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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."
... but it seems a shitty research, based on the article:
> Pi never scored less than a B on the tests, and in one case outperformed all the RNGs, which in addition to mathematical algorithms included a device that uses turbulence in a fluid as its source of randomness. But in most cases, pi lost out to at least one RNG, and in several it finished decidedly in the middle of the pack.
Obviously. There is no reason that pi would beat every RNG out there on a sample of numbers. It should just be slightly ahead the pack (if some RNG are bad), or just in the middle (if all are good).
> "Our work showed no correlations or patterns in pi's number set - in short, pi is indeed a good source of randomness," Fischbach said. "However, there were times when pi's performance was outdone by the RNGs."
Well, there is a reason why mathematicians consider that statistics are not a branch of mathematic. And such article are a proof of it.
pi output on the statistical tests were correct (if they werer not, then it would be an important news, as it would imply correlations). The fact that some other RNG generated "better" output for the (relatively) small sample they used is meaningless.
Not only that, but the five trillionth, forty trillionth, and the quadrillionth bits of Pi are all zero... I did all that work, and it all came to naught.
Tarsnap: Online backups for the truly paranoid
The fun thing about this is that if pi really is "normal", then if you compute long enough, you'll not only eventually find pictures of circles in base 11, you'll also find an MPEG-4 of NTS video of a hand writing, with goose-quill pen, "I exist, yours sincerely, God."
What's worse is that somewhere else is NTS video of the same hand, writing "I don't exist after all, yours sincerely, God."
(I leave the proof of this as an exercise for the interested student.)
Even quantum physics, although theoretically 'random', is generally predictable and reliably recreatable for a large T distribution over time.
If you want truly unpredictable, unrecreatable, random numbers - let my wife balance your checkbook.
Glonoinha the MebiByte Slayer
I must tell you a story.
In the first half of the 15th century the Persian mathematician Al-Kashi calculated pi to 14 places. It would be over a hundred years until a European calculated it to 9 places. But that's not what makes Al-Kashi cool, the Arabs where so much better at math in that period. What made him cool was that he stopped. He observed that, with his pi, the calculation of the circumference of a circle with a radius twice the size of Earth would have a margin of error smaller than a "horse hair" (a Persian unit). Problem solved, next problem. Meanwhile, people are still today using computers to get pi to _hundreds_of_billions_of_decimal_places!! As if there's something unique about pi because it's irrational and transcendental, when this is in fact true of the vast majority of all real numbers. Here's to Al-Kashi, a sane man and a pragmatic!
Pi is a transcendental number
Yes, that's right...
and therefore cannot be exactly determined
Er, that depends on what you mean by "exactly determined". Do we need to know the digits in decimal expansion (base 10) to "determine" pi? How about saying that pi is exactly "1.000" in "base pi"? IMHO, whether or not a number can be exactly determined is independent of whether its decimal expansion is known. By your logic, sqrt(2) cannot be exactly determined, as it is an irrational number and has infinitely many digits (and they aren't periodic, unlike 1/3=0.33333333333... which also has infinitely many digits). But I am not entirely comfortable with saying that sqrt(2) cannot be exactly determined. After all, we know exactly what it is -- the positive number whose square is two.
I expect e and the square root of 2 to be better choices
WTF? How is e a better choice? It is also a transcendental number, just like pi. And sqrt(2) isn't even transcendental!