typodupeerror

## Pi Computed To 10 Trillion Digits414

Posted by samzenpus
from the because-he-can dept.
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."
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## Pi Computed To 10 Trillion Digits

• #### What Does This Mean? (Score:5, Insightful)

on Monday October 17, 2011 @01:07AM (#37735836)

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?

• #### Re: (Score:2, Funny)

by Anonymous Coward

a message from god shows up in binary once you get to 20 trillion digits.

• #### Re: (Score:2)

A couple dozen digits of pi exceeds all practical necessity. Calculating it to 10 trillion digits is obviously pointless.
• #### Re:What Does This Mean? (Score:5, Interesting)

<`moc.liamg' `ta' `noitarutcan'> on Monday October 17, 2011 @02:28AM (#37736208) Journal

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

• #### Re: (Score:2, Insightful)

by Anonymous Coward

If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.

• #### Re: (Score:3)

If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.

You can navigate in a perfect circle, but when you reach the end of the perfect circle there will be a little left over because the number you were using for pi to calculate the circumference was off.

However, don't let me interrupt what must be a satisfying eye roll for you. I'm glad to see cowards on Slashdot have remained as polite as ever.

• #### Re: (Score:3)

People think in binary here. It's either perfect or not. In your case, it is not.

• #### Re:What Does This Mean? (Score:5, Funny)

<`moc.liamg' `ta' `noitarutcan'> on Monday October 17, 2011 @03:17AM (#37736416) Journal

How irrational of me.

• #### Re:What Does This Mean? (Score:4, Funny)

on Monday October 17, 2011 @05:24AM (#37736834)

How irrational of me.

Get real.

• #### Re: (Score:2)

Well if they search long enough. They will find the collected work of shakespear hiding in pi.

• #### Re: (Score:2)

You mean if they search along the circumference of the universe for Shakespeare? What a strange notion. Or perhaps you replied to the wrong post.

• #### Re: (Score:3)

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

To put numbers on that.

pi ~= 3.14159265358979323846264338327950

The first zero in pi appears 33 digits in. Memorising digits up to this first zero gives an error of less than 10^(-32). The radius of the known universe is 4.6 * 10^10, light years, and since a li

• #### Re:What Does This Mean? (Score:4, Interesting)

on Monday October 17, 2011 @07:18AM (#37737364) Homepage
It's not useless for those interested in computational efficiency with huge datasets. (Things like weather modelling, climate modelling, nuke aging analysis, fusion research, etc.)

If you look at a naive theoretical model for a computer, then you would predict that certain classes of algorithms would be most efficient for calculating digits of pi. (These algorithms use huge FFTs in order to do bignum arithmetic.) Several world records were broken using this technique. However, as the problem size grew, the FFTs started to become impractical, as the communication overhead started to dominate, and eventually algorithms that didn't have such a communication overhead became favoured. Better models of computational efficiency were arrived at, and new records were broken. We now understand time/space trade-offs better.

However, your loaf of bread won't be cheaper because of this, nor will the number of homeless on the street decrease.
• #### That is only true for measuring circles (Score:3)

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.

• #### Re:What Does This Mean? (Score:5, Funny)

on Monday October 17, 2011 @01:20AM (#37735890) Homepage
I believe that the correct term is "mathsturbation"
• #### Re:What Does This Mean? (Score:5, Funny)

on Monday October 17, 2011 @05:57AM (#37736946) Homepage

I believe that the correct term is "mathsturbation"

Given that Pi never ends, could we also call it "onanonanonanonanism"?

• #### Re: (Score:3, Informative)

by Anonymous Coward

No, you only need about 50 decimal places to have an accurate enough approximation to calculate the circumference of the entire universe with less than 1 planck length of error.

