10: Pi Equals
Title text: My most famous drawing, and one of the first I did for the site
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 (a number that has an endlessly long decimal that never repeats) 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 never ends and does not follow any sort of known pattern, if each number pair were assigned a letter from the alphabet, or if it was converted to base-26 (or preferably ASCII or some other form of text encoding, if you desire capitalization and punctuation), 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); although 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 title text, Randall notes that this became one of his most famous comics (at the time it was re-released on the new xkcd site on the 1st of January 2006.) He also notes that it was one of his first drawings for the site (it was the 11th posted originally). See trivia below.
- [A huge π to the left, then a large equal-to sign, and then five rows of text.]
- π =
- This was the 11th comic originally posted to LiveJournal.
- Comic #36 was originally posted as a duplicate of comic 10: Pi Equals. This was corrected some time between April 23, 2006 and July 5, 2006 when the current version showed up in the web archive (see the links).
- This comic kept its original title: "Pi Equals"
- There were no original Randall quotes for this comic.
- This was one of the thirteen first comics posted to LiveJournal within 12 minutes on Friday September 30, 2005.
- This comic was posted on xkcd when the web site opened on Sunday the 1st of January 2006.
- It was posted along with all 41 comics posted before that on LiveJournal as well as a few others.
- The latter explaining why the numbers of these 41 LiveJournal comics ranges from 1-44.
- One of the original drawings drawn on checkered paper.
- The book version of this comic (in xkcd: volume 0) has 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."
- "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