Listen With Others

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Listener 4195, Sum by Hotspur: A Setter’s Blog

Posted by Listen With Others on 14 July 2012

For decades, I had been both intrigued and saddened by the tragic story of the brilliant Alan Turing, hounded to death in my own lifetime. During a career in information technology, I often thought how he might be celebrated in a crossword, but it was not until after I retired that I set myself seriously to the task.

The image I had in my mind was that of a continuous reel of paper-tape, constantly updating the computer’s stored program. My (slightly simplified) view of the inherent process representable in the puzzle – but one found in authoritative reference works – was as follows: “The process used mimics the action of a Turing machine, which is determined by (1) the current state of the machine (2) the symbol in the cell currently being scanned by the head and (3) a table of transition rules, which serve as the ‘program’ for the machine.” Thus I conceived a process of splitting a row of twelve cells artificially into two, after which the set of incoming letters and their correspondents in storage, taken individually, would result in a new letter, by performing a ‘sum’ of the two, and this process could be infinitely repeatable.

Could this work? What proportion of the grid could support such a mechanism? Would enough real words emerge? Would they support a valid number of checked letters? It seems that I would have to accommodate a good number of jumbles, but the latter would have to be restrained, and could not be allowed to leak too deeply into the puzzle. And I wanted to include the key word ‘ENIGMA’ in the structure, as a reminder of Turing’s work at Bletchley Park.

After much trial and error (and no software aids!), I came up with the result. I also wanted to use a quotation to provide the mask for the clues. What I recalled vaguely I found in the Oxford Dictionary of Scientific Quotations – also available on the Web, of course. On reflection, I could have used the germ of ‘Can machines think?’ as a selective misprint device, which would have made cluing a lot easier, but the length was perfect for the puzzle size. My first stab for the word to be identified was weak, and the editors diligently prodded me to come up with a more integrative response. ‘COGITO’ fortunately had six letters, and the phrase ‘COGITO ERGO SUM’ provided an appropriate link for the title (which I had conceived early in the process). [Unfortunately, this is when the error occurred: one of my own making, which somehow eluded all checks. My apologies to all solvers.]

Writing clues took much longer than creating the grid. I happen to favour misprints, and the device of allowing them to appear anywhere in the clue gave me more freedom – much needed, given that every clue except one had its misprinted letter determined. I tried to make both versions of clue make some sort of sense, but that was not always possible. I had problems with the preamble – trying to make it concise and accurate without giving too much away. Again, the editors helped considerably with this aspect.

The puzzle had lain dormant for quite a while until the new Editors looked at it in 2010. After much negotiation (and I thank them publicly for their patience and insights), I gained approval. Then I realised that, with Turing’s centenary coming up in June 2012 – on a Saturday, as well! – it would be appropriate to delay publication until then. I suspected that that might make the puzzle easier to solve, given the attention given to Turing, and maybe solvers’ expectations that he would be commemorated in some way.

Incidentally, shortly before publication, I happened to be re-reading Peter Wright’s Spycatcher. In Chapter 13 he writes: “To send a message using a one-time pad, the addresser translates each word of the message into a four-figure group of numbers, using a codebook. So if the first word of the message is ‘defense’ [sic!], this might become 3765. The figure 3765 is then added to the first group on the one-time pad, say 1196, using the Fibonacci system, which makes 4851. It is, in effect, a double encipherment. (The Fibonacci system is also knows as Chinese arithmetic, where numbers greater than 9 are not carried forward. All cipher system work on the Fibonacci system, because carrying numbers forward creates nonrandom distribution.)” It occurred to me that this process – the obverse of the modifiable stored program concept, whereby the initial ‘one-time pad’ is replaced by a new one – was also represented by the mechanism I used in the puzzle.


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