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Nicholas Sze of Yahoo Finds Two-Quadrillionth Digit of Pi
gregg writes "A researcher has calculated the 2,000,000,000,000,000th digit of pi — and a few digits either side of it. Nicholas Sze, of technology firm Yahoo, determined that the digit — when expressed in binary — is 0."
an so are an infinite other digits in that number
don't cut it off www.mgmbill.org
Well, the 243,000,500,000,000,000,002th digit of pi is "4".
Go on, prove me wrong.
Or hex?
i misread that statement and i thought Pi finally have an ending to its story! Guess not.
BFD
*facepalm* So that's 9 in decimal, right?
No folly is more costly than the folly of intolerant idealism. - Winston Churchill
Just say'in
...move along people, nothing to see here.
He'll definitely get some action for sure!
Good to know they're putting those idle datacenters to good use. It's not like Yahoo has any real users anymore to generate load.
"Interestingly, by some algebraic manipulations, (our) formula can compute pi with some bits skipped; in other words, it allows computing specific bits of pi," Mr Sze explained to BBC News.
So why don't they just use their formula to compute the last digit of Pi already?
That would be the rational approach. Who cares about the two quadrillionth digit??
either that or 1
Geez, even I could have gotten it right half the time.
http://www.tauday.com/
2,000,000,000,000,000 digits takes about from 200 TB (binary digits) to 3600 TB (hexadecimal digits).
So, do you have to keep the whole number in the memory to calculate some more digits? Or can you keep the whole thing on the hard disk because it is not needed to calculate more digits?
If the first is the case, how do they do it? It is more than 100 hard disks worth of memory, who has that?
If the second is the case, why don't they just calculate the digits from wherever the last record ended...
Word. This discovery is useless. Now, if he'd managed to prove that the digit, when expressed in binary, is 2... That'd be something to shout about!
the digit — when expressed in binary — is 0.
Jeez, what are the odds of that?
The interesting thing about this article is how they calculated the digits. They broke the problem up into small pieces and had them calculated in parallel. This approach isn't something that's new or all the unique, but what is is applied to is. Most mathematical calculations are done in a near linear fashion, not in parallel. So for them to be able to do this is a big step forward in how we approach these types of problem in the future.
Of course I'm very interested in this since it seems I'll be doing something like it in the near future as part of getting my master's degree.
I think it's safe to assume the number never repeats.
Get some !!
further evidence of the media's lack of communication skills;-}
"Technology firm Yahoo"? Does it need such an introduction now?
Also I can calculate with 50% certainty that the next digit is 0 also. Do I get a prize?
I've always wondered about these ridiculously precise values of pi - doesn't that imply a measurement (of circumference or diameter) smaller than the Planck length? What's the point of 2 trillion decimals of precision?
No folly is more costly than the folly of intolerant idealism. - Winston Churchill
Bailey–Borwein–Plouffe formula lets you calculate the n-th digit of pi without calculating the n-1 digits.
I wonder what formula was used to calculate the digit here.
Before you know it all computers around the world will be consumed with finding the complete number set of PI
does this bit from TFA strike anyone else as a bit odd?
"The computation took 23 days on 1,000 of Yahoo's computers, racking up the equivalent of more than 500 years of a single computer's efforts."
So.... 1000 machines, 23 days, assuming embarrassingly parallel that's 23000 days of computation on 1 machine.
23000/365 = 63.0136986 years
now each of those could have 8 cores and they meant 500 years on a single core processor of course.
but still odd phrasing.
And, we know this is correct how ?
Amazing, so is Yahoo's profit projections within five years!
The world's burning. Moped Jesus spotted on I50. Details at 11.
Is that a way of saying they have a lot of engineers, but little to show for it?
This article actually explains it better, and uses the phrase "piece of pi". I love it.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
Does Fuzzy Math have a hair-pi?
I have something in common with Stephen Hawking...
just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.
It's actually 13 orders of magnitude less significant than the 200th.
"Who is the Journal of Quantum Physics going to believe?" --Stephen Hawking
just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.
Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less than a power of 2. We can determine if such numbers are prime using a very efficient test called the Lucas-Lehmer test. The largest such prime known today is 2^43,112,609-1. This is much, much larger than any number we'd want to practically factor (for example numbers used in RSA encryption are generally on the order of a few hundred digits. It is believed that numbers with 2000 or so digits will be secure for the indefinite future). So yeah, finding large primes is about as useful as this when it comes to practical factoring. There are other somewhat good reasons to be interested in finding large primes, but factoring isn't one of them.
I bet he googled the answer...
dnuof eruc rof aixelsid
It's actually 13 orders of magnitude less significant than the 200th.
Yeah, I knew some smart ass would say that. I almost didn't use the word "significant" but the meaning of the word is ambiguous. So we are both right.
The horror, they used map reduce instead of a acid compliant database server.
Got Code?
It is 1 in binary.
That quote really doesn't work. If that digit, expressed in binary, is 0 then the (decimal) digit is also 0. /. summaries would at least get that right. (Yeah, I'm new here.)
But that cannot be what they meant, so I think they meant that the nth binary digit is 0, in which case the title should have been something like "Nicholas Sze of Yahoo finds two quadrillionth binary digit of pi".
You'd think that
In any case, this is the interesting bit of the article:
"Interestingly, by some algebraic manipulations, (our) formula can compute pi with some bits skipped; in other words, it allows computing specific bits of pi," Mr Sze explained to BBC News.
The rest is pretty much filler and brand tossing.
just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.
Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less than a power of 2. We can determine if such numbers are prime using a very efficient test called the Lucas-Lehmer test. The largest such prime known today is 2^43,112,609-1. This is much, much larger than any number we'd want to practically factor (for example numbers used in RSA encryption are generally on the order of a few hundred digits. It is believed that numbers with 2000 or so digits will be secure for the indefinite future). So yeah, finding large primes is about as useful as this when it comes to practical factoring. There are other somewhat good reasons to be interested in finding large primes, but factoring isn't one of them.
Yeah, I know all of that. That wasn't my point. Reread what I wrote.
The attention to detail one pays in one field of endeavor is somewhat of an indicator of how much attention to detail one pays overall. Sure, your defense is the SAT separates the two, but the brain doesn't work on different problem classes completely independently!
There are two ways to express uncaring: "I could not care less", meaning I care as little as possible for this thing, in fact it is not possible for me to care any less than I do right now.
Then there's the somewhat intricate (for minds like yours) "I could care less", meaning that although it is possible that I could care less for this thing, it would require more effort than I'm willing to put forth, so I'm happy to stick with the current amount of caring I have for this thing.
Welcome to fifth grade English.
I feel fantastic, and I'm still alive.
They are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
IIRC to represent any other number (other than 1 or 0) you'll display it accumulatively.
For example:
0b = 0
1b = 1
10b = 2
11b = 3
100b = 4
so on and so forth. So if this number is expressed in binary as 0, then the number is actually 0 in decimal, right?
And I have calculated that if he is incorrect and the value is one and not zero that I have a 50% chance of being correct.
Ok. Reread it. Now confused. What did you mean when you said "At least with primes you reduce the time for factorization"?
The computation took 23 days on 1,000 of Yahoo's computers, racking up the equivalent of more than 500 years of a single computer's efforts.
And before answering, the computer paused and said, "You're not going to like it ..."
the meaning of the word is ambiguous. So we are both right.
Also, you're both wrong.
I'd rather you rationally disagree than irrationally agree.
I was hoping for a funny rather than the informative I got, to be honest.
"Who is the Journal of Quantum Physics going to believe?" --Stephen Hawking
It's actually about 10^13 orders of magnitude less significant than the 200th.
It is 1 in binary.
Hast du ein?
The Admin and the Engineer
Oh thank God that Nicholas Sze was finally able to think of a clever way to finish that calculation - the anticipation has kept me awake for at least the last twenty-three days!
