10: Pi Equals

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Pi Equals

Original title: Pi equals

Title text: My most famous drawing, and one of the first I did for the site

Explanation

This was the eleventh comic originally posted to LiveJournal. The previous one was 9: Serenity is coming out tomorrow, and the next one was 14: Copyright. It was among the first thirteen comics posted to LiveJournal within 12 minutes on September 30, 2005, on the first day of the xkcd LiveJournal account.

There are two possible references here. One is from the book Contact by Carl Sagan, where the existence of God was shown in the last chapter to be encoded in the digits of pi. The other is an old joke of a fortune cookie with a fortune that reads, "Help! I'm trapped in a fortune cookie factory!" Similar jokes are often repeated for any mass-manufactured personalized item, often implying that the worker who made the item is working in a sweatshop somewhere or is literally trapped inside a factory and calling for help via the items they produce. This joke is also referenced in 327: Exploits of a Mom's title text, where Mrs. Roberts' daughter's name is "Help I'm trapped in a driver's license factory." The most literal interpretation of the joke would be that some being who helped to create the universe in a "universe factory" snuck a message into the digits of pi, asking for help to get out. Mathematical concepts being manufactured in a factory is the main mental image here. One can't help but wonder if the primordial beings who labored on the universe to produce things like the gravitational constant and pi have a labor union. Judging by the fact that they're calling for help, it seems they don't.

Since pi is irrational (it has an infinite, non-repeating decimal representation), if each number pair were assigned a letter from the alphabet, or if it was converted to base-26, ASCII, or some other encoding, the entire works of Shakespeare, as well as any other expressible piece of information, including the message in this comic, could presumably be found. It is not really known that pi really has this property, but the absence of this property would in itself be an extraordinary coincidence. However, the probability of finding any given string of numbers within a calculable range of digits of pi diminishes rapidly as the string length increases.

In the novel Contact by Carl Sagan, he includes a "Signature of God." In brief, the signature consists of a very long string of 1s and 0s far out (after some 10^20 seemingly random numbers) in the base-11 expansion of pi that when arranged in a square of a specific size yields a clear drawing of a circle with a diameter of several hundred digits. The existence of this pattern was hinted to the protagonist by a member of an advanced alien civilization as being encoded in physics by an even more advanced civilization with the ability to create universes. Interestingly enough, this could also work for pictures: if you assign a set of nine numbers to equal an RGB hexadecimal color value, eventually you will find the Mona Lisa.

In the book xkcd: volume 0, this comic has a red text at the bottom of the page: CNEG BAR BS RVTUG VA URK: RR AVAR RVTUG SVIR BAR BAR RVTUG. It's ROT13 for "PART ONE OF EIGHT IN HEX: EE NINE EIGHT FIVE ONE ONE EIGHT". "7108914" appears in position 13,709,690 of pi, suggesting that the length of the string of "digits" that is 'helpimtrappedinauniversefactory' is correspondent to a good 13,709,675 digits long, meaning each individual letter corresponds to about 456989.166667 digits. Aggravatingly, however, if the string was instead "71089314", it would appear at position 2533.

• If the letters correspond to the phone keypad, then these digits are wrong: 3.14159265358979343574687277334628648377332286797108914
• If the words correspond to their length, then these digits are wrong: 3.14159265358979342721877108914
• And if the words are omitted altogether, then these digits are wrong: 3.1415926535897937108914

In the title text, Randall notes that this is one of his first drawings and it became one of his most famous comics. At the time, it was re-released on xkcd.com on January 1, 2006, with the number 10, but it was the eleventh comic posted to LiveJournal. See the trivia section below. In xkcd: volume 0, this comic has a different title text: "I've put rescue instructions in e. You'll need the cheat codes for your universe, which I hid in the square root of two.".

The volume 0 title text is a message styled so that it would appear to come from the maker(s) of this universe, detailing how to escape it. A cheat code is a type of utility in certain video games, that, when inputted, gives the player things not normally granted in normal gameplay. As the universe is not such a game^{[citation needed]}, such a concept would be somewhat nonsensical. The hex number "EE985118" is 4,002,959,640 in decimal, so that could be the answer to the number in the title-text.

