Re: "All random number generators eventually exhibit periodicity"?????

From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 08/04/04 

Date: 04 Aug 2004 12:44:43 +0300

"r.e.s." <r.s@ZZmindspring.com> writes:
> "Phil Carmody" <thefatphil_demunged@yahoo.co.uk> wrote ...
>
> > Mahler is probably the strongest indication that pi isn't normal, but
> > certainly isn't an actual indication that it isn't.
>
> For an argument that Mahler's theorem does *not* indicate non-normality
> of pi, see ...
> http://groups.google.com/groups?threadm=qKs3c.12089$%06.8336@newsread2.news.pas.earthlink.net
> or
> http://tinyurl.com/6gl4y

It's an interesting argument, as David remarks. Note - I don't believe
that Mahler does actually indicate for or against normality, simply
that it deals with concepts related to normality, and proves that the
digits are not IID. Normality is independent of that property, of course.

I worded my post deliberately, playing epsilontics; Mahler is (to
my mind) the strongest indication, where its strength is epsilon,
such that for any number delta greater than zero, epsilon<delta.

Phil 

-- 
1st bug in MS win2k source code found after 20 minutes: scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending on the CRTL)