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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.programming
Subject: Re: Another little puzzle
Date: Sun, 08 Jan 2023 19:59:14 +0000
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Ben Bacarisse <ben.usenet@bsb.me.uk> writes:

> Tim Rentsch <tr.17687@z991.linuxsc.com> writes:
>
>> Ben Bacarisse <ben.usenet@bsb.me.uk> writes:
> <cut>
>>> 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.