Download PI

Florentg @ 2006-05-25 22:09:24

Hey man, you've juste discovered the best way on earth to compress data ! Just store the position :D

Anonymous Coward @ 2006-05-25 22:51:37

Finding long continuous sequences in PI that exactly match the byte values in, say, a 6 MB MP3 is intractable. In fact, for anything but trivial sequences (such as your INFO example), the problem is intractable.

You could provide a bunch of offsets, however, say one for every longword in the data. But this definitely isn't compression; the bits representing the offsets will very likely be as large, if not larger, than the original data.

You are essentially describing a one-time pad, except that it won't work for encryption purposes because everyone knows the codebook.

vince @ 2006-05-26 00:38:05

An old idea. Hardly feasible.

If you first consider data compression. It's not about actually compressing anything but creating a mapping from numbers to numbers. We give the big numbers we like (data) a smaller representation as another number, and the numbers we don't like (noise) some big number. While on other numbers we win, with others we lose. Nothing is compressed. It just seems that way. For every compression algorithm there is a kooky other one somewhere brewing that can compress everything into a single bit. The directions on which program to use for decompression are part of the file.

Also, it wouldn't do squat for the copyright laws. It is not that the PI decimals would be illegal. It wouldn't be too hard to argue that no matter what the method of producing a string of bytes constituting a copyrighted work, distributing those means or methods should be illegal.

For instance, there is nothing illegal in you encrypting an mp3 and representing the bits as a noise image on a website. Only if you include the image with directions on how to unravel the mp3, you commit yourself.

I for one believe there is no good way to solve the 'problem' like there is no good way to solve any problem that involves some (any) form of a resource.

cyber_rigger @ 2006-05-26 05:30:45

Compression isn't the issue.

Theoretically strings of copyrighted material are contained in pi,
therefore making the distribution of pi to infringe on these copyrights.

Since pi was here first then these "copyrighted" works are plagerisms of pi.

vince @ 2006-05-26 09:31:53

PI doesn't sound like anything or make it to the boxoffice (well...).

Like all laws copyright laws are about an agreement.We do want there to be copyright laws to protect people who create things and we don't want these laws to be too strong. But we do want the laws to be there. Thus we agree to find a way to apply them and with that we agree to not let sleight of hand abolish those laws.

In the same way a set of natural numbers can be considered containing all copyrighted works there is. Just make a program to go through all the permutations and stop when the desired work is at the beginning.

I guess it is like some artists say: "They didn't create anything, they just had to find them."

Copyright laws are not going anywhere. As much as I hate the side effects I do think they are neccessary.

hueblur @ 2006-05-27 04:40:45

Um...

no.

Adam Lyttle @ 2006-05-27 04:59:01

That is a fantastic idea, I am going to take the challenge and develop a program which compresses files using the method you described!

Derek @ 2006-05-27 05:03:35

The digits of pi are not "random" in the computational sense because we can write a fairly short program that computes the i'th number of the sequence. They just appear random to the human eye. In fact, Pi does not contain more information than the number of bytes required to write a program to calculate it in an average programming language, which is say far less than < 1000 bytes.

Even something as simple as a computationally random 640 x 480 x 32 bit image (by random I mean very difficult to compress) has potentially 2^20 bytes more information than is contained in Pi.

Therefore, in order to express that image in terms of PI, you'd need an offset that on average contained this 2^20 bytes of missing information... kind of pointless. It's just a translation from one set of numbers (the data) into another (the offsets).

