1.7 Billion Digits Of Pi On CD

H0ek writes "Not that there is any use for this whatsoever, but there is a torrent available for 1.7 billion digits of pi on a CD. The data is everything after the '3.' on one line, bzipped. There are a couple of the Cygwin tools on the disk as well as source for a small search tool (because grep just didn't cut it this time). Inside the ISO there's links to the source of the data, in case you want the rest of the 4.2 billion digits available. Wear your geek badge with pride! Be the first kid on your block to have the entire set!"

Comments

On a T-Shirt

[stu_coates]

...and it's available on a T-Shirt from ThinkGeek... only in size XXXXXXXL. ;-)

Why not DVD?

[ichimunki]

You could probably get another several billion digits on there!

Re:Why not DVD?

[m_chan]

Spoiler ahead:

The last digit is 4.

I also wrote a compression algorithm that will get you all the digits in 11 characters. Feel free to share with your friends:

0123456789.

pi memorization contests

[gothzilla]

Me and a friend of mine had a contest once to see who could memorize PI to the most number of decimals. He beat me badly. Needless to say he became a successful wealthy programmer while I still fix pc's for a living.
Never underestimate the power of PI. :)

Re:pi memorization contests

[miTcixelsyD]

Needless to say, he's living at home with Mom and you're actually dating women! :-p

Re:pi memorization contests

[Aerion]

You should challenge him to another contest ... this time, to memorize pi backwards.

No 3?

[SilkBD]

The data is everything after the '3.' on one line, bzipped.

What? They couldn't fit the '3' on the disc???

Re:No 3?

[stienman]

What? They couldn't fit the '3' on the disc???

Duh! It's 30 times larger than the next digit, which is 2.5 times bigger than the next digit, etc.

The biggest savings occurs by chopping off the "3."

-Adam

Useless?

[Xaroth]

"Not that there is any use for this whatsoever..."

I'm not so sure. Given that there are all sorts of interesting things about the number (a quick google search turned up this as an example), having a CD with the first couple billion digits could be useful for anyone playing around with statistical analysis of it.

Re:Useless?

[WolfWithoutAClause]

And a statistical analysis of the digits of Pi would be useful because? :-)

Re:Useless?

[Zocalo]

Interesting, and a step beyond just using Pi (or e, or...) as a source of sequences of random numbers but I can't help but feel that there is an element of "Bible Code Syndrome" here. There seems to be a similar obsession with finding a pattern in Pi as some have with finding messages from God in the Bible. What happens if we do a statistical analysis of every nth digit? What happens if we do an analysis of all the odd digits? Or even digits? What if we reverse the sequence and try again? Try again in other number bases?

It's an infinite data set; apply an infinite number of methods of analysis and the odds are good that some of them will give results that might be considered meaningful. Even if you do find something, whether it's a something profound about the structure of the universe or even a message from God, you then have another problem. How are you then supposed to prove that it's not a statistical fluke keeping in mind that an infinite random data string will contain within itself every possible sequence?

Re:Useless?

[illuvata]

Why wouldn't they just generate it themself? For most people, downloading an ISO and extracting the archive would be slower than just to use something like this.

Re:Useless?

[museumpeace]

Far be it from me to step in a pile of God doodoo, especially on /. but...
There is a pattern of sorts in the digits of Pi. Providing you don't mind working in hexadecimal, [why that base and no other?...any math PhD's in the audiance?] formula 29 on this page gives you a way to calculate any arbitrary digit of Pi without running a series calculation up to that digit's precision. If a formula for any digit, with independence from all other digits doesn't stretch the definition too much, I'll call it a pattern in the digits of Pi.
I for one welcome a creator who would leave us such puzzles.

Re:Useless?

[gstoddart]

Why wouldn't they just generate it themself? For most people, downloading an ISO and extracting the archive would be slower than just to use something like this.

Oh, man, you just spoiled this guys whole business model.

Guess it's back to underpants.

Re:Useless?

[Zocalo]

Yeah, I'd come across that formula before which is where my reference to trying other numeric bases came from. Similarly the reference to the message from God in Pi was from "Contact" by Carl Sagan (the book, rather than the film, as well as a nice link back to the Bible Code. And that's where I have a problem; the usual approach is more akin to looking for a hidden message rather than finding a reason *why*.

My own personal view is that few, if any, of these universal constants, whether mathematical like Pi and e, or physical like the speed of light and Plank's constant, are entirely arbitrary. There is a *reason* why Pi is 3.14159... instead of some other constant value, a reason why light travels at the speed that it does in a vacuum, and so on. While some of those reaons may be quite mundane, I think there are some profound insights into the nature and underlying structure of the universe hidden behind all those digits. Whether you would want to see that as pure science or looking for God's signature is entirely up to you.

