Tuesday, December 08, 2009

A musing on mathematics and the existence of God

Either humans are capable of understanding everything in the universe or we're not. Given the facts of our fallible, fragile, and finite conciousness and comprehension, "we're not" is far more likely.

Just have a look at the Euler formula: e^ipi+1=0. It's a beautiful mathematical expression that contains all the fundamentals of mathematics: the fundamental constants e, i, pi, 1, and 0; and the fundamental operations addition, multiplication, exponentiation, and equality.

The constants in this elegant equation are all vitally important for describing and understanding reality. One is unity - existence iteself. Zero is nothing, except that it's not really nothing. (I had an interesting discussion a week or so ago with a very smart friend who noted that zero actually carries more semantic meaning than one. In a digital signal, no-voltage can mean Zero, or it can mean Off. Which is which makes a big difference.)

Pi of course is the ratio of the radius of a circle to its circumfrence. E is the natural logarithm, which is useful in all sorts of calculations involving real-world phenomena such as fluid flow. And note that both e and pi are by defintion irrational numbers - in any base number system (except base e or base pi), their decimals repeat *infinitely*.

And then there's i, which again is very useful for describing real-world phenomena, especially fractals, which shows the similarity between the jaggedness of the cost of Norway as seen from space, and the jaggedness of a pebble in a fjord when seen under a microscope. i is defined as the square root of negative one, a number that cannot exist in the real world. It's called "the *imaginary* number."

So... if the infinite, the irrational and the imaginary are so valuable in describing the reality that we *can* understand, why is it so difficult for people to accept the existence of an infinite, trancendent, and unseen God that we *cannot* understand?