God in $n$-space

So here’s a question about the nature of God that’s probably atypical. But I should probably preface this by saying that this is purely an academic exercise and thought experiment and that I’m not really looking to establish any deep theological truths. It’s entirely possible that I’m horribly wrong.

One of the things Christians do when describing God’s eternal nature is to say that because he has no beginning and no end, he exists outside of time.

I’ve never really understood what this meant.

The rationale for this kind of explanation is that our finite minds can’t comprehend infinity. As a mathematician, that notion seems kind of silly. Here, I’ll give an example of something we’re all familiar with that doesn’t have a beginning or end: $\mathbb Z$, the set of integers. We’re even able to distinguish between different cardinalities of infinity and have developed useful number systems in which we can, yