Ah, then when you were referring to the ant example, you are assuming the constraint that the ant is moving only along the string. You did not specify that cons

Ah, then when you were referring to the ant example, you are assuming the constraint that the ant is moving only along the string. You did not specify that constraint in your original phrasing, and I imagined it as -- if the string was rolled into a ball, the ant can travel in any direction on the ball. This would cause it to appear to teleport if observed from a 1D point of view. My question about dimensionality would be about the decomposition of the 2D coordinate of the chessboard into a 1D state space. First of all, all games with discrete positions would be 1D games, correct? Even the 5D chess game, since time and timelines can also be encoded into state space. This would also seem to apply to every computer game as well, since the state space can be taken to be the snapshot of any data at a certain time step in the computer. And finally, if we take that to the limit, as we approach infinitely small time steps, the state space would get infinitely less granular, and we could map any N-dimensional space into 1D. That doesn't seem right, where is the fallacy in this line of reasoning?