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# Nicholas Sze of Yahoo Finds Two-Quadrillionth Digit of Pi

#### timothy posted about 4 years ago | from the I'm-a-good-guesser-in-binary-too dept.

299

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."

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### an so are an infinite other digits in that number (1)

#### viking80 (697716) | about 4 years ago | (#33605370)

an so are an infinite other digits in that number

### Re:an so are an infinite other digits in that numb (4, Funny)

#### Anonymous Coward | about 4 years ago | (#33605554)

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!

### Re:an so are an infinite other digits in that numb (2, Insightful)

#### HungryHobo (1314109) | about 4 years ago | (#33605700)

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.

### Re:an so are an infinite other digits in that numb (4, Funny)

#### MightyMartian (840721) | about 4 years ago | (#33605716)

the digit -- when expressed in binary -- is 0.

Amazing, so is Yahoo's profit projections within five years!

### Oh yeah? (4, Funny)

Well, the 243,000,500,000,000,000,002th digit of pi is "4".

Go on, prove me wrong.

2th?

### Re:Oh yeah? (4, Funny)

#### Kinky Bass Junk (880011) | about 4 years ago | (#33605640)

He might be the 2th fairy.

### Re:Oh yeah? (0, Offtopic)

#### Kinky Bass Junk (880011) | about 4 years ago | (#33605880)

I can't believe people actually modded that lame joke as funny.

### Re:Oh yeah? (3, Funny)

#### Dthief (1700318) | about 4 years ago | (#33605508)

I would argue the opposite

### Re:Oh yeah? (0)

#### Anonymous Coward | about 4 years ago | (#33605660)

I would argue the opposite

And I could care less.

### Re:Oh yeah? (2)

#### Peach Rings (1782482) | about 4 years ago | (#33605726)

I couldn't care more!

?

### Re:Oh yeah? (3, Insightful)

#### cmdahler (1428601) | about 4 years ago | (#33605744)

Really? You "could care less"? So... that means that you actually do care, right? I mean, since you just said it is possible for you to care less than you do. I'm just sayin'... Just for your edification, the proper way to say what you are trying to say is, "I could not care less." And with regard to the subject at hand in this thread, the idea that someone's poor English skills could have any bearing whatsoever on his or her skills at mathematics is just laughable and shows how little anyone presuming such preposterously arrogant nonsense actually knows about mathematics or the history of the brilliant minds in non-English-speaking cultures who have contributed to it. In other words, total bullshit.

### Re:Oh yeah? (0)

#### Anonymous Coward | about 4 years ago | (#33605802)

Really? You "could care less"?

Whoosh.

### Re:Oh yeah? (1)

#### asCii88 (1017788) | about 4 years ago | (#33605852)

Relax, you're answering to an Anonymous Coward!

### Re:Oh yeah? (0)

#### mark-t (151149) | about 4 years ago | (#33605604)

I had once formulated a somewhat bizarre proof that showed that the "infitieth" digit of pi was 5, based on the distribution of digits among fractions with non-terminating decimal representations.

### Re:Oh yeah? (1)

#### Peach Rings (1782482) | about 4 years ago | (#33605738)

In other words, the proof wasn't valid? Watch, I can do the same thing:
Many hills are green. Therefore, the "infitieth" (???) digit of Pi is 27. QED.

### Re:Oh yeah? (1)

#### Surt (22457) | about 4 years ago | (#33605854)

You call that 'somewhat' bizarre? Marginally bizarre at best. Where are the pink unicorns?

### Re:Oh yeah? (3, Funny)

#### blair1q (305137) | about 4 years ago | (#33605608)

No it's not. Because I say so.

(See, I have a 90% chance of being right and you have a 10% chance of being right, so I win Monte Carlo testing, and I provided more evidence than you, so I win in a civil suit.)

### Re:Oh yeah? (0)

#### Anonymous Coward | about 4 years ago | (#33605686)

Well, that's easy: there is no such 243,000,500,000,000,000,002th digit. There might be a 243,000,500,000,000,000,002ND digit that has the value of 4, but I'm sure I've already made my point.

### Re:Oh yeah? (1)

#### TexNA55 (1338761) | about 4 years ago | (#33605694)

Actually I dont think it would be too hard-just CBF working it out and quoting the command. On a konsole generate pi; pipe to a file; grep your 243,000,500,000,000,000,002 digit then check the tail of the file.. No doubt the more geeky will give the exact command; and probably an easier way by piping straight to a konsole. Cheers,

### Re:Oh yeah? (1)

#### camperdave (969942) | about 4 years ago | (#33605944)

I just tried it, and my computer started screaming "Redjack", there was some maniacal laughter, and the lights started flickering.

