“My soul as a computer programmer cries out against the idea of representing N particles with N^2 distances between them; it seems wasteful”
Given 3 non-collinear points on a plane, any other point is fixed by its distances from these three points; and similar results hold in higher dimensions. You need O(N) numbers, not O(N^2) numbers to describe N particles.
“My soul as a computer programmer cries out against the idea of representing N particles with N^2 distances between them; it seems wasteful”
Given 3 non-collinear points on a plane, any other point is fixed by its distances from these three points; and similar results hold in higher dimensions. You need O(N) numbers, not O(N^2) numbers to describe N particles.