As a physics layperson I wonder if there are helpful analogies between a (high-dimensional and historically dynamic) semantic space and the curvature of physical space(-time?).
Maybe someone can help me understand the latter better?: Is its curvature like an additional dimension, with the peculiarity that it is not orthogonal but related to the other dimensions?
(I am trying to form an imagination in terms of vectors (or even a spreadsheet table if you will) rather than of 3D spatial analogies but I am not sure what "happens" there with adding curvature either.)