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Share The Pi!

Hemos posted more than 12 years ago | from the 'merica-mom-and-apple-pi dept.

Science 380

freedumb writes "From this article in Nature: "Two mathematicians have now taken the first step towards proving that pi contains not a single message but every conceivable message, meaningful or not."" Actually, it's a discussion concerning whether "that all strings of the same length appear in pi with the same frequency: 87,435 appears as often as 30,752, and 451 as often as 862, a property known as normality."

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380 comments

Where's the code ? (1)

Anonymous Coward | more than 12 years ago | (#2201093)

Does anyone have working source code for the algorithm to calculate a digit of pi with out knowing the previous digits ? Is this something that my laptop can handle ?

On a related note... (1)

Anonymous Coward | more than 12 years ago | (#2201094)

...some guy found 424242 in Pi [angio.net] at position 242424 (counting the the decimal point.)

π Code Red Alert!!! (1)

Anonymous Coward | more than 12 years ago | (#2201095)

But, but, but... that means pi contains the Code-Red worm code! (In binary and source form!) Those bastards have infected !

Re:What's the big deal with Pi? (1)

Anonymous Coward | more than 12 years ago | (#2201096)

Other irrational numbers obviously do not contain every possible sequence, like 1.01001000100001.. Although there are random irrational numbers that do. Pi is somewhere in between, more complex but obviously not random. (There is no way of talking about a specific random irrational number.) It can be described as the sum of many infinite sequences, some of which are actually rather simple (something like pi/4 = 1-1/3+1/5-1/7.., as I remember). The digits appear "random", but because the series is simple to write out, it's strange that some digits do not appear slightly more than others, but it will be interesting if they can prove it one way or the other.

you missed the point (1)

Anonymous Coward | more than 12 years ago | (#2201097)

the size of this "position number" would probably be many many times the size of the text you are trying to compress - i.e., useless.

Wow... (2)

Anonymous Coward | more than 12 years ago | (#2201104)


An amazing finding...
...next thing you know, they'll be finding secret messages hidden in the Bible
using some sort of letter skipping technique.

Re:source code for windows? (2)

Anonymous Coward | more than 12 years ago | (#2201105)

What is even more interesting is that NetBSD is a subset of this

Re:Definition of frequency? (1)

Olivier Galibert (774) | more than 12 years ago | (#2201108)

The point is, nobody ever has proven that Pi contains every possible string of numbers. I'm not even sure it has been proven that all the digits are equi-probable.

OG.

Badass compression algorithm? (5)

defile (1059) | more than 12 years ago | (#2201109)

Soo.. if pi contained every possible message (ie, was truly random), couldn't you in theory find a specific position where pi prints out say, the Max Payne ISO, and distribute that position to friends?

Then, said friends, start calculating pi from that offset (wasn't there a story on slashdot about calculating any N digit of pi without having to calculate the first N-1 digits). Voila, kickass compression.

Of course, the small snags here are:

  • Searching pi until you find that right position that matches your Max Payne ISO, which could be located on the far end of infinity.
  • Distributing what could be a multi-trillion digit number to your friends.

But once you get over these boring details, pi-based-compression can make for some very neat applications

order in the chaos of Pi (2)

Tumbleweed (3706) | more than 12 years ago | (#2201112)

> If we could just get enough of the message contained in Pi, maybe some order would magically appear.

I'm sure once it's calculated to an infinite number of digits, the true meaning will become clear.

La bibliothèque de Babel (1)

whatever (7319) | more than 12 years ago | (#2201119)


Make me think about this article in a French science magazine about "La bibliothèque de Babel". Sorry, don't remember the title.

translation : "The Babel library"

Named after the guy who "invented" it.

This virtual library contains _many_ books...but a finite number of books.

The books contains 60 chars per line, 30 lines per page, and 500 pages per book...so 90000 chars total. (not sure about the numbers, but it's not important)

If the books uses an alphabet of 26 chars (a to z...sorry no caps), the space (" ") and the period char (".") we have 27 possible chars.

So 27^90000 different books (possibilities).

A book with all "a"s. The same book (all "a"s) but with one "b" at the end, a book about your life, a book about your life minus 20 years, a book on how the universe was created, etc... _And_ you have the same version in many languages (all the languages that uses this alphabet). In short, and infinite number of story...hrm wait a minute...it's a finite number (27^90000). :)


P.S. Sorry for my english

Pi is not really "Random" (1)

dido (9125) | more than 12 years ago | (#2201120)

If you think about it, the digits of pi are not really a "random sequence" at all, at least according to Gregory J. Chiatin's [auckland.ac.nz] theory of algorithmic information theory. The digits of Pi are of course compressible. You can write a computer program which is of finite size that will generate the digits of Pi, and that's definitely smaller than all the digits! The "randomness" only arises from our choice of base, actually. If you would use a factorial base representation (for instance) to write Pi, it wouldn't look very random...

What's the big deal with Pi? (1)

HomerJ (11142) | more than 12 years ago | (#2201122)

It's an irrational number. It doesn't end. Nothing more to see, go back to your homes.

If you have an infinate list of numbers, of course you can pull whatever you want out of them. Eventually something interesting will come up. I'm sure places 495865749584 to 495857498745 in binary are linux kernel 6.2.4 compiled perfectly for my hardware. In some other goofy place is DeCSS, and in another is any goofy message you want to look into it.