### Re:Oh yeah? (1)

#### curtix7 (1429475) | about 4 years ago | (#33605762)

Shoulda stuck to binary for the 50/50 chance.

### Re:Oh yeah? (1, Informative)

#### Anonymous Coward | about 4 years ago | (#33605778)

You're wrong, because TFA is discussing the binary representation of pi. It's either a 1 or a 0.

Or hex?

### Re:So, what is the digit in decimal? (2, Funny)

#### froggymana (1896008) | about 4 years ago | (#33605444)

I think it would be neater to be done in binary. Or perhaps convert it to ASCII to see if pi actually represents a story of some kind that is being told to us by the aliens.

### Re:So, what is the digit in decimal? (3, Funny)

#### Gerald (9696) | about 4 years ago | (#33605596)

It is, but it's encoded in UTF-35, not ASCII.

### Re:So, what is the digit in decimal? (1)

#### Zero__Kelvin (151819) | about 4 years ago | (#33605948)

It is also ROT 13'ed 2^100 times!

### Re:So, what is the digit in decimal? (1)

#### spblat (26399) | about 4 years ago | (#33605602)

Or perhaps convert it to ASCII to see if pi actually represents a story of some kind that is being told to us by the aliens.

You know that's the revelation at the end of a sci-fi novel by a certain revered astronomer, right?

### Re:So, what is the digit in decimal? (3, Informative)

#### Anonymous Coward | about 4 years ago | (#33605494)

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

### Re:So, what is the digit in decimal? (4, Informative)

#### Haxamanish (1564673) | about 4 years ago | (#33605692)

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s [maa.org] . So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.

### Re:So, what is the digit in decimal? (0, Flamebait)

#### Utopia (149375) | about 4 years ago | (#33605758)

Not quite true. See Bellard's formula [wikimedia.org] and Bailey's formula on which it is based.

### Re:So, what is the digit in decimal? (1)

#### Haxamanish (1564673) | about 4 years ago | (#33605950)

Can you please explain where I went wrong? Thx.

BTW, the link I provided is to an article about Bailey's formula.

### Happy Ending is but an illusion (1)

#### Maxhrk (680390) | about 4 years ago | (#33605412)

i misread that statement and i thought Pi finally have an ending to its story! Guess not.

BFD

### You fail math forever (4, Funny)

#### \$RANDOMLUSER (804576) | about 4 years ago | (#33605424)

the digit - when expressed in binary - is 0.

*facepalm* So that's 9 in decimal, right?

### Re:You fail math forever (1)

#### almightyons (1842868) | about 4 years ago | (#33605486)

I agree, but perhaps they're talking about the 2-quadrillionth binary digit. The 0 from b1,1110 is 'different' then the zero of d1,1110.

### Re:You fail math forever (0)

#### Anonymous Coward | about 4 years ago | (#33605510)

There are 10 kinds of people in the world. Those who understand binary math and those who don't.

### Re:You fail math forever (0)

#### Anonymous Coward | about 4 years ago | (#33605754)

And those who confuse it with ternary.

### Re:You fail math forever (0)

#### Anonymous Coward | about 4 years ago | (#33605536)

Here I was thinking...

0 - 0
1 - 1
10 - 2
11 - 3
100 - 3
101 - 4
111 - 5

100-4
101-5
110-6
111-7

### Re:You fail math forever (2, Informative)

#### voutasaurus (1895138) | about 4 years ago | (#33605540)

What they should have said is: The two quadrillionth digit in the binary expansion of pi is 0.

### indeed (0)

#### Anonymous Coward | about 4 years ago | (#33605636)

further evidence of the media's lack of communication skills;-}

Is it?

### Re:You fail math forever (1)

#### LambdaWolf (1561517) | about 4 years ago | (#33605804)

Agreed. Let's look at the exact phrasing.

A researcher has calculated the 2,000,000,000,000,000th digit of pi [...] the digit – when expressed in binary – is 0.

"Digit" without qualification usually means decimal digit. So presumably, he found the two quadrillionth decimal digit, which, in binary, is 0. Let me just convert that to decimal...

*uses calculator*

Apparently that's equivalent to 0.

### Re:You fail math forever (3, Funny)

#### jd (1658) | about 4 years ago | (#33605916)

Are you sure? 0, for large values of 0, approaches 1, for small values of 1.

