Pi: Less Random Than We Thought

[cypherpunk]

>    [1]Autoversicherung writes "Physicists including Purdue's Ephraim
>    Fischbach have completed a study [2]comparing the 'randomness' in pi
>    to that produced by 30 software random-number generators and one
>    chaos-generating physical machine. After conducting several tests,
>    they have found that while sequences of digits from pi are indeed an
>    acceptable source of randomness -- often an important factor in data
>    encryption and in solving certain physics problems -- pi's digit
>    string does not always produce randomness as effectively as
>    manufactured generators do."
>    1. https://autoversicherung.einsurance.de/
>    2. http://news.uns.purdue.edu/UNS/html4ever/2005/050426.Fischbach.pi.html

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