> I understand what you are trying to say, but I don't think it is entirely accurate to say that being able to define any point by a single coordinate is what makes it "one-dimensional."
You're missing the fact that several different definitions of dimension exist. If we're talking about topological dimension, then yes, the fact that you need exactly one parameter to define a point is what makes it one-dimensional.
I played around with this idea. First transforming the visual representation of the chess board and then seeing how I would describe the moves of the pieces and whether it was more / less intuitive.
It is easy to view the board as 64 consecutive spaces (left-to-right through the ranks, then snaking through the ranks, and then a circular representation. The circle was cool because the moves became rotations (a rook can stay in its octant or move an exact multiple of 45 degrees...). I did some 2D transformations with a one space skew on each rank (this made the bishop act simultaneously like a rook and knight which was interesting).
So it is easy to preserve the rules of chess and create a different visual representation of the board. Of course, every one I tried just made the game more difficult to understand. I wonder if there is a transform that could aid in understanding chess.
You're missing the fact that several different definitions of dimension exist. If we're talking about topological dimension, then yes, the fact that you need exactly one parameter to define a point is what makes it one-dimensional.