Re: Another little puzzle

Newsgroups	comp.programming
Date	2022-12-30 18:18 -0800
References	(2 earlier) <tnv0ia$uein$3@dont-email.me> <874jtovgao.fsf@bsb.me.uk> <tnvhb2$1vkb$1@gioia.aioe.org> <tnvocb$1i1c$1@gioia.aioe.org> <tnvvb3$ot1$1@gioia.aioe.org>
Message-ID	<7566d2c0-42d5-41fa-a9fc-d561b8f18131n@googlegroups.com> (permalink)
Subject	Re: Another little puzzle
From	Ǝ <angel00000100000@mail.ee>

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You !



On Wednesday, December 21, 2022 at 11:54:47 PM UTC+2, Dmitry A. Kazakov wrote:
> On 2022-12-21 20:55, Mike Terry wrote: 
> 
> > The OP was probably deliberately rather vague on this point!  The 
> > easiest definition for "average" literally doesn't make sense in a 
> > modulo context:  we can ADD the modular values, but in general dividing 
> > in such a mathematical setting doesn't make much sense, so 
> > 
> >     Average ([i=1,2,..n] x_i)  =[def]=  Sum ([i=1,2,..n] x_i) /n 
> > 
> > would be inappropriate due to the /n operation.
> Unless you calculate everything as reals or integers and then take the 
> remainder of 24. Which is kind of most natural definition, at least to me.
> > HOWEVER, there's another characterisation for the average of a set, 
> > which looks more promising in a modular (or other more general) 
> > setting:  the average is the value of V which MINIMISES THE "ERROR" 
> > calculated by 
> > 
> >     error = Sum ([i=1,2,..n] (V - x_i)^2) 
> > 
> > that is, minimises the sum of squares of differences from V.
> This has exactly same problem as above, because subtraction and 
> multiplication (power of two) have different semantics in modular 
> arithmetic.
> > [Incidentally, if we minimise the sum of absolute differeces from V, 
> > that characterises the mode (aka "midpoint") of the sample, but I think 
> > the median is more what is wanted here...]
> Actually it is the same beast. Median is the least C-norm defined as |x-y|. 
> 
> Mean is the least Euclidean norm (squares), the thing you proposed. 
> 
> Mean and average are same for real numbers. 
> 
> You are right that median (and C-norm) can be unambiguously defined in 
> modular numbers. But nobody would ever qualify this as a puzzle! (:-)) 
> 
> [...]
> > Now, as to how to CALCULATE the V above???
> As I said, in real numbers V is the mean, i.e. 
> 
> V = Sum (Xi) =def= mean({Xi | i=1..n}) 
> i=1..n 
> 
> Any numeric method is in the end mapping Xi to some normal number, 
> calculating a classic mean, mapping back. The problem is with the 
> forward mapping being ambiguous. One method to disambiguate is staying 
> within the same day. Another could be taking a median and considering 12 
> hours before and 12 hours after it. And there are many more. 
> 
> P.S. There are differences between the average and mean. OP referred the 
> average, which may mean something completely counterintuitive (no pun 
> intended (:-))
> -- 
> Regards, 
> Dmitry A. Kazakov 
> http://www.dmitry-kazakov.de

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Re: Another little puzzle Richard Heathfield <rjh@cpax.org.uk> - 2022-12-21 13:09 +0000
  Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-12-21 17:05 +0000
    Re: Another little puzzle Richard Heathfield <rjh@cpax.org.uk> - 2022-12-21 17:21 +0000
    Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-12-21 18:55 +0100
      Re: Another little puzzle Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-12-21 19:55 +0000
        Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-12-21 22:54 +0100
          Re: Another little puzzle Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-12-22 00:01 +0000
            Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-21 16:05 -0800
              Re: Another little puzzle David Brown <david.brown@hesbynett.no> - 2022-12-22 16:50 +0100
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-22 08:30 -0800
                Re: Another little puzzle David Brown <david.brown@hesbynett.no> - 2022-12-22 22:06 +0100
                Re: Another little puzzle Richard Heathfield <rjh@cpax.org.uk> - 2022-12-22 21:30 +0000
                Re: Another little puzzle David Brown <david.brown@hesbynett.no> - 2022-12-23 13:46 +0100
                Re: Another little puzzle Y A <angel0000000001000000000000@mail.ee> - 2023-01-09 21:26 -0800
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-22 14:15 -0800
                Re: Another little puzzle David Brown <david.brown@hesbynett.no> - 2022-12-23 13:47 +0100
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-23 08:33 -0800
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-25 15:52 -0800
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-26 06:32 -0800
                Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-26 06:34 -0800
              Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-23 08:35 -0800
            Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-12-22 09:10 +0100
          Re: Another little puzzle Ǝ <angel00000100000@mail.ee> - 2022-12-30 18:18 -0800
        Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-21 14:47 -0800
          Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-23 08:35 -0800
          Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-25 15:52 -0800
            Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-26 06:32 -0800
          Re: Another little puzzle Julio Di Egidio <julio@diegidio.name> - 2022-12-26 06:33 -0800
          Re: Another little puzzle Y A <angel0000000001000000000000@mail.ee> - 2023-01-09 21:26 -0800

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