# How do you calculate Pi? Build a supercomputer.

September 9, 2010 1:28 PM Subscribe

How do you calculate Pi? Build a supercomputer.

*The Mountains of Pi*, a New Yorker profile of the mathematician (sic) the Chudnovsky brothers. Warning: the article is from 1992, and internet is missing its definite article. (Previously)Interesting. "Internets" used to be singular.

posted by found missing at 1:33 PM on September 9, 2010 [1 favorite]

posted by found missing at 1:33 PM on September 9, 2010 [1 favorite]

I had a math teacher in the 8th grade that told me that the way mathematicians calculated pi was by measuring an actual circle and dividing the circumference by the diameter. More accurate values required more accurate tape measures, according to him.

Not only was it, of course, total horseshit, but it wasted an opportunity to reward an interest in higher math. It was the absolute nadir of my public education experience, and if I ever meet the guy again I think I might have to kick him in the shins.

posted by jedicus at 2:01 PM on September 9, 2010 [2 favorites]

Not only was it, of course, total horseshit, but it wasted an opportunity to reward an interest in higher math. It was the absolute nadir of my public education experience, and if I ever meet the guy again I think I might have to kick him in the shins.

posted by jedicus at 2:01 PM on September 9, 2010 [2 favorites]

Now I want to make cornbread.

posted by longsleeves at 2:09 PM on September 9, 2010

posted by longsleeves at 2:09 PM on September 9, 2010

This is really interesting, thanks. Had not heard of these two, or of m0.

posted by everichon at 2:13 PM on September 9, 2010

posted by everichon at 2:13 PM on September 9, 2010

Thank you for posting this article and allowing me to read it through Internet.

posted by chinston at 2:26 PM on September 9, 2010

posted by chinston at 2:26 PM on September 9, 2010

One of these days a computer is going to discover that pi is actually not an infinite series, but terminates somewhere near the googolth decimal place, and millions of nerds will weep as their favorite pastime is completely invalidated overnight.

posted by The Winsome Parker Lewis at 2:26 PM on September 9, 2010

posted by The Winsome Parker Lewis at 2:26 PM on September 9, 2010

*"Internet" is still singular.*

Woosh.

posted by coolguymichael at 2:33 PM on September 9, 2010 [1 favorite]

Also, this makes me nostalgic for the days of long-long-form New Yorker pieces.

posted by everichon at 2:36 PM on September 9, 2010

posted by everichon at 2:36 PM on September 9, 2010

I still wonder are there any practical applications of calculating Pi beyond the first 100 places or so?

The article states

Planck length (ℓP) is 16.163×10^−36 m.

So the universe is (1.476x10^27m)/(16.163×10^−36 m/ℓP) = 9.13x10^61 Planck lengths wide, give or take.

If I wanted to calculate the circumference of the universe, and I knew the *exact* width of the universe in Planck lengths, I still wouldn't need more than the first 62 digits of Pi.

The article also mentions that even if we turned the entire universe into a computer, we still could not calculate more than about 10^77 digits of Pi. So why do people keep at it?

posted by fings at 2:43 PM on September 9, 2010 [1 favorite]

The article states

an expansion of pi to only forty-seven decimal places would be sufficiently precise to inscribe a circle around the visible universe that doesn’t deviate from perfect circularity by more than the distance across a single proton.I had actually run a similar calculation last week. According to science, the universe is 156 billion light years wide (1.56x10^11ly). A light year is 9.461×10^15 meters, so that makes the universe about 1.476x10^27m wide.

Planck length (ℓP) is 16.163×10^−36 m.

So the universe is (1.476x10^27m)/(16.163×10^−36 m/ℓP) = 9.13x10^61 Planck lengths wide, give or take.

If I wanted to calculate the circumference of the universe, and I knew the *exact* width of the universe in Planck lengths, I still wouldn't need more than the first 62 digits of Pi.

