Harry R. Schwartz

If you like chess but think it has too many dimensions, one of these one-dimensional chess variants might be the game for you. You might also want to avoid certain other variants, unless you’re a truly devout Star Trek fan.

I’ve seen references to four- and five-dimensional chess (which look like they might still be borderline-human-playable games), but a search for “n-dimensional chess” shows that not a lot of progress has been made for the general case. It seems like it wouldn’t be too hard to develop rules… rooks could move an arbitrary distance on paths parallel to the basis vectors, bishops could move diagonally on any plane, etc. Certainly the number of pieces would have to scale up, and it might be tricky to prove that checkmate is possible for all n, but someone who wasn’t prepping for finals could probably develop a consistent set of “playable” rules without too much trouble.

The real trick, of course, would be a consistent set of rules for chess in Hilbert space, a task which should perhaps be left to the real mathematicians.