5 Trillion Digits of Pi — a New World Record 299
KPexEA writes "Alexander J. Yee & Shigeru Kondo claim to have calculated the number pi to 5 trillion places, on a single desktop and in record time. The main computation took 90 days on Shigeru Kondo's desktop. Verification was done using two separate computers. The program that was used for the main computation is y-cruncher v0.5.4.9138 Alpha." Looks like the chart of computer-era approximations of Pi here might need an update.
Mind-numbing computational outsourcing (Score:5, Funny)
Re:Mind-numbing computational outsourcing (Score:5, Funny)
Re: Comfortably Numb (Score:3, Funny)
You set someone up there with a perfect Pink Floyd joke, but I can't find the best algorithm...
Re:Mind-numbing computational outsourcing (Score:4, Funny)
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Yes, but how could they verify that we bested hamlet?
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The same way the robots know they've finished calculating Pi.
KGB it! (Score:2)
You know the KGB commercials? I'd find it funny if someone were to ask them what the 5 trillionth and one decimal digit of Pi is.
Re:KGB it! (Score:5, Insightful)
Re:KGB it! (Score:5, Funny)
Okay, so what's the last digit of Pi?
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f(infinity+1) ... where f is the computation algorithm.
Re:KGB it! (Score:5, Interesting)
The moment we know, the stars will start to fade out. [lucis.net]
Re:KGB it! (Score:4, Funny)
in binary, it's either a 1 or a 0, so you have a 50/50 chance of being right.
Re:KGB it! (Score:4, Informative)
Actually the last digit of PI is 1 in binary.
As 0.1b is the same as 0.10b
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Re:KGB it! (Score:4, Interesting)
in binary, it's either a 1 or a 0, so you have a 50/50 chance of being right.
In unary it's just 0. It's zeroes all the way down. Easy to calculate too, you just turn off your computer forever. Dead computing is the new trend.
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I don't think that's true. As far as I see, you can't represent the last digit of pi at all in unary. You can represent the positive integers in unary. I suppose you could represent the negative integers. You cannot represent zero. You can represent real numbers as a fraction, but as far as I know, not as a decimal (sic).
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Errr....really I meant you can represent rational numbers as a fraction. You can't represent irrational numbers as a fraction for all the obvious reasons.
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unary moderation, everyone is a troll all the way down.
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In base Pi, it's zero.
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no, in base Pi, Pi=1*Pi^1 + 0*Pi^0 + 0*Pi^-1 + 0*Pi^-2 + 0*Pi^-3 + 0*Pi^-4...
hence, in base Pi, Pi= 10.0000000000..., like in base 10, 10=10.00000000000..., like in base 2, 2=10.0000000...
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Chuck Norris.
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Okay, so what's the last digit of Pi?
We here in Flatland always get a hearty chuckle when we read about human antics. As you know, we are a Base-pi society as opposed to basing our number system on something as arbitrary as the number of digits we have (btw, what's a digit again?).
So does that answer your question?
Re:KGB it! (Score:4, Informative)
The BBP formulas handle this. A quick Google for Bailey-Borwein-Plouffe should give you all the citations you ever need.
A working example of the BBP formula can be found in Javascript on this webpage. http://www.csc.liv.ac.uk/~acollins/pi
Warning: it WILL hang some web browsers as the author does not use web worker API.
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Pi has decimal digit extractors. In fact, I think there's an arbitrary base algorithm.
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I was thinking, you should ask them for Pi to 10 trillion decimal places... but then I thought, by the time they sent you the first half of all those text messages (something like ~31 billion assuming 161 characters max), they would have enough time to calculate the next 5 trillion, along with making a crapload of money from all the fees.
So is there a message (from God?) (Score:4, Funny)
I've heard that in the book (not movie) "Contact" that when Jodie Foster's character meets the uber-aliens she asks them:
"Do you believe in God?"
-"Yes"
Taken aback "Really, why?"
-"We have proof, when PI is expended out to (some number), there is a message"...
I really wish I read the book to know what the message is (maybe "Nietsche is dead"?)