The article also mentions that even if we turned the entire universe into a computer, we still could not calculate more than about 10^77 digits of Pi. So why do people keep at it?

posted by fings at 2:43 PM on September 9, 2010 [1 favorite]

*One of these days a computer is going to discover that pi is actually not an infinite series, but terminates somewhere near the googolth decimal place*

Last piece of pi?

posted by Blazecock Pileon at 2:44 PM on September 9, 2010 [2 favorites]

OmieWise: "

I thought, "who calls it

posted by boo_radley at 2:45 PM on September 9, 2010

*internet is missing its definite article.*"I thought, "who calls it

*the pi*?"posted by boo_radley at 2:45 PM on September 9, 2010

These guys did a tour of academic institutions around the time this was published. The meetings at University of Washington, at least, were invitation-only affairs, and I heard (from one of those invited), that they did a lot of listening and evaded questions about their own work.

This was right at the end of the time when custom silicon could compete with the commodity guys (DEC Alpha, Intel and Motorola were all duking it out, along with custom CPUs from Tera and Cray). Those days ended when the fabrication technology of the really big guys leapt so far ahead of the little guys that the little guys couldn't compete. More recently parallelism and FPGA's have become interesting compute fabrics, such as the techniques used to determine that the Van der Waerden number W(2,6) = 1132 (sadly, pay-only access)

posted by dylanjames at 3:00 PM on September 9, 2010 [1 favorite]

This was right at the end of the time when custom silicon could compete with the commodity guys (DEC Alpha, Intel and Motorola were all duking it out, along with custom CPUs from Tera and Cray). Those days ended when the fabrication technology of the really big guys leapt so far ahead of the little guys that the little guys couldn't compete. More recently parallelism and FPGA's have become interesting compute fabrics, such as the techniques used to determine that the Van der Waerden number W(2,6) = 1132 (sadly, pay-only access)

posted by dylanjames at 3:00 PM on September 9, 2010 [1 favorite]

I read this in 1992, and it's still one of the best New Yorker articles I have ever read.

posted by briank at 3:12 PM on September 9, 2010 [1 favorite]

posted by briank at 3:12 PM on September 9, 2010 [1 favorite]

Suggested alternate post title: 12:45, restate my assumptions.

The author wrote a follow-up article in 2005: Capturing the Unicorn, and they were also featured in a NOVA profile around the same time. Watching them finishing each other's sentences on video really shows how well the author captured their interactions.

posted by lantius at 3:30 PM on September 9, 2010 [1 favorite]

The author wrote a follow-up article in 2005: Capturing the Unicorn, and they were also featured in a NOVA profile around the same time. Watching them finishing each other's sentences on video really shows how well the author captured their interactions.

posted by lantius at 3:30 PM on September 9, 2010 [1 favorite]

One of the practical applications for calculating Pi to zillions of places is basically to check if your computer works.

posted by madcaptenor at 3:31 PM on September 9, 2010 [1 favorite]

posted by madcaptenor at 3:31 PM on September 9, 2010 [1 favorite]

I always figured these guys as the inspiration behind the movie Pi.

posted by Hactar at 3:50 PM on September 9, 2010 [2 favorites]

posted by Hactar at 3:50 PM on September 9, 2010 [2 favorites]

*pi ... terminates ... and millions of nerds will weep as their favorite pastime is completely invalidated overnight.*

If π were to be found to be rational, all of math and logic would be out the window.

posted by phliar at 5:21 PM on September 9, 2010 [1 favorite]

I presume these results are in seconds so it looks like you can do a billion places in a little over half an hour these days if you have the right processor (using the same formula).

posted by tallus at 6:27 PM on September 9, 2010

posted by tallus at 6:27 PM on September 9, 2010

I still remember this article from when it came out, and think of it quite often; something about envy of access to resources. I don't recall it being in the New Yorker though, that doesn't seem to be the sort of thing I would have been reading when I was 22.

posted by thrind at 7:22 PM on September 9, 2010

posted by thrind at 7:22 PM on September 9, 2010

Pi possibly first entered human consciousness in Egypt. The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 B.C. by a scribe named Ahmes. Showing a restrained appreciation for his own work that is not uncommon in a mathematician, Ahmes began his scroll with the words “The Entrance Into the Knowledge of All Existing Things.”

