People tell me that God is infinite. Infinite in power, scope, beauty, presence – many different things. When I was younger, I heard it in church; I don’t think the idea is biblical so much as Platonic, but appears to be a fairly universal belief within Christianity. I still hear it, from Christianity and Judaism and New Age religions, and I understand it to be a tenet of mono- and uni-theism.

People would tell me that I can’t comprehend what it means to be infinite, even when I told them I could – I’d spent enough time thinking about it maths that I could understand it as well as I could understand the concept of 2 or red or yesterday – that is to say, vaguely, but enough to move on to other topics. (But it’s really, really big! Yes, I know. Really BIG! Yes – it’s much more difficult to understand exceptionally large non-infinite numbers than it is infinity, because then you have to reference a scale.)

But I had a problem with God being infinite – I understood it to mean that we must necessarily be a part of God. If God is infinitely everywhere and infinitely powerful, all places and powers must be caught up in him, including my power, right now, to do evil. Right?

But I had fallen into the trap of understanding all infinities equally. It’s the same trap that some writers have made when they say: given an infinite number of worlds in an infinite universe, it is statistically impossible that we don’t exist an infinite number of times simultaneously, or: give enough monkeys enough time on enough typewriters, and one of them will produce Hamlet.

But there are different kinds of infinities. There are an infinite number of numbers, right? You can keep counting forever. Infinity. But if you take away all of the even numbers, how many numbers do you have? An infinite number. But a lesser infinity, right? Yes. No. No. It’s still infinite, though it’s a non-comprehensive subset of the first infinitity. You could only count factors of 10: 1, 10, 100, 1000, … and still end up with an infinite set that is not any smaller than our original set, though as a subset it’s rather limited. Then, of course, we have all sorts of infinities squeezed into each member of our infinite set. Take all numbers: 1/2, 1/3, 1/4, 1/5, … There’s an infinite number of them, though they all fit between 1 and 0. Even if we add them up, we don’t any smaller of a number than if we add up any of our other infinities.

I’m no maths expert (even though I once thought I was), but I can only really distinguish two types of infinity – infinity and pleni-infinity. Perhaps there is a better word somewhere than pleni-infinity, but I don’t know it, so I resorted to crafting a new word. Pleni-infinity is not an infinite set, but the complete set of all sets, infinite and otherwise. It’s every single number, ever. All of them. Thought of one that’s not in there? Nope, it’s in there. Hah!

What does all of this have to do with religion and God? Well, God can be infinite in characteristics without including all aspects of those characterstics. His power could be infinite in might without being infinite in scope; it could be infinite in scope, and still not need to include those regions of power which involve flicking your sister’s earlobe until she loses her temper. Infinite, but not pleni-infinite. Not every possible aspect of power need be in his scope of power for it to be infinite.

This comes to mind as I’m reading the Urantia Book, and it describes in very minute detail the infinitude of God – in this chapter, the infinity of his personality. And instead of being put off by the word “infinite”, I say: Oh, why that means that his personality could be delved without reaching bottom – you could get to know him for as long as you like and still have more to learn than you know.

So maybe I get infinity a little better now.