Yes, this has absolutely nothing to do with my usual topics of discussion … well, God is supposed to be infinite, so maybe there is a connection. Anyway, I’m interested in the concept of infinity. How well do we understand it? For myself, I know it gives me a headache every time I try to think about it. Sometimes I think it’s the coolest thing ever discovered. Other times I think it’s just a mental trick, a mathematical miscalculation.
One of the coolest things is the fact that there is more than one type of infinity. And I don’t just mean the distinction between the infinitely large and the infinitely small (infinitesimal). That’s a cool distinction to make. But even cooler is the fact that there is more than one infinite number. Without getting bogged down in the mathematics of it, there are more points on a line segment than there are integers. And the number of points on a line segment are not the largest infinite number. There are an infinite number of infinite numbers. There’s a whole field of mathematics devoted to things like this called “Transfinite Set Theory.” For myself, I lack the background to give a full discussion of Transfinite Set Theory; I only know a few bits and pieces—enough to recognize that it is a really cool subject.
But is it all based on a mental trick? We get our first inkling of infinity when we learn to add and realize there is no last number. Then you start finding paradoxes, like Xeno’s Paradoxes of Motion and a few other mathematical such things. Wherever infinity comes up, our understanding balks and fails.
Is the universe infinite? From what I gather from the scientists I’ve spoken to, the answer is no. But a good portion of them think math is a game, anyway. They might be right, and, if so, infinity may be the perfect example of such a contention.
What about God? If He exists, He is supposed to be infinite. In fact, He is supposed to be The Infinite. The final ultimate infinite number/being whatever. The Universal Set itself, or what have you. And, I guess, that adds to part of the mystery and our curiousity about the subject.