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Re: Entropy Definition : Request for Comments

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On Wednesday, March 14, 2012 9:16:47 PM UTC, Thomas Richter wrote:
> On 14.03.2012 19:34, lawcounsels@gmail.com wrote:
> 
> >
> > An interesting related phenoma would be to ask :
> >
> > if complete random binary file of length N bits were to be REVERSIBLE 'transformed' / 'randomised' / 'jumbled' by any methods ,
> > will the resultant 'jumbled' of exact same N bits EXHIBIT any particular
> > patterns / restrictions  on any portion of the resultant file BEYOND those normally associated with 'random' file ( like the 1Million Random Digits file )
> 
> This is not exactly related. What is "exact the same N bits". If the 
> bits are exactly the same, the file is identical, so there is nothing to 
> say. If the transformation is reversible, then any reversible transform 
> on a finite set is just a permutation on the base space, and as the 
> entropy is a sum over the full base space, any permutation doesn't 
> change this sum at all - IOW, the entropy is invariant under reversible 
> transformations of a base space into itself. [As intuition also 
> suggests, of course].
> 
> So this is not exactly "interesting". The answer is immediate, and 
> exactly what is expected.
> 
> More interesting things happen if you map this to a smaller set, say, 
> you consider for example sums of random variables. Then, under mild 
> constraints of the source, you get something called the "central limit 
> theorem", i.e. your distribution approaches Gaussians (or stable 
> distributions under less constrained conditions).
> 
> Greetings,
> 	Thomas

we are both on the right wavelengths here 

myself would 100 times out of 100 immediate says the exact same you did here without hesitations ... EXCEPT the INVARIABLE REVERSIBLE resultant transformed file of same N bits long ALWAYS GIVES sizeable portions with unmistakable particularly strong patterns / restrictions ( UNMISTAKABLY UNAMBIGUOUS LOW ENTROPY bits sequences at unmistakable unambiguous ascertainable 'start' / 'end'  bits positions .... mathematics proven instantiated with the described Entropy Definition formula on ALL real transformed resultant files )



LawCounsels
 

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Entropy Definition : Request for Comments LawCounsels <LawCounsels@aol.com> - 2012-03-13 01:40 -0700
  Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-13 10:13 +0100
    Re: Entropy Definition : Request for Comments LawCounsels <lawcounsels@gmail.com> - 2012-03-13 10:03 -0700
      Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-13 19:25 +0100
        Re: Entropy Definition : Request for Comments LawCounsels <lawcounsels@gmail.com> - 2012-03-13 11:56 -0700
          Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-13 20:38 +0100
            Re: Entropy Definition : Request for Comments lawcounsels@gmail.com - 2012-03-14 01:43 -0700
              Re: Entropy Definition : Request for Comments lawcounsels@gmail.com - 2012-03-14 01:46 -0700
                Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-14 12:09 +0100
                Re: Entropy Definition : Request for Comments LawCounsels <LawCounsels@aol.com> - 2012-03-14 08:52 -0700
                Re: Entropy Definition : Request for Comments lawcounsels@gmail.com - 2012-03-14 11:34 -0700
                Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-14 22:16 +0100
                Re: Entropy Definition : Request for Comments lawcounsels@gmail.com - 2012-03-14 23:29 -0700
                Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-15 12:10 +0100
                Re: Entropy Definition : Request for Comments lawcounsels@gmail.com - 2012-03-15 06:23 -0700
                Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-15 16:45 +0100
                Re: Entropy Definition : Request for Comments LawCounsels <LawCounsels@aol.com> - 2012-03-20 18:08 -0700
                Re: Entropy Definition : Request for Comments Thomas Richter <thor@math.tu-berlin.de> - 2012-03-14 22:10 +0100
  Re: Entropy Definition : Request for Comments jacko <jackokring@gmail.com> - 2012-03-15 16:27 -0700
  Re: Entropy Definition : Request for Comments jacko <jackokring@gmail.com> - 2012-03-15 16:40 -0700
    Re: Entropy Definition : Request for Comments jacko <jackokring@gmail.com> - 2012-03-15 17:14 -0700
      Re: Entropy Definition : Request for Comments jacko <jackokring@gmail.com> - 2012-03-15 17:24 -0700
        Re: Entropy Definition : Request for Comments LawCounsels@aol.com - 2012-03-31 10:30 -0700

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