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[Fwd: Re: bimodal ditribution form counting signs of Pi digits differences]

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  • Roger Bagula
    ... Subject: Re: bimodal ditribution form counting signs of Pi digits differences Date: Mon, 01 Nov 2004 08:26:03 -0800 From: Roger Bagula
    Message 1 of 1 , Nov 1, 2004
      -------- Original Message --------
      Subject: Re: bimodal ditribution form counting signs of Pi digits
      differences
      Date: Mon, 01 Nov 2004 08:26:03 -0800
      From: Roger Bagula <tftn@...>
      Reply-To: tftn@...
      Organization: tftn/bmftg
      Newsgroups: comp.soft-sys.math.mathematica
      References: <clst68$3nf$1@...> <cm4rh8$6oo$1@...>



      It appears that both this version and the built in ( rule 30 based)
      random are Markov based ( depend on their own previous history )
      to produce randomness.
      It appears that Pi by measure doesn't and is, thus, more "ideally" random.
      Questions associated with all such dependent randomness ( not just rule 30)
      are well known.
      By my experiments the "traditional" pseudorandom
      seems more random than the rule 30 based version.
      But still less than the ideal for which Pi seems better suited?
      I've been told that my experimentation with this area of thought for my
      own personal
      gratification is "futile".
      It seems mostly that there is a "doctrinaire" tide in place and if it
      questions
      Mathematica's integrity it is "futile".
      That "doctrinaire" tide is not a scientific
      or mathematical attitude that stand up to any critical comment.
      Association with such thought patterns is personally repulsive for me as
      well.
      Many current professional level development systems
      give access to more than one way to produce pseudorandom
      numbers for simulations. It is well known that not all such
      randomness systems are "equal" in their measures of randomness.
      Suppression of personal research for doctrinaire reasons
      is one of the worst results of a commerial enterprise
      in a scientific sense.
      Roger Bagula wrote:

      >A second crack at a null hypothesis using an
      >independent pseudorandom generator.
      >Results from this generator are more variable than the Mathematica built in
      > as you can change both the seed start number and the irrational it is
      >based on.
      >It too gives a different result than the Pi digits.
      > >Mathematica code:
      >Clear[r,s,a,c1,d1]
      >s=5
      >(*Pseudorandom number algorithm from Forcasting on Your
      >Microcomuter,nickell, tab books, 1983*)
      >SeedRandom[123]
      >r[n_Integer]:=r[n]=Mod[(E+r[n-1])^s,1]
      >r[0]=Random[]
      >digits =50000
      >a=Table[Mod[Floor[10*r[n]],10],{n,1,digits}];
      >c1=Drop[FoldList[Plus,0,Sign[Drop[a,1]-Drop[a,-1]]],1];
      >ListPlot[c1,PlotJoined->True];
      >(* Rowe Count*)
      >d1=Flatten@{0,Length/@Split[Sort@c1], 0}
      >ListPlot[d1,PlotJoined->True];
      >
      >Roger Bagula wrote:
      >
      > >
      >>This program is real slow on my machine.
      >>Show a lean toward positive differences that is "slight" at 2000 digits.
      >>
      >>Digits=2000
      >>$MaxExtraPrecision = Digits
      >>(* Sum of the sign of the differences between the first 2000 digits of Pi*)
      >>f[m_]=Sum[Sign[Floor[Mod[10^(n+1)*Pi,10]]-Floor[Mod[10^n*Pi,10]]],{n,0,m}]
      >>a=Table[{n,f[n]},{n,0,Digits-1}];
      >>ListPlot[a,PlotJoined->True]
      >>b=Table[a[[n]][[2]],{n,1,Dimensions[a][[1]]}];
      >>(* distribution of the noise that results*)
      >>c=Table[Count[b,m],{m,-12,12}]
      >>ListPlot[c,PlotJoined->True]
      >>
      >>Respectfully, Roger L. Bagula
      >>tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      >>alternative email: rlbtftn@...
      >>URL : http://home.earthlink.net/~tftn
      >>
      >> >>
      >> >>
      >
      > >

      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      alternative email: rlbtftn@...
      URL : http://home.earthlink.net/~tftn






      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      alternative email: rlbtftn@...
      URL : http://home.earthlink.net/~tftn
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