Gryfft @ 2006-05-27 05:05:12

See, the thing is, EVERYTHING is in there. Everything. Movies, books, all our life stories-- books that haven't been written yet, games that will never be published. The problem is that it is SO RIDICULOUSLY FAR DOWN in Pi that the position of that movie, game, book, song, complete human genome, complete genome for, I don't know, real Tribbles, would be far longer than the actual representation of that piece of media. Like, if every atom in the Earth was a digit, there wouldn't be enough digits to express the place number of said position of Pi. So yeah, it's all in Pi... but it's a few Googolplexes down in there. Unless you have an overclocked quantum supercomputer sitting around, I doubt you'll be getting anywhere within the lifetime of the Universe.

arredja @ 2006-05-27 05:05:41

Besides wouldnt you need to have that copyrighted work before you could even begin to look for it therefor breaking copyright anyway?

foobario @ 2006-05-27 05:27:14

This thought pops up with astounding regularity on the net. Without fail, the same logical error is made every time: distributing Pi does not violate any copyright. Distributing the offsets and encoding method for the location of a sequence that represents a copyrighted work does violate copyright... it's not really any different from distributing the location of a .torrent in the long string of numbers that make up the net.

snood @ 2006-05-27 05:27:50

this sound similar to primary number encryption..

Adalgiso @ 2006-05-27 05:39:18

I'd like to add that using making the argument that Pi contains all possible sequences of numbers is like saying the dictionary infringes on copyrights because words could be put together from its pages that form lyrics to a song.

Dan @ 2006-05-27 05:40:21

First of all, copyrighted materials are not 'plaigarized from Pi' because any given number of the size of, say, a 250kb picture has certainly not been discovered yet. So, unless you can prove that the creators of the material had the knowledge that the paticular string of digits in question already existed within Pi, they have done nothing wrong.

Furthermore, suppose I took all of the bits of an mp3 and mixed them up so that the file could no longer be used to hear the song. If you downloaded this new file, would you be infringing on a copyright? No, because the owner of the song does not lose any money by you having it - you still have to purchase a CD if you actually want to listen to the song. It is only when you acquire the information to de-scramble the file does the copyright holder lose business. (If this were not true, then most novels wouldn't be legal - I'm sure you often can rearrange the letters of one novel to make another, albeit shorter, copyrighted story).

By this logic, simply downloading Pi would not be illegal - only when you acquire the offset(s) would you be breaking the law. And judging by how difficult it is even to find a 1000 digit number in Pi, I suspect that most offsets would be extremely large. This means that it would not be reasonable to argue that you stumbled upon that information by chance - you had to have knowingly and proactively searched for it. Thus, you had acted upon an intent to acquire copyrighted material illegally, and could be prosecuted.

Anonymous @ 2006-05-27 05:47:16

i'd rather be s @ 2006-05-27 05:48:25

This is completely retarded. Changing 24 to 56 does no compress anything. All you are going to do is change the code into another equally long code. Complete waste of Digg space.

jb @ 2006-05-27 06:00:44

This website: http://www.angio.net/pi/piquery searches the first 200 million digits of pi. The odds of finding anything over about 8 digits is awfully low, and dropping exponentially. This makes no sense.

graffiti @ 2006-05-27 06:11:56

So where's PI inside PI?

Anonymous @ 2006-05-27 06:15:00

It would be a great research project. The problem of processing power could be overcome by new grid technologies. In fact, I am shifting my Xgrid project to focus on this (I needed a monster job to test anyway).

Soon I will apply a 10x3GHz test grid to different algorithms have run them 24/7. This will allow a 'search' algorithm to evolve and steamline. After alpha testing, a 400x1.25GHz grid will be invoked (June '06 timetable).

I envision the 'search' function to occupy the majority of the computational requirements (considering you have to search pi(i..i+n) for each ith position (binary file length n) to find a match. Retrieval would be on an exponentially smaller computation requirement, as both i and n are known.

A production grid 5x proposed size would be available with minor difficulty provided success. Any interested and serious parties that wish to contribute to this project email me bstrauch@harnett.k12.nc.us

Hardware specs:
10x3GHz G5 servers as dedicated grid agents. (test environment)
Production agents are 1.25GHz emacs.
Controllers are duel Xeon 3.4GHz Xserves with 4GB ram and 1TB raid5.

