From: ben.usenet@bsb.me.uk   
      
   Tim Rentsch  writes:   
      
   > Ben Bacarisse  writes:   
      
   >> The "other" average, minimises the sum of the of the angular   
   >> distances.   
   >   
   > I think you mean it minimizes the sum of the squares of the   
   > angular distances.   
      
   Yes thanks.  I originally thought I'd write an abbreviation but then I   
   convinced myself I would not forget any of the "squares of"s.  Proof   
   reading might have been useful too.   
      
   >>> and the center of mass is never on the unit   
   >>> circle (not counting the case when all the time values are the   
   >>> same).  Even so it's an interesting way to view the distinction.   
   >>   
   >> It's more interesting because it really is about chords!   
   >   
   > I don't buy the "really" here.  The center of mass is fundamental   
   > and always well-defined.  Furthermore it works for collections of   
   > points that are not all on the same circle or sphere.  Looking at   
   > the problem in terms of chords seems somewhat artificial, or at   
   > least less fundamental.   
      
   There are other ways for something to be interesting (at least to me).   
   When you plot the two averages, and look at the chords vs the arcs, it   
   becomes clear why one average "looks" more average than the other.   
      
   --   
   Ben.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)