Not being a troll, but I still don't see the big deal about one irrational number.

Re:What's the big deal with Pi? (1)

HeghmoH (13204) | more than 12 years ago | (#2201123)

The number 0.11010010001000010000010000001... is irrational, infinite in length, and yet does not contain every concievable message.

Re:Badass compression algorithm? (1)

HeghmoH (13204) | more than 12 years ago | (#2201124)

Two problems.

1) The search will probably take many trillions of years.

2) The number specifying which digit to start with will probably be larger than the ISO was in the first place.

Re:Badass compression algorithm? (1)

Jeremi (14640) | more than 12 years ago | (#2201127)

Actually, all you need to do is FIND it. Not that this is a trivial task

Indeed. I'll buy a case of beer for the first guy who builds a quantum computer that can search all the digits of pi simultaneously to do this. ;^)

Re:Useless Pi Fact (3)

wirefarm (18470) | more than 12 years ago | (#2201130)

Oddly, my ICQ number is at position 19724810 counting from the first digit after the decimal point.
What're the odds of *that*?
;-)
Cheers,
Jim in Tokyo


Have no clue about firewalls? [mmdc.net]

More about normal numbers ... (1)

rkmath (26375) | more than 12 years ago | (#2201140)

It is not hard to prove that essentially any number is a normal number - in the sense that any number you pick at random between say 0 and 1 (uniform distribution) (More precisely, the set of normal numbers in [0,1] is a set of full measure - one proof goes via the strong law of large numbers - ask your local probabilist for an explanation). What is hard is showing that a particular number is a normal number (I didn't even know that one had any explicit examples).

Normal numbers being essentially all numbers is more subtle than the fact that "essentially all numbers are transcendental". The set of non-normal numbers is actually uncountably infinite (not countably infinite like algebraic numbers).

Re:Badass compression algorithm? (4)

The Raven (30575) | more than 12 years ago | (#2201143)

It wouldn't work. With a completely random (normal) data set, the address of any particular string of numbers is of equal length to... the particular string of numbers! Thus, the average distance into pi of a four digit number... is a four digit number. I don't really care to do the exact math, but the end result is that the number of bits you wish to find and encode the address of would, on average, require an address with an equal number of bits.

Raven


And my soul from out that shadow that lies floating on the floor

Re:Badass compression algorithm? (2)

Restil (31903) | more than 12 years ago | (#2201144)

Actually, all you need to do is FIND it. Not that this is a trivial task, but if you know the position, you can retrieve the digits with multiple ease with a simple fast algorithm (at least if the digits are binary)

However, like you said, FINDING it would take far longer than just sending a damn copy of the thing. :) If we ever had really REALLY fast computers some day, this could do wonders for data compression. Any value could be represented by a simple position.

Of course, if the position was somewhere after a googolplex digits, sending the position would be an order of magnitude more complex than just sending the data.

Forget I said anything.

-Restil

Why is this then worthy... (1)

mefus (34481) | more than 12 years ago | (#2201145)

...of an article in Nature, if as they say:
Mathematicians have known for more than two centuries that the number is an infinite,

non-repeating decimal.
I mean, isn't that the implication being made by that Nature [nature.com] article?

If it has now been shown, then Nature (Ma Nature, not the journal) has given us the proverbial infinite monkeys, and I'm going to look for Shakespearean sonnets in that number. <g>

Re:What's the big deal with Pi? (1)

mefus (34481) | more than 12 years ago | (#2201146)

???

at position 2^300+1 the next 600,222 bytes are the Linux kernel compiled for Io Rover VII (or whatever)

What's uncompressed about that?

Re:Random bits that are in Pi somewhere (1)

mefus (34481) | more than 12 years ago | (#2201147)

That pattern (1828...) breaks down after awhile, if that's what you mean.

Re:Random bits that are in Pi somewhere (1)

mefus (34481) | more than 12 years ago | (#2201148)

I think that would make PI a repeating pattern...

so... IANAM, but I think that's been ruled out.

Damn, slashcode thinks I'm cowboyNeal, and won't let me post!

Random bits that are in Pi somewhere (3)

BigKahuna (41476) | more than 12 years ago | (#2201157)

Why concentrate on just pi? If they show it's true for all trancendental numbers, they've got it for pi, e, etc.

Can pi appear in pi anywhere? I guess not, since that would mean that pi repeats. Could e be in pi? I suppose if e was in pi, and pi was in e, then pi would be in pi, which I guessed earlier it couldn't be. But, maybe I'm wrong and there's a loophole since if pi contains itself, there's an infinite recursion going on.

If there were an infinite number of monkeys typing on an infinite number of keyboards would they eventually produce all the works of Shakespeare? Not exactly - they would produce them immediately (as quickly as a monkey can type). That's infinity for you. The lazy 8. It goes on and on...

Every message? (2)

[amorphis] (45762) | more than 12 years ago | (#2201161)

So, does it contain the 7 line DeCSS implementation? how about just the ascii "Natalie Portman"? goatse.cx?

Re:Useless Pi Fact (2)

alteridem (46954) | more than 12 years ago | (#2201162)

and seven 7's [angio.net] is found at position 3346228, six 6's [angio.net] is found at position 252499, five 5's [angio.net] is found at 24466, and so on...

What am I trying to say? So what!

Upgrade Time (1)

pnatural (59329) | more than 12 years ago | (#2201171)

Quoth the article:

The quest to conquer pi's infinite expanse has led some mathematicians into fierce calculating competitions. The current record, achieved with the help of supercomputers, is 500 billion digits.


