# 3.14159265itwasthebestoftimesitwastheworstofti...

December 4, 2007 7:20 PM Subscribe

Ever wondered if and where a specific set of numbers could be found in pi? Maybe you'd like to know where your birthday is? Or maybe just something funny. [prev. here, here]

Psh, that's child's play. Old news. If you wanna be hip and play with the big boys and girls, you're gonna have to think bigger [previously]. Since computer files are simply numbers, then, in theory,

images, audio, video, even wikipedia articles all exist in pi. In fact, all existing data in the universe must be somewhere in pi since it is an infinite, non-repeating sequence of numbers which appear with equal probability (so the theory goes).

Some have suggested this is a useful file compression/encryption mechanism. Some have to see a doctor after hearing about it. And some just find its implications amusing.

Too bad

it's all bunk. But don't lose hope, there may be alternatives. My solution to the debate? -- f*ck it, let's just call it 3.

I was surprised by the number of references to this all-things-in-pi concept throughout MeFi, but there was no post explicitly on the subject. I tried to give credit where it was due. Enjoy!

Psh, that's child's play. Old news. If you wanna be hip and play with the big boys and girls, you're gonna have to think bigger [previously]. Since computer files are simply numbers, then, in theory,

images, audio, video, even wikipedia articles all exist in pi. In fact, all existing data in the universe must be somewhere in pi since it is an infinite, non-repeating sequence of numbers which appear with equal probability (so the theory goes).

Some have suggested this is a useful file compression/encryption mechanism. Some have to see a doctor after hearing about it. And some just find its implications amusing.

Too bad

it's all bunk. But don't lose hope, there may be alternatives. My solution to the debate? -- f*ck it, let's just call it 3.

I was surprised by the number of references to this all-things-in-pi concept throughout MeFi, but there was no post explicitly on the subject. I tried to give credit where it was due. Enjoy!

The string 0123456789 did not occur in the first 200000000 digits of pi after position 0.

posted by grumblebee at 7:34 PM on December 4, 2007

posted by grumblebee at 7:34 PM on December 4, 2007

For us non-math adepts, can someone explain what's being said in the "too bad it's all bunk" links?

posted by Sangermaine at 7:35 PM on December 4, 2007

posted by Sangermaine at 7:35 PM on December 4, 2007

The string 01234567 occurs at position 112,099,767 counting from the first digit after the decimal point. The 3. is not counted.

But...

The string 012345678 did not occur in the first 200000000 digits of pi after position 0

posted by grumblebee at 7:36 PM on December 4, 2007

But...

The string 012345678 did not occur in the first 200000000 digits of pi after position 0

posted by grumblebee at 7:36 PM on December 4, 2007

"The string 8675309 occurs at position 9,202,591 counting from the first digit after the decimal point."

posted by Keith Talent at 7:38 PM on December 4, 2007 [2 favorites]

posted by Keith Talent at 7:38 PM on December 4, 2007 [2 favorites]

I thought statistically every single number combination occurs somewhere in pi.

posted by spiderskull at 7:39 PM on December 4, 2007

posted by spiderskull at 7:39 PM on December 4, 2007

*80081355 occurs at position 38,683,948 counting from the first digit after the decimal point. The 3. is not counted.*

HEHE.

posted by Samuel Farrow at 7:39 PM on December 4, 2007 [1 favorite]

"The string 14 occurs at position 1 counting from the first digit after the decimal point. The 3. is not counted."

posted by Rumple at 7:40 PM on December 4, 2007

*leaping lizards*posted by Rumple at 7:40 PM on December 4, 2007

[less inside]

posted by stavrosthewonderchicken at 7:40 PM on December 4, 2007

posted by stavrosthewonderchicken at 7:40 PM on December 4, 2007

*80081355*

Boobiess?

Boobiess?

Boobless. Though, why anyone would search for something like that on the internet is beyond me.

posted by flatluigi at 7:47 PM on December 4, 2007

*paging*

More like 17485, amirite?

posted by Horace Rumpole at 7:48 PM on December 4, 2007 [1 favorite]

Does this mean there is an infinitely long representation of e somewhere in pi? What about root(2)?