Transcript

[A huge π to the left, then a large equal-to sign, and then five rows of text.]

π = 3.14159265

3589793help

imtrappedin

auniversefac

tory7108914...

Trivia

• 36: Scientists was initially published as a duplicate of this comic. Over three months after the original posting, Randall noticed the error and corrected it sometime between April 23, 2006 and July 5, 2006, when the updated version appeared in the Web Archive. He likely found an old drawing that was never meant for publication and used it instead, so it wouldn't appear out of place among the other comics from that period. This is why 36: Scientists doesn't have a date like most other comics.
• This used to be one of the footer comics featured in the bottom segment of xkcd.com.

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Discussion

Interestingly, 7108914 does not occur in the first 100,000 digits of pi. However, 71089 does occur at roughly around the 2,500 digit mark. --DanB (talk) 18:17, 6 August 2012‎ (UTC)

7108914 position 13,709,690 counting from the first digit after the decimal point. The 3. is not included. --whitecat (talk) 10:43, 7 August 2012‎ (UTC)

There is a children's book called "Help, I'm a prisoner in a toothpaste factory". 86.30.117.77 (talk) 17:13, 7 January 2013‎ (UTC) (please sign your comments with ~~~~)

or it's reference of the Mac OS 6 and 7 "BlueMeanies" easter egg "Help! Help! We're being held prisoner in a system software factory!". 46.126.181.133 (talk) 08:59, 7 January 2013‎ (UTC) (please sign your comments with ~~~~)

In my profession - simplifications of π is equal perfection, I can throw a recurring function at it, but it will just give me more pages of numbers. Remember that pi will ultimately equal 22/7, and you'll be alright. - E-inspired (talk) 09:17, 3 March 2013 (UTC)

We still have to find "helpimtrappedinauniversefactory" @pi, even when Randall also does not know.--Dgbrt (talk) 20:48, 23 June 2013 (UTC)

You know, we could convert "helpimtrappedinauniversefactory" to the ASCII numbers and then use one of those algorithms that searches pi for a particular string of numbers... 108.162.219.36 22:40, 13 November 2013 (UTC)

While the string 72697680 (HELP) appears multiple times throughout the first 200,000,000 digits of pi (not counting the 3.), none of the resulting ASCII strings makes sense. The closest (7269768022774869990317421141) is at position 31,961,494 with the resulting string as "HELP�M0E". Note that it is the number "0" and not the letter "O". The string "104101108112" ("help") does not occur in the first 200,000,000 digits. -108.162.250.114 08:15, 30 December 2013 (UTC)

Umm... "Of course, because pi never ends and never repeats, if you assign each number pair a letter from the alphabet and look through the digits of pi, somewhere within it is the entire work of Shakespeare, or any other piece of information that could be expressed with human language. So, ironically, somewhere in pi, there actually is the phrase stated in the comic, in a sense." This isn't guaranteed. Just because it's infinite and non-repeating doesn't mean that every possible pattern exists within it. 0.1010010001000010000010000001... is infinite and non-repeating, but it most certainly doesn't contain Shakespeare. It would only be guaranteed if the series was perfectly random over an infinite amount of time. 108.162.237.64 23:47, 14 March 2014 (UTC)

Ah, but in 0.1010010001... there is a pattern, isn't there? 1, then n number of zeroes, where n is incremented by 1 each time it is used. I don't see such patterns in 3.14159... myself. :PNSDCars5 (talk) 12:56, 23 May 2014 (UTC)

That you don't see a pattern doesn't mean there is one. That there is no pattern doesn't mean it contains every possible sequence. --108.162.231.98 12:14, 6 August 2014 (UTC)

Have edited it to add that this requires a proof that pi is normal. For readers, to see the flaw in NSDCars5's reasoning, consider how he might have seen the entire infinite sequence of pi's digits, then realize it's impossible without a formal proof. Which is what the proof of pi being normal would solve. As it is, we don't have that proof yet, and so we cannot say for sure that pi has every possible finite sequence. 103.22.201.63 16:31, 12 August 2014 (UTC)

