General Report on Tunny

---

23X Page 106

(e.g. at least ¾), unless B₁ is unusually small. Therefore, in most cases, the factor in favour of T₃ not allowing for competition is approximately q. It follows now by the general form of Bayes’ Theorem (21(f)) that the odds of theory T₁ allowing for all the evidence mentioned is usually approximated by
Where S₁ S₂ are the best and second best sigma-ages. The estimate of q must be based on statistics. It depends on the link and end and on N, d, quality of interception and B₂. However it is a reasonable approximation to assume to be independent of N and this enables the decibannage of the odds to be calculated easily, with the help of tables of

and

This is how the 'Χ–setting scoring charts' were constructed. The tables required for all types of runs are the form

Discussion of the subject may be found in R2 pp. 7, 27, 30 and R5 pp. 66, 73, 74, 83, 89.

23X     THEORY OF COALESCENCE (R4 pp. 83- 85)

Suppose that we know the setting of Χ₂, μ₆₁.μ₃₇ for a particular message on Χ₂ + Ψ'₁ limitation. Consider two different hypotheses about the Ψ₁ setting at a particular letter of the message. If these two Ψ₁ settings differ by s (s = 2, 3,...) it is a reasonable approximation to suppose that at the next BM dot there is a chance ½ that they will remain s apart, a chance ¼ that they will become (s+1) apart and chance ¼ that they will become (s-1) apart. The probabilities in the case of s = 0 and 1 (when the streams can even cross over) are more complicated. It is worth making the assumption that for s = 1 the probabilities are the same as for s > 1 and that coalescence is complete if s = 0. These assumptions simplify the problem and are unlikely to produce any serious error.

---

< previous

next >

Back to General Report on Tunny. Contents.

Back to The Enigma and the Bombe main page

Home