Do they exist in each other? Does this mean there is in fact one infinitely long irrational number that contains all others, and itself, to an arbitrary length?

Show full working please ;-)

posted by sien at 7:51 PM on December 4, 2007 [5 favorites]

Do they exist in each other? Does this mean there is in fact one infinitely long irrational number that contains all others, and itself, to an arbitrary length?

Show full working please ;-)

posted by sien at 7:51 PM on December 4, 2007 [5 favorites]

That discussion subsumes a lot of the "think bigger" link, sien.

Cool stuff. There is no 999999999 in the first 200000000 digits, but there is 666666666. COINCIDENCE?!?!?

posted by yhbc at 7:54 PM on December 4, 2007

Cool stuff. There is no 999999999 in the first 200000000 digits, but there is 666666666. COINCIDENCE?!?!?

posted by yhbc at 7:54 PM on December 4, 2007

*"For us non-math adepts, can someone explain what's being said in the "too bad it's all bunk" links?"*

Essentially, you can represent information simply as the offset into pi (or any other random string of numbers). If I want to tell you my phone number is 4159265, I can just tell you my phone number starts at the second decimal place in pi. Theoretically this method could be used to communicate any information, because any set of numbers is found in pi somewhere.

Unfortunately, for any arbitrary string of numbers, it will usually take more numbers for the placeholder than the data itself. So there is no shortcut for quickly communicating data. Its easier to tell you my actual phone number than to tell you the offset into pi.

For a good example, see grumblebee's comment

posted by jpdoane at 7:56 PM on December 4, 2007 [3 favorites]

"The string 4815162342 did not occur in the first 200000000 digits of pi after position 0."

Darn it.

posted by brownpau at 7:58 PM on December 4, 2007

Darn it.

posted by brownpau at 7:58 PM on December 4, 2007

*Ever wondered if and where a specific set of numbers could be found in pi?*

Not really since AFAIK recently it was proven that PI is NORMAL

This mean it will contain mine and your phone number and not only the collected works of Shakespeare but also every book that ever has been written and all the books that ever will be written. I guess finding the position in PI will be the tough part ;-)

posted by yoyo_nyc at 8:05 PM on December 4, 2007

In Carl Sagan's novel

posted by pax digita at 8:11 PM on December 4, 2007

*Contact*, there's a surprise ending of sorts involving pi.posted by pax digita at 8:11 PM on December 4, 2007

The string [my social security number] occurs at position 186,xxx,xxx counting from the first digit after the decimal point.

That can't possibly be good.

posted by wendell at 8:12 PM on December 4, 2007

That can't possibly be good.

posted by wendell at 8:12 PM on December 4, 2007

A

posted by Justinian at 8:13 PM on December 4, 2007

*happy*ending? That's what I want from my numbers.posted by Justinian at 8:13 PM on December 4, 2007

Seems like a good time to read about Kolmogorov complexity if you're thinking that an offset into pi might be a useful compression technique.

posted by jewzilla at 8:16 PM on December 4, 2007

posted by jewzilla at 8:16 PM on December 4, 2007

*Cool stuff. There is no 999999999 in the first 200000000 digits, but there is 666666666. COINCIDENCE?!?!?*

Meh. If a 6 turns out to be 9, I don't mind.

posted by The World Famous at 8:22 PM on December 4, 2007 [4 favorites]

**jpdoane**'s point is true in general for compression algorithms — it's impossible to have a single algorithm that compresses all files to a size smaller than the original size. In fact, it's impossible to have a single algorithm that losslessly compresses all files by a single bit.

Suppose you did have such a compression algorithm. Then you could use it to compress all possible files of length, say,

*n*bits (of which there are 2

^{n}), to files of length

*n*- 1 bits. But there are only 2

^{n - 1}possible files of length

*n*- 1, half as much as 2

^{n}. Since the number of possible files that go

*into*the compression algorithm (the "domain") is larger than the number that can come

*out*(the "range"), there must be some pair of distinct input files that compress to the same output file. (This is what the pigeonhole principle is all about.) But that can't work because you'll end up getting the same file for both when you go to decompress it. Therefore, such an algorithm can't exist.

