amok: aye, but it is not about the geometry as such, but how you move within it. The geometry are arguably Euclidean. take away the character and how it moves, and that's more or less what you are left with.
Starmaker: When you take away the character and how he moves, it's all just pixels on a flat screen.
that's a bit silly, as it boils everything and nothing down to... well... nothing. We can discuss the geometry of a virtual space without relating it to characters and movements within it, just by how it is constructed. or, if you like, how the pixels have been arraigned. You can have a virtual space with a geography, without any characters. Going with this, the virtual geography do not need to be flat, even though your representation (the screen) is. This would be to argue that the world is flat, because I have an image (i.e. an representation) of the earth and it is flat.
Starmaker: Now, because everythin boils down to pixels on a flat screen, several things make DROD notable.
- It's a game about advanced math.
- the Chebyshev distance is an intentional design decision, presented front and center, and is the only scoring metric. Even chess doesn't feature it as prominently, because how fast a king can cross the board straight vs diagonally is never an issue in actual play.
- what the game represents using it (a human walking over a tiled floor) cannot be realized in the real world even with constraints. Manhattan distance exists IRL, it's in the name; it models and corresponds to an actual lived IRL seamless 3d experience without the need for mathematical constructs. Chebyshev distance is "what if I charge you the same amount of arbitrary points for moving diagonally".
and then, the above, again becomes not a discussion of the geometry, but about the vectors and movement space within the set geometry. even though the game score you this numbers.