500 billion digits? that's all? my nt box calculates that many instructions every time it boots. maybe the mathematicians should upgrade.

Pi = Infinite Monkeys (1)

Toodles (60042) | more than 12 years ago | (#2201172)

Ever since the post late last week about the predictability of pi, I can't help but think about the infinite monkey/infinite time scenario. It would seem that embedded within the number pi is the script to Hamlet. Ford Prefect would be proud.

There is/was a German hacker's convention scheduled for this year, one of the topics for discussion that I haven't seen posted in /. is the 'illegal prime'. A prime number, when written in base 16, that becomes a .gz file with the deccs code imbedded within. Its about 1400 digits long, viewable here [utm.edu] How long till a digit place and count to find it in pi becomes available? The smalled deccs code in c is about 430 charachters. Remove the CR/LF, encode as 7 bit, and it should be much easier to find inside pi.

With the predictability of pi digits outlines a couple of days ago, making a program to accept a place and length to output a planned file is very realistic. However, I believe we are far behind in the computing power to actually take an arbitrary file of more than a few bite's in size and find that location/length pair in pi. Let's hoep quantum computing changes that.

On an aside, all of the information on finding digits of pi are base 10. Are there any articles on predictability based on a binary representation?

Toodles

everything? (1)

ankit (70020) | more than 12 years ago | (#2201177)

so pi contains everything? information about everything?
so everything is out in the open. forget about privacy and the like.

source code for windows? (5)

ankit (70020) | more than 12 years ago | (#2201178)

this is the latest : microsoft sues pi for containing the complete source code to windoze.
btw, the code starts at position 4200394298 (in the binary expansion of pi), and continues for well, as long as anyone ccan read the stuff...

Pi is PRIOR ART! (1)

pcx (72024) | more than 12 years ago | (#2201182)

FLASH! All patents are declared null and void because all patents previously awarded have been found to exist within PI. Although mathematicians have not proven yet that PI has existed since the beginning of the universe, they have conceeded that not only has PI been around "a very long time" but that it has probably been around longer than Compuserve's GIF patents.

An anonymous scientist has even gone so far as to say it has probably been around longer than the human genome, rendering new drug company patents on human DNA void for the prior art contained within PI.

A roman catholic biship was overheard to have said, "Not only does this prove that there is a God, but it finally proves once and for all that he hates lawyers."

An anonymous lawyer who wondered if God's prior art could be nullified for His refusal to defend His prior art was killed by a stray lightning bolt in the middle of the Sahara desert in a highly unusual but unrelated incident.

Re:Normality (2)

BlueUnderwear (73957) | more than 12 years ago | (#2201184)

> If every known string would be found. They what about finding Pi with one digit off?

All finite strings.

Re:New cult... (5)

BlueUnderwear (73957) | more than 12 years ago | (#2201188)

With your username, you should know one egregious example of funny strings in Pi at funny positions:

42424242 at position 242424.

Oddly enough, according to the pi search page [angio.net] , the same string can be found again at position 1404114, which is also below 100000000. On a normal pi, you'd expect a single occurrance of 42424242 below 100000000, and at a completely random position...

Re:not EVERY possible message... (1)

nebular (76369) | more than 12 years ago | (#2201192)

Actually it is possible. If you read an earlier post there is a string of eight 8s

The nature of Pi will not allow a repeating pattern of numbers, so long as no continuous pattern of those numbers appears to infinity, Pi can have every possible piece of information contained within.

Scary when you actually think about it

Re:Badass compression algorithm? (2)

Speare (84249) | more than 12 years ago | (#2201194)

Searching pi until you find that right position that matches your Max Payne ISO, which could be located on the far end of infinity.

Distributing what could be a multi-trillion digit number to your friends.

The second problem is easy, prima facie. Just "compress" it with your compression scheme until you've minimized the energy. Establish a convention: if the position'th digit is a known pattern, then the following minimum-compliant-digits describe the even-more-distant starting place for the actual content (or another copy of the known pattern to loop again yet-further-out). If you can't find the key digits of your position before the position itself in pi, then you've got the optimum key. Of course, the drawback is this: minimizing the energy a normal-to-base-10^n-for-all-n number is not going to be all that likely. The best key Y that encodes Max Payne's starting point of X may be such that Y > X!

The first problem's not that hard, but the storage for it is a big problem. You have to keep around all of the pi digits prior to the end of your most distant dataset instance. The upside: you can store Max Payne and Linux 6.5.3 ISO and DeCSS all in one archive. The downside: poor retrieval. There are a few helpful indexing methods for searching through all those digits fast, of course. See Knuth.

First Application Of This... (2)

Greyfox (87712) | more than 12 years ago | (#2201198)

The first application of this should be a search for the decss source code. The resulting start digit will be illegal. I have this really weird feeling that if you looked in the vicinity of the prime number that gunzips to the decss source code, you might find it there. (Possibly gzipped.)

The second application should be the start digit of a Metallica MP3.

Anyone want to start up a distributed network to look for these?