Interestingly, I'm pretty sure that what's said in the "Too" link is incorrect. The set of finite bit strings is countable (being the union of the set of strings of length 0, 1, 2, etc., which is countable, and each of which are finite), so its cardinality is ℵ

_{0},

*not*2

^{ℵ0}, and it's still possible that all finite bit strings show up in the digits of π. The poster might have been confusing it with the set of all bit

*sequences*, which is indeed uncountable.

posted by pmdboi at 8:25 PM on December 4, 2007 [3 favorites]

*Not really since AFAIK recently it was proven that PI is NORMAL*

My understanding from the resources I found was that it is not known if Pi is normal.

Mathworld

Wikipedia

Unfortunately, I don't have enough of a background in set theory to make any sort of argument. Has the paper you linked to been peer-reviewed?

posted by TimeTravelSpeed at 8:25 PM on December 4, 2007

*Unfortunately, for any arbitrary string of numbers, it will usually take more numbers for the placeholder than the data itself.*

That's true. And from a purely practical perspective, even if you could keep the "compressed" file size smaller than the file, this wouldn't be an efficient method: you still have to store an enormous number (pi out to a sufficient digit) which has probably a trillion useless digits for every useful one. This is a huge waste of space.

Ideally, you'd have some algorithm which can quickly calculate pi real-time starting at the correct digit. I would guess this is impossible, but maybe someone more mathy than me can elaborate.

posted by TimeTravelSpeed at 8:46 PM on December 4, 2007

*This mean it will contain mine and your phone number and not only the collected works of Shakespeare but also every book that ever has been written and all the books that ever will be written.*

See also Borges' The Library of Babel.

posted by Mapes at 8:46 PM on December 4, 2007

Here's an arbitrary but fun game:

Take a number and see at what place it falls in pi. That that number and find its place. How far can you go until your number is beyond 200,000,000 or until it goes into an infinite loop?

(666 takes 24 steps, 42 takes 29 steps and 93 goes into infinite loop at 3!

posted by Cat Pie Hurts at 8:48 PM on December 4, 2007

Take a number and see at what place it falls in pi. That that number and find its place. How far can you go until your number is beyond 200,000,000 or until it goes into an infinite loop?

(666 takes 24 steps, 42 takes 29 steps and 93 goes into infinite loop at 3!

posted by Cat Pie Hurts at 8:48 PM on December 4, 2007

*80081355*

I think you mean

`55318008`?

posted by misterbrandt at 8:52 PM on December 4, 2007 [2 favorites]

*How far can you go until your number is beyond 200,000,000 or until it goes into an infinite loop?*

It took me 11 steps for my user id (41529 -- which is very close to the 4th through 8th digits of pi)

posted by TimeTravelSpeed at 8:56 PM on December 4, 2007

*I think you mean 55318008?*

Of course not! You'd have to turn pi upside down which would just make an infinite mess on the kitchen floor.

posted by TimeTravelSpeed at 8:58 PM on December 4, 2007 [1 favorite]

*"The string 4815162342 did not occur in the first 200000000 digits of pi after position 0."*

Darn it.

posted by brownpau at 7:58 PM on December 4 [+] [!] No other comments.

Darn it.

posted by brownpau at 7:58 PM on December 4 [+] [!] No other comments.

4815162342 is not a phone number. I tried. Darn it.

posted by iamkimiam at 8:59 PM on December 4, 2007

macadamiaranch's user id nearly goes into a loop in one step!

posted by TimeTravelSpeed at 9:01 PM on December 4, 2007

posted by TimeTravelSpeed at 9:01 PM on December 4, 2007

There's a whole bunch of bad math and CS in the links. The "encryption mechanism" link, for instance. The reason why one-time pads are secure is that they have as many bits of "randomness" as there are bits in the message you're trying to encode. So if I have a given ciphertext, there's no way I can even theoretically find the plaintext from it: since given any plaintext, there exists some key that would produce the ciphertext I have (and since all keys are equally likely due to the random selection) I have no way of deciding between two plaintexts of the same length.

If you pick a digit of pi to start at, you don't magically get extra randomness. The "key" isn't the list of digits starting at that point--it's just the digit you start at. This means that to decrypt your message, I could just test all of the digits of pi starting from one and going until I got a plausible plaintext. Of course, you could pick a starting point such that the number of bits it takes to express the digit you picked is about as big as the number of bits in your message--but then you haven't gained anything.