I no longer login because I feel that while attacking a company's products is fair game (specifically Apple), having stories singling out their users as "selfish" and unkind is not "news for nerds stuff that matters". Am I an Apple fanboi? Let's just say I've used NIX for decades (yes I'm old) and I'm not talking OS X.
Re:So is there a message (from God?) (Score:5, Informative)
The aliens are vague about the location of the message (it might be in pi) so the Foster character runs software to search for it. Right at the end of the book her program finds a pattern (A circle drawn in 1s and 0s in an 11 by 11 matrix). This pulls together the thread in the book about belief in god vs religion. It turns out that somebody made the universe after all, and the Christians had been (sort of) right all along, though the scientists were right to demand evidence.
I love both the book and film. Thats unusual for me. The Postman was a fantastic book. Don't get me started on the movie.
I often put the DVD of Contact on just to watch the sequence where Fosters character first hears the signal and her crew reconfigure the telescope to analyse it. Its a classic tech scene.
"Once upon a time I was a hell of an engineer"
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Right at the end of the book her program finds a pattern (A circle drawn in 1s and 0s in an 11 by 11 matrix).
Wait, so the message from God is a circle? I find this one a little more convincing:
http://dresdencodak.com/2009/07/12/fabulous-prizes/ [dresdencodak.com]
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I always found that concept, encoding a message in pi, to be staggeringly stupid. The value of pi doesn't depend on physics, which is why we are able to determine it algorithmically rather than experimentally. (Some people argue 'but pi is the ratio of the circumference of a circle to its diameter, and that depends on physics'. Yes, that ratio depends on physics, for physical circles, provided that some other physical geometry besides 'flat' is possible. But a non-flat geometry would just mean that the
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But maybe that just demonstrates the limits of our thinking. We re used to the parameters of our universe and have trouble imagining how things could be different.
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But maybe that just demonstrates the limits of our thinking. We re used to the parameters of our universe and have trouble imagining how things could be different.
Of course there are many, many, marvelous things that are beyond our imagination. But the abstraction pi can be understood to be what it is, within the framework that defines it. This isn't affected by those other unknown things. If there were a 'different' pi that could be conceived of in some other realm, it would have other properties and relationships, and could be given a different name to distinguish it from the one we work with. It is not physical, is not measured, is not a 'parameter of our univ
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I think that it's one of those big things that we just don't quite can wrap our minds around. What does it mean that there's a certain structure and properties to geometries, that topology of things looks just like so and not some other way, etc? Do those things depend at all on the universe we live in? Would, somehow, someone in another universe find, that PI has a different value even though it's not a physical constant as far as we can tell? And maybe we're just mistaken and it is really a physical const
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I think that it's one of those big things that we just don't quite can wrap our minds around.
OK. Speak for yourself.
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I'm serious. How would you even start an argument about PI not being a physical constant? It's really just a matter of definition, and in that sense there's no argument.
But we say that physical constants are some things we measure, and other seemingly fundamental things we can measure are not (like PI). PI can be of course measured to a good few digits by manufacturing a sphere or a disk/cylinder, and then measuring the circumference and radius. We then also have mathematical theories that can come up with
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The aliens are vague about the location of the message (it might be in pi) so the Foster character runs software to search for it. Right at the end of the book her program finds a pattern (A circle drawn in 1s and 0s in an 11 by 11 matrix). This pulls together the thread in the book about belief in god vs religion. It turns out that somebody made the universe after all, and the Christians had been (sort of) right all along, though the scientists were right to demand evidence.
If you're given a free hand at the decryption code, you can find any message you want. Presumably the infinite non-repeating sequence of digits is full of marvelous patterns when displayed on a grid as well.
Maybe *every* pattern on every grid size, but I'm not sure of that. (The digits aren't actually independent random numbers.)
It's just a matter of time until some charlatan claims to find a message in our DNA. In a society that can't grok what's the deal with The Bible Codes, people will believe him.
