https://pointatinfinityblog.wordpress.com/2018/01/22/independence/comment-page-1/#comment-318

the squared distance from the origin when taking independent steps in one dimension is the same as when taking dependent steps, where each step is in a new dimension.

if you take as inner product the statistical expectation, then independent vectors are orthogonal. Independent things are formally analogous to orthogonal things! Nice

Matroid theory?