[Doctor Stochastic]

It's trivial to see that the first of the (curse of dimensionality) guy's pictures looks random and the second doesn't. It's obvious that he want's to define "random" as something different from what the rest of the world means. He is confused by the terms "random" and "equally distributed." A random choice of points will be equally distributed but it will not be expected to be the most equally distributed set of points in a region.

I did use the term "Curse of Dimensionality" in my dissertation about 30 years ago. I think I got the term from Bellman.

[Alamo-Girl]

Thank y’all so much for your posts!

I was working on a reply last night, but a giant thunderstorm came through and I lost it. Sigh...

Your experiment sounds very interesting, Doctor Stochastic! Please let us know if you follow-through on it!

It seems to me that time is a dimension in wave propagation and hence time is contiguous in 4D, i.e. jumping is a technical deficiency of numbering and not time. But continuity of time is turned on its head when we examine betty boop's extra time dimension possibility! IOW, I believe betty has trumped Lynds.

It seems we always come back to randomness, Doctor Stochastic. I am not aware of any randomness that is uncaused (including Brownian motion) and thus the very definition of “random” as a natural event is a tongue-in-cheeker for me.

But with regard to the “Curse of Dimensionality” article – I read his use of the term “random points” as if it were “arbitrary points.” The bottom line is that the article is helpful to me in conceptualizing higher dimensions, e.g. hypercubes.