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• High-Dimensional Spaces Are Counterintuitive, Part Five

  All of this stuff about high dimensional geometry has been known for quite a while. The novel bit that this paper is all about is how to actually build a fast index for searching a high-dimensional space where the query has a strong likelihood of being Read More... Posted Monday, June 20, 2005 10:48 AM by Eric Lippert | 2 Comments Filed under: Performance, Rarefied Heights, Mathematics, High Dimensional Spaces

• High-Dimensional Spaces Are Counterintuitive, Part Four

  It's reasonably common to have a database containing a few thousand or million points in some high-dimensional space. If you have some "query point" in that space you might like to know whether there is a match in your database. If you're looking for Read More... Posted Thursday, June 09, 2005 1:57 PM by Eric Lippert | 5 Comments Filed under: Performance, Rarefied Heights, Mathematics, High Dimensional Spaces

• High-Dimensional Spaces Are Counterintuitive, Part Three

  My next book project is ready for copyediting, the wedding invitations are sent out, my bug count is under control, I've got a layer of levelling compound poured in the basement, there's no more ivy on my roof, and I’m rigging my sailboat some time this Read More... Posted Monday, June 06, 2005 3:57 PM by Eric Lippert | 6 Comments Filed under: Performance, Rarefied Heights, Mathematics, High Dimensional Spaces

• High-Dimensional Spaces Are Counterintuitive, Part Two

  The volume of an n-cube of edge length s is easy to work out. A 2-cube has s 2 units of area. A 3-cube has s 3 units of volume. A 4-cube has s 4 units of 4-volume, and so on -- an n-cube has s n units of n-volume. If the n-cube has edge of s>1, say Read More... Posted Friday, May 13, 2005 11:27 AM by Eric Lippert | 0 Comments Filed under: Performance, Rarefied Heights, Mathematics, High Dimensional Spaces

• High-Dimensional Spaces Are Counterintuitive, Part One

  A friend of mine over in Microsoft Research pointed out to me the other day that high-dimensional spaces are really counterintuitive. He'd just attended a lecture by the research guys who wrote this excellent paper and we were geeking out at a party about Read More... Posted Wednesday, May 11, 2005 1:24 PM by Eric Lippert | 10 Comments Filed under: Performance, Rarefied Heights, Mathematics, High Dimensional Spaces