True, But... (2)

Greyfox (87712) | more than 12 years ago | (#2201199)

I'm sure there's a lot of cool stuff in the first 2^128 digits. If 128 bits is a long on an itanium system, I'm sure we could have a lot of fun searching the first 2^128 digits of pi for stuff without even breaking out of the long address space. If 2^128 seems small, how about 2^256? 2^1024? 2^65536? That's not a lot of bytes, but it's a hell of a lot of space to search. Probably more than modern computers will be able to handle for years (Even if we do start up a distributed net type search engine to look for things.) Who knows. My next computer might have to include a pi coprocessor...

Re:but can it fortell assasinations (1)

Jotham (89116) | more than 12 years ago | (#2201200)

heh.. you can try, but it's common knowledge that those messages are really broadcast via TV static every night around 2:32am.

Definition of frequency? (2)

Ryu2 (89645) | more than 12 years ago | (#2201201)

If pi does contain every possible string of numbers, then it follows that any finite-length string must appear an infinite number of times.

So, yes, trivially, all strings appear an infinite number of times. Or are we talking about another measure of frequency (number of appearances in a substring of pi's digits of a given length?)

Re:Useless Pi Fact (1)

mberman (93546) | more than 12 years ago | (#2201203)

Eight 8's happening early enough in pi that we'd notice is extremely unlikely, as we can all imagine. This makes it, on first inspection, pretty damn cool that it happens. But then, when you think about it a little more, you realize that while eight 8's is unlikely, "something that humans find interesting" is very likely, mostly because we find so many strings of digits interesting. From that point, it's just random which particular interesting string crops up, since we know one is going to, eventually.

More Pi Weirdness (1)

mberman (93546) | more than 12 years ago | (#2201204)

One of the weirdest facts about pi that i've ever heard is the following: the length of a sailboat, in feet, divided by its hull speed (the maximum speed a boat can go, at which point its bow and stern waves cross so that it can no longer accelerate without planing), in knots, is, you guessed it pretty damn close to pi! Now, by "pretty damn close", I don't mean by an irrational number researcher's standards...it's more like 2 or 3 decimal places...but to a sailor, that's close enough that the "pi" button on the galley's calculator works perfectly.

Re:Random bits that are in Pi somewhere (1)

Chan (93764) | more than 12 years ago | (#2201205)

It would seem to me that if e is in pi, then that would be the only independent irrational sequence in pi, since you couldn't fit two infinite sets of numbers together "end to end" since there is no end. Therefore no other irrational number could be in pi. Unless (spooky) that other irrational number is contained in e.
Nesting irrational sequences...
Time to go to bed.

New cult... (3)

Zaphod B (94313) | more than 12 years ago | (#2201206)

It will start a whole new branch of numerology dedicated to finding entire new holy books... the Book of the Damned, I Microsoft, II Microsoft, the letter of BOFH to the Great Unwashed, and, of course, the source code to Office (which will take up the space between 2^8 and 2^40906) ...


Zaphod B

Re:Normality (3)

Mister Attack (95347) | more than 12 years ago | (#2201207)

The article states specifically that the researchers are working in binary. The property they are looking for to prove normality is a property of a binary number. The base-10 numbers they gave were probably just examples that "normal" people would understand.

So if anything, they are proving normality to base 2^n, NOT base 10^n. And it may actually be that their proof is general enough to show normality in all bases - the article is not clear on that point.

Re:Badass compression algorithm? (1)

SirStanley (95545) | more than 12 years ago | (#2201208)

Well. If it did start on say the Trinllionth trillionth Digit of pi. Just store digits as powers. That way we can make em smaller. Then use LZW on that number. =) But for compression you'd have to store not only the starting digit but how many digits it needs. And doing all this fun math should be a snap on a 64-way Sun E10000 loaded with the 900mhz Ultra Sparc IIIs (not a configuration yet...)

Re:Normality (1)

SirStanley (95545) | more than 12 years ago | (#2201209)

If every known string would be found. They what about finding Pi with one digit off? Like Where we found Pi and every digit in pi is the same except say the trillionth digit. Now. Start your recursive looop engines and figure out the rest

Re:Badass compression algorithm? -- NOT (1)

naoursla (99850) | more than 12 years ago | (#2201212)

Unfortunately, you need to specify the index to the beginning of the message. Since your message is probably a very long way into Pi, the index will likely be more bits than the message itself. I discovered this property of compression when I tried to build a compression routine based on Godel numbers. Most compression algorithms use the assumption that there are repeatable elements that can be compressed. This is sort of like using fewer bits to represent the low frequency component of a signal. If the message doesn't have much repetition, that algorithm will do poorly. You could also write a compression algorithm that knew commonly used phrases - this algorithm will only work well on phrases in the domain for which it was designed. All of this is related to Wolpert's No Free Lunch theorem.

Re:Useless Pi Fact (1)

jareds (100340) | more than 12 years ago | (#2201213)

You're right that we're likely to find a few interesting sequences earlier than we expect. However, this isn't one of them. Finding 88888888 (~8.9*10^7) at or before position 46663520 (~4.7*10^7) is clearly not unlikely. It should be around 37% probability.

Re:Definition of frequency? (1)

jareds (100340) | more than 12 years ago | (#2201214)

I'm sure we're talking about the limit of the frequency in the first n digits of pi as n approaches infinity, or some similar definition. Frequency of course refers to the ratio of the number of ocurrences to the size of the string of digits.

Re:Normality (1)

jareds (100340) | more than 12 years ago | (#2201215)

I don't want to go off on a tangent about proofs... but I'm curious - what happens when a rule of mathematics is challenged? For example, some defenitions seem so arbitrary to me. 1 is not considered a prime number because it has only itself as a factor... I don't like that reason and I don't kow why. Years of work would be invalidated should such rules be thrown out, right?

