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Re: Simple random number generator?
Posted:
Dec 3, 2012 5:34 PM
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In article <011220121921576414%chenrich@monmouth.com>, "Christopher J. Henrich" <chenrich@monmouth.com> writes:
>In article <pChMbSKOZRuQFw+m@invalid.uk.co.demon.merlyn.invalid>, Dr J R Stockton <reply1248@merlyn.demon.co.uk.invalid> wrote:
>> In sci.math message <50b6cabe$0$24749$607ed4bc@cv.net>, Wed, 28 Nov 2012 21:38:34, Existential Angst <fitcat@optonline.net> 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>
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