Pi Calculated To Record 2.5 Trillion Digits 432
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."
Congratulations! (Score:4, Funny)
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.
Re:Congratulations! (Score:4, Funny)
I hear those black hole's are pretty loose, and CERN is working on one so who knows, maybe it will be used.
If you find a singularity "pretty loose" (Score:2, Funny)
having effectively zero size, your girlfriend must wish you were throwing a hotdog through the halway :P
Re:Congratulations! (Score:5, Funny)
I hear those black hole's are pretty loose
Racist!
Re:Congratulations! (Score:5, Funny)
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.
Re:Congratulations! (Score:5, Funny)
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:Congratulations! (Score:5, Funny)
Hey! That's my job.
They make a machine to take every job. Before I know it they'll have a machine loafing at the corner bar, smoking cigarettes and downing Jim Beam and Coke like it was water.
Re:Congratulations! (Score:5, Insightful)
They make a machine to take every job. Before I know it they'll have a machine loafing at the corner bar, smoking cigarettes and downing Jim Beam and Coke like it was water.
I see you've met Bender.
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It'll say, "Don't bother me, I'm working on that entropy problem. But don't worry, I'm still collecting data."
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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.
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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.
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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)
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.
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But yes, In general I agree that this is largely for the benefit of computer science and not mathematics.
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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?
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Every possible pattern, interesting or not, occurs in the digits of Pi because they go on forever and do not repeat
Your conclusion does not follow from your premise.
Liouville's constant is trancendental. It goes on forever, it does not repeat, and it consists almost entirely of zeros with an occasional 1 and no other digits at all.
http://en.wikipedia.org/wiki/Liouville_number#Liouville_constant [wikipedia.org]
Tim.
Re:Congratulations! (Score:5, Insightful)
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.
Hah! If My Math is Bad, Your Logic is TERRIBLE (Score:2)
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.
Please don't mod me up, except maybe +1 funny (Score:3, Funny)
Re:Congratulations! (Score:5, Funny)
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!
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On the other hand the ability to calculate pi just proves that we have a computer capable of making a vast number of calculations. I could well run the same numbers through my GPU - it just might take a little longer - to prove the same thi
So.... (Score:4, Funny)
...have they found the circle yet?
Of course there's a pattern! (Score:5, Insightful)
Otherwise how would you calculate it? The "pattern" is it matches the stream of digits produced by a simple algorithm!
100 years from now... (Score:5, Funny)
Researchers will find that Pi begins to repeat after 2,500,000,000,001 digits.
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Damn, having seen this same joke on 2 other sites that posted this story days ago... it just proves that no one can come up with an original thought anymore.
It just goes to show, this joke is circular.
No pattern = a very good thing (Score:2, Insightful)
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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.
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Huh?
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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.
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No one needs more than 50 digits (Score:5, Informative)
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
Re:No one needs more than 50 digits (Score:4, Insightful)
So you are criticising my preparation for the afterlife? Other people memorise wodges of religious texts, I choose to memorise digits of pi ...
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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:
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Of course... If you count the improperly formatted characters from my previous post, Pi may have a few errors... :|
Re:No one needs more than 50 digits (Score:5, Funny)
No one needs more than 640 digits
Fixed that for you.
Re:No one needs more than 50 digits (Score:5, Insightful)
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
wouldn't it be awesome (Score:2)
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)
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.
Question about Pi and circles. . . (Score:3, Interesting)
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?
Re:Question about Pi and circles. . . (Score:5, Funny)
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Re:Question about Pi and circles. . . (Score:5, Informative)
Pi was shown to be irrational in 1768 and transcendental in 1882, finally putting to rest the ancient problem of "squaring the circle".
Re:Question about Pi and circles. . . (Score:5, Informative)
I believe you are confusing rational numbers and real numbers. rational numbers are those that can be expressed as p/q where p and q are prime integers. The existence of real numbers that are not rational follows from cantor's diagonal argument : http://en.wikipedia.org/wiki/Cantor's_diagonal_argument [wikipedia.org]
Proofs of the irrationality of pi can be found on wikipedia : proof [wikipedia.org]
The sqr root of a negative is not defined in the real set but only in the complex set. http://en.wikipedia.org/wiki/Complex_numbers [wikipedia.org]
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rational numbers are those that can be expressed as p/q where p and q are prime integers.
Under your definition of "rational", 4/5 (0.8) is an irrational number. In order for a number to be rational, p and q need only be integers. Whether they are prime is irrelevant.
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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.
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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
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But to construct the circumference perfectly, wouldn't you have to have a fraction of an atom in the perimeter somewhere?
Re:Question about Pi and circles. . . (Score:5, Insightful)
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To travel from one point to another, an object must pass through all the points in between. There are an infinite number of points "in between," thus to move at all, an object must travel through an infinite number of points in a finite time. Clearly this definition of reality is flawed: stop using it.
Actually, I don't think the GP mentioned travelling at all!
Re:Question about Pi and circles. . . (Score:5, Insightful)
Not necessarily. We can't really know about anything smaller than the Planck length, so in practical terms your paradox probably fails. The universe may be discrete on those scales.
Re:Question about Pi and circles. . . (Score:5, Informative)
Not necessarily. We can't really know about anything smaller than the Planck length, so in practical terms your paradox probably fails. The universe may be discrete on those scales.
