It seems to me like with 1 space dimension and 1 time dimension, different streams of information would not be able to cross each other. Intuitively the natural abstraction model makes sense and I would expect this stuff to work with more space dimensions too—but just to be on the safe side, have you verified it in 2 or 3 spatial dimensions?
(… 🤔 isn’t there supposedly something about certain properties undergoing a phase shift beyond 4 dimensions? I have no idea whether that would come up here because I don’t know the geometry to know the answer. I assume it wouldn’t make a difference, as long as the size of the graph is big enough compare to the number of dimensions. But it might be fun to see if there’s some number of dimensions where it just completely stops working.)
Well, it worked reasonably well with ER graphs (which naturally embed into quite high dimensions), so it should definitely work at least that well. (I expect it would work better.)
Another question:
It seems to me like with 1 space dimension and 1 time dimension, different streams of information would not be able to cross each other. Intuitively the natural abstraction model makes sense and I would expect this stuff to work with more space dimensions too—but just to be on the safe side, have you verified it in 2 or 3 spatial dimensions?
(… 🤔 isn’t there supposedly something about certain properties undergoing a phase shift beyond 4 dimensions? I have no idea whether that would come up here because I don’t know the geometry to know the answer. I assume it wouldn’t make a difference, as long as the size of the graph is big enough compare to the number of dimensions. But it might be fun to see if there’s some number of dimensions where it just completely stops working.)
Well, it worked reasonably well with ER graphs (which naturally embed into quite high dimensions), so it should definitely work at least that well. (I expect it would work better.)