This is just a "because we can" exercise. (Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)

• #### Re:What Does This Mean? (Score:5, Informative)

on Monday October 17, 2011 @01:51AM (#37736034)

(Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)

What? There's a mathematical proof that pi is irrational (in fact, transcendental). Specifically, if it were not, -1 would be irrational (in fact, transcendental) thanks to the Lindemann-Weierstrass theorem [wikipedia.org] and the fact that e^(pi*i) = -1. The digits cannot simply start repeating after a while (in particular, they cannot eventually just become 0, as happens with, for instance, 1/2 = 0.5000... .

• #### Re: (Score:3, Informative)

IIRC pi has not been proven to be normal yet, so there's some value in gathering statistical evidence on that.
• #### Re: (Score:2)

Any 1st year calculus student should know both that it's been proven that Pi is irrational and does NOT repeat, but should be able to do that proof on their own.

• #### Re: (Score:2)

pi is irrational (not the ratio of two numbers)
pi is transcendental (not the solution to an algebraic formula)

pi might not be normal - the distribution of digits might not be balanced and even ...it looks like it is but it has not been proven to to be...

• #### Re:What Does This Mean? (Score:5, Informative)

on Monday October 17, 2011 @01:37AM (#37735980)

The only practical application I've ever heard of for projects like this is as an integrity check on new supercomputers. They compute the first X digits of pi and then compare it to a known result which someone computed and verified earlier.

On a completely separate note, it's "pi", not "Pi". The Greek letter used is lowercase, and the standard English version is similarly lowercase.

• #### Re: (Score:2)

Which if you think about it is really strange for pi to not be a proper noun.

• #### Re: (Score:2)

Perhaps it is a proper noun which just breaks the typical capitalization rule since it's the transliteration of a lower case letter. That is, capitalizing it would change the meaning of the translation.
• #### Re: (Score:2)

Indeed. The symbol indicating the ratio between a circle's diameter and its circumference (pi) means something totally different in math when upper-cased. There it's used to express the product of the terms of a series. Given that, upper-casing it (except when it's the start of a sentence) really would change the meaning hugely.

• #### Re: (Score:2)

I've never seen "Pi" written out to indicate a product in standard writing, so I'm not sure if there's any issue here (in reality that is; theoretically the issue clearly might occur). That I've never seen it is probably just because "Pi" (now I want to write \Pi) is only really used in higher level contexts than "pi".
• #### Re: (Score:2)

No more stranger than one, two three, four, five, fi or e.

• #### Re: (Score:2)

Do you mean "phi" instead of "fi", that is, the golden ratio (which is also for some reason not a proper noun)?
• #### Re: (Score:2)

Yes, if they keep looking they will eventually find the DNA of our beloved overlords.
• #### Re: (Score:2)

It depends how it's done. Many record holders develop new algorithmic or implementation techniques in the process, and that's actually very useful.

• #### The calculation was commissioned (Score:3)

The calculation was commissioned by an anonymous group known as Occu-Pi.

• #### Why not (Score:2)

would just using =Right(Pi, 1) be quicker?

• #### Re: (Score:2)

would just using =Right(Pi, 1) be quicker?

There is an overflow risk. Try Right(Pi,1,10000000000000) instead.

• #### Re: (Score:2)

That only works in Haskell, which nobody uses.
• #### Ham Radio Callsign (Score:3, Insightful)

on Monday October 17, 2011 @01:14AM (#37735866)

Kind of obvious to me, being one. Here is his info:

http://hamcall.net/call/JA0HXV [hamcall.net]

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

• #### Re: (Score:2)

Damm, you beat me to it. Yes Shigeru, as a fellow ham operator I salute you and your work. Tim VK4YEH
• #### Quantum Computing? (Score:2)

Supposedly, this ran for nearly a year -- imagine how fast someone can come to the same result if he/she was dealing in qubits.

• #### Re: (Score:2)

Quantum computing is about algorithmic efficiency, not speed. So calculating pi will be a whole lot slower until you find and implement an quantum algorithm that is more efficient than classical solutions.

