Linear Chess

Published 22 Nov 2010.
Tags: chess, games, math.

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.