> we are really not that great thinking in higher dimensions.
Normally when you've hit 4d arrays, are you not dealing with a grid of grids?
That is say you've got a 2×3×4×5 array, another way to think about that is you've got a 2×3 matrix of 4×5 matrices. (APL example to show what I mean: https://tryapl.org/?clear&q=%7B%E2%8D%B5%2C%E2%8D%A5%E2%8A%8...)