SImPSON | 421
probably relied on his judgement, taking other considerations into account too, rather than on
an automatic threshold.
The Banburies in the roof
I am grateful to Bletchley Park for enabling me to study the papers found in the roof of Hut
6 in some detail. Banbury One (see Fig. 13.2) is roughly torn off at column 114. The writing
along its top, ‘with TGC 11xx/159’, is explained in Chapter 13 as meaning: ‘when this message
and another with indicator TGC were compared, with an overlap of 159 letters, 11 repeats were
found of which four came as two bigrams’. There must have been much more to come beyond
column 114 to make an overlap of 159 possible. Banbury Two (see Fig. 13.3) lacks its first 36
columns through rough tearing, and ends (apparently through careful tearing, perhaps along a
crease) at column 160. The near coincidence of this figure with the 159 overlap invites conjec-
ture, but no plausible significance can yet be attributed to it.
Given these 11 repeats, how plausible is this alignment? By simple averaging, we should
expect 159 comparisons to yield 6 repeats if the alignment is false (repeat rate 1:26 for ran-
dom letters) or 9 repeats if it is true (repeat rate 1:17 for Naval German). Finding 11 repeats is
encouraging, so we turn to Bayes factors. The Bayes factor for 11 repeats in 159 comparisons
is (26/17)^11 × (16/17 × 26/25)^148 , which works out at about 4.7. Colloquially, this make-up of
159 comparisons is about 4.7 times as likely to occur in a true alignment as in a false one. The
logarithm of 4.7 is 0.6701, and (moving to the one-twentieth scoring units) 20 times this is 13.4.
So the alignment scores 13.4.
By the shortcut method using scoring units instead of Bayes factors, 11 repeats each scoring
3.7 make 40.7, while 148 no-repeats, each scoring –0.184, make –27.2, giving a net score of 13.5,
near enough to the 13.4 above. Unless there is other supporting evidence, this is far short of
what is needed to accept the alignment as probably true.
It is tempting to conjecture that Banbury Two, which carries no identification (probably
because its first 36 columns are missing), is the one with indicator TGC. But scoring them at the
alignment which provides a 159-letter overlap makes this look very unlikely.
The back of Banbury Two had been used for workings. It had been turned over and placed
vertically on the table with its torn left (starting) end at the top, and a column of letter sets jotted
down. The column is headed ‘105’ and then ‘GOY’ with the G in the characteristic hand of ‘with
TGC’ on Banbury One. There follow sets of five letters grouped as three and two and spaced
as ‘AAN NB’, in alphabetical order; perhaps some 50 sets in all. Some are marked ‘?’, others
‘poss’. Beyond the observation that these workings probably relate to the indicator system, their
purpose has not yet been discerned.
Decibans
In 1950 Jack Good recorded that:^9
Turing suggested further that it would be convenient to take over from acoustics and electrical
engineering the notation of bels and decibels (db). In acoustics, for example, the bel is the loga-
rithm to base 10 of the ratio of two intensities of sound.