So, I'm reading *Le ton beau de Marot* by Douglas Hofstadter (the guy who did *Godel Escher Bach*), which is about translation and communication and language.

In it, it uses a metaphor. It postulates a game of "chesh", which is identical to the game of chess, such that you could understand a play-by-play description of chess/chesh and consider them to be the same (i.e. a translation of chess to chesh is perfect - you can see the analogy to language I hope).

Anyway, Hofstadter asks a simple question about chesh - how would bishops be considered? There's no real "diagonal" on the hexagon board. He goes through various iterations of what diagonal might mean on a square lattice. There's the notion of 45-degree angles, which doesn't lend itself to exportation to hexagons (and 45 degrees with respect to what, exactly, on a hexagon board?).

From there, he goes to the idea of diagonal being about squares that "kiss" at their common corners, and nowhere else. But that doesn't really work on the hexagon structure either.

And from THERE he goes to the idea of "moving to the nearest neighbor of the same color." So you need to make sure your hexagons don't have any neighbors of one color. A two-color board doesn't work, but with three colors, you reach the 'aha' moment. From here we can go to answer "how will a chesh bishop move?" and now we have an answer.

What's more interesting is that these "diagonal" moves radiate out from each corner, so while they aren't close enough to "kiss" their neighbors, they can still blow each other kisses, so to speak. You move along the 'crease' between other hexes to get there.

Anyway - I want to do to wuxia what Hofstadter did to chess. But… what is the "square board" of wuxia? That's what I'm trying to investigate.