As to intuition, I started wondering whether your sentences produce averages of distances between two random points, or between the origin and a random point (=vector length). Or whether that might be the same (?) For two points at a time I get:
avg %: +/ *: -/?2 1000 1000$0 12.8989 avg %: +/ *: -/?2 4000 1000$0 25.8177 avg %: +/ *: -/?2 10000 1000$0 40.8296 (if I'm not mistaken) So it is not the same. In 1D it's 0.33 vs. 0.5 and that ratio seems to hold in any dimension (which makes sense. Intuitively). Greetings, Ben On Fri, 15 Nov 2019 at 03:47, Raul Miller <[email protected]> wrote: > For example, here's an illustration of the concept that the average > distance between random points in a unit hypercube increases with the > number of dimensions: > > (+/%#)+/&.:*:?1000 1000$0 > 18.2652 > (+/%#)+/&.:*:?4000 1000$0 > 36.5102 > (+/%#)+/&.:*:?10000 1000$0 > 57.7314 > > Thanks, > > -- > Raul > > On Thu, Nov 14, 2019 at 11:16 AM Raul Miller <[email protected]> > wrote: > > > > I stumbled across this today: > > https://github.com/leopd/geometric-intuition accompanied by an > > assertion that you can find the eigenvectors for a hermitian matrix > > from its eigenvalues and the eigenvalues of its submatrices. I have > > not yet worked through the details of that, but it sounds plausible > > and might be of interest to some of you, here. > > > > But the repository itself covers a lot more ground than that. > > > > Anyways, the code is python, but a lot of it is fairly straightforward > > to re-implement, and there's good english descriptions and > > illustrations, also. So this looks like fun. > > > > FYI, > > -- > > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