Mod parent up - AC or not... I had to scroll a LONG way before seeing this argument and was going to post it myself if no-one else had. There's a lot of "weird" points about the universe that just don't seem to make sense. Posts such as the GP saying, "Clearly this definition of reality is flawed: stop using it." (with regard to travelling through an infinite number of points in a finite time) are all well and good, but don't go anywhere towards explaining WHY this definition is flawed. By defining the universe as discrete rather than continuous, it is no longer flawed, as with many other oddities and apparent paradoxes.
This would also potentially have an interesting effect on Pi in that if the number itself is truly irrational, then it's also wrong for every case we're using it - we actually should HAVE TO round it off somewhere to be correct when using it in models of the physical universe.
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Definitions (Score:2)
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.
The pattern. (Score:5, Funny)
Of course there's a pattern. I mean, otherwise, I wouldn't be able to match it with 3.[0-9]{1,}
Come ON, folks! (Score:2)
Pi does have many patterns. (Score:2)
So what? (Score:2)
Rational PI FYI (Score:2, Funny)
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.
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There is a pattern (Score:4, Interesting)
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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)
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)
Wait, we can record a ridiculous amount of data (2.5 trillion digits!) just by calculating pi?
Best.
Compression Algorithm.
Evar!
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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].
why we do this sort of stuff (Score:5, Insightful)
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.
obligatory very early xkcd reference (Score:3, Funny)
"Unfortunanely, there seems to be no pattern yet", but what about secret messages? [xkcd.com]
Re:Well... (Score:5, Insightful)
I fail to see how not understanding the word "seems" is insightful.
Re:Well... (Score:5, Funny)
00001110 001110000
00110000 000001100
01000000 000000010
01000000 000000010
01000000 000000010
00110000 000001100
00001110 001110000
00000001 110000000
About two trillin digits down the line, in base 2, scientists discovered a curious pattern... is it purely random, or perhaps a message from the Creators?
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Re:Well... (Score:5, Informative)
Re:Well... (Score:4, Informative)
0.123456789012345678901234567890... = 1234567890 / 9999999999
Any recurring decimal can trivially be written as a fraction.
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In the example you give, perhaps you're thinking of Champernowne's number, 0.123456789101112....
This is an irrational number, and was the first number proven to be normal [wikipedia.org].
Re:Well... (Score:5, Informative)
There are, however, irrational--indeed, transcendental--numbers that follow a discernible decimal pattern, like the Liouville constant [wikipedia.org].
12345678910 (Score:3, Informative)
0.123456789101112131415161718192021....
Re:Well... (Score:5, Interesting)
Of course there's a pattern, even a simple and elegant one. It's equal to:
4 * (1 -1/3 + 1/5 -1/7 +1/9 -1/11 +1/13 -1/15 etc., etc., etc.)
Just because the pattern doesn't come out pretty in a decimal representation doesn't mean it's not elegant or not a pattern.
I've got an even more simple pattern (Score:5, Funny)
Re:I've got an even more simple pattern (Score:5, Interesting)
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It can be exactly defined by a finite amount of information. And it's not impossible, in general, for a transcendental number to have some sort of pattern in the numerical representation. For instance, the Champernowne constant -- .12345678910111213...
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Actually, the program itself is a perfectly fine way of representing pi. See: computable numbers [wikipedia.org]. Note that almost all [wikipedia.org] real numbers are not computable, so it is a non-trivial property.
It also takes an infinite amount of time to write out the decimal expansion of 1/9, but that can be written very concisely as a rational number. Also note that pi is irrational [wikipedia.org] so its decimal expansion is infinite in all bases [wikipedia.org].
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Actually, the program itself is a perfectly fine way of representing pi.
So... random honest question. How do they know the program (or its output) is correct? Is it possible to create a proof that the program will generate correct output?
I mean, sure, we can look at the first nine digits and say "yeah, that looks right". But does anyone really know if digits 1.2 trillion through 2.5 trillion in the output are correct?
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Wikipedia has pretty good article(s) on everything PI - how to calculate it in different ways, history, and all those quirks you don't even imagine to think about, before you read about them :-)
Re:I've got an even more simple pattern (Score:4, Insightful)
The grandparent post already answered that...
PI = C/D
Or even simpler: "PI is the circumference of a circle of diameter 1".
Or how about "PI radians = 180 degrees"
Just because it's not easily representable in a base-10 number system, doesn't mean you can't exactly define it.
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Or even simpler: "PI is the circumference of a circle of diameter 1".
OK, so where do I find the circumference?
Pardon the pun, but this definition seems circular to me.
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i is the perimeter of your happy place.
In grue feet.
Re:Well... (Score:5, Interesting)
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Just because nobody has detected a pattern doesn't mean there isn't one.
Don't you think that's an irrational conclusion?
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They better keep on going, 'cos what if the pattern is that the SECOND three trillion digits are the same as the FIRST three trillion digits, except like BACKWARDS! :O
Man, that'd be SO AWESOME.
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Just because nobody has detected a pattern doesn't mean there is one.
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Ever stopped to think that throwing more computing power at a problem is about as productive as throwing more money at a problem or more man power? You can only do so much before an effort becomes either redundant or the return on investment is as dismal as the stock market has been this past year.
I don't honestly know what the practical value of knowing Pi to the 2.5 trillionth digit is but I'd like to think that there are enough resources in play that the fight f
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