Is Your Entire Life History Really Encoded in the Digits of Pi?

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April 17 2013 4:43 PM

Your Life in Pi

Everything in your past—and future—is encoded in the digits of pi.

Life Encoded in Pi

Illustration by Robert Neubecker

"Pi is an infinite, nonrepeating decimal - meaning that every possible number combination exists somewhere in pi. Converted into ASCII text, somewhere in that infinite string of digits is the name of every person you will ever love, the date, time, and manner of your death, and the answers to all the great questions of the universe. Converted into a bitmap, somewhere in that infinite string of digits is a pixel-perfect representation of the first thing you saw on this earth, the last thing you will see before your life leaves you, and all the moments, momentous and mundane, that will occur between those two points.

All information that has ever existed or will ever exist, the DNA of every being in the universe, EVERYTHING: all contained in the ratio of a circumference and a diameter."

From what I can tell, this meme comes from Redditor kenfoldsfive's answer to the question, "Reddit, what's the most mind-blowing sentence you can think of?" It's been bouncing around the Internet for several months now and got a little boost recently when George Takei's Facebook page shared it with nearly 4 million followers earlier this month. It certainly is a mind-blowing idea! Infinity is always hard for our puny finite brains to handle, and I admit that the vastness of irrational numbers blows my mind whenever I accidentally think about it for too long. We're talking about a number that encodes not only my life story, but also a version in which my fly wasn't down the first time I taught a class.

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The only problem is, it isn't true. Or, it's probably true, but we don't know for sure, and get off my lawn. At least that's what the Huffington Post said last week. (On Tuesday it posted a more cheerful story about pi with some interesting illustrations.) The article makes some good points, but I think it misses the forest for the trees. If you look at it the right way, pi really does have it all.

The sticking point is the first assertion of the meme: Does pi contain every possible finite combination of digits? All irrational numbers, including pi, have infinite, nonrepeating decimal representations, but this is not enough to ensure that they include all strings. For example, 0.1010010001 … is a perfectly acceptable irrational number, and it never even includes the digit 2.

In an edit to the original post, kenfoldsfive notes that the statement is true if pi is a "normal number," meaning that every finite string occurs with exactly the frequency you'd expect if the digits were random. For example, 10 percent of digits are 1s, 10 percent are 2s, and so on. (This is for numbers written in base 10. Normality can be defined for binary, hexadecimal, or any other base.) In 1909, mathematician Émile Borel proved that "almost every" real number is normal. The mathematical meaning of "almost every" is more extreme than the typical English meaning. Borel showed that there is basically a 0 percent chance that if you pick a real number truly randomly, you'll get one that isn't normal.

For this reason and analysis of the first few trillion digits of pi, most people who care about such things believe that pi is indeed normal. There's no reason to think it isn't, except that no one has proved it yet. There's a lot we don't know about pi. After all, we only know 10 trillion digits of it, a mere speck in the grand scheme of things. We don't even know whether every digit appears infinitely often. Maybe there are only 101,000 7s.

But the focus on whether or not pi is normal misses an interesting question: Exactly how would we translate an irrational number into a bunch of text? At its heart, the meme is saying that there is something essentially infinite about irrationality that can be used to represent everything contained in our finite world. And that's right, if you choose your "code" correctly.

The meme suggests ASCII, a method of rendering characters using either seven or eight binary digits. (There is a decimal version as well.) Ignoring some technical details about how ASCII is really implemented, let's pretend that every two-digit combination from 00 to 99 encodes a different letter, number, space, or punctuation mark. Then we just go through the digits of pi two at a time and get some string of symbols out. If pi is normal, your life story is in there somewhere.

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