Too lazy to RTFA, but spigot algorithms (specifically the BBP algorithm for calculating pi) ALL have the capability of extracting arbitrary digits from irrational numbers without calculating previous ones first.
http://en.wikipedia.org/wiki/Spigot_algorithm
My understanding is there are actually only two digits in that number: digit zero and digit one.
If enithin kan gow rong it whil. (Murfey)
And I had '1' in the pool!
When will the mathematicians give up on Pi as some sort of grand benchmark.... couldn't they do better things to benchmark their systems... like running a folding@home client, or some such thing?
Honestly.. the first thing I thought when I saw this was... wow.. how.. uncreative...
How is this going to help them beat out Google and MS again ?
Not to bash on Yahoo.. they were once a great service/company... but they're quickly becoming a has-been. What they desperately need, and what everyone in this sector needs, is creativity. This sort of horn tooting doesn't really impress me, so much as it depresses me that people are benchmarking their systems on the same old problem again and again.
I can give them any digit in the binary representation of pi with 50% accuracy.
I think I would have had a halfway-decent chance of guessing that.
It's really only when you examine the unary representation of pi that the fascinating patterns tend to emerge:
000.000000000000000000000[...]00000000000000000000000000000000000000000000000000[...]000000000000000000000000000000000 and so forth.
You're forgetting all the zombie networks that connect to Yahoo. There's probably a few billion nodes there, and there's not a friggin' chance Yahoo will admit to knowing about them.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
The 2,000,000,000,000,000th digit of pi is 13 orders of magnitude less significant than the 200th, at least in base 10.
http://en.wikipedia.org/wiki/Order_of_magnitude
"Who is the Journal of Quantum Physics going to believe?" --Stephen Hawking
The computation took 23 days on 1,000 of Yahoo's computers, racking up the equivalent of more than 500 years of a single computer's efforts.
1000 computers * 23 days * (1 year / 365 days) = ~63 computer years
The additional 437 years are due to the single computer's constant procrastination, frequent partying and numerous hangovers.
The guy at Yahoo later calculated the 10^100th digit of pi, and some guy from the marketing department came up behind him and whacked him with a 2x4.
Blah
Then there's the somewhat intricate (for minds like yours) "I could care less", meaning that although it is possible that I could care less for this thing, it would require more effort than I'm willing to put forth, so I'm happy to stick with the current amount of caring I have for this thing.
Welcome to fifth grade English.
That's like when I visit my family for vacation. Mom keeps asking me if I want more mashed potatoes, more roast beef, more salad... and at the end of the meal I say "I could eat more". She looks all puzzled for a while until I explain to her that while it's possible that I could eat more, I'm so full that it would likely rupture my stomach if I did, so I'm happy to stick with the current amount of food that I've consumed.
I guess Mom didn't finish fifth grade.
Want to improve your Karma? Instead of "Post Anonymously", try the "Post Humously" option.
He could have just asked Yahoo! Answers
That'd be 42, not zero.
Maybe Computers will never be as intelligent as Humans.
For sure they won't ever become so stupid. [VR-1988]
Can anyone explain to me how 0s and 1s expressed in binary is "0"? WTF does that mean?
WTF for?
Knowing it to about twenty digits is enough to locate a proton anywhere in the solar system (actually that may not be entirely accurate but I *did* once calculate that the 355/113 ratio was enough to find a spot on the surface of the Earth to within the length of a car).
Do we really need more accuracy than that?
Backing up even farther, I thought you could calculate a specified digit of pi without calculating all those that came before it. Or do the numbers simply get so big that even regular operations like multiplication and division start to take extreme amounts of computing power?
To answer my own question (yes, I know I should have looked before asking in the first place) the most efficient digit extraction algorithm known is O(n^2), so I imagine finding the Two-quadrillianth digit would still take quite a while.
.01=10^-2 is an order of magnitude less significant than 0.1=10^-1. 0.0000000000001 (13th digit) is 13 orders of magnitude less significant than 1. Not just one order of magnitude. The kth digit contributes n_k 10^-k in the decimal expansion where n_k is the kth digit. So, indeed, n_k's contribution is indeed k-k' orders of magnitude more significant than the k'-th digit.
