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Math Supercomputing

Pi Calculated To Record 2.5 Trillion Digits 432

Posted by samzenpus
from the almost-there dept.
Joshua writes "Researchers from Japan have calculated Pi to over 2.5 trillion decimals using the T2K Open Supercomputer (which is currently ranked 47th in the world according to a June, 2009 report from Top500.org). This new number more than doubles the previous record of about 1.2 trillion decimals set in 2002 by another Japanese research team. Unfortunately, there still seems to be no pattern."
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Pi Calculated To Record 2.5 Trillion Digits

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  • by Petersko (564140) on Wednesday August 19, 2009 @09:40PM (#29128385)
    These researchers are now in possession of the most useless piece of information in science.

    3.14 was very useful. 3.1415? Even more so. But after that it's diminishing returns, baby. 2.5 trillion digits? Good heavens. Of course it never repeats - we kind of knew that already.

    Pointless mathematical dick-sizing. Problem is, this dick is so huge no vagina will ever make use of it.
    • by AnonGCB (1398517) <7spams&gmail,com> on Wednesday August 19, 2009 @09:42PM (#29128401)

      I hear those black hole's are pretty loose, and CERN is working on one so who knows, maybe it will be used.

    • by Anonymous Coward on Wednesday August 19, 2009 @09:47PM (#29128453)

      The point is that someday, a computer instructed to compute pi indefinitely will simply respond, "Why don't you just go fuck yourself?" Then we'll know that the machine has achieved sentience.

      • by Snarfangel (203258) on Wednesday August 19, 2009 @09:53PM (#29128497) Homepage

        The point is that someday, a computer instructed to compute pi indefinitely will simply respond, "Why don't you just go fuck yourself?" Then we'll know that the machine has achieved sentience.

        I'd be even more impressed if it said "Sure thing, I'll get right on it!" and then pretended to work while surfing the web.

      • Re: (Score:2, Funny)

        by olsmeister (1488789)
        Yeah. Either that, or it's from New Jersey.
      • Re: (Score:3, Funny)

        by Sark666 (756464)

        It'll say, "Don't bother me, I'm working on that entropy problem. But don't worry, I'm still collecting data."

      • Re: (Score:3, Funny)

        If the computer were really smart, it would say, "Interesting. Yes, I can do that, but it will take some time. Seven and a half million years." Then it will relax while appearing to give the problem deep thought.
        • Re: (Score:2, Funny)

          by mldi (1598123)

          If the computer were really smart, it would say, "Interesting. Yes, I can do that, but it will take some time. Seven and a half million years." Then it will relax while appearing to give the problem deep thought.

          Nope, it'd come back and tell you it's 42.

    • Re: (Score:3, Interesting)

      by SpottedKuh (855161)

      Of course it never repeats - we kind of knew that already.

      You're absolutely right: pi is irrational, and as such, there won't be any repeats. However, that doesn't mean there isn't a pattern. For example, 0.12112111211112111112... is irrational, but there's a clear pattern that you could extend to an infinite number of digits. Does such a pattern exist once you get to a certain number of digits in pi? We don't know.

    • Re: (Score:3, Insightful)

      by Fluffeh (1273756)

      Of course it never repeats - we kind of knew that already.

      Goodness me, so many holes in this.

      Firstly, just because something isn't repeating doesn't mean there isn't a pattern.
      1,2,4,8 isn't repeating, but the pattern is there. (Each number doubles the previous)
      1,1.5,2.25,3.375 also doesn't repeat but there is a pattern.(Each number is the previous number plus half the previous number)

      Knowing (thinking) that something doesn't repeat and PROVING that it doesn't repeat are two ENTIRELY different things. I am guessing your maths/science education either stoppe

      • Re:Congratulations! (Score:5, Informative)

        by daver00 (1336845) on Wednesday August 19, 2009 @10:29PM (#29128737)

        We know without a doubt that it never repeats - if it did it would be a rational number, it has been proven to be an irrational number, moreso it is transcendental. We also know the exact pattern, take the taylor series of sin about pi/4, you get an elegant and simple series solution for pi.

        That is not the point. The point is and exercise in computing, everything we do in computing involves rational numbers only (floats) and there is substantial error involved with this. It is computationally difficult to deal with large numbers, hence any method to do this more effectively is a gain for science.

        • We know an exact pattern. This could conceivably reveal another representation.