Uh, changing a definition is hardly throwing out a rule. If you don't like one being prime, just take any mathematical work and replace every reference to 'primes' with 'primes other than one'. Whether you like how things are named has nothing whatsoever to do with validity. Definitions aren't really arbitrary, but they could be without messing anything up.

Re:Random bits that are in Pi somewhere (1)

jareds (100340) | more than 12 years ago | (#2201216)

It is possible to have an infinite number that contians smaller sets of infinite numbers. Like the set of whole numbers of infinite. The set of even numbers is infinite. The size of the whole number set is larger than the set of even numbers. The even numbers could never hold the whole numbers, but the whole numbers do hold the even numbers.

This is just dead wrong. The set of even numbers and the set of whole numbers are the same size, because you can map then in a one to one correspondence.

Re:Badass compression algorithm? (4)

localman (111171) | more than 12 years ago | (#2201228)

Distributing what could be a multi-trillion digit number to your friends.

Easy! All you have to do then is search pi for the multi-trillion digit number and then send it's offset. If that offset is still to long you can just do it again until you ended up with, like, a single digit!

Pi is three (2)

zerocool^ (112121) | more than 12 years ago | (#2201229)

PI IS THREE!!

froin laven, i didn't think i'd have to use that.


Irrationality (3)

sigwinch (115375) | more than 12 years ago | (#2201230)

Not being a troll, but I still don't see the big deal about one irrational number.
'Irrational' means literally 'cannot be written as a ratio'. This doesn't necessarily mean that the digits are random. You can have numbers like
3.44333444443333334444444...
that are irrational, but whose digits are trivially deterministic. Boring.

Then there are the 'dirty' irrational numbers like pi and e that seem to have random digits. The research mentioned has moved a big step closer to proving that the digits of pi don't just seem random, they truly are random (at least in the sense that all possible combinations occur).

The part that'll really blow your mind is that somebody found an equation that tells you any binary digit of pi you want, without having to calculate any of the other binary digits. (See here [doe.gov] .) That is why people are excited by the conjectured normality of pi: if normal, it produces all possible strings of bits from a trivial deterministic equation. This mixture of randomness with order is at the heart of many interesting questions in chaos theory, computational theory, and cryptography.

Well, I know one thing this will mean... (3)

Antaeus Feldspar (118374) | more than 12 years ago | (#2201231)

And that is a pain in the neck for everyone in comp.compression.

There is a frequent fallacy among those who almost understand how compression works, that works like this:

"Wait a minute! I bet that every set of digits that someone could be trying to encode can be found somewhere in the digits of pi! Therefore, we can compress any sequence by simply reducing it to the number of digits in the sequence, and the offset in the digits of pi where an identical sequence begins!

The assumption, of course, is that the number of digits and the offset can be encoded in a form that will be smaller than the original sequence. There is nothing to warrant that assumption. The fact is that the number of possible inputs that a lossless compression method can handle places lower bounds on the average length of its outputs. This means that no lossless compression method can achieve a lower average length for its outputs than would be achieved by simply numbering them all with the non-negative integers.

In fact, 'compressing' a sequence of digits into a (length, offset) pair will do substantially worse, since there are multiple (length, offset) pairs that will correspond to a given digit sequence; for instance, "1" could be encoded as (1,0) or (1,2). This duplication means that (1,2) is essentially wasted, since it could be representing a sequence that currently has a longer representation.

Lossless compression methods need to be used in conjunction with models: some criteria that separates the data we will want to compress from the vast majority of files, about which we do not care. The accuracy of this model affects how many of our inputs we can actually compress, and its precision affects the average compression ratio.

Re:Badass compression algorithm? (1)

Leven Valera (127099) | more than 12 years ago | (#2201243)

I've read an Arthur C. Clarke story where an alien visits the Earth, spends decades learning all of human knowledge, then runs that knowledge through a massively-complicated equation. After that, the alien marks humanity's position on a storage rod as a # of marks from the top, and goes on his way.

Weird.

Re:Normality (3)

BadDoggie (145310) | more than 12 years ago | (#2201261)

This has happened before, when mathematicians realised they had been basing proofs on a couple assumptions which themselves had never been proven. You can read about it in Simon Singh's "Fermat's Last Theorem", an extremely readable and enjoyable look into both Fermat and mathematics in general.

A teacher, a physicist and a mathemetician are having drinks together in a Scottish pub when the teacher looks out the window and sees a white sheep. The teacher says, "There are white sheep in Scotland". The physicist looks out the window and declares, "There are sheep in Scotland; we have already detected and confirmed white ones." The mathematician says, "In Scotland there is at least one sheep, at least one side of which is hite."

No, I didn't pull that from Singh (it's there, though). It's an old mathematician's joke but it's true. The most anal Rainman you've ever seen is incredibly chaotic compared to mathematicians (at least when they're working on a proof or theorem).

woof.

"No ma. You don't have to worry about Code Red. Yes, I know CNN told you that you do. Ma, do you run a Web server? No, Netscape is a browser, not a server. Yes, there's a difference. You don't want to know. No, and the Internet didn't die last week, either..." -- my side of a phone call two nights ago.