(And besides, we don't even know if pi is "normal", so it's an open question whether every digit sequence appears in pi or not.)

posted by goingonit at 9:04 PM on December 4, 2007

If you pick a digit of pi to start at, you don't magically get extra randomness. The "key" isn't the list of digits starting at that point--it's just the digit you start at. This means that to decrypt your message, I could just test all of the digits of pi starting from one and going until I got a plausible plaintext. Of course, you could pick a starting point such that the number of bits it takes to express the digit you picked is about as big as the number of bits in your message--but then you haven't gained anything.

(And besides, we don't even know if pi is "normal", so it's an open question whether every digit sequence appears in pi or not.)

posted by goingonit at 9:04 PM on December 4, 2007

They used to say that a million typing monkeys could produce the works of Shakespeare. But now that we have Metafilter, we know that this is not true.

posted by jonp72 at 9:07 PM on December 4, 2007 [2 favorites]

posted by jonp72 at 9:07 PM on December 4, 2007 [2 favorites]

74553050682034962524

Here I am, at position 2,108.

posted by 517 at 9:11 PM on December 4, 2007 [1 favorite]

**517**49399651431429809190Here I am, at position 2,108.

posted by 517 at 9:11 PM on December 4, 2007 [1 favorite]

If π is normal then it contains every bit of porn on earth in every possible media format. Which makes you wonder why your netnanny doesn't block it.

posted by George_Spiggott at 9:13 PM on December 4, 2007 [1 favorite]

posted by George_Spiggott at 9:13 PM on December 4, 2007 [1 favorite]

And the "Too" link in the ...bunk section is false. There are not more than aleph-null finite bit strings. Every unique "finite bit string" is the binary representation of a unique natural number, and there are only aleph-null natural numbers by definition.

So really don't trust anything you read in the links in this FPP.

posted by goingonit at 9:15 PM on December 4, 2007

So really don't trust anything you read in the links in this FPP.

posted by goingonit at 9:15 PM on December 4, 2007

yoyo_nyc, was that paper supposed to be the proof that pi is normal? It actually says "proofs of normality for fundamental constants such as log(2), pi, zeta(3) and sqrt(2) remain elusive" on the second page.

Here's a statement about one of the authors describing his work. It says:

Here's a statement about one of the authors describing his work. It says:

Bailey emphasizes that the new result he and Crandall have obtained does not constitute a proof that pi or log(2) is normal (since this is predicated on the unproven Hypothesis A). "What we have done is translate a heretofore unapproachable problem, namely the normality of pi and other constants, to a more tractable question in the field of chaotic processes."posted by aneel at 9:24 PM on December 4, 2007

*Maybe you'd like to know where your birthday is?*

I'll be damned--there it is. Thanks. I was wondering where the hell it went.

posted by weapons-grade pandemonium at 9:48 PM on December 4, 2007 [3 favorites]

All right, I have just found my phone number, my social security number, my birthdate, and my checking account number hidden in pi.

WHY ARE YOU FUCKING WITH ME GOD?

posted by Astro Zombie at 10:04 PM on December 4, 2007

WHY ARE YOU FUCKING WITH ME GOD?

posted by Astro Zombie at 10:04 PM on December 4, 2007

God is too busy to do things like hide your checking acount number in pi. Occam's razor says it must be the other way around. Pi is in your checking account.

posted by weapons-grade pandemonium at 10:10 PM on December 4, 2007

posted by weapons-grade pandemonium at 10:10 PM on December 4, 2007

I found Jenny @ string 8675309 occurs at position 9,202,591 counting from the first digit after the decimal point.

posted by hortense at 10:20 PM on December 4, 2007

posted by hortense at 10:20 PM on December 4, 2007

Does pi contain pi?

What if C-A-T spelled "dog"?

posted by papakwanz at 10:21 PM on December 4, 2007 [2 favorites]

What if C-A-T spelled "dog"?

posted by papakwanz at 10:21 PM on December 4, 2007 [2 favorites]

It was the best of times, it was the blurst of times...

Stupid monkeys.