          But yes, In general I agree that this is largely for the benefit of computer science and not mathematics.
      • If there are interesting patterns in Pi, it'll be discovered through analytical research, not calculating digits out to some indeterminate end. I mean honestly, do they think the 2.5 trillion and one digit is going to hold the secret to one of the simplest shapes in mathematics?

        • No, but you may be surprised at how much mathematics is done computationally today. Many number theorists, for instance, spend an inordinate amount of time writing computer programs with the general intention of finding the answer first and determining the reason (i.e. proving it) second.
      • by sys.stdout.write (1551563) on Wednesday August 19, 2009 @10:39PM (#29128833)

        Knowing (thinking) that something doesn't repeat and PROVING that it doesn't repeat are two ENTIRELY different things. I am guessing your maths/science education either stopped very early or you didn't do too well in either.

        I think it's funny that you are insulting someone's math education immediately after you imply that no proof exists showing pi not to repeat.

      • "Knowing (thinking) that something doesn't repeat and PROVING that it doesn't repeat are two ENTIRELY different things. I am guessing your maths/science education either stopped very early or you didn't do too well in either."

        I wish I'd noticed this earlier, so I could belittle you proper. I'll leave it to you and your superior science/math brain to figure out why I find this amusing.
    • While I think that the computing horsepower was misdirected (covered elsewhere), and the last trillion digits could have waited, this post is mostly here for me to be arrogantly dismissive and make dick / vagina jokes.
    • by commodoresloat (172735) * on Thursday August 20, 2009 @12:09AM (#29129431)

      Pointless mathematical dick-sizing. Problem is, this dick is so huge no vagina will ever make use of it.

      Huge? What are you talking about? It's barely over 3 inches!

  • So.... (Score:4, Funny)

    by MichaelSmith (789609) on Wednesday August 19, 2009 @09:42PM (#29128403) Homepage Journal

    ...have they found the circle yet?

  • by Anonymous Coward on Wednesday August 19, 2009 @09:42PM (#29128405)

    Otherwise how would you calculate it? The "pattern" is it matches the stream of digits produced by a simple algorithm!

  • by Anonymous Coward on Wednesday August 19, 2009 @09:48PM (#29128457)

    Researchers will find that Pi begins to repeat after 2,500,000,000,001 digits.

  • Otherwise it would mean other non-predictable numbers could actually be predictable, potentially make breaking cryptography easier (much like finding out that a prime really isnt), would generally disrupt a bunch of mathematical theorems probably pissing off a whole sect of mathematicians, and turn a lot of things we think we know upside down.
    • Re: (Score:2, Informative)

      by Taikutusu (1479335)

      Cryptography has nothing to do with a prime "not being a prime". It's to do with quick factorization of primes.

      Besides, I don't see why pi having any sort of repeating pattern would disrupt any theorems. I honestly can't think of any theorem that requires such a thing. Irrational and transcendental yes, but no repeating decimal pattern?

      Maybe you can enlighten me to such a theorem.

      • quick factorization of primes

        Huh?

      • Your post is not informative. Please reference elliptic curve cryptography [wikipedia.org] for why research in this field might actually yield valuable insights in the field of crytography. If you can't grasp it after a cursory overview of the topic, you probably shouldn't have replied to the GP, even given the fact that s/he was obviously misguided on the whole prime-or-not concept.
    • Re: (Score:3, Funny)

      by daver00 (1336845)

      Ahhh! what is wrong with you geeks! Hand in your cards, all of you.

      There is an extremely simple pattern to pi, just not in base10 decimal expansion. Its already been said but here we go:

      pi = 4(1-1/3+1/5-1/7+1/9-1/11+...)

      Mathematicians were all over this stuff years ago, try to think about what the implications of this are for precision in scientific computing.

    • by JoshuaZ (1134087)
      Wrong. At multiple levels. First of all, no form of cryptography relies on the digits of Pi not having a "pattern"(whatever that means). There is cryptography that relies on the conjecture (note, not theorem, but conjecture) that factoring numbers into primes is difficult. More specially, it is conjectured that factorization cannot be done in polynomial time. However, there's nothing at all connected to the digits of Pi, nor is there is anything connected numbers that one might think are prime that aren't.
  • by Anonymous Coward on Wednesday August 19, 2009 @09:49PM (#29128463)

    A nice little article on why it's useless to know pi to more than 50 digits in this universe.
    http://everything2.com/title/Too%2520small%2520a%2520Universe%2520to%2520memorize%2520Pi

    • by kipling (24579) on Wednesday August 19, 2009 @10:53PM (#29128919) Homepage

      So you are criticising my preparation for the afterlife? Other people memorise wodges of religious texts, I choose to memorise digits of pi ...