Craziness with transcendental and imaginary #s (3)

proxima (165692) | more than 12 years ago | (#2201283)

Trying to imagine why every n digit number shows up the exact same amount of times is hard to imagine at first. But then, once you think about it, on an infinite scale, it would seem to attest to Pi's true randomness.

On a side note, I had a Calc II professor awhile back that wrote on the board:

e^(i*Pi) = -1 (of course, using the real symbols).

Then, he proved it. I have the proof written down in a notebook and I even managed to work through the final parts of the proof (it uses a standard solution for finding e^(i*A*X) without using it. If anyone is really interested in seeing it, I can post it (in rough ascii math =) For those of you with TI-92s that don't believe me, type it in. That magical machine can do more than I give it credit for sometimes.

Anyway, I just thought it was absolutely incredible that you could mix the two most popular transcendental numbers with the imaginary number (square root of -1) and spit out plain old -1.

Pi is a circumvention device... (1)

gnomer (179654) | more than 12 years ago | (#2201292)

...for every copyright protection scheme ever invented! And for every one that ever will be invented, for that matter. Not only that, it contains my entire illegal mp3 collection (and yours too).

Am I in violation of the DMCA every time I divide the circumference of a circle by twice its radius? Hmmmmm....

Re:What's the big deal with Pi? (1)

Sydney Weidman (187981) | more than 12 years ago | (#2201299)

0.11010010001000010000010000001

Would this be considered non-repeating? It seems like it should, but it's so damn orderly.

Great contrast... (2)

Sydney Weidman (187981) | more than 12 years ago | (#2201300)

  • It's amazing to think that something as orderly and perfect as a circle has this incredibly chaotic quality.
  • If we could just get enough of the message contained in Pi, maybe some order would magically appear.
  • If you could read a circle like a book, what would it say?

wouldnt that just mean... (1)

rootofevil (188401) | more than 12 years ago | (#2201303)

that pi is totally and completely random?

Re:Badass compression algorithm? (2)

quintessent (197518) | more than 12 years ago | (#2201306)

If PI has the property they are theorizing, to find a number n digits long in PI, you'll likely look through about 10^n digits of PI. So, storing its location in PI should take about as many digits as the message you are trying to compress.

The Zen PI (1)

sasha328 (203458) | more than 12 years ago | (#2201312)

I remember when I was working on engineering design that PI=3.1416.
That was good enough for us.

Re:Maybe we haven't dug deep enough into Pi (1)

tswinzig (210999) | more than 12 years ago | (#2201315)

So according to Contact, embedded into the digits of Pi is the picture of a perfect symbol.

Err I mean "the picture of a perfect circle."

Maybe we haven't dug deep enough into Pi (2)

tswinzig (210999) | more than 12 years ago | (#2201316)

Not being a troll, but I still don't see the big deal about one irrational number.

In Carl Sagan's book, Contact, there is an interesting revelation made to Ellie by the alien she visits light years away. It tells her that buried deep in Pi is an important message.

(Here's where my memory gets a little iffy.)

So when she returns home, she writes a program that searches for non-random data in Pi, in multiple bases, and sure enough she finds a message in base-11 composed of all 1's and 0's.

When laid out in rows of equal columns, a perfect circle is formed out of 1's, with 0's as the background.

So according to Contact, embedded into the digits of Pi is the picture of a perfect symbol. If this were true, it would be proof that the universe was created by intelligent life.

Or at least a real funny joke.

Useless Pi Fact (2)

Fatal0E (230910) | more than 12 years ago | (#2201337)

I remember watching Northern Exposure when I was about 13 and there was this episode where Chris Stevens dates this mathematician chic and she talks about a string of eight 8's [angio.net] . Years later when I read about a Pi search engine I tried it and was actually surprised to see it worked.

alcohol + /. = useless posts.
:o)

Re:Maybe we haven't dug deep enough into Pi (1)

3prong (241218) | more than 12 years ago | (#2201347)

I loved that part of the book, but it always kind of bothered me, too. Bitmaps of circles always look like crap (thanks to the jaggies) unless they are a) very high resolution or b) anti-aliased. Would the creator of the universe put a low-res, very imperfect rendering of a circle in such an important place, even as a cutesy joke?

Unavoidable Bad Pun (1)

shorti9 (307602) | more than 12 years ago | (#2201384)

"Information wants to be pi"

-josh, who needs to do something better with his time

Re:Where's the code ? (2)

Angry Toad (314562) | more than 12 years ago | (#2201388)


Right here in C [nersc.gov]

Ban the circle! (5)

Telal (314917) | more than 12 years ago | (#2201390)

If pi has all conceivable messages, pi must contain all of the US military's secrets, DeCSS, kiddie pr0n, violent and explicit sexual films beyond anyone's imagination and much much more. It must therefore be banned. When you get the death penalty for circle possession, don't say I didn't warn you...

Remember This? (1)

robbyjo (315601) | more than 12 years ago | (#2201391)

Hmm... Check this out [slashdot.org] .

Check this formula too [doe.gov] . If the formula is so simple (like taking the sigma out of a mere factors of fractions), pi couldn't be containing any message. I simply skeptic about that....

Normality (2)

Spling (317404) | more than 12 years ago | (#2201394)

Strictly speaking, the property mentioned isn't actually normality, but normality to base 10^n for all n. Normality to base b means that if you write down the base-b expression for the number then every base-b digit occurs with equal frequency. So normality to base 10 means that in the usual decimal expansion, 3 and 7 occur with equal frequency, for instance. Normality to base 100 means that, e.g., in the decimal expansion 34 and 87 occur with equal frequency.

