Monday, 4 March 2019

Shannon, Entropy and Guardian Crosswords...

As part of the Fifteensquared discussion of a Crossword by Brummie in the Guardian last Wednesday, this thread started:-

Dr. Whatson says:
There’s something about Brummie you folks may find interesting.  His puzzles have the most helpful crossers of all setters here.   This is following the notion that the more unusual the letter (e.g. Z, J) the more helpful it is as a crosser, the more common (e.g. E, T) the less helpful.  I won’t go into details, but you can calculate the helpfulness via entropy, and his numbers are statistically significantly higher than the average.  At the other end of the spectrum is Chifonie, with Pan nipping at his heels.  Nobody else stands out. I don’t imagine this is intentional on any of their parts, but rather a side-effect of their grid-filling methods/software.
How is this useful?  Probably not much, except if you’re stuck on a Brummie, maybe that crosser is a B or a C.

thezed says:
Dr. Whatson @1 – re entropy, the first time I came across comments on this was in Claude Shannon (engineer, inventor of a juggling robot and, more famously, the man who invented information and communication theory, giving us Shannon’s Law) who discussed information contained in language in terms of its entropy. In his seminal paper “A Mathematical Theory of Communication” (free link) on page 15 he even briefly detours into the necessary redundancy in a language in order to be able to make crosswords possible. English is well-suited it turns out. He goes into more detail on language, but not on crosswords, in his “Prediction and Entropy of Printed English” (here). I’ve not read a biography recently so do not know if he was a cruciverbalist on top of his other talents, but I’ve always treasured that little detour in one of the most important papers of the 20th century.

Well, crikey, I thought.