I just ran across a very poetic meme about the number pi .
Pi is an infinite, non-repeating decimal — meaning that every possible number combination exists somewhere in pi. Converted into ASCII text [computer representation], 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 [computer image], 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 these two points.
All the 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.
Googling around for more about this, I saw someone point out that if the universe is finite, then pi must somewhere contain a representation of the entire universe.
I find this beautiful and very appealing. Judging by all the “Wow!” comments on the Internet, a lot of other people are equally fascinated.
The only problem is, it ain’t necessarily so. The non-sequitur is in the very first sentence: “Pi is an infinite, non-repeating decimal — meaning that every possible number combination exists somewhere in pi.” I studied a lot of math in college, and I admit that the error slipped by me. Before I knew it, I was carried away by the poetry and joined in the chorus of “Wow!”
The error (obvious now!) is that just because a number never repeats itself into all infinity, it does not follow that every possible number combination occurs. For example, maybe there are no sevens after the trillionth digit, but the other nine digits continue without repeating. If you’re looking for a sequence that contains a seven, and you don’t find it in the first trillion digits, you will never find it.
Sadly, the frisson I felt while reading transcendent thoughts about everyone’s favorite transcendental number was … unwarranted. Even a methodological naturalist like me must be careful to practice shaphat.
After further Googling, I learned that it could be true that pi contains all finite sequences. In fact, mathematicians suspect that it is true, even though it has not been proven one way or the other.
Now … how tempted am I to believe without proof, just because it’s beautiful?
I’ll leave that question with you as an exercise in shaphat. Can you refrain from judging what’s in my head when you have no proof? :)