[bear8642]

> 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...)

[cycomanic]

I agree in principle, but if you try to do operations about submatrices (and in a way that's what the article is about) it gets tricky quite quickly. I actually often find it even harder to understand if there are multiple nested loops, but that might also be because I use numpy much more often.

[thaumasiotes]

> 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.

No, a grid of grids is the same thing as a grid.

You can lay out some 4×5 matrices within a 2×3 pattern to have something to look at, but the result is significantly less structured than the 4-dimensional space that the array represents.

    ***** ***** *****
    *A*** ***** *****
    ***** ***** *****
    ***** ***** *****
    
    ***** ***** *****
    ***** ***** *****
    ***** ***** *****
    ***** **B** *****

How close are the points A and B? The taxicab distance is 5.