Pi: Less Random Than We Thought
Tyler Durden
camera_lumina at hotmail.com
Thu May 5 07:49:09 PDT 2005
Cypherpunk:
While I respect your forthrightness you are unfortunately wrong. Read the
chapters on Randon Mumber generation from "Numerical Recipes in C" and you
get just a small glimpse of how sticky the issue is, particularly when it
comes to computers (which are innately non-random, by the way).
As a very simple example, imagine that after 10 billion digits we found that
the "average" value was actually 5.000000001. This would make it, in your
book, not random at all, but I suspect that for almost many uses it would be
random enough.
And then, imagine that the cumulative average of the digits of pi oscillated
around 5 (to one part in a zillion) with a period of 100 Billion...is this
random enough for you?
Let us remember, of course, that the digits of "pi" are not random
whatsoever: they are the digits of pi! "Random is in the eye of the
beholder."
I was hoping Cordian would grumpily reply...he's a number theorist or
something.
-TD
>From: Sarad AV <jtrjtrjtr2001 at yahoo.com>
>To: cyphrpunk at gmail.com
>CC: cypherpunks at al-qaeda.net
>Subject: Re: Pi: Less Random Than We Thought
>Date: Thu, 5 May 2005 05:43:35 -0700 (PDT)
>
>hi,
>
>If you remember D.E Knuth's book on Semi-Numerical
>Algorithms he shows some annoying subsequences of pi
>in it which are far from random.
>
>Sarad.
>
>
>--- cypherpunk <cyphrpunk at gmail.com> wrote:
>
> > This doesn't really make sense. Either the digits
> > are random or they
> > are not. You can't be a little bit random. Well, you
> > can be, but the
> > point is that you either pass the test or you don't.
> >
> > If pi's digits fail a test of randomness in a
> > statistically
> > significant way, that is big news. If they pass it,
> > then there is no
> > meaningful way to compare them with another RNG that
> > also passes. It's
> > just a statistical quirk due to random variation as
> > to which will do
> > better than another on any given test.
> >
> > The bottom line is still that either an RNG passes
> > the tests
> > acceptably or it does not. From what they say (or
> > don't say), pi does
> > pass. It doesn't make sense to say that other RNGs
> > do better.
> >
> > CP
> >
> >
>
>
>
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