Re:Useless?

[Alsee]

What if we reverse the sequence and try again?

During step two you get laid.

-

Re:Useless?

[HighlyVerbal]

Zocalo says: "keeping in mind that an infinite random data string will contain within itself every possible sequence" Two objections to Zocalo's reasoning: 1) the digits of pi are infinite and non-repeating but certainly not random - any digit is provably (in)correct 2) infinite non-repeating strings do NOT guarantee every possible sequence ... ie: 1.9119111911119 -- although if one mistakenly believed pi's digits to be random one might think the odds approached 100% of any given string appearing Fun thought of the day: if a infinite non-repeating string DID contain any given string, would they all be the same? We could then express irrationals by just naming the starting point on the "omni-string." Cheers!

Alas, firewalls...

[CAlworth1]

While there is probably nothing useful that I could do with this file, there is also no way for me to be able to get it, even if I had something to do with it - One of the wonderful things about going college in the day and age where it is bad to share information is that bitTorrent is not allowed.... mirror of pi anyone?

Having said that, it seems interesting to be asking, literally, for a mirror of the real world - as numbers go, this is pretty real.

Unlikely!

[JaxWeb]

Be the first kid on your block to have the entire set!

You're unlikely to be the first kid on the block to have the whole set of Pie digits...

Not yet, I'll wait a few months...

[Rahga]

I figure the director's cut on DVD will include even more content.

Shouldn't compress well

[crow]

At first, I was thrown off by the idea of compressing something like pi, as it shouldn't compress. The answer is that they're storing ASCII decimal digits, which require less than 4 bits per number, instead of 8. So you should get at least a 50% compression ratio, which would be 850 million bytes. But it's actually 3.something bits of information per byte, so they're able to fit it on a CD. I would be surprised if bzip could do any better than that.

Re:Shouldn't compress well

[slamb]

At first, I was thrown off by the idea of compressing something like pi, as it shouldn't compress. The answer is that they're storing ASCII decimal digits, which require less than 4 bits per number, instead of 8. So you should get at least a 50% compression ratio, which would be 850 million bytes. But it's actually 3.something bits of information per byte, so they're able to fit it on a CD. I would be surprised if bzip could do any better than that.

I had the same thought. To put it in dirt-simple terms, they're only using 10 out of the 256 possible values in every byte, due to the ASCII encoding. This is how bzip2 is able to find any redundancy; pi itself has none.[*]

So the best compression ratio (just compressed size/uncompressed size, right? so lower is better) is ln(10) / ln(256) = 41.5%. On a 700 MiB CD with no filesystem and nothing but pi, this means 700 * 2^20 / ln(256) * ln(10) = 1.77 billion digits (1767655840, with almost room for one more).

You'd do better than bzip2 by just using fixed blocks of N bytes to represent M digits. (Larger choices would get you closer to that best ratio; lower choices would less work to decode each block, which might make seeking more practical and reduce memory requirements.) This would be superior to bzip2 in that it'd get somewhat better compression, use a lot less CPU time, and be seekable. You could encode and decode with a one-line Perl script.

[*] - I suppose you could simply include the algorithm they used to generate the digits...but it'd take a long time to run, negating the whole point of putting pi on a CD.

Re:Shouldn't compress well

[EnronHaliburton2004]

I would be surprised if bzip could do any better than that.

Out of curiosity--

Bzip could could only improve on that if it found some repeating data the stream, right? Any improvement beyond the 50% compression ratio would be pretty revolutionary...

Re:Shouldn't compress well

[whydna]

Assuming that the ASCII digits of pi are evenly distributed between '0' and '9', then you should have log2(10) = 3.322 bits per digit. At 3.322 bits per digit and 700MiB (5872025600 bits at 8 bits per byte) we should have about 1,767,655,841
digits. Assuming that they're publishing exactly 1.7 Billion digits, they're within 3.8% of ideal compression, assuming an eactly even distribution of digits.

Where it gets interesting is if there's NOT an even distribution of digits (which I don't believe is actually the case for digits of pi, but humor me). For example, assume that one digit, say 0, occurs 100 times more frequently than each of the other digits, with the remain 9 digis occuring evenly. If you use something like huffman encoding and represent '0' with 1 bit, and the remaining bits with an average of 4.22 bits per digit (based on my back-of-the-envelope huffman encoding), you'd wind up averaging 1.266 bits per digit (100/109 * 1 bit + 9/10 * 4.22 bits). Clearly, as the frequency of this digit approaches infinity, the average bits per digit approachs 1. With the scheme described above, any distribution with 0 occuring at least 27.95% of the time (and an even distribution of the remaining digits), this basic encoding will perform better than the ideal encoding described in the first paragraph. For the curious, my huffman encoded values in this scenario were (0, 1000, 1001, 1010, 1011, 1100, 1101, 11100, 11101, 1111) for 0-9 respectively.