### Re:You fail math forever (1)

#### internettoughguy (1478741) | about 4 years ago | (#33605760)

In that case; there is a fifty percent chance that septillionth digit is 1.

### Re:You fail math forever (1)

#### Peach Rings (1782482) | about 4 years ago | (#33605768)

Why do people keep saying digit and being ambiguous? It's called a bit. The two quadrillionth bit.

### Re:You fail math forever (1)

#### Peach Rings (1782482) | about 4 years ago | (#33605776)

I don't get it. What does 9 have to do with anything?

### Re:You fail math forever (1)

#### Facegarden (967477) | about 4 years ago | (#33605794)

the digit - when expressed in binary - is 0.

*facepalm* So that's 9 in decimal, right?

Yeah, that's just fucking terrible. Honestly I'm getting so sick of people writing terrible, terrible blog postings on supposedly high tech blogs. If this were a cat blog, I would understand, but its just silly for slashdot to post such crap. Why does this happen?
-Taylor

### Re:You fail math forever (2, Funny)

#### MattGWU (86623) | about 4 years ago | (#33605844)

Yeah, I've seen more credible technical journalism on the blog the guy at the yarn museum does.

Told you I'd use it.

Just say'in

### If zero equals nothing then... (3, Funny)

#### Daneurysm (732825) | about 4 years ago | (#33605436)

...move along people, nothing to see here.

### Re:If zero equals nothing then... (0)

#### Anonymous Coward | about 4 years ago | (#33605942)

exactly, wtf cares
anything beyond digit 4 is pro'ly useless
i'm also very drunk right now

### Chicks'll find this sooooo hot (1, Funny)

#### Anonymous Coward | about 4 years ago | (#33605438)

He'll definitely get some action for sure!

### Put to good use (5, Funny)

#### Anonymous Coward | about 4 years ago | (#33605440)

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.

### Last Digit? (5, Funny)

#### fandingo (1541045) | about 4 years ago | (#33605450)

"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??

### Re:Last Digit? (3, Funny)

#### JesseL (107722) | about 4 years ago | (#33605512)

Irrational numbers care not for your "rational approach".

### Re:Last Digit? (1)

#### PhxBlue (562201) | about 4 years ago | (#33605600)

That would be the rational approach. Who cares about the two quadrillionth digit??

I see what you did there.

either that or 1

### In binary? (4, Funny)

#### silverpig (814884) | about 4 years ago | (#33605502)

Geez, even I could have gotten it right half the time.

### how do they do it (1)

#### mestar (121800) | about 4 years ago | (#33605552)

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...

### Re:how do they do it (0)

#### Anonymous Coward | about 4 years ago | (#33605598)

You know, if you're really interested, you could have just skimmed the article:

Instead, each of the Hadoop computers was working on a formula that turns a complicated equation for pi into a small set of mathematical steps, returning just one, specific piece of pi.

### Re:how do they do it (0)

#### Anonymous Coward | about 4 years ago | (#33605622)

TFA:

He said the current, single-digit record is "more a demonstration of the Hadoop parallelisation framework... it can demonstrate the power of new algorithms which could be useful in other fields".
[...]
Mr Sze added that the calculation was also a good test for the Hadoop hardware and approach.
"This kind of calculation is useful in benchmarking and testing," he said.
"We have used it to compare the [processor] performance among our clusters."

### Re:how do they do it (-1, Flamebait)

#### Anonymous Coward | about 4 years ago | (#33605646)

really tough to answer that sorry... guess you will have to go ahead and READ THE FUCKING ARTICLE?!@#

### Re:how do they do it (0)

#### Anonymous Coward | about 4 years ago | (#33605690)

There are several ways to calculate pi. There are a bunch of methods to calculate all the digits, starting from 3.something and continuing until an arbitrary number of digits. There is also a way to calculate what a single digit will be, without calculating all the digits to that point. I know this method is slower, and I suspect it's a binary approach. In fact I'm pretty sure it is - it calculates what a single binary digit is.

It is called the Bailey-Borwein-Plouffe formula, if you would like to read more.

### Re:how do they do it (2, Informative)

#### Surt (22457) | about 4 years ago | (#33605772)

Regardless of what actually happened, there isn't any computation that requires keeping data in memory rather than hard disk. Memory is just faster, if you need more space for the computation, you can always actually use the 100 disks.

### What are the odds? (5, Funny)

#### grot (57003) | about 4 years ago | (#33605582)

the digit — when expressed in binary — is 0.

Jeez, what are the odds of that?

