NaBloPoMo: Infinity

11/06/2010 By Shawn Burns

Count to infinity. I’ll wait.

Oh, you’re back. That was quick. I actually didn’t expect to hear from you again. Oh, you counted to ‘1’ and stopped? That seems like cheating. I know that the distance between ‘0’ and ‘1’ is infinite, in the sense that you can always divide the space further, but that doesn’t mean you can just count to ‘1’ and claim to have completed an infinite series.

We used to confuse “infinite” with “all” on a pretty regular basis. For instance, when some medieval philosophers used to define the infinite as that which cannot be increased. This seems a little counter-intuitive to those of us who think of the infinite as something like the indefinite, a sequence that can always be increased.

Descartes thought that God was infinite, while sequences like the counting numbers were merely indefinite. The difference for him was that while we can always add another number, or more matter, or increase the quantity of whatever the sequence contained, God did not have any limits (as far as positive qualities went). God was infinitely good, powerful intelligent, etc….

That version of infinite is more like an “all” definition than what we usually think of, and it prompted Spinoza, following Descartes, to theorize that there was only one thing, God. God is limitless, therefore everything must be in God.

Now infinity is more a mathematical tool than a metaphysical one. But that development is younger than the United States.