Heh.

I also read this when it came out, but my grandfather was a mathematics professor, and subscribed to the magazine, giving it to us in paper grocery sacks stuffed to the gills not unlike the manila folders used by the Chudnovskys.

posted by dhartung at 9:49 PM on September 9, 2010

Heh.

I also read this when it came out, but my grandfather was a mathematics professor, and subscribed to the magazine, giving it to us in paper grocery sacks stuffed to the gills not unlike the manila folders used by the Chudnovskys.

posted by dhartung at 9:49 PM on September 9, 2010

*One of the practical applications for calculating Pi to zillions of places is basically to check if your computer works.*

In the article:

*the brothers had concluded that it would be cheaper and more convenient to build a supercomputer in Gregory’s apartment. Then they could crash their own machine all they wanted, while they opened doors in the house of numbers. The brothers planned to compute two billion digits of pi on their new machine to try to double their old world record. They thought it would be a good way to test their supercomputer: a maiden voyage into pi would put a terrible strain on their machine, might blow it up.*

I also like this bit:

...the thought of a billion decimals of pi oppresses even some mathematicians, who declare the Chudnovskys’ effort trivial. I once asked Gregory if a certain impression I had of mathematicians was true, that they spent immoderate amounts of time declaring each other’s work trivial. “It is true,” he admitted. “There is actually a reason for this. Because once you know the solution to a problem it usually is trivial.”

posted by dhartung at 10:06 PM on September 9, 2010

Am I the only person who's bothered by the writing? I can't quite put my finger on how this is accomplished, but this piece feels

His condition doesn’t seem to be getting better, and doesn’t seem to be getting worse. He developed the disease when he was twelve years old, in the city of Kiev, Ukraine, where he and David grew up. He spends his days sitting or lying on a bed heaped with pillows, in a bedroom down the hall from the room that houses the supercomputer. Gregory’s bedroom is filled with paper; it contains at least a ton of paper. He calls the place his junk yard. The room faces east, and would be full of sunlight in the morning if he ever raised the shades, but he keeps them lowered, because light hurts his eyes. (article)

posted by d. z. wang at 10:09 PM on September 9, 2010

*rushed*. Reading it is like listening to someone speak just a little bit too fast. There's a certain rat-a-tat rhythm to it that I just find extraordinarily discomfiting, and I don't know why that is.His condition doesn’t seem to be getting better, and doesn’t seem to be getting worse. He developed the disease when he was twelve years old, in the city of Kiev, Ukraine, where he and David grew up. He spends his days sitting or lying on a bed heaped with pillows, in a bedroom down the hall from the room that houses the supercomputer. Gregory’s bedroom is filled with paper; it contains at least a ton of paper. He calls the place his junk yard. The room faces east, and would be full of sunlight in the morning if he ever raised the shades, but he keeps them lowered, because light hurts his eyes. (article)

posted by d. z. wang at 10:09 PM on September 9, 2010

Now that I've finished the article, I'm mostly disappointed by how little it said about m0 itself.

posted by d. z. wang at 10:28 PM on September 9, 2010

posted by d. z. wang at 10:28 PM on September 9, 2010

d. z. wang: I read the article a while ago, but my understanding (reading a bit between the lines to make up for the lack of detail) is that what they built was basically a very early compute cluster using commodity parts. I assume they had to write some fairly clever custom software to parallelize and distribute the work, but I've never seen any evidence that they released or published it. Which is too bad, because in retrospect they might have been ahead of the field by a few years — the first commodity-cluster I remember reading about was Beowulf (the original NASA one) in the mid 90s (WP says it was 1994).

There's a comment about the interconnect topology being fully connected (every node to every other node) which makes me curious what sort of networking they were running. Token Ring would have been big at the time, but wasn't point-to-point; I've wondered if it wasn't something homebrew based on RS232, the cards for which would have been a lot easier to come by at the time. Given the amount of time and effort they put into it, imagining they they wrote their own networking stack doesn't seem that hard to believe.

