The Mystery of the Aleph

Let's look at a number line. You know, the kind we learned about in school with has marks along a single line that have numbers underneath them. In the middle is 0, with 1, 2, 3, 4, etc. to the right and, if you'd like, -1, -2, -3, etc. to the left. It's just a simple number line.

Imagine a man is standing on 1. His desire is to walk to 2. Every step he takes takes him half way between himself and his goal (in other words, he crossed half the distance with each step). From his perspective, his first step is huge. He crossed half the distance between 1 and 2 with little effort.

There's another thing we learned about in school. When you divide a number (or thing) in half (by two), and then divide it in half, and keep on doing this, there is no end. You will end up with exquisitely small things, yes, but never will you reach the next integer.

Step by step he realizes that despite the great journey he's taken, he will never reach the next number, the next hash mark on the line. He will walk for all eternity. There is infinity between 1 and 2. Since there is nothing beyond infinity, if this is the case, then "2" doesn't really exist.

Since he could just have easily gone left instead of right, infinity lies that direction as well. The only "number" at all is the starting point, which is really an arbitrarily chosen spot in the vast infinity. We have an idea of numbers that serves our purposes, but these really are nothing more than created symbols set in place to help us quantify something than is, in actuality, unquantifiable.