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 <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] CC: [EMAIL PROTECTED] 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 <[EMAIL PROTECTED]> 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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