Anonymous @ 2006-05-27 06:29:03

...continued

What is grid computing?
http://en.wikipedia.org/wiki/Grid_computing

My grid:
http://www.apple.com/server/macosx/features/xgrid.html

I am not pursuing copywriting issues, let lawyers play with that.

I am not researching compression methods, too many ways to compress already. (Compression might be utilized, as search time is proportional to binary file length.)

I am not encrypting. Let NSA play with that.

I am basing all this on the author's original idea: finding a representation of a binary file in PI at the ith position.

If hypothesis holds true, the search would require the supercomputer. Once i and n are found, the generation would take far less time and could theoretically be run in an end user environment.

Anonymous @ 2006-05-27 06:47:29

http://www.geocities.com/hjsmithh/Pi/PiQPCpp.html calculates digits of pi in hex, without calculating any of the digits that come before it.

Anonymous @ 2006-05-27 06:51:53

An infinite series of numbers is not an exhaustive set of numbers. Another way to say that is just because there are an infinite number of digits in Pi does not mean that any particular combination of numbers must exist. You might be able to find your phone number or social security number quite easily, but good luck finding any series of numbers that represents a program, music, or anything else. Not that it is impossible, it is just very very improbable.

To further explain why Pi is not an exhaustive set, let's assume that all number sequences exist in Pi. That statement means that I should be able to find a series of 100 fives, or 1000 fives, or a billion billion billion fives, and even an infinite number of fives. Any number of fives (or any other number) is a valid series of numbers, so it would have to be found if our assumption were true. It also would mean that I should be able to find all the numbers for e (Euler's number) as well. Since e is a non-repeating, non-terminating number like Pi, its number sequence cannot be found within Pi.

Also, Pi is not a random series of numbers. By the simple fact that you can write a program to predict the digits of Pi means it is not random. Just because there is no repeating pattern does not mean it is random. Random, by definition, is not predictable.

The assumptions you made are common mistakes that I have made myself.

Seth @ 2006-05-27 06:57:44

I'm no statistician here, but finding The DaVinci Code inside pi, no matter what kind of code you adopted, would be tantamount to a roomful of chimps typing the complete works of Shakespeare. It's probably close to the same order of magnitude of information, at any rate.

The amount of computing power it would take just to calculate pi to the requisite length (let alone searching it for such an enormous sequence) likely won't ever be achieved, if only because you'd need to calculate pi out to somewhere around 10^n digits, where n represents any number you'd care to pick greater than the number of elementary particles in the universe. So while technically you're right that given an infinitely long random string you can pick out any given sequence of digits, once that sequence becomes long enough, the probability is small enough for us to regard it as zero.

scruffy dan @ 2006-05-27 06:59:39

If this works, you would not need to download anything, you computer would be able to generate the movie/song/media from pi.

Cool concept, but how powerful would computers have to be for this to work

Seth @ 2006-05-27 07:00:19

The guy above me is right too, so disregard the first part of my last sentence above.

swordphish @ 2006-05-27 07:01:57

"So where's PI inside PI?"

At offset 0.

This is an interesting concept, no matter how infeasible - let people dream - who knows what might emerge.

Paul Gnuyen @ 2006-05-27 07:42:04

Um. Okay there's a sequence of numbers which is just as good for this... the integers. In order. The whole movie just just a number, finding the offset in PI that this number is at on average, will be the same as just giving the number directly. That is, in your info example you can say, take the 73,787,079th number in the integers instead of the 8,223,688th in PI. This is just a one time pad that's hard to calculate.

You can say, all things can be represented as numbers, and people can copyright things, therefore there are some numbers that are copyrighted. Yeah, really long numbers when used in a certain way.

Leif @ 2006-05-27 07:50:42

As as stated in comments above, finding a reasonably large file in Pi will take an unreasonably long time and also the information describing the offset in pi will be larger than the the information in the original file. BUT you should really checkout http://en.wikipedia.org/wiki/Illegal_prime for another novel way to say FUCK COPYRIGHT LAW.

scarabic @ 2006-05-27 07:58:58

Interesting idea!