A few minutes of Googling doesn't turn up anything else on m0 besides the New Yorker article, and some newer articles on systems that the Chudnovskys have worked on or built since then. I've always been curious about it though.

posted by Kadin2048 at 12:21 AM on September 10, 2010

There's a comment about the interconnect topology being fully connected (every node to every other node) which makes me curious what sort of networking they were running. Token Ring would have been big at the time, but wasn't point-to-point; I've wondered if it wasn't something homebrew based on RS232, the cards for which would have been a lot easier to come by at the time. Given the amount of time and effort they put into it, imagining they they wrote their own networking stack doesn't seem that hard to believe.

A few minutes of Googling doesn't turn up anything else on m0 besides the New Yorker article, and some newer articles on systems that the Chudnovskys have worked on or built since then. I've always been curious about it though.

posted by Kadin2048 at 12:21 AM on September 10, 2010

*According to science, the universe is 156 billion light years wide*

That article is wrong. It's more like 93.

posted by Rhomboid at 1:37 AM on September 10, 2010

*I assume they had to write some fairly clever custom software to parallelize and distribute the work*

The Bailey–Borwein–Plouffe formula allows for calculating arbitrary binary digits of Pi without first having to compute any of the preceding ones. Its refinement, Bellard's formula, was used in 1998-2000 as the basis for a distributed computing project that computed short runs of Pi at bit positions 5 trillion, 40 trillion, and one quadrillion, the last of which still holds the record for farthest bits of Pi ever calculated.

However the BBP algorithm was published in 1995 so either the Chudnovsky brothers came across it on their own and never disclosed it (possible) or they used some other custom method.

posted by Rhomboid at 2:02 AM on September 10, 2010

Kadin2048, I had the same intriguement over the supercomputer (more than the math, which is more interesting to me now). I wonder if it was ever written up in any obscure, out-of-print computer magazine (Dr. Dobbs? Byte?).

You can see a bit of the then-current version of the device in this NOVA profile, at about the two-minute mark.

posted by dhartung at 10:17 AM on September 10, 2010

You can see a bit of the then-current version of the device in this NOVA profile, at about the two-minute mark.

posted by dhartung at 10:17 AM on September 10, 2010

However the BBP algorithm was published in 1995 so either the Chudnovsky brothers came across it on their own and never disclosed it (possible) or they used some other custom method. (Rhomboid)

I didn't see this in the article, but, if they were doing this around 1992, I would guess that they used their own 1989 algorithm, which certainly looks like it would allow each term to be calculated separately.

Given the amount of time and effort they put into it, imagining they they wrote their own networking stack doesn't seem that hard to believe. (Kadin2048)

Yes, and probably their own arbitrary-precision arithmetic, too. I've never actually used FORTRAN, but wikipedia only lists two multiple-precision packages. One still doesn't handle more than a few thousand digits and the other doesn't seem to have been more than a proof of concept in 1989, with the library finally released in 1991.

posted by d. z. wang at 10:52 AM on September 10, 2010

I didn't see this in the article, but, if they were doing this around 1992, I would guess that they used their own 1989 algorithm, which certainly looks like it would allow each term to be calculated separately.

Given the amount of time and effort they put into it, imagining they they wrote their own networking stack doesn't seem that hard to believe. (Kadin2048)

Yes, and probably their own arbitrary-precision arithmetic, too. I've never actually used FORTRAN, but wikipedia only lists two multiple-precision packages. One still doesn't handle more than a few thousand digits and the other doesn't seem to have been more than a proof of concept in 1989, with the library finally released in 1991.

posted by d. z. wang at 10:52 AM on September 10, 2010

Err, never mind that about writing their own arbitrary-precision math. I just started reading the articles on the FM library, and it cites an MP package by Brent which was first released in 1978. So I guess the Chudnovsky brothers "only" built a commodity cluster on their own fully connected network.

posted by d. z. wang at 10:54 AM on September 10, 2010

posted by d. z. wang at 10:54 AM on September 10, 2010

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