• #### Contact (Score:3)

on Monday October 17, 2011 @01:20AM (#37735894) Homepage
The big question is, does it turn out to contain the plans for a teleporting device?
• #### Re: (Score:3)

The big question is, does it turn out to contain the plans for a teleporting device?

Undoubtedly it does, embedded somewhere in the sequence.

Also the text of every novel that will ever be written.

Just got to figure out what the encoding is. And figure out where the relevant substring starts.

• #### Re: (Score:2)

No, the Teleporting device plans came by radio singnal (along with a few prime numbers and the TV broadcast of Hitler at the 36 olympics.

The first message that was found in pi was a circle drawn in 1's and zeros in base eleven.

This was in the book anyway, I think they left the whole pi thing out of the movie.

• #### Even better (Score:3)

on Monday October 17, 2011 @01:32AM (#37735962)
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.
• #### Re: (Score:2)

This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.

Wonderful stuff. I read so many short stories in my youth, I can't remember many, what I do remember though is the slightly-musty smell of the books in a library and immediately having to go to the toilette for a nice bowel movement... olfactory tri

• #### Re: (Score:2)

This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.

Do you mean Clarke's "The Nine Billion Names of God?" [wikipedia.org]

• #### Re: (Score:2)

Sounds to me like you're thinking of Aurthur C. Clarke's The Nine Billion Names Of God [wikipedia.org].

• #### What's the message? (Score:2)

Isn't that one of the plot ideas in the book (which the movie was based on) "Contact"?

"Do you believe in God?"

(A little surprised) "Why?"

"We have proof"

(Very surprised) "Proof?! What is it!"

"If you calculate Pi to the n-th digit you will find a message..."

Since I didn't read the book, I'm not sure this is how the exchange went, nor do I know what the "message" was. But it makes a good story! (I th

• #### Re: (Score:3)

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.

• #### Re: (Score:3)

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.
• #### Re: (Score:2)

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.

Can we have xkcd [xkcd.com] now?

• #### Re: (Score:2)

Anyway how would you determine, when looking at an infinitely long string of "random" numbers, what is a "message"?

And I suppose people are thinking it's going to be something in a current language... But I'm thinking some DNA-like thing instead.

• #### Re: (Score:2)

Good question.
http://en.wikipedia.org/wiki/Normal_number [wikipedia.org]

We're not sure pi is normal.
So it is believed that the complete works of Shakespeare in Klingon are hidden in pi, but you'll probably need a whole library to describe its location.

• #### Re:What's the message? (Score:5, Informative)

on Monday October 17, 2011 @03:35AM (#37736482)

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.

• #### Re: (Score:2, Informative)

by Anonymous Coward

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.

• #### Sagemath.org can do many digits (Score:2)

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

• #### Computers get faster and faster (Score:2)

So the record will be broken over and over and over again...

• #### Thanks for the answers (so far) (Score:2)

Thanks for the answers to some of my questions. I didn't read the book, but might if it recommended (and if it's an e-book).

Likewise, never heard of "normal" numbers before (like I said, I'm not a mathematician). So thinks for the info.

Uh, is there any way to check this person's answer (short of duplicating the entire calculation)? Like I heard there's a way of confirming If a number is prime that's easier than figuring out what's the next prime number.

• #### Mistake (Score:4, Funny)

on Monday October 17, 2011 @03:19AM (#37736428)

It looks to me like there is a mistake in the 34,518,296,721th digit. Could you repeat and compare please?

• #### Actually calculated 10 billion digits (Score:2)

The guy is using short scale [wikipedia.org].
This being Slashdot, you could have written 10^13, that being unambiguous.
Call me back when someone actually computes 10 trillion (10^19) decimals of Pi :)

• #### Is there a prize (Score:2)

Is there a prize for memorizing, and then reciting all 10 trillion digits?

• #### Tau, not Pi! (Score:4, Informative)

<!@phrogz.net> on Monday October 17, 2011 @07:52AM (#37737684) Homepage

That's all well and good, but what about digits of tau [tauday.com]?

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