From: ben.usenet@bsb.me.uk   
      
   Ben Bacarisse  writes:   
      
   > 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.   
      
   I can see a possible misunderstanding here.  You might have taken my "it   
   really is about chords" to mean "it is fundamentally about chords", but   
   I said "it really is about chords" because you thought I'd used the word   
   chord incorrectly to refer to the lines between the centre of mass and   
   the data points.  I was saying "I really did mean chords".   
      
   --   
   Ben.   
      
   --- SoupGate-Win32 v1.05   
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