    • by Burning1 (204959)

      Seems like an appropriate place to mention it. A gentleman who does music based on listener requests has created a mnemonic for the first 50 digits of Pi [songstowearpantsto.com].

      Here are the lyrics:

      Man, I canâ(TM)t - I shanâ(TM)t! - formulate an anthem where the words comprise mnemonics. Dreaded mnemonics for piâ¦

      The numerals just bother me, always - even the dry anterior. Try to request something lower (zero) in numerary aptitude. Even I, pantaloon gallant, I cannot actualize the requested mnemonics. The leadi

      • by Burning1 (204959)

        Of course... If you count the improperly formatted characters from my previous post, Pi may have a few errors... :|

    • by commodoresloat (172735) * on Thursday August 20, 2009 @12:11AM (#29129437)

      No one needs more than 640 digits

      Fixed that for you.

    • by LS (57954) on Thursday August 20, 2009 @01:36AM (#29129837) Homepage

      The article isn't really that informative. It takes things too literally, using the known size of the universe to determine the largest possible physical circle and the smallest possible length (planck length) to determine the maximum precision and he comes up with 50 digits. But it wouldn't be too hard to come up with an application that uses more than 50 digits of pi. A new encryption algorithm could use sequences in pi, but this has nothing to do with physical circles. Math is abstraction, and there are fields in math that are so abstract that you can't even correlate them with a physical measure. It's very silly to say that knowing pi to more that 50 digits is useless.

      LS

  • if they found a repeat at say, 3 trillion digits?*

    just so that certain science/ math completists/ perfectionists, who would consider it their duty to know pi exactly, their brains would explode in an attempt to remember the digits

    (*i don't think it is possible for pi to repeat at all, i think pi's irrationality is essential to what pi represents)

  • Choose your pattern (Score:3, Interesting)

    by iris-n (1276146) on Wednesday August 19, 2009 @09:50PM (#29128473)

    Of course there's a pattern. In fact, an infinite number of them. My favourite is the one in the generalised continued fraction [wikipedia.org] expansion of pi.

  • by JSBiff (87824) on Wednesday August 19, 2009 @09:50PM (#29128481) Journal

    Since Pi is irrational, does that mean that a "perfect" circle cannot actually exist? If you don't understand my question, think about it like this. Let's say I want to construct a circle of radius R. To create a "perfect" circle, it seems like I would need a length of material to build the circle out of that was exactly 2*Pi*R, but since Pi is irrational, it seems that you could never actually get any length which is an exact multiple of Pi? If Pi really expands out infinitely, even a circle with a radius the size of a galaxy, or a cluster of galaxies, could never be *exactly* the right length?

    • by e9th (652576) <e9th@t[ ]dex.com ['upo' in gap]> on Wednesday August 19, 2009 @10:00PM (#29128563)
      I've constructed a perfect circle, with a circumference of 1 meter. It's the diameter I'm having trouble with.
    • If I use a base Pi number system, then a circle of radius 1 will simply have a circumference of 20. It's just our inferior number system that holds us back.
    • Question for the mathematicians... Can it really be proven that Pi is irrational or did it just get that reputation since it is a number that has no known end? I understand that from the laws and proofs of maths certain numbers can't exist as rational numbers (the sqr root of a negative) but Pi, in my limited knowledge of math, doesn't seem to fit into that. Is there an easy way to determine if a number is irrational?
    • by daver00 (1336845)

      No.

      This is just zeno's paradox in disguise, if it were the case you could therefore never move from point a to point b and achilles could never catch up to the turtle.

    • by russotto (537200)

      If you don't understand my question, think about it like this. Let's say I want to construct a circle of radius R. To create a "perfect" circle, it seems like I would need a length of material to build the circle out of that was exactly 2*Pi*R, but since Pi is irrational, it seems that you could never actually get any length which is an exact multiple of Pi?

      In an ideal world? Just take a unit of material and roll it into a circle. You'll never be able to measure the radius exactly, but you'll have your

  • Perhaps value derives from the lack of pattern in this particular instance. Some math junkie might look at the problem from that point of view and see what pops up.