I'm not sure all images, all content is "inside pi." You can use PI as an encoding key to express lots of data, but as you point out, you'd quickly need to invent an encoding/decoding scheme rather than scan through all of pi looking for the specific numeric sequnce that spells out a JPEG image (for example).

At this point, using pi positions to encode data affords little protection against intellectual property laws. Pi may be public domain, but a stream of pi positions that spells out a copyrighted work... that's something different. That set of pi positions is NOT public domain, although pi, itself, may be.

Dogwelder @ 2006-05-27 08:00:26

Stupid concept. Pi may extend infinitely, but that doesn't mean it contains every possible series of numbers. Even if it did, it would be non-feasible to transmit information just by sending an offset. Think of a number that really does contain every possible finite series of numbers, by listing every permutation of 1 digit, then every permutation of 2 digits, etc.: 0.1234567900010203... By the time you got around to the number that represents the latest travesty from American Idol in MP3 format, the offset is a number that takes exponentially more time to transmit than the MP3 itself. And then you have to spend the rest of the universe calculating the 900 kazillionth bazillionth digit just to decode it. Just download your shit from BT like the rest of us.. life's too short.

Anonymous @ 2006-05-27 08:00:49

Thats the same as saying if you put enough monkeys in a room with enough typewriters, one of them would write Shakespeare. I dont think so!

Anonymous @ 2006-05-27 08:03:36

Searching for the entire binary representation in a single substring would be inefficient.

Take the Da Vinci Code for example. One representation of this work is in a basic .txt file. Compress this text file into a .zip which is 20% original size. The binary representation of that .zip file is your search string.

Now one could start out looking for this search string as one long substring within PI. When you find that string, you're done. That's the least efficient method O(t).

Another way would be to search for the first half of that substring, then the second half, then join. Now you have O(t/2).

Continue division and independent searches in this manner, and you decrease your O(t) proportional to the size of the generation algoritm that is being extrapolated.

Boundaries on division would exist at 1 (search for entire string) and X (where generation function to rejoin substrings approaches size of original file).

We are still assuming here that extrapolating the generation function is the computational intensive portion of the process and once a matching generation algorithm has been obtained regeneration could be accomplished with end user resources.

~bstrauch

NTDaley @ 2006-05-27 08:06:03

1:
Downloading PI would not be illegal.
Downloading the offset and length for pirated software/music/etc would be, as this is just a way of encoding the data. It is illegal to download pirated software whether you download it as binary data, a tar file, Base64 encoded data, ... So because the offset and length in PI are a way of encoding the pirated software, it would be illegal to download the offset and length.

2:Using an offset and length into PI as a compression scheme would not work. On average this information would use the same or slightly more data than the original data.

truth machine @ 2006-05-27 13:05:29

"We would need a very very very long binary expansion of pi and some kick-ass interface for searching for a file"

No, we would only need to be able calculate it -- and, as is noted above, the hexadecimal expansion of pi has the advantage of being calculable from any starting point, so no significant amount of processing power is required. OTOH, downloading the start and end positions of an arbitrary item would generally require longer than the life of the universe and more storage than there is matter.

"This thought pops up with astounding regularity on the net. Without fail, the same logical error is made every time"

The thought pops up frequently because there's a nearly inexhaustible supply of sloppy thinkers -- and the same logical error is made every time because anyone recognizing the error immediately dismisses the thought.

"An infinite series of numbers is not an exhaustive set of numbers. Another way to say that is just because there are an infinite number of digits in Pi does not mean that any particular combination of numbers must exist. You might be able to find your phone number or social security number quite easily, but good luck finding any series of numbers that represents a program, music, or anything else. Not that it is impossible, it is just very very improbable."

