of those repeated letters, be aligned in depth. An
arithmetic was needed for deciding how much evidence was ‘enough’—that is, sufficient to
decide that a particular speculative alignment could be relied upon before using it in the com-
plex reconstruction process that was to follow. Donald Michie, echoing Max Newman, called
the scoring system that Turing devised for this purpose his ‘greatest intellectual contribution
during the war’.^17
Neither of the histories explains the derivation of this arithmetic: it was in fact based on
Bayes’ theorem and the calculation of the mathematical probabilities of different numbers of
repeats, as Chapter 38 explains. But with the Enigma details changing daily and the Battle of
the Atlantic in the balance, there was no time for calculating individual probabilities. Instead,
Hut 8 devised a streamlined process of scores that required only to be added or subtracted by
non-mathematical (but clever) ‘girls’. This process borrowed the ready-to-hand decibel unit
from acoustics and re-named it the ‘deciban’, and eventually worked in units half that size, the
half-deciban or hdB. Chapter 38 fills in the main details of this most elegant procedure.
Then the really hard bit
So far this chapter has considered only the first part of the cryptographic dictionary’s definition
of ‘Banburismus’. The second part of the definition is opaque, because the process it describes