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Pi Computed To 10 Trillion Digits
An anonymous reader writes "A Japanese programmer that goes by the handle JA0HXV announced that he has computed Pi to 10 trillion digits. This breaks the previous world record of 5 trillion digits. Computation began in October of 2010 and finished yesterday after multiple hard disk problems, he said. Details in English are not fully available yet, but the Japanese page gives further details. JA0HXV has held computation records for Pi in the past."
Is there any practical application to this sort of thing, either having the number itself, or whatever method this guy used to arrive at it? Or is this a thumb gazing exercise?
If you want news from today, you have to come back tomorrow.
Kind of obvious to me, being one. Here is his info:
http://hamcall.net/call/JA0HXV
And although I'm not first, let me congratulate Shigeru on a job well done! Oh, and to the idiot complaining of all the wasted CO2, please turn in your geek/nerd card now: computing Pi (and e and...) is NEVER a waste! :P
Supposedly, this ran for nearly a year -- imagine how fast someone can come to the same result if he/she was dealing in qubits.
"Good, Fast, Cheap: Pick any two" -- RFC 1925
The big question is, does it turn out to contain the plans for a teleporting device?
The last three trillion digits were all 0, since pi turned out to be rational after all, which turned out to be the key in efficiently factoring large numbers and proving that P=NP. So, we can all go home now, math is done.
Wen calculating pie in a given number base (I forget which base), there was an abnormally long string of zeros and ones. The length of this string was the product of two prime numbers.
Arrange the zeros and ones into a two-dimensional matrix with one prime's units on the X axis, and the other prime's units on the Y axis.
The result was a "picture" of a circle.
- Spryguy
There are three kinds of people in this world: those that can count and those that can't
Probably not nearly as much as other useless endeavors, such as playing computer games, updating facebook status, or watching super bowl. And reading slashdot, of course.
Yeah, if I remember right, at some point deep inside pi, there is a message primer. It establishes that there is a message to get your attention. Then you begin to decode it, like you said. The trippy part of that is that the message is embedded into the very fabric of the universe through math.
Authority questions you. Return the favor.
A one time pad that can generated perfectly by anyone using simple maths and published techniques? Try worst pad set ever, by telling your adversary the pad is found in the first 10 trillion digits of pi, you just reduced the search space to at worst log2(10*10^12) 45 bits.
The sagemath.org open source computation engine has a 2 line benchmark that computes Pi to 5 million digits.
It took my Atom desktop computer about 15 minutes. I watched it with Top. It sucked up 99 to 100% of the CPU and strangely only 200 Mb out of 2 Gig of RAM.
Also, it didn't use the Linux swap at all. It kind of got me puzzling that my Ubuntu Linux might be missing some performance optimizations.
What to do with it? Resume studying mathematics. Make a pretty good symmetric encryption gadget with a CD of huge encryption keys.
easy:
sage: numerical_approx(pi,digits=50)
3.141592653589793238462643383279502884197169399
takes a long time:
sage: time a = N(pi, digits=5000000)
Yes, like reading about it on slashdot and complaining that he's wasting time :)
Hey! Without reading Slashdot we wouldn't know about those useless endeavours, let alone be able to discuss them. That in itself proves already that reading Slashdot is not a useless endeavour.
I think there are formulas for calculating the nth digit without knowing the previous ones. Assuming this is so, you can get a probabilistic proof very easily: just pick 100 random digits, compute their values, and check against the claim. (It may require some computational power to do this, but it should still be plenty tractable.) If they all match, you've got solid evidence it is correct.
So I'm sort of right and sort of wrong. There are digit-extraction methods for pi, but according to wikipedia, they work in O(n^2) time (for the n'th digit). But it also looks like there's an algorithm to compute up to the nth digit in time O(n log(n) log(log(n))).
Which means that asymptotically, if the storage requirements of the second alogrithm don't preclude its use in those cases, there's some N for which it's actually faster to compute all of the first N digits than just do the N'th digit directly.
It looks to me like there is a mistake in the 34,518,296,721th digit. Could you repeat and compare please?
To decipher the math-speak on that page for the less mathematically inclined, here's my explanation of what a normal number is, geared towards a programmer.
Say you generated a number by randomly picking digits 0-9. After generating 100 digits, you'd expect close to 10 of them to be "7" (1/10). After generating 1000 digits, you'd expect about 100 to be "7" (1/10 again), but you'd expect only about 10 copies of the string "57" (10/1000 = 1/100), since there are 100 possible two-digit strings ("00", "01", ..." 99") and there are about 1000 length-2 substrings in a string of 1000 digits (999, to be precise). In general, for such a string of length N, we'd expect about 1/10th of the digits to be "7" and 1/100th = 1/10^2 of the substrings to be "57". If we made N very large we would also expect these estimates to get closer and closer to the truth.
You might get some strange abberations by random number generation. For instance, with astronomical bad luck you might generate 0 each time, and then your estimated fraction of "5"'s would be completely wrong. Still, the above properties are pretty good measures of how "well mixed" the digits of a number are, and they're taken (with mild generalizations) as the defining conditions of a normal number.
Specifically, for a given number x, imagine writing out its (infinitely many) digits in base b. Pick a substring of length m that you're interested in--say an encoding of Shakespeare's complete works in the original Klingon. In the first N digits, we would like to require the fraction of substrings matching our given string to be 1/b^m in analogy with the above (1/10^2 came about from b=10, m=2). That's too much to ask, so instead specify a small tolerance above and below 1/b^m. The key condition for normality is that if we look at the first N digits where N is larger than some number (which depends on the tolerances, the substring we picked, and x itself), the actual fraction of matching substrings will be within our tolerances of 1/b^m. A normal number is one where you can perform this operation in any base, with any substring, and with any tolerances.
If pi were normal, there would have to be at least one (indeed, infinitely many) occurrence of a given encoding of Shakespeare's works, since otherwise for N large enough the number of matching substrings would be near 0, and we could specify our tolerances to be between, say, 1/2 * 1/b^m and 3/2 * 1/b^m, which is strictly greater than the fraction of matches for N large enough since that fraction tends to 0, so it can't be within these bounds.
It's not too surprising that proving the normality of a number is much harder than believing it. Essentially, any number whose decimal digits appear "quite random" feels normal.
>All that CO2 for nothing!
All those digits were calculated with Occupy San Fran bicycle-powered laptops, you insensitive clod!
I'm not a lawyer, but I play one on the Internet. Blog
The calculation was commissioned by an anonymous group known as Occu-Pi.
I do not fail; I succeed at finding out what does not work.
And how much CO2 did those people breathe out while pedaling? And how much extra did they have to eat afterwards? Where did that food come from? Etc...
Pi is exactly 1, if your numbering system uses base pi.
"Good news, everyone!"
That's all well and good, but what about digits of tau?
The usual method is calculate it twice, using different algorithms, then compare the results and claim up to the point that the two methods start to differ
There is a lot more to Pi than calculating circle sizes. There are open mathematical questions about Pi.
For example, is Pi a normal number? (A normal number is one in which all digits appear with the same frequency in every base). And if this product turns out to be true for the at least the first 10 trillion digits, it can be a great random number generator.
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