It's known that in a certain precise sense, almost all numbers are normal (i.e. normal to *all* bases). But to this day, not one single specific number has been *proved* to be normal!

Re:What's the big deal with Pi? (1)

Chakat (320875) | more than 12 years ago | (#2201398)

Well, now that they've proven that Pi's completely irrational, combined with the formula to determine an arbitrary number of pi, there are a few interesting things that can be performed. Like the aforementioned kernel source example you gave. I know you were being silly, but in low bandwidth/high latency situations, such as deep space, if one could find the string of numbers you want to send, one could probably save a good deal of time transmitting. There's also the usage as a one time pad, a cheap source for "random" numbers.

Yeah, it's not as exciting as finding a cure for cancer, but it's still pretty cool

D - M - C - A

Re:An Infinite Random Irrational Number (1)

preternatural (322346) | more than 12 years ago | (#2201400)

If Pi is infinitely long, non-repeating and random, then isn't the rule that any such number must contain all finite numbers ... eventually?

Not necessarily. Consider pi, written base 10. Now replace every occurrence of the digit 7 with the digit 2. The resulting number is still infinitely long, non-repeating, and random (but I suppose this depends on what your definition of random is). It doesn't contain any finite number that contains a 7 and thus doesn't contain all finite numbers.

Re:Great contrast... (1)

Kynde (324134) | more than 12 years ago | (#2201402)

It's amazing to think that something as orderly and perfect as a circle has this incredibly chaotic quality.

Circle has hardly anything to do with this "chaotic quality", since most of the real numbers also have this quality.

If we could just get enough of the message contained in Pi, maybe some order would magically appear.

Did you not understand the randomness in question? That's exactly what will not happen, ever, since that's the essense in randomness. It's like saying that by throwin the dice more and more maybe you'll find a pattern. The thing with randomness is that these "patterns" cannot compress the sequence. (worth noting is that the sequence of Pi is anything but random in a information science sense, since it's well known and can be compressed to, say, "Pi")

If you could read a circle like a book, what would it say?

The expectation value of the position of any certain string of numbers is actually as long as that certain string. It might be easier to wait for some hwrandom() to produce Romeo and Juliet.

---


---

I've said it once and I'll say it again... (1)

Uttles (324447) | more than 12 years ago | (#2201403)

WHO CARES!

OK so the ratio of the circumference of a circle to it's diameter just happens to be a number that has infinite decimal places and contains an equal distribution of all possible base 10 numbers... what in the hell does this prove? First of all, it's not proven anyway, and second of all, do these people think that Pi is the secret to life or something? Really folks, it's just a number, and since we have no practical means of measuring anything past the... oh... say... 1,000,000,000ths digit, why bother?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The Movie (1)

skinney (395862) | more than 12 years ago | (#2201407)

I think that this is very similar, if memory serves, to what was described in the movie PI.
Is it possiable that the numbers that are extracted from the irrational number have some kind of signifigant meaning in nature?

The key to GUT'S in a piece of PI??

~Shane

Re:Stephen King, author, dead at 54 (1)

skinney (395862) | more than 12 years ago | (#2201408)

Whatever....you post this same shit all the time. Find something better to do with your time you fuckin _troll_

but can it fortell assasinations (1)

beanerspace (443710) | more than 12 years ago | (#2201417)

If PI contains every concievable message, then do you suppose we could use to predict the future ? Not the normal boring stuff, like will my daughter run off with tall swarthy mediterranean, but important stuff, like assasinations [anu.edu.au] ?

roll your own PI (5)

beanerspace (443710) | more than 12 years ago | (#2201418)

For those of you with a spare machine and time on your hands, here are some links that show you how to calculate your own value for PI:

Re:Normality (1)

6EQUJ5 (446008) | more than 12 years ago | (#2201421)

I don't want to go off on a tangent about proofs... but I'm curious - what happens when a rule of mathematics is challenged? For example, some defenitions seem so arbitrary to me. 1 is not considered a prime number because it has only itself as a factor... I don't like that reason and I don't kow why. Years of work would be invalidated should such rules be thrown out, right?

Re:Normality (2)

MarkusQ (450076) | more than 12 years ago | (#2201423)

I think he said "almost every number..." or something very like. There are, of course, some exceptions (such as the integers, and rational fractions, etc.) but they make up a very small subset of "the numbers," amost all of which are too lengthy to write in this margin.

-- MarkusQ

Re:Ban the circle! (3)

MarkusQ (450076) | more than 12 years ago | (#2201425)

If pi has all conceivable messages, pi must contain all of the US military's secrets, DeCSS, kiddie pr0n, violent and explicit sexual films beyond anyone's imagination and much much more. It must therefore be banned.

It must also contain all finite length MP3s. Therefore under the DMCA it already is banned.

The sad part is, I'm not joking. The DMCA is so absurdly broad that you could easily raise a cogent case for using it to ban the concept of Pi for this very reason.

-- MarkusQ

Re:Random bits that are in Pi somewhere (1)

NHaedhroes (451415) | more than 12 years ago | (#2201426)

err....isn't e 2.7818281828......?there's only room for one infinite-digits number. Or is there...

