From: ben.usenet@bsb.me.uk   
      
   Mike Terry  writes:   
      
   > On 24/12/2022 22:30, Ben Bacarisse wrote:   
   >> Mike Terry  writes:   
      
   >>> Another way of thinking of this approach is "balancing" the 24-hour   
   >>> modular circle, where we've put unit weights at each of the times x_i.   
   >>> E.g. we look for a balancing line through the centre of the circle.   
   >>   
   >> Is that the same?  For {0, 8, 16} any of the three lines through 0, 8 or   
   >> 16 balances, but the vector sum interpretation is undefined.  And for   
   >> {0, 6, 12, 18} there are two balance lines, neither of which seems to be   
   >> a natural answer for the average.   
   >   
   > Yes, it's logically the same, in so far as WHEN the x_i aren't already   
   > balanced [aka they /have/ a meaningful average] we get the same   
   > average both ways.  (Adding vectors is effectively a way of   
   > calculating moments of the weights in the balancing view of things.)   
      
   Oh, yes, I see what you mean.  Sorry.   
      
   --   
   Ben.   
      
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