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Pi: Less Random Than We Thought
Autoversicherung writes "Physicists including Purdue's Ephraim Fischbach have completed a study 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."
ScienceNews article (2001) on Randomness of Pi's digits
Interesting work from Johan on Testing the a-periodic randomness of and comparing it with a Quantum Mechanical source.
But are the digits truely random ? In 1996, NERSC Chief Technologist David H. Bailey, together with Canadian mathematicians Peter Borwein and Simon Plouffe, found a new formula for pi. This formula permits one to calculate the n-th binary or hexadecimal digits of pi, without having to calculate any of the preceding n-1 digits. This formula was discovered by a computer, using Bailey's implementation of Ferguson's PSLQ algorithm
Mod parent down, he needs to take a basic number theory class. It has not been proven that pi is normal. It has been proven that there are all kinds of infinite sequences which are not normal. Random is not the same as normal
Yes, picking every 14th digit of Pi may share the properties of a good random number (although, once again, the article points out that it is not as good as a RNG). However, actually using said digits for anything would be very unwise, since it wouldn't be that hard to determine that you were using a periodic subsequence of Pi's digits. I.e. don't use this for cryptographic keys.
Being able to reproduce random sequences is a good thing. Let's say you want to set up a test that feeds random data into a program until it crashes. It would be nice to be able to rerun that sequence (without having to store the sequence) to make sure the problem gets fixed.
That's why most random number generators let you specify a seed value. As long as you use the same seed value, you get the same sequence back. If you want a new sequence every time, peg your seed value to some number that varies, like the current time...
I just remember that it was possible because pi was periodic in some obscure fractional base.
I don't believe that's true. Pi is a transcendental number, which pretty much precludes it being periodic in an fractional base.
(Assuming by "fractional" you mean "rational", the ratio of two whole numbers. Sorry to be picky; I'm just trying to be complete.)
You can compute arbitrary digits of pi in hexadecimal (and binary and octal and any other 2^n base), but as far as I'm aware there isn't any corresponding algorithm for decimal numbers. I'm not certain it's been precluded, either, but I'm fairly certain you won't find pi to be periodic in any fractional base.
If there does exist a proof that you can't do it in decimal, I suspect it will involve the fact that there exist fractions in base 10 that don't have terminating representations in base 16 (e.g. 1/5). That'll make it hard to apply the algorithm from base 16 back to base 10; a one-bit change in the base 16 representation will have dramatic effects all over the base 10 representation.
(I'm not a mathematician, but I used to be, which is why this post is so maddeningly vague. I hope somebody gives you a better answer than I just did.)