24D Page 122
converging, but only those which score reasonably well, say more then 10 pips. The others are 'doubted', i.e. ignored. The start is usually made from very few characters, more being added at each stage: towards the end, the standard of 10 pips may need to be lowered, and finally all characters are taken. While doubting is in use, the score does not necessarily increase at each stage.
Note 1: To take a wheel through write out ΔΧ1 (say) on a strip of paper which can be placed against each row in turn. It will suffice to include only new or changed characters, the earlier score for ΔΧ2 being added in.
Note 2: Taking a wheel through is in fact a short wheel-breaking run (25A: R1 pp 92, 94) and can be done on Colossus (25A) but computer time is often cheaper than Colossus time.
Note 3: For a suggested automatic converging machine R1 p 91.
Note 4: For the standard in taking characters during convergence R2 pp 9, 11, 15.
24D STARTS FOR CONVERGING RECTANGLES
(a) In the following paragraphs several methods will be described. All have been used operationally: the 9 x 9 flag and "E2" are probably the most popular with computers, who are normally allowed considerable freedom of choice. The skeleton was rather neglected, probably because it is unsuitable for depth 8, at one time the maximum for a Colossus rectangle. (R2 pp 4, 14, 17, 19. R3 p 21. R4 p 23.)
(b) Flagging.
In 24W(A) an "accurate" system of scoring the evidence that two wheels are alike (or opposite) is given. This may be applied to two rows of a rectangle to find weather the corresponding characters of ΔΧ2 are alike or unlike. The calculation is too long for starting rectangles quickly, but there are two simple approximations
(i) the sum of products of corresponding entries (Scalar product)
(ii) the sum of the smaller of every two corresponding entries, with a positive or negative sign according to whether the two entries are alike or unlike (Jacob flagging).
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