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If you're given a free hand at the decryption code, you can find any message you want... Maybe *every* pattern on every grid size"
Yes, given infinite digits, every pattern would appear eventually. However, the point that was made in the book was that the probability of a particular pattern appearing is vanishingly small. In the book Contact, the embedded circle of 1's in and 11 x 11 grid appeared after a LONG (>10^6) sequence of just 0's... and followed by one too. Then PI continued as always. As
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The problem is, if you look long enough, hard enough, any message you can think of will appear in pi. Put it in Base 26 and you'll eventually find the complete works of Shakespeare (it might be 10^10^10^10 digits down, but it will be there). I was kind of disappointing in the book that Sagan didn't at least discuss the probability of finding something that appears significant by the time they reached the depth they were at.
Re:So is there a message (from God?) (Score:5, Funny)
I no longer login because I was modded down to terrible karma when I tried to stand up for one of Apple's gay products, and subsequently bragged about performing fellatio on Steve Jobs. People thought I was trolling but actually I was telling the truth.. Am I an Apple fanboi? Yes Indeed.
FTFY.
Re:So is there a message (from God?) (Score:5, Informative)
"Taken aback "Really, why?"
-"We have proof, when PI is expended out to (some number), there is a message"..."
Duh.
http://everything2.com/title/Converting+Pi+to+binary%253A+Don%2527t+do+it%2521 [everything2.com]
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Actually, it's quite safe to calculate Pi in binary, if you do enough of it. After all, somewhere in it you'll find a message from each copyright owner, signed with his secret key, that you are allowed to have a copy of the copyrighted work. Moreover, you'll have documents about everyone on earth which reveal facts they rather would not like to be published. So actually having enough digits of Pi in binary gives you near-absolute power! That's why THEY want to scare you away from calculating Pi in binary.
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"We have proof, when PI is expended out to (some number), there is a message"
"Five trillion digits ought to be enough for anybody - God"
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"We have proof, when PI is expended out to (some number), there is a message"...
Of course, pi is normal [wikipedia.org] in binary. Every possible message will occur eventually. So if we expand pi far enough, we might even find a positive review for Carrot Top's act. Turns out that math can be wrong.
Wow. (Score:2, Offtopic)
A tour de force of math and computing hardware and software skills.
Makes me want to turn in my geek card.
Obviously a fraud (Score:2, Funny)
They just took the number 3.14159 and added a load of random digits to the end - let's face it, nobody's going to check!
Re:Obviously a fraud (Score:5, Interesting)
They just took the number 3.14159 and added a load of random digits to the end - let's face it, nobody's going to check!
Reminds me of the MAX light rail station in the zoo tunnel in Portland, Oregon. Apparently there is the first 100 (1000?) digits of pi chiseled into one of the walls. A writer noticed that the first digits were correct, but quickly went astray. But later in the sequence, there was a recognizable early string of digits. The writer sleuthed that the sculptor had used the Book of Pi, which has the numbers in blocks of ten digits in five (or so) columns. In the book, you read the first row and then the next row.* The sculptor had read the first column, then the next column...
* or the other way around
Soon there'll be a competition to calculate... (Score:2)
... how many digits someone will calculate Pi too each year.
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I don't write this question as a troll... (Score:2)
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Not a lot. Except to prove that your supercomputer is reliable when calculating numbers like that, and how fast it can do it. Usually, I think it's just used as a test of the computer's abilities rather than anything serious.
Even in the precision engineering world, more than about 10 digits of accuracy for pi is a bit silly. Pi will never really, practically, be required in more depth than what your processor's registers can hold.
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Hmm, I can think of an interesting and useful use of it: doing various statistics and randomness tests on those digits, finding patterns in their order, and so on.
But I don't suppose that's what those contests to find the most PI digits are about.
Re:I don't write this question as a troll... (Score:4, Funny)
what is the real significance of learning Pi to a more accurate measurement?
The same as the damage a bulldozer would suffer if it were allowed to run over you.
Re:I don't write this question as a troll... (Score:4, Funny)
what is the real significance of learning Pi to a more accurate measurement?
The same as the damage a bulldozer would suffer if it were allowed to run over you.
The frustrating bit is that PI is available to 100 trillion digits in the local planning office on Alpha Centauri.
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Trillion? (Score:3, Insightful)
Trillion in which language? How many zeros does it have?