Too bad you have no idea what you're talking about. The digits of pi aren't just "an infinite series of numbers", they are the decimal expansion of a transcendental number. While it's not proven that every finite string of digits occurs within the decimal expansion of pi, it is very very likely, not "very very improbable", that any specific finite string does appear. The vast majority of mathematicians believes this to be the case, as there is absolutely no reason to expect otherwise, and it is known that the first 30 million digits of pi are very uniformly distributed.

"To further explain why Pi is not an exhaustive set, let's assume that all number sequences exist in Pi. That statement means that I should be able to find a series of 100 fives, or 1000 fives, or a billion billion billion fives, and even an infinite number of fives. Any number of fives (or any other number) is a valid series of numbers, so it would have to be found if our assumption were true."

This does not "further explain why Pi is not an exhaustive set" -- it is to be expected that all of those different sequences occurs at some point in the *infinite* string of digits of the decimal expansion of pi. If pi contains all strings of digits, then they all occur; if it does not, then one or more may not occur. Rather than "explain why Pi is not an exhaustive set", you have offered a simple case of petitio principii.

To see why it is almost certainly true that all these sequences occur, imagine breaking up the decimal expansion of pi into blocks of a billion billion billion digits. There 10^27 different such blocks, but an infinity of such blocks in the expansion, and we have no reason to expect any of these blocks to occur any more than any other; we certainly don't have any reason to expect any of them to never occur -- and that's the case for the block of all 5's. So not only should we expect such a sequence to occur, but we should expect it to occur infinitely many times.

"It also would mean that I should be able to find all the numbers for e (Euler's number) as well. Since e is a non-repeating, non-terminating number like Pi, its number sequence cannot be found within Pi."

Um, do you know of any images, music, etc. of infinite length? e and other infinite sequences are irrelevant. But we should expect any finite subsequence of the decimal expansion of e to occur within the decimal expansion of pi. Certainly you have offered no reason not to expect that, and there is every reason to expect that, as the digits of pi show no statistical patterns and there is no known reason why there would be any.

anie @ 2006-05-27 16:35:48

you have rediscovered the bicycle man

Jayesh @ 2006-05-27 16:39:30

Good idea. I am wondering if you have read Carl Segan's 'The Contact' (book not the movie). At the end of this novel he talks about finding a message from an alien civilization hidden inside the expansion of PI. When I first read it, I was amazed by the idea of 'Modulating the Facts' to store information. Your blog reminded me of the book. If you haven't read it, give it a try.

MS @ 2006-05-27 16:55:49

To answer graffiti's question, pi cannot appear inside pi.

Lets say the digits of pi were repeated after the nth digit. Let's call the value of pi, up to but not including that digit, x. Then, we can actually use infinite series to calculate a fractional representation of pi as such:

Knowing that the sum of the infinite series x + x*10^(-n) + x*10^(-2n) + x*10^(-3n) + ... is equal to

x/(1-10^(-n))

And knowing that the sum is also equal to pi, we have just expressed pi in fractional form, which contradicts pi's irrationality. It follows that such an expansion cannot exist, and pi cannot be inside pi.

Daniel @ 2006-05-27 19:55:27

Wait a minute...

For every digit that you add to your number that you are searching for, the difficulty of finding that number will increase by a power of 10. So if you are looking for 7 digit number, your odds of finding it are 1: 1,000,000. Odds are you're position in pi will be at least a 6 digit number... hardly a good compression scheme. If you are trying to get a 5MB mp3 file somewhere in pi, if you even find it, the number that you'll use to express that position will be so big that you might as well just send the MP3.

Rob @ 2006-05-27 20:38:59

You never proved your assertion that "any sequence of digits is in pi."

I don't believe this is true.

saichu @ 2006-05-27 21:04:36

Ok, look.

Screw pi. Stop thinking about it, it doesn't matter.

The fact is, I can make a floating point number (in any base) that contains every finite string. I can do it quite easily, in fact.

Let me illustrate in base 2.