Obviously, the digits of pi are NOT distributed as disproportionately as I mentioned above, so a simple huffman encoding scheme is unlikely to produce better than ideal encoding. In fact, assuming an even distribution of digits, a back-of-the-envelope huffman encoding would yield encoded values of (1100, 1101, 1110, 1111, 000, 001, 010, 011, 100, 101) for 0-9. With this, you'd average 3.4 bits/digit, which is only just over 5% away from ideal encoding (this also agrees with the estimate from above, especially since bzip2 uses huffman encoding).

Of course, huffman encoding is not the only option. You could consider checking for multiple-digit combinations and determining the frequency of each combo. Or you could look at actual bit patterns, which is similar to run-length-encoding.

All of this is discounting the fact that the digits of PI are computable, and thus encoding them can be completely avoided if you're willing to spend considerable resources calculating the values yourself. In this case you need 0 bits per digit (discounting the size of your "decompression program"). This is the most computationally intense option, but yields the most optimal compression ratio.

Wow.

[Anonymous Coward]

If that torrent gets past 5 seeders, I will EAT A BRICK.
How about just linking to the software included on the cd and not the whole cd proper?
I'll say this: the BAD thing about BitTorrent is not the fact that 80% of its use is illegal, rather that it lowers the barrier of entry to hosting huge (and incidentally useless, in this case) files from random hole-in-the-wall ISPs.

I'll take back everything I said if that's a huge torrent of porn disguised as a PI cd.

Re:Wow.

[H0ek]

Less than two hours after the posting of the article to the public it's hit 6 seeders. Let me present to you your BRICK.

This from a site on a 500MHz P3 sitting on a little cable modem on a public utility style ISP providing 100KB/s upload speed. I love BitTorrent.

Re:Wow.

[Alsee]

I'll take back everything I said if that's a huge torrent of porn disguised as a PI cd.

Dude! 1.7 BILLION digits of Pi *is* geek porn.

-

Mathematical Music

[Marillion]

Burn it as an audio CD. The static will still sound better than most of the recently released music.

Who uses PI?

[vettemph]

I use pie all the time in an Engineering lab. typically out to 3 or 4 decimals. Does anyone NEED to use PI to a greater level of accuracy? If so, what application and how many decimal places do you require?

Re:Who uses PI?

[Daniel Dvorkin]

Our microscopic image processing software uses pi to considerable precision. This is, I admit, a pretty specialized application.

Woo Hoo!

[forty-2]

Now I can finally find my phone number in pi.

Re:Woo Hoo!

[stienman]

You could do that before:
PI Phone Number Search Engine

-Adam

Go to pi.com! ;-)

[xmas2003]

http://3.14159265358979323846264338327950288419716 9399375105820974944592.com/ which is the longest you can do in DNS currently ...

Uncountable versus countable infinities

[benhocking]

Better yet, since pi only contains a countable number of infinite digits, and there are uncountably infinite numbers of problems (see any decent book on theory of computing), the digits of pi most likely solve an infinite number of problems. Of course, since we can only describe a finite number of problems (in a finite amount of time), there are far fewer of these. The digits of pi do solve, for example, the problem of the ratio of a circle's circumference to its diameter. Of course, the question we're really looking at is what are the digits telling us in some non-geometrical sense (presumably), and, better yet, is there anything they're telling us that is independent of the number base (e.g., decimal vs. binary vs. trinary)? Of course, your argument still holds.

I've got a bunch of digits of pi

[Xtifr]

Since pi is infinite and irrational, I'm pretty sure that the data on every CD I own appears somewhere in pi. So, can I distribute these too? :)

Re:I've got a bunch of digits of pi

[mdielmann]

I'm pretty sure that the data on every CD I own appears somewhere in pi.

Oh great, just what I need. Now every time I see a circle, I'll be reminded that pi contains Britney Spears' Greatest Hits. Bastard.

On the plus side, it also contains every snide remark made about her. Including this one.

Re:I've got a bunch of digits of pi

[DustMagnet]

Since pi is infinite and irrational, I'm pretty sure that the data on every CD I own appears somewhere in pi. So, can I distribute these too? :)

Cute concept.

