What I thought about last night when I was falling asleep.

March 17, 2010

Irrational numbers.

Actually, I was really thinking about Transcendental Numbers. There are just so many of them, and we don't even know how to describe almost all of them. And we'll never know how to describe most of them because they simply can't be described. They're just an infinite string of seemingly random digits with possibly no pattern at all. There are infinitely many transcendental numbers that obey no rule, and since they obey no rule, they can't be described without just enumerating their infinite digits, which of course is impossible.

I mean, there are nice ones that are easy to describe, such as e. I can write e down in just a line:

$ \sum_{n=0}^{\inf} \frac{1}{n!} $

Thus, I can calculate any digit given enough time and effort.

But there are numbers that I can't even describe, and I can't label in any meaningful way since I don't even know what I'm trying to label.

They simply exist on the number line, never to be seen or described. It's a bit sad, in a way.