On Dec 3, 2:34 pm, mstem...@walkabout.empros.com (Michael Stemper) wrote: > In article <011220121921576414%chenr...@monmouth.com>, "Christopher J. Henrich" <chenr...@monmouth.com> writes: > > > > > > > > > > >In article <pChMbSKOZRuQF...@invalid.uk.co.demon.merlyn.invalid>, Dr J R Stockton <reply1...@merlyn.demon.co.uk.invalid> wrote: > >> In sci.math message <50b6cabe$0$24749$607ed...@cv.net>, Wed, 28 Nov 2012 21:38:34, Existential Angst <fit...@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> > Visualize whirled peas!