Re:Trillion? (Score:4, Informative)
This page has more details [numberworld.org], what I find interesting is that he needed 96.0 GB of ram to do the number crunching.
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last time i checked, trillion was not a proper SI prefix.
what you probably mean is "tera-", but in my native language a trillion is 10^18, which would be the "exa-" SI prefix.
check this: http://en.wikipedia.org/wiki/Long_and_short_scales
They're doing it wrong (Score:2, Funny)
They're calculating Pi in base 10, which is the wrong path.
Pi should be calculated in base 3.141593...
It's a paradox, people.
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Pi should be calculated in base 3.141593...
You're out on the 6th decimal digit (unless you're going to stop there). Pi is greater than 3.1415926 and less than 3.1415927.
Have I been trolled?
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No, it's not. Your answer is 10.
Aww. (Score:2)
When I read the title, I thought someone had successfully memorized 5 trillion digits of Pi. They just computed it? What a letdown.
Still no pattern in there? (Score:2)
5 trillion digits are a *lot* of digits! no patterns yet in there?
Was there any pattern after 2 billion digits? (Score:2)
My passwd (Score:2)
Hmm, I'm not I like this. Has anybody considered the security impact of this? Pi being a proper irrational number is bound to have, as substrings of digits in it's decimal representation, all possible combinations of characters represented as eg. UTF-8, so somebody could easily find all passwords currently in use in there, lined up alphabetically. Somebody clearly hasn't thought this through.
Time to sing some Pi carols! (Score:2)
It's a Wonderful Day for Pi [youtube.com]
Pi - full version [youtube.com] / just the numbers [youtube.com]
.
Pi Calculated to 5 trillion digits (Score:2)
So, is it still between 3.14 and 3.15?
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It is even between 3.1416 and 3.1417
pi is Wrong (Score:2, Informative)
Value of Pi (Score:2)
Here's What /. Readers Really Want (Score:2)
Also, anyone else also notice the partially cropped off friend, it's not Clippy [wikipedia.org], on the final result screenshot?
What was sitting on the desktop? (Score:2)
How big was this desk, and what was sitting on its top that was doing the actual calculation? It's odd to simply refer to a piece of furniture as doing the calculation.
Print it out! (Score:2)
The "world's fastest laser printer" prints about 60 ppm. At one page a second, 10,000 digits per page, it would take 500 million seconds or fifteen years to print it out. So one might hope to live to see all the known digits of pi printed out... unless those pesky computer scientists calculate more of them. But, really, 5 trillion digits ought to be enough for anybody.
And it would only require a million reams of paper.
Re:Update... (Score:4, Informative)
Wikipedia has a much better page available.
http://en.wikipedia.org/wiki/Chronology_of_computation_of_%CF%80 [wikipedia.org]
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The PDF version http://numbers.computation.free.fr/Constants/Pi/piCompute.pdf [computation.free.fr] of the page is up to date, but for some reason the html is behind. Also the PDF correctly displays the mathematical formula, while the html doesn't for me.
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Re:Are they exact? (Score:5, Funny)
How can we be sure all those digits are correct?
Use it to draw a circle. If the circle ends up looking more square than round then you know they've made a mistake. Seriously, do I have to do everything around here?
Re:Are they exact? (Score:5, Informative)
If you want to prove that all the digits are correct, you only have to check a few things:
1. There is a sound mathematical proof that the algorithm used in fact does generate the digits of pi, and
2. The algorithm was coded correctly. This should be even easier to check, though likely more tedious.
Now, what it's good for is a little harder. There is no physical application for such a highly accurate value of pi (39 digits should be sufficient to calculate the circumference of the known universe given its radius to within the diameter of a hydrogen atom). However, large numbers of digits of pi are useful as arguments in number theory, statistics, and information theory. For instance, there is no real proof that pi is a normal number [wikipedia.org], but as more digits of pi are found and the statistical properties of the digits are analyzed and shown to be consistent with the definition of normal numbers, that makes the conjecture that pi is actually normal a little closer to being true (see experimental mathematics [wikipedia.org]).
Re:Are they exact? (Score:5, Insightful)
Knowing that the algorithm is correct and the implementation was codec correctly doesn't help you when you have faulty RAM that flips a bit.
