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? > > > > > > > > > >
