The diagonal argument of Georg Cantor is an elegant introduction to the world of infinities. You write down multidigit numbers, generally arranged in columns, and then change the first digit in the first, the second digit in the second, and so on. The number revealed by reading down the diagonal (and which crossword solver doesn’t enjoy reading down diagonals?) is necessarily not in your original list. That remains true however long your list may be, even unto infinity and beyond.
And, of course, presentations of the diagonal argument tend to use square arrays of numbers. Look, says the eye, there’s something like a crossword grid on this page/site.
The EV Crossword has limited space, so an infinite diagonal was not on the cards. Cantor’s own name was a sensible length, and ‘diagonal argument’ being (8,8) simply begged for symmetrical positioning.
I can’t now recall quite how I settled on the grid as presented. I certainly wanted solvers to amend a fixed 6×6 square of letters, which meant establishing that square first. It might be possible to produce a grid where such a square lurks within normally clued across and down answers. The additional constraint of having word 1 alterable by changing letter 1 to C, word 2 ditto with letter 2 to A, and so on, looked a bit fearsome. So I imagine that is how I ended up with the sort of doughnut shape.
Cramming the six initial words also into the dough of the nut, along with DIAGONAL ARGUMENT, took multiple iterations and tweaks, far more than usual, especially with the added requirement of the hidden 6-letter entries protruding into the ‘hole’ to provide some structure for the central entries. Change one of those, and you changed one of the six central entries (with added constraint), which fed back into the outer section, which led to a change in one of the hidden 6-letter words…and so on. Even my ‘final’ copy had a note saying ‘grid changed’ and the wrong clue numbering as a result of bars shifting.
Got there in the end, even if WARMED to WARTED still rankles. It’s probably the nearest to a numerical puzzle you’ll get from me!
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