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

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: Simple random number generator?
Posted: Dec 3, 2012 5:34 PM
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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
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