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Or some kind of wierd, rare CPU bug. (I was going to mention ram bits getting flipped by cosmic rays and not error corrected, but you've basically covered that with the faulty RAM thing). Oh, you could also have a faulty sector on a hard drive/NAS that you are saving the result too. Or maybe a random network error that corrupts the data (if it gets transmitted over any kind of network). Maybe some wierd glitch in the Front Side Bus (or other hardware on the MoBo which interconnects things).
There's all sorts
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The problem with normality is that every digit, including the infinitely many that we haven't calculated (and the infinitely many that we never will) are equally significant. We are no closer to determining
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If you want to prove that all the digits are correct, you only have to check a few things:
1. There is a sound mathematical proof that the algorithm used in fact does generate the digits of pi, and 2. The algorithm was coded correctly. This should be even easier to check, though likely more tedious.
Actually, 1 isn't very hard. It's known that the series expansion used approaches pi in the limit. If you mean each of the algorithms that they use to break down the Chudnovsky formula, then that's harder. 2 is the real kicker along with hardware errors as others have noted. Basically it was not fully verified that the coding was done correctly. How many things really have mathematically proven and truly 0 bug coding anyway? I don't think even medical or nuclear installations have that.
But because of imp
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No, that isn't practical or sufficient, and it's not how they actually did it [numberworld.org]. Proving nontrivial pieces of software to be correct is basically impossible, and really you'd also need to prove that the compiler
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2 x ( 2/1 . 2/3 . 4/3 . 4/5 . 6/5 . 6/7 . 8/7 . 8/9
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...
That would take forever to calculate, I presume.
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"How can we be sure all those digits are correct?"
Manual comparison. They read the first million or so digits aloud, and if those digits don't match the ones from previous programs then there is something wrong in the algorithm.
"And, more important question, what are they for?"
Comparison of size of course, people do that all the time. But in this case it's more about who is able to write the most optimal application than anything else.
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How can we be sure all those digits are correct?
You mathematically prove the algorithm is correct, and that the program faithfully implements the algorithm.
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Why?
Why not?
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segfault
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There might actually be something interesting in there. Lots of discoveries have been made by people who were just trying things out or seeing what they could see.
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Put labour last in the senate, Aug 21
Why?
You think I should preference the Sceptics Party first? Or the Citizens Electoral Council?
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Vote how you like. I am a Victorian so this is my Big Chance to vote Stephen Conroy out.
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Conroy is a twat, all agreed.
I have already voted - did it today - sex party 1 in the senate...
Certainly didn't put Labor last tho - there are seriously derange lunatics to preference well after Labor.
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First off, it's a simple test. A proving ground of sorts. It's also a good place for a programmer to cut his teeth on a lot of concept that he can relate to with other programmers since it is so wide spread.
Corrections follow... (Score:5, Informative)
Yes, we do. Mathematical algorithms, i.e., equations on paper.
Absolutely not. The algorithms have to run on practical, exists-on-the-Earth-today computers. Try to multiply two, million-digit numbers together on your laptop and you'll see what I mean. These achievements are all about computational optimizations. RTFA -- especially the sections entitled "Arithmetic Algorithms" and "Maximizing Scalability." Even the algorithm used for multiplication changes (dynamically!) during the program's execution, based on the size of the operands.
Not even close. The computations are so long, and so intense, that errors caused by hardware imperfections can be expected, so error detection and correction algorithms have to be added. If "I left my pi calculating program running longer than the last guy" it would not produce the correct result -- even if the data structures and algorithms it used were up to the task.
In a word, yes. Could you do it? It's a very, very difficult technical feat, one that required hardware powers and software abilities far beyond those of mortal men. Besides, you're worried about newsworthiness when the two previous /. articles are on wall-climbing robots and the popularity of video game arcades in New York?
This isn't about needing pi to 5 trillion digits. This is about learning how to do large computations faster. Like, improving the state of the art.
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Yes. Avoid floating-point.
Either used fixed-point (yuck), symbolic calculations and then only finding the decimal expansion at the last stage, or rewrite your formula to avoid any possible lack of precision (i.e. any division).