Pi: Less Random Than We Thought

Gil Hamilton gil_hamilton at hotmail.com
Thu May 5 07:48:04 PDT 2005

Sarad writes:
>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.

I don't have Knuth's book handy to look at, but it's not really correct
to speak of a particular sequence or subsequence of digits as being
random or non-random.  For example, is this sequence of bits random:
01100100010?  How about this one: 0000000000?  From a true random number
generator, both are completely possible and equally valid.

(Furthermore, I would contend that the digits of pi are *non-random* by

>--- 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.
> > 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.

One can only do statistical analyses of sequences of digits to determine
whether they *appear* to have a uniform distribution of individual
digits and subsequences.

Of course the result of such a test (positive *or* negative) doesn't 
positively confirm
whether a given digit source is truly random.

Wikipedia has a good article on randomness:


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