For some inexplicable reason, I've always been interested in constants. Like in physics and math. The gravitational constant, planks' constant, e, pi, etc. It's those little numbers that are stuck into equations that are nothing other than a number, but without them, nothing works. The natural question is always, "why is the constant what it is? why is pi 3.14... and not 3.15...?" I've never read one of them, but my understanding is that intelligent design books often take off on this. If any of these numbers, they argue, was different by a billionth, then the universe falls apart and therefore something must have designed it.
Before we start, remember that pi is the ratio of the circumference of a circle to its diameter. c/d. A better way to understand that is that if you took the line out of a circle that represented its diameter and then wrapped it around the circle, you'd find that it wraps around pi times or 3.14.... times. It takes 3.14... diameters to be the same length as a circle's circumference. But pi is a rather odd number. It's apparently been calculated out now to over 1 trillion places (yes, a trillion) and no one's ever seen a pattern. It's just this random sequence of numbers going on and on forever. There is no way, if it's random, to predict what a later number would be based upon an earlier number. But pi is used in a vast number of mathematical and physical descriptions of the universe from anything involving a circle to relativity to quantum mechanics to a million other things. Why is there this random series of numbers seemingly embedded in the very fabric of the universe?
I've been reading a non-mathematical intro to superstring theory called The Elegant Universe with which to fall asleep. (I mean that in the best way.) So far, no strings. To get to strings, the author has to walk us through Einsteinian relativity and quantum physics, because the main purpose of superstring theory is to unify the two well-confirmed theories. All of this is new to me, so I'm good.
General Relativity, as I understand it, provides the first successful account of the mechanism of gravitation. Newton previously was able to describe describe gravity's effects, calculate its effects, unify actions on Earth and around the solar system with it, but he admitted he had no idea how this mysterious force worked, what it was. How does the Sun actually affect the Earth 83 million miles away? Einstein reformulated gravity as the effects of mass on space-time. Mass curves space-time and it is through the warping / curving of space-time that gravitation acts. (To know more, read the book! :) )
One implication from general relativity is that pi is no longer the ratio of circumference to diameter when space-time is curved. Pi assumes flat (Euclidian) space. Only when space is flat is pi the number you want.
Paca's lightbulb. A-ha! So why is pi the number it is? Well, pi only holds when space-time is not curved. And so pi, in a sense, is the expression of idealized flat space. Could one define what it means for space-time to be flat, and therefore find a natural process which "generates" pi? If something generates the number, it's not random anymore, but has structure.
I'm sure this is all illogical to people who know stuff, but it's cool to me.