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Big Numbers Are Big

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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.

Evelyn Lamb About the Author: Evelyn Lamb is a postdoc at the University of Utah. She writes about mathematics and other cool stuff. Follow on Twitter @evelynjlamb.

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

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  1. 1. virgilll 8:46 pm 04/17/2013

    Human imagination is unique to every one of us…… and though at 46 I do actually believe that every human emotion has been felt in our past 50+ thousand yrs of existence …… the point of life is for each person to feel and grow as much as possible… and some day we will actually be able to define what consciousness means!!! In the mean time…. I will always trust a human over a piece of machinery!!!!!! Math is just one way of expressing human imagination… and you are right that it is just one more “tool” !!!!!

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  2. 2. phalaris 2:26 am 04/18/2013

    An amusing reminder of probabilities and infinity.
    When I was at school, some kid would assert: in an infinite universe, there would somewhere be an army of monkeys randomly hitting the keys on typewriters and producing the complete works of Shakespeare.

    The sonnet example brings home just how big infinite is…

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  3. 3. gizmowiz 2:26 am 04/18/2013

    Few numbers are more big than Obama’s $16.6 trillion and counting….

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  4. 4. jtdwyer 6:40 am 04/18/2013

    The reason for your failure is that you’ve made a fundamental error – the encoding scheme begins 0-9, followed by A-Z…

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  5. 5. whatmeworry 4:09 pm 04/18/2013

    At some point in the expansion of pi, it must repeat the previous sequence of numbers. Call that sequence S1. So pi = S1S1… Then there must be another sequence S2 such that pi = S2S2S2… Ultimately you have an infinite repeating decimal so pi is rational. Heh never mind.

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