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Re: bimodal ditribution form counting signs of Pi digits differences
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51793] Re: bimodal ditribution form counting signs of Pi digits differences
*From*: Roger Bagula <tftn at earthlink.net>
*Date*: Tue, 2 Nov 2004 02:05:21 -0500 (EST)
*References*: <clst68$3nf$1@smc.vnet.net> <cm4rh8$6oo$1@smc.vnet.net>
*Reply-to*: tftn at earthlink.net
*Sender*: owner-wri-mathgroup at wolfram.com
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 at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
>>alternative email: rlbtftn at netscape.net
>>URL : http://home.earthlink.net/~tftn
>>
>>
>>
>>
>>
>
>
>
--
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL : http://home.earthlink.net/~tftn
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