I loved the Ask Me thread linked in the FPP. At Thanksgiving my electronic engineer uncle and I were discussing and trying to explain quantum cryptography and computing (as we understand it) to my 85 year old grandfather. I think it went pretty well. He still refuses to use a computer, but I can understand that. He thinks Trig is the shit though.

And being thanksgiving, there was great pi.

posted by afflatus at 10:31 PM on December 4, 2007

Stupid monkeys.

I loved the Ask Me thread linked in the FPP. At Thanksgiving my electronic engineer uncle and I were discussing and trying to explain quantum cryptography and computing (as we understand it) to my 85 year old grandfather. I think it went pretty well. He still refuses to use a computer, but I can understand that. He thinks Trig is the shit though.

And being thanksgiving, there was great pi.

posted by afflatus at 10:31 PM on December 4, 2007

*If π is normal then it contains every bit of porn on earth in every possible media format. Which makes you wonder why your netnanny doesn't block it.*

Well, the thing is, you see, it also contains all perfectly convincing arguments as to why netnanny

*can't*block it.

And

*can*.

posted by aeschenkarnos at 10:38 PM on December 4, 2007 [1 favorite]

*Does pi contain pi?*

Good question. I'm pretty sure the answer is no, because the words "contains pi" are invalid, in the same way that "outside the universe" or "negative absolute value" are invalid - the elements required to construct these concepts contradict each other, under the system of logic through which they are given meaning.

posted by aeschenkarnos at 10:45 PM on December 4, 2007 [1 favorite]

Astro Zombie:

Tell me you didn't just give all of that information to a stranger's website.

posted by Mikey-San at 10:45 PM on December 4, 2007

Tell me you didn't just give all of that information to a stranger's website.

posted by Mikey-San at 10:45 PM on December 4, 2007

This sentence contains all the information in the universe.

posted by Citizen Premier at 10:50 PM on December 4, 2007

posted by Citizen Premier at 10:50 PM on December 4, 2007

*Tell me you didn't just give all of that information to a stranger's website.*

No problem, the stranger already had it.

posted by aeschenkarnos at 10:50 PM on December 4, 2007 [4 favorites]

pax digita, on my last reading of the book I understood how ambiguous the ending really is.

posted by jiawen at 11:29 PM on December 4, 2007

posted by jiawen at 11:29 PM on December 4, 2007

A while back while investigating methods of encryption and data compression I snapped a piece of dry spaghetti such that the quotient of the two lengths was binary code for all of my personal information. So I carried it everywhere and it worked fine for a while but I forgot to take relative humidity into account and so ended up buying a telescope with some random dude's credit card number.

posted by weapons-grade pandemonium at 11:31 PM on December 4, 2007 [3 favorites]

posted by weapons-grade pandemonium at 11:31 PM on December 4, 2007 [3 favorites]

No, pi does not contain pi. Suppose it did: then you would have

3.1415926..........31415926

at which point it would repeat forever. Since the only numbers that repeat forever are the rationals, and pi is not rational, pi cannot contain itself.

posted by Pyry at 12:07 AM on December 5, 2007

3.1415926..........31415926

at which point it would repeat forever. Since the only numbers that repeat forever are the rationals, and pi is not rational, pi cannot contain itself.

posted by Pyry at 12:07 AM on December 5, 2007

I think a more accurate argument as to why pi doesn't contain pi is that pi has no end, so you would never know anyway.

posted by blacklite at 1:15 AM on December 5, 2007

posted by blacklite at 1:15 AM on December 5, 2007

Not true. π is irrational. If π contained π, then π would repeat (if the π valued subsequence starts at digit

We know that π is irrational, so we know that it does not contain itself without actually looking at any of its digits.

posted by agent at 1:27 AM on December 5, 2007

*n*, then it repeats at digit*kn*for all integers*k*). Thus it would be rational. Bang, contradiction, so π must not contain π.We know that π is irrational, so we know that it does not contain itself without actually looking at any of its digits.

posted by agent at 1:27 AM on December 5, 2007

Pi isn't irrational if you use as a base for your number system, just like 1/3 in base 3 is 0.1 (I know, 1/3 is not irrational). A nice tool based on this idea is the "pi tape" that converts circumference to diameter.