The hexadecimal digit extraction formula for PI (that allows you to skip calculating the previous hex digits) is already known. It can calulcuate the N'th hexadecimaldigit of Pi without calculating most of the previous digits: http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
A slower generalized version that can extract the n'th digit of Pi in any base (including decimal) has also been found: http://web.archive.org/web/19990116223856/www.lacim.uqam.ca/plouffe/Simon/articlepi.html
Stylish sheet to fix many problems in Slashdot's D3: https://gist.github.com/801524
Was the base 43?
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
I think you're off by a few trillion orders of magnitude there!
The thing that I find funny, is that had they used the Bailey-Borwein-Plouffe formula, they could have saved themselves some very considerable computing resources.
[FUCK BETA]
is enough for PRACTICAL purposes - if you need more decimal places, use 22/7 :-)
" 2,000,000,000,000,000 digits" is just tits on a bull.
1.Convert PI to binary
2.Interpret binary PI as ASCII
3.Search for the complete works of William Shakespeare
4.Once found, use number to produce compact William Shakespeare quote generator.
Yeah, a wildly inefficient demonstration... What's next? Will they attempt to use cloud computing to add 1+1+1+1+1 etc. until they know how many ones you need to add to reach 'infinite'?
the meaning of the word is ambiguous. So we are both right.
Also, you're both wrong.
Stop being so ambiguous.
And I predict that the 4,000,000,000,000,000th digit of pi will be a 1. I've got a 50% chance of being right if it's in binary.
To have a right to do a thing is not at all the same as to be right in doing it
No. It's actually 20,000,000,000,000 orders of magnitude less significant. Think small: The 10th digit is 10 OOM, the 20th is 20 OOM etc. less significant.
I've got a 110010% chance of being right if it's in binary.
FTFY
... since it is in binary. Unless there is some pattern.
It's sad that so much work has been done to find digits of one-half of the REAL circle constant, Tau. http://tauday.com/
No comment.
3!
Is that actually provable? And if so, how?
Forget magic. Any technology distinguishable from divine power is insufficiently advanced.
**sigh**
now i may die in peace, the secret i have been searching for is revealed. my life is now complete
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
There is no 2
For binary it is trivial:
Since it is an infinite, noncyclical number, there must be a zero some finite digits after any one. This must repeat ad infinity, so there must be an infinite numbe of zeroes.
Alternative would be that all digits after, say, digit 1,000,000,000 are ones. This could be written as a fraction, and would not be an irrational number.
You can make a similar argument for a decimal representation for pi. If you can come up with a good one, please reply.
don't cut it off www.mgmbill.org
It is believed that numbers with 2000 or so digits will be secure for the indefinite future.
Digits? or bits? Because most RSA keys are in the 1024-4096 bit range if I understand the math correctly. Which is a lot less then 2000 decimal digits (2^4096 is roughly 1.044e1233 or about 1234 decimal digits while 2^2048 is only 3.23e616 or about 617 decimal digits).
Wolde you bothe eate your cake, and have your cake?
Already done (with 50% probability)
Why do I hear Comic Book Guy when I read this article.
That's nice, but shows what's wrong with the slashdot approval system, since the pointer to the source arXiv:1008.3171 was already posted here a month ago:
http://slashdot.org/submission/1317438/A-new-record-the-Two-Quadrillionth-Bit-of-Pi-is-0.
Why is it more interesting because the BBC finally got around to covering it?
Yes, sorry I think I was thinking "binary digits" and then somehow dropped a word. Either that or there was a generic stupidity moment on my part.
when expressed in binary — is 0
Hmmk, but when 5 is expressed in binary, it is: 101 and 15 expressed in binary, is: 1111 So how is 3.14_ expressed in binary as 0?
"had they used the Bailey-Borwein-Plouffe formula"...
You don't think calling the implementation "DistBbp" suggests they did?