### Re:What are the odds? (2, Insightful)

#### The Living Fractal (162153) | about 4 years ago | (#33605654)

Apparently, 100%. :D

### Re:What are the odds? (1)

#### HungryHobo (1314109) | about 4 years ago | (#33605656)

gotta be a 1 in a million chance that, of all the numbers it could be... that it'd be zero!

3 out 2?

### Re:What are the odds? (0)

#### Anonymous Coward | about 4 years ago | (#33605672)

The odds would be 1...

#### Nemesisghost (1720424) | about 4 years ago | (#33605586)

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.

#### DerekLyons (302214) | about 4 years ago | (#33605718)

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.

At least with regards to calculating Pi, it's isn't particularly new. They first used this parallel method back in the 1980's.

### Out on a limb... (1)

#### Titan1080 (1328519) | about 4 years ago | (#33605606)

I think it's safe to assume the number never repeats.

Get some !!

### Yahoo (0, Redundant)

#### immakiku (777365) | about 4 years ago | (#33605638)

"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?

### Re:Yahoo (1)

#### RyuuzakiTetsuya (195424) | about 4 years ago | (#33605756)

Yeah, given their slides, I'm surprised they're not introduced as, "Advertising Brokerage firm, Yahoo!"

### Re:Yahoo (2, Funny)

#### Surt (22457) | about 4 years ago | (#33605824)

Well, it will help to date the story to this year, compared to stories that run in 2012 that will say 'defunct technology firm yahoo ...'

### A serious question (3, Interesting)

#### \$RANDOMLUSER (804576) | about 4 years ago | (#33605648)

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?

### Re:A serious question (1)

#### Nimey (114278) | about 4 years ago | (#33605736)

Because it's there. Also, everyone with a third-grade education knows what pi is, so it's useful for popularization of science.

### Re:A serious question (2, Interesting)

#### Black Gold Alchemist (1747136) | about 4 years ago | (#33605752)

Well, the radius of the visible universe is roughly 7.6 * 10^6 Planck lengths [google.com] . That means the volume is on the order of 10^183 cubic Planck lengths. So, if you can calculate PI to 200 digits or so, you're really accurate. At some point, more accurate than spacetime itself.

### Re:A serious question (0)

#### Anonymous Coward | about 4 years ago | (#33605810)

You never know when you'll need the 2,000,000,000,000,000th digit of pi to calculate the circumference of the universe to within a Planck length.

### Re:A serious question (1)

#### Surt (22457) | about 4 years ago | (#33605836)

It proves he had access to more useless cpu cycles than anyone else. A 'mine's bigger' sort of competition, if you know what I mean, and if you don't, seriously, what are you doing here?

### Bailey–Borwein–Plouffe formula (2, Interesting)

#### Utopia (149375) | about 4 years ago | (#33605650)

Bailey–Borwein–Plouffe formula [wikimedia.org] 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.

### Re:Bailey–Borwein–Plouffe formula (0)

#### Anonymous Coward | about 4 years ago | (#33605870)

They used Bellard's formula [wikimedia.org] . Here's the original article [arxiv.org] .

### All computers consumed (0)

#### Anonymous Coward | about 4 years ago | (#33605668)

Before you know it all computers around the world will be consumed with finding the complete number set of PI

### Confirmation ? (2, Insightful)

#### mbone (558574) | about 4 years ago | (#33605710)

And, we know this is correct how ?

Netcraft.

### Re:Confirmation ? (1)

#### Surt (22457) | about 4 years ago | (#33605790)

Beyond having proven the algorithm, and verifying the implementation of the algorithm on known digits of pi, we do not and will not.

### Re:Confirmation ? (2, Funny)

#### devnulljapan (316200) | about 4 years ago | (#33605918)

They asked some autistic dude who has it memorised to 3 quadrillion digits and he said "yes"

### "technology firm"? (0)

#### Anonymous Coward | about 4 years ago | (#33605732)

Is that a way of saying they have a lot of engineers, but little to show for it?

### Best article (1)

#### istartedi (132515) | about 4 years ago | (#33605764)

This article [radionz.co.nz] actually explains it better, and uses the phrase "piece of pi". I love it.

### Fuzzy Math (1)

#### Penguinshit (591885) | about 4 years ago | (#33605800)

Does Fuzzy Math have a hair-pi?

### Uh, so what? There are an infinite number of them (1)

#### divisionbyzero (300681) | about 4 years ago | (#33605902)

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.

### Re:Uh, so what? There are an infinite number of th (3, Funny)

#### Surt (22457) | about 4 years ago | (#33605938)

It's actually 13 orders of magnitude less significant than the 200th.

Function reject.

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