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Topic: Simple random number generator?
Replies: 8   Last Post: Dec 12, 2012 12:01 AM

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Posts: 2,720
Registered: 2/15/09
Re: Simple random number generator?
Posted: Dec 12, 2012 12:01 AM
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On Dec 3, 2:34 pm, (Michael Stemper)
> In article <>, "Christopher J. Henrich" <> writes:

> >In article <>, Dr J R Stockton <> wrote:
> >> In sci.math message <50b6cabe$0$24749$>, Wed, 28 Nov 2012 21:38:34, Existential Angst <> posted:
> >> >So are the digits of pi random or not?
> >> 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).

> >> 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.

> >> A real mathematician could put that more precisely.
> >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.

> 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...
> Is my understanding correct, or have any numbers that are otherwise
> interesting been proven normal?
> --
> Michael F. Stemper
> #include <Standard_Disclaimer>
> Visualize whirled peas!

"Borel v. Combinatorics"

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