Roots of Unity

Roots of Unity

Mathematics: learning it, doing it, celebrating it.

Big Numbers Are Big


SOS, 181418, appears starting at the 1,377,767th digit of pi. Image: xkcd.

Today I have a piece in Slate about that pi meme that's been going around. According to the meme, your life story is encoded in pi somewhere. My life story would probably include the word "Evelyn" at some point. (I'm going out on a limb, but stay with me.) In a code that assigns the string 00 to A and 25 to Z, EVELYN is 042104112413. It does not occur in the first 2 billion digits of pi, according to this pi search page.

At first, I was a bit surprised. 2 billion is a lot of digits, and I was only trying to match 12 of them. But there are 1012—1 trillion—12-digit strings, so only about 0.2 percent of them are present in the first 2 billion digits. In other words, at least 99.8 percent of possible 6-letter words won't occur in the first 2 billion digits of pi. When it comes to encoding entire sentences, the numbers quickly get out of hand.

If you're looking for, say, the works of Shakespeare in pi, you'll need the 618 characters of Sonnet 18 in there, which will require 1236 digits to encode. There are 101236 possible 618-character strings, and 101236-1 are impostor sonnets. The amount of time it would take to sift out all the garbage and find that comparison to a summer's day is simply unfathomable. To give you a frame of reference, the universe has been around for about 1017 seconds and contains approximately 1080 atoms.

So if you're worried that human creativity is worthless because every possible piece of literature, the MP3 of every song anyone will ever sing, the choreography of every ballet, along with the DNA of every person who will ever perform it, is encoded in pi, don't despair. No one with any sense will be switching to a pi-mining strategy to write the next great American novel or record the next "Gangnam Style." The messy, complicated, frustrating, exhilarating inner workings of the human brain are still the most efficient tools for creating profound new art, or meaningful new ideas in any field. At least until we become the sniveling slaves of our robot masters.

The views expressed are those of the author and are not necessarily those of Scientific American.

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