This number, represented as an infinite string, will be a set of substrings concatenated to each other. Specifically, it will be the string

"0."

concatenated to the set of all binary strings of length 1, concatenated to the set of all binary strings of length 2 (let us denote these as [1] and [2], and in general, [3], etc).

So how do I guarantee that all binary strings of length 1, 2, etc are in my concatenation? Simple. I count upwards.

The binary strings of length 2, for instance, are

00
01
10
11

So the string 00011011 (which is counting up in [2]) is the string that contains all strings of length 2.

Similarly, the string that contains all strings of length 1 is 01.

Thus, the beginning decimals of my number, appending these first two sets, is 0.0100011011...

The same principle can be applied to any other base. For decimals, for instance, it would start as 0.12345678900010203040506070809101112...

The algorithm for computing this number can easily find out what the number at the nth decimal place is.

Similarly, given any finite substring, I can easily find its first occurance in my number.

Say the substring is of value x, and it has length n. The first occurance is simply x + [SIGMA from i = 1 upto i = n-1 (i*2^i)]

In other words, the digital form of any song you might write is already in that number. Show me the binary representation, and it's as simple as plugging into that formula.

So why can't I just copywrite this number and force you all to pay royalties?

---

Ok, so if the patent office has a problem with infinite decimal numbers.. well, that is easily solved.

Very few works of music or theatre, after all, have binary representations greater than 10 gigabytes in length. So all we have to do is produce a binary string (it doesn't have to be a floating point this time; it can be integral) that contains all strings 10 gigabytes in length. (It will also contain all strings less than 10 gigabytes in length.) The same principle can apply.

If you want the number to be prime, you can just keep adding on more digits to it until you get a prime number.

In other words, screw pi, we don't need to know whether pi contains every infinite string. I already have a number that is sure to, and an algorithm that can find the offset for this string. Now, where do we go from here?

Martin @ 2006-05-30 22:25:24

@ saichu

Brilliant!

My first thought was, "Start generating that file!", but after some calculations it turned out that if we only want to cover all 1kb files it requires more harddrivespace than exists on earth:

2 > 2^2=4*2 = 8
3 > 2^3=8*3 = 24
4 > 2^4=16*4 = 64
5 > 2^5=32*5 = 160
6 > 2^6=64*6 = 384

1kb = 1024 byte = 1024*8 bits = 8192

2^8192*8192 = 8,7259850849553274357038739578703e+2466 bits =
1,0907481356194159294629842447338e+2466 byte =
1,0651837261908358686161955514978e+2463 kb =
1,0402184826082381529455034682596e+2460 mb =
1,0158383619221075712358432307223e+2457 gb =
9,9202965031455817503500315500222e+2453 tb

So I guess we'll have to wait for bigger harddrives, but then the movies will probably also be made in better quality so it seems to be a moment 22.

But i still think your idea is great!

godfather @ 2006-06-04 18:53:58

Thankss!!!!

school student @ 2006-06-18 17:04:53

well this is an interesting website, but im just trying to find what set of numbers that Pi belongs to!!! ahhhh any help????? thanks anyway,
School Student.

Wi11 R @ 2006-09-04 20:52:00

Recently Pi was proven to have the property that every finite sequence of arbitrary length is in fact in its expansion. In fact, I was trying to find the name of that property when google brought me here... Damn I wish a scrapbooked that webpage.

Random is not the correct term, as has been pointed out.

This also does not change much for copyright law as has been pointed out.

It matters tons to math nerds who care about this though...

sounded something like 'totem p-something...', 'teut.... ',
bah

Wi11 R @ 2006-09-04 20:53:08

Recently Pi was proven to have the property that every finite sequence of arbitrary length is in fact in its expansion. In fact, I was trying to find the name of that property when google brought me here... Damn I wish a scrapbooked that webpage.

Random is not the correct term, as has been pointed out.

This also does not change much for copyright law as has been pointed out.

It matters tons to math nerds who care about this though...

sounded something like 'totem p-something...', 'teut.... ',
bah

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