  • by Anonymous Coward on Wednesday August 19, 2009 @09:54PM (#29128503)

    Of course there's a pattern. I mean, otherwise, I wouldn't be able to match it with 3.[0-9]{1,}

  • Haven't you seen Contact? Get out your different-sized graph papers!
  • First of all, Pi appears to be normal (that is the digits actually meet certain statistical tests for randomness). That is a pattern in some sense. In any event, digits to any base (even base 2 or base 3) are in many ways a very artificial way of thinking about numbers. A far more natural way is to represent numbers as continued fractions http://en.wikipedia.org/wiki/Continued_fraction [wikipedia.org], When considering generalized continued fractions, Pi has a variety of different very elegant patterns.
  • I wonder, who needs that?
  • by NCamero (35481)

    FYI
    The reason the Babylonians, and the Egyptians, and we use 360 degrees is this:

    355/113 = 3.14159292035
    pi `= 3.14159265359

    A difference of 8.5x10-6%

    Which makes 355/113 close enough to pi. 360 is close to 355 which is why we use 360 degrees for angles and time.

    • by godrik (1287354)
      heu? what is the point of dividing by 113 ? being able to revert back to radiant "easily". I would thought we use 360 because it is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360 which is fairly convenient.
  • There is a pattern (Score:4, Interesting)

    by SolusSD (680489) on Wednesday August 19, 2009 @10:55PM (#29128937) Homepage
    The pattern just isn't in base 10. It's in base e. Why does anyone expect to see a numerical pattern in an arbitrary number base like 10? Just because we have 10 fingers doesn't make it the "correct" base for anything.
    • Re: (Score:3, Insightful)

      by cryptoluddite (658517)

      Because if there's a pattern in one base, there's a pattern in all bases. It's just maybe less obvious and easy to describe in some.

  • Pi should be 2 pi (Score:4, Interesting)

    by The_Duck271 (1494641) on Wednesday August 19, 2009 @11:29PM (#29129179)
    There's a good argument that the choice of pi = (circumference / diameter) was unfortunate; it should have been (circumference / radius). In the light of modern mathematics it seems clear that the radius is more "fundamental" than the diameter; choosing pi = (circumference / radius) = 6.28... gives a number of nice things like:
    A = (1/2)pi r^2, just as E = (1/2)m v^2 or d = (1/2)a t^2, and for the same reason.
    In general, in the current convention, 2pi seems to show up a lot more than pi, e.g. there are 2pi radians in a circle, sin(x) has period 2pi, etc. All these would become simply pi with the (circumference / radius) convention
  • Compression (Score:5, Funny)

    by The_mad_linguist (1019680) on Wednesday August 19, 2009 @11:32PM (#29129193)

    Wait, we can record a ridiculous amount of data (2.5 trillion digits!) just by calculating pi?

    Best.

    Compression Algorithm.

    Evar!

    • Re: (Score:3, Interesting)

      by Pflipp (130638)

      Yeah. Pi acts like Infinite Monkeys. All _we_ have to do is to point to the monkey that actually does write Shakespeare, i.e.: the index of Pi which actually represents Kill Bill Complete in AVI format.

      The only problem is the size of that index, but hey, if you zip that number and take its MD5, you have achieved something similar to this [wikipedia.org].

  • by wickerprints (1094741) on Thursday August 20, 2009 @02:04AM (#29129973)

    It's a great way to test the performance of these supercomputers, to ensure that their calculations are correct. The calculation of pi to additional decimal places beyond what was previously known is never done with just a single method--otherwise, it is impossible to verify the additional digits. It is always done with two different algorithms to ensure that the result is valid. There are many rapidly converging algorithms (e.g., variations on AM-GM methods can be quadratically convergent or better; BBP-type digit extraction methods; and of course, classic Ramanujan series-type methods). However, computing pi to so many decimal places has much less to do with the chosen algorithm than it has to do with the memory- and computing time-efficient implementations of such algorithms in massively parallel architectures. Thus these calculations serve as very good tests for the robustness of supercomputers. The result is also verifiable to previously known digits, and even beyond the previous record, it is possible to perform statistical analyses to determine whether there are any significant deviations in the distribution of digit frequencies.

    So, in summary, it is hardly a useless computation. Not that you're going to get an explanation like this from your usual news sources, which generally do not write for technical audiences.

    Also note that distributed computing resources such as Folding@home, or even the Great Internet Mersenne Prime Search don't bother with calculating pi, as the purpose of these projects is to make new discovers in their respective fields of interest.

  • by phaunt (1079975) * on Thursday August 20, 2009 @06:22AM (#29131131)
    I'm surprised that nobody posted this yet.
    "Unfortunanely, there seems to be no pattern yet", but what about secret messages? [xkcd.com]

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