Of course you mean that the number of digits in pi is infinite. We both know pi isn't infinite since it's greater than three and less than four. Of course all irrational numbers have an infinite number of digits, so it works better to say, "Since pi is irrational, etc".

While I don't know about pi, an irrational number does not have to contain every combination of digits. For example, take this irrational number:
3.131131113111131111131111113111111311111113...
While irrational, it doesn't match any of your CDs. At least, I hope it doesn't.

1.7 billion digits of pi on a CD, WITH A BONUS!

[EnronHaliburton2004]

1.7 billion digits of pi on a CD.

And if you have trouble visualizing what Pi calculated to 1.7billion digits, the CD conveniently comes in the shape of a near-perfect circle for reference.

Torrent

[bcmm]

As this is actually an article about a torrent, I feel that it is legitimate and on-topic to say:
Please stop leaching. You should open at least port 6881 for incoming connections, and leave your bittorrent client open until you have uploaded at least as much as you have downloaded. It's only fair.
Thank you.

(I assume that you are all actually downloading this and not just laughing about it, right?)

Hidden messages

[jsveiga]

If all you want to do is search for mystic stuff inside the number, you don't need the CD with its measly 1.7bi digits.

Save your bandwidth and just go here to search within 4bi digits.

Expansion Pack

[MankyD]

The '3' will be included in the expansion pack, slated for release in early 2006.

Compressing Pi

[rdwald]

The data is everything after the '3.' on one line, bzipped.

So, in order to reduce the space on the CD, they bzipped it? I could see that helping for the search code, etc., but for pi itself, isn't it impossible to represent it in less space than it already takes without actually using a mathematical formula which defines pi? I would think the only way to actually save space would be to use some non-ASCII encoding scheme such that each byte could hold two digits, not one. Or encode it in hexadecimal, and use five bits per digit.

Re:Compressing Pi

[MankyD]

If each digit is was stored as ascii, you could use a Huffman code (the basic zip encoding) to shrink it down. This returns a result much like you suggested. If for those not familiar with Huffman Codes, I'll give a quick and dirty summary:

Say each char takes 8 bytes but, in this case, you're only using 10 chars, so you don't need 8 bytes to represent it all. Huffman codes do a quick count of character frequencies and create tree of shorter bit representations for each character. Characters that have a higher frequence (say the number 0 occurred a lot) are given a shorter code. A tree is used to mantain uniqueness so that no ambiguity occurs. For instance:

0 - 0
1 - 100
2 - 101
3 - 11000
4 - 11001
5 - 11010
6 - 11011
7 - 11100
8 - 11101
9 - 11110

If I give you the bits "011000101" you can translate that to "0 - 3 - 2". Use google for those who want to learn more.

Algorithm

[FullMetalAlchemist]

Does anyone have a link to the algorithm where one can calculate the digits of pi at any given position without knowing the result from the preceding digits?

Re:Algorithm

[JaxWeb]

Yeah, http://crd.lbl.gov/~dhbailey/

Enjoy.

You're a genius!

[FiloEleven]

Since nothing is going horribly wrong at work today, I took your advice. You will not believe what is encoded in the sequence!

Most of it is awful noise, but after the first two or three minutes it ceases being pure white noise and you get some interesting texture. At this point, I turned up the volume a bit and kept surfing Slashdot. Until my mind was blown.

Right around 7 minutes 6 seconds into the track, the textures resolve into a whispery voice. I know this sounds nuts, and I wouldn't believe it either if I hadn't heard it myself. There's still a lot of fuzz, but ifyou listen carefully you can make out some of what it says:

"...four simultaneous [unintelligible] four hour days...[unintelligible]...rotation of the earth"
"ineffable truth and wisdom"
"four corner [unintelligible] metamorphic human"

This stuff goes on and on, but I need to clean up the audio to understand everything! Does anyone have recommendations for heuristic filtering software? This is absolutely amazing. I wonder what it all means?

Applicable poem

[H0ek]

The nifty thing about sharing links like this is you get fun mail, like this poem from a friend:

Now I will a rhyme construct
By chosen words the youth instruct
Cunningly devised endeavour
Con it and remember ever
Widths in circle, here you see
Sketched out in strange obscurity

I might just have to memorize it. ;-)

PI server

[JVolkman]

http://3.14159265358979323846264338327950288419716 9399375105820974944592.jp
I believe this server keeps sending digits of PI indefinitely (most likely using the fun Nth-digit-of-PI formula). It's already a slow site, and will probably be slashdotted quickly. (This is not a dupe of the .com posted earlier)