posted by 445supermag at 5:59 AM on December 5, 2007

posted by 445supermag at 5:59 AM on December 5, 2007

My birthday was not found and it was only seven digits.

posted by Brian B. at 6:32 AM on December 5, 2007

posted by Brian B. at 6:32 AM on December 5, 2007

**agent**: The question that will really bake your noodle is whether it's possible for π to contain itself but "half as fast," i.e., π ends up looking something like

3.14159...4

**3**7

**1**9

**4**0

**1**2

**5**2

**9**3...

Such a number can still be irrational. There might still be some reason why the above is impossible, though, probably having to do with power series. :)

posted by pmdboi at 6:40 AM on December 5, 2007 [1 favorite]

aren't we a few months early on this post? March 14th anyone? beuller?

on an off-note if you taped a slice of buttered toast to a pi and dropped it on the floor would you then create an infinite improbability drive?

Or would you need a toast-pi-toast matrix to make such a thing actually feasable... what if it were cat pi? toast-catpi-toast matrix? or would PETA come after you for cruelty to infinite strings?

posted by Sam.Burdick at 7:09 AM on December 5, 2007

on an off-note if you taped a slice of buttered toast to a pi and dropped it on the floor would you then create an infinite improbability drive?

Or would you need a toast-pi-toast matrix to make such a thing actually feasable... what if it were cat pi? toast-catpi-toast matrix? or would PETA come after you for cruelty to infinite strings?

posted by Sam.Burdick at 7:09 AM on December 5, 2007

Several years ago, I also pondered using 'Pi addresses' as a way of storing information. Want this year's edition of the Encyclopedia Britannica? Start at this number.

The trouble is, the address would usually take up more space than the encyclopedia.

One other thing: we know that Pi is infinitely long and doesn't contain repeat in the sense of 13.333333333... or 13.131131131131...

How do we know it doesn't have a different sort of pattern that nonetheless precludes the inclusion of all possible strings of numbers in Pi. For instance: 13.10100100010000100000

Obviously, it would be a much more complex pattern, but the possibility would invalidate some of the ideas described in the post above.

posted by sindark at 7:55 AM on December 5, 2007

The trouble is, the address would usually take up more space than the encyclopedia.

One other thing: we know that Pi is infinitely long and doesn't contain repeat in the sense of 13.333333333... or 13.131131131131...

How do we know it doesn't have a different sort of pattern that nonetheless precludes the inclusion of all possible strings of numbers in Pi. For instance: 13.10100100010000100000

Obviously, it would be a much more complex pattern, but the possibility would invalidate some of the ideas described in the post above.

posted by sindark at 7:55 AM on December 5, 2007

*Since computer files are simply numbers, then, in theory,*

images, audio, video, even wikipedia articles all exist in pi.

images, audio, video, even wikipedia articles all exist in pi.

So how long before this site gets their own special cease and desist letter from the RIAA?

And if my social security number is included within, say, 'Free Bird', shouldn't the record companies be paying some royalties to

**me**?

posted by wabashbdw at 10:34 AM on December 5, 2007

**yoyo_nyc:**

*This mean it will contain mine and your phone number and not only the collected works of Shakespeare but also every book that ever has been written and all the books that ever will be written. I guess finding the position in PI will be the tough part ;-)*

Are you sure? IANAM but doesn't Cantors diagonal argument apply to this problem?

linky

All though there might still be many good books in there :)

posted by larsso at 12:38 PM on December 5, 2007

Someone should do a DaVinci or Bible code deal with Pi. (SEE! It was predicted - by Pi! - Whoa dude! Can I subscribe to your religion/newsletter/blog?)

posted by Smedleyman at 3:42 PM on December 5, 2007

posted by Smedleyman at 3:42 PM on December 5, 2007

1111111111111

1111100011111

1111011101111

1110111110111

1110111110111

1110111110111

1111011101111

1111100011111

1111111111111

<>Contact >

posted by John of Michigan at 4:48 PM on December 5, 2007

1111100011111

1111011101111

1110111110111

1110111110111

1110111110111

1111011101111

1111100011111

1111111111111

<>Contact >

posted by John of Michigan at 4:48 PM on December 5, 2007

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