Re:Badass compression algorithm? (1)

NHaedhroes (451415) | more than 12 years ago | (#2201427)

err....you're all a little caught up on what you know, what you can think about, it seems. Advanced search, storage, retrieval, interpretation techniques. Just think. Technology as an adjunct to more technology, not tricks made by playing with a number. One person mentioned transcendental numbers. Transcendental indeed. Something about mapping out hyperspace. Geblurp.

An Infinite Random Irrational Number (1)

catsidhe (454589) | more than 12 years ago | (#2201431)

If Pi is irrational, does that not imply that its fractional part is infinite and non-repeating in all bases? (Except possibly base pi...)

If Pi is infinitely long, non-repeating and random, then isn't the rule that any such number must contain all finite numbers ... eventually?

But, by extrapolation, does this not imply that while pi may contain the complete source code to Office 2000, it also contains all possible incorrect versions, and it is impossible to know which one you have found. And it is impossible to know which base to look in. And it is impossible to know how far in it is. And, and, and,...

Essentially, if you find anything meaningful in pi (or e, or ...), then it is a: accidental, and b: not actually meaningful.

The mathematics of trans-finite numbers will make your brain melt if you think about them long enough.


--------
I see no THERMONUCLEAR WARHEAD here.

You are at Y2.

Re:Random bits that are in Pi somewhere (1)

catsidhe (454589) | more than 12 years ago | (#2201432)

Can pi appear in pi anywhere? I guess not, since that would mean that pi repeats. Could
e be in pi?

I would have said 'no', but then I remembered the story about how it is, in theory, possible to fit an infinite number of people into a hotel with an infinite number of rooms that were already full... (source?)

Could the same principle be used to justify squeezing one infinite length string of digits into another?

I wonder. (Common sense says that the concept is ridiculous, but as I have said before, when dealing with trans-finite numbers, check your common sense at the door.)


--------
I see no THERMONUCLEAR WARHEAD here.

You are at Y2.

Re:An Infinite Random Irrational Number (1)

catsidhe (454589) | more than 12 years ago | (#2201433)

I would have thought that this would not be random because for the digits [1,3..6,8..0] there is a probability of 0.1 of their appearance, but a probability for '7' of 0.0, and a probability for '2' of 0.2.

Whether this measurable discontinuity would carry over when the fiddled pi is in other bases is another question entirely, and one for number theorists, not me.
--------
I see no THERMONUCLEAR WARHEAD here.

You are at Y2.

Chaitin's Omega (1)

NotoriousQ (457789) | more than 12 years ago | (#2201437)

The fact that they are looking for patterns is kinda cool. Anyone else think that they should compare it with pattern's in Chaitin's Omoga. Would be nice, if you could calculate it though. Unfortunately, knowing a single digit of that number without calculating its compononts is a paradox, sigh.

Re:An Infinite Random Irrational Number (1)

cakoose (460295) | more than 12 years ago | (#2201441)

How can you have base PI? I though only integer bases were possible. Maybe the digits are: {0, 1, 2, 3, PI} ???

Re:Useless Pi Fact (1)

DNS-and-BIND (461968) | more than 12 years ago | (#2201443)

Big deal...since Pi is an irrational number, and never ends, at some point there is a string of 5,646,498,765 8's all in a row.

Re:roll your own PI (1)

DNS-and-BIND (461968) | more than 12 years ago | (#2201444)

So, can we start a distributed computing project to find the DeCSS code in Pi?

Re:What's the big deal with Pi? (1)

marvin tph (462349) | more than 12 years ago | (#2201445)

If I understand you correctly you want to send the start index and length of your msg as it appears in pi. I think its safe to assume that this would in fact be a longer than the msg itself.
Try writting out every 2 digit sequence (00..99)
Done? You should have 200 digits down. Now if you wanted to send the msg "99" you would send 197. That's an extra digit. When you start doing this for arbitrary length expressions the losses are going to get even worse.

---------------------------------------------

Re:Random bits that are in Pi somewhere (1)

snilloc (470200) | more than 12 years ago | (#2201454)

IANAM (I am not a mathematician), but I don't think you could put pi (or any other irrational number) in pi

3.14....lots of numbers.... infinite number of numbers....lots more numbers.....

You'd never get to the end of INON (that is, pi) in order to tack LMN to the end... In order to put pi inside of pi, pi would have to be infinitely self-referential, thus giving it repetition... and making it a rational number.

Assume: On the x-th digit of pi, insert pi....
but on the (x*2)th digit (the xth digit of the second iteration of pi) you'd start pi again...
Therefore, pi is repeating (rational)
But, pi is not rational
Therefore, the assumption that pi contains pi cannot be true. ????

The puzzle/story (1)

snilloc (470200) | more than 12 years ago | (#2201455)

The first task for the new employee at Hotel Infinite was to add one guest to an infinitely booked hotel... Solution: tell the new guest to go to room 1 and tell the guest in 1 to go to 2, 2 to 3, 3 to 4....

The second task was to add an infinite number of guests to the hotel... Solution: Tell every current guest to move to the room number double his/her current room. Tell the new guests to go to the odd numbered rooms.

Sorry, I don't where this story was first published...

Pi (1)

E-Rock-23 (470500) | more than 12 years ago | (#2201458)

Funny. My mom can never seem to slice pi with the same kind of normality. Then again, my mom is as odd as pi anyway...

Finding messages (2)

Captain_Jackass (472496) | more than 12 years ago | (#2201462)

Yeah, but what's the point of finding, "First Post!", in pi if it's not first?
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