
Re: Simple random number generator?
Posted:
Dec 3, 2012 5:34 PM


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 subsequence 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 subsequences 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!

