In article <firstname.lastname@example.org>, "Christopher J. Henrich" <email@example.com> writes: >In article <pChMbSKOZRuQFwfirstname.lastname@example.org>, Dr J R Stockton <email@example.com> wrote: >> In sci.math message <firstname.lastname@example.org>, Wed, 28 Nov 2012 21:38:34, Existential Angst <email@example.com> 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!