Thanks, folks. On Fri, Jul 22, 2011 at 2:55 PM, Ted Dunning <[email protected]> wrote: > Sean is correct. > > And this will change the distances, but not the ratios of the distances > because small patch of the sphere is nearly isometric with the original > space. > > > On Fri, Jul 22, 2011 at 12:46 AM, Sean Owen <[email protected]> wrote: > >> I think Ted is suggesting augmenting the vectors to (1,0,0,100) and >> (10,0,0,100) and projecting onto the unit sphere in 4 dimensions. Then the >> distance is not 0 on the surface of that sphere. >> >> On Fri, Jul 22, 2011 at 7:29 AM, Jake Mannix <[email protected]> >> wrote: >> >> > (1, 0, 0) and (10, 0, 0) have very large distance in R^3, but 0 when >> > projected onto >> > the a patch near the north pole of S^4, while other pairs of vectors may >> > have >> > (nearly) unchanged distances. >> > >> > Am I misunderstanding what the question was? >> > >> > On Thu, Jul 21, 2011 at 9:43 PM, Ted Dunning <[email protected]> >> > wrote: >> > >> > > Embed onto a very small part of S^4 >> > > >> > > On Thu, Jul 21, 2011 at 9:14 PM, Jake Mannix <[email protected]> >> > > wrote: >> > > >> > > > Think about it in 3-dimensions, how can this work? >> > > > >> > > >> > >> >
-- Lance Norskog [email protected]