I vote we modify that. It's almost certainly true that pi does include the entire works of Shakespeare, but good luck proving that. 108.162.216.58 07:29, 30 November 2014 (UTC)

If you would argue that, statistically, even one line of Hamlet or Romeo and Juliet could be found within Pi, then statistically, it would be found thousands of time with typos or mistakes first. By the time someone found ALL of Shakespeare's works lined up, first we would have found the individual works separated, millions of times, with all manner of mutations that would result from random chance. Something to consider. 108.162.221.44 16:30, 28 June 2015 (UTC)

I feel like there should be a mention that, since pi is a mathematical constant rather than a physical constant, even if you did create the universe you'd have no control over it. You might be able to influence the directions math takes and exert some control over what constants seem important, but that will only give you a few bits of control, meaning that you can only encode a message a few bits long. You could easily encode messages into the fine structure constant, but if you stick it too close to the beginning it might inhibit life, and if you stick it too far nobody will be able to measure it accurately enough to find it. 108.162.216.58 07:29, 30 November 2014 (UTC)

Yes, manipulating such a mathematical constant would require changing in some incomprehensible way basic rules of logic or arithmetic, which seems much farther beyond human comprehension than physical constants which human physicist still don't fully understand a clear reason behind their known value needing to be what it is and can only deduce by calculating them based on experimental results. However some being outside the universe making universes including fine tuning their details would have to be in some way beyond human comprehension anyway. This was a topic in the Contact book btw, with a conversation with the Alien like "how could a message be hidden inside pi? It's part of the fabric of the universe!" To which the alien replied "exactly." Note that most of this topic, like a ton of other stuff was left out of the movie supposedly based on it.--108.162.216.215 23:21, 3 October 2022 (UTC)

Whereas the fictional prisoner in a Fortune Cookies Factory may harbor hopes that once his message gets out and the finder of the message take it to the authorities who will trace it's origins and affect a rescue; no such hopes are available to the Universe Factory prisoner. Not unless the residents of the created universe have a manner of interfacing with the creators civilization. Which brings up an interesting question: Once an intelligence has deciphered a message from a higher being, do they just move on as if nothing happened, or do they now focus their resources toward ascending into the higher realm just revealed. If the latter, than our Universe Factory prisoner may have some hope after all... Mountain Hikes (talk) 08:52, 31 August 2015 (UTC)

The link to TV tropes yields "403 Forbidden", please find a different link. 108.162.210.220 18:15, 8 September 2016 (UTC)

Though the fortune cookie story is fictional, I once read a credible seeming article about someone buying a Halloween decoration made in China and finding a hand written letter inside asking for help.--172.70.178.221 23:23, 3 October 2022 (UTC)

The fact that the digits 7108914 appear at position 13709690 of pi doesn't mean that it is the string that is represented in the comic. The 7108914 in the comic might be one of the 19 other times it appears in the first 200 million digits of pi. "helpimtrappedinauniversefactory" might represent a longer string of digits and each letter might represent a whole number of digits in pi. 1234231587678 (talk) 01:17, 2 January 2024 (UTC)

Using A=1, B=2 … instead of ASCII makes messages shorter ⇒ more probable. HELP→851216 occurs 17x in the 1st 10M digits of π alone, sadly none followed by I=9. HELPME→851216135 is absent, too. RANDA→1811441 occurs 2x, none followed by L=12. I find 6x MUN→132114 and 87x ROE→18155 in the 1st 10M digits, but not consecutively. What does this tell us? That my lunch break's been over for a while and I'd better stop now. :) --172.70.230.94 21:43, 7 October 2024 (UTC)

Brief comment: If A=1, and L=11, then what does …11… in a sequence decode to? Either/both?

Requiring A to be …01… is one solution, but then there are sequences (…00… and …27… to …99…) that disqualify themselves from decoding. You could treat invalid numeric pairs as null-encoding (but then …019999999901… as as much "AA" as any other block of 'ignorables' between two 'A's, so might give many other new matches for resolvable strings), though you might also assign other numbers to other non-alphabetic characters like spaces, punctuation or even formatting-associated markup. Which is not far from ASCII/ANSI/Unicode/etc! 172.70.85.138 22:50, 7 October 2024 (UTC)