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Re: Simple random number generator?
Posted:
Dec 12, 2012 12:01 AM
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On Dec 3, 2:34 pm, mstem...@walkabout.empros.com (Michael Stemper)
wrote:
> In article <011220121921576414%chenr...@monmouth.com>, "Christopher J. Henrich" <chenr...@monmouth.com> writes:
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> >In article <pChMbSKOZRuQF...@invalid.uk.co.demon.merlyn.invalid>, Dr J R Stockton <reply1...@merlyn.demon.co.uk.invalid> wrote:
> >> In sci.math message <50b6cabe$0$24749$607ed...@cv.net>, Wed, 28 Nov 2012 21:38:34, Existential Angst <fit...@optonline.net> posted:
> >> >So are the digits of pi random or not?
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> >> The digits of pi are not random, because, unless the base is changed,
> >> they are the same every time and can be defined relatively briefly, even
> >> without assuming a definition of pi (which pi may formally lack).
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> >> But any arbitrarily chosen sub-sequence of the digits of pi will, I
> >> believe, pass an appropriate proportion of the usual tests for
> >> randomness. Note that the full expansion of the digits of pi contains
> >> as sub-sequences of a given length all possible digit strings of that
> >> length, some of which will not look random to the untutored eye, such as
> >> yours.
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> >> A real mathematician could put that more precisely.
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> >If the digits of a number are uniformly distributed, so that in the
> >(infinitely) long run 0's, 1's, 2's, etc. occur equally often, then the
> >number is said to be "simply normal" (in base 10).
> >Most of the irrational numbers that are interesting (such as sqrt(2) or
> >pi) appear to be normal.
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> This topic is far from what little knowledge I have, but I've heard that
> the only numbers proven to be normal were created for the purpose of
> illustrating this property -- numbers like 0.1234567891011121314...
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> Is my understanding correct, or have any numbers that are otherwise
> interesting been proven normal?
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> --
> Michael F. Stemper
> #include <Standard_Disclaimer>
> Visualize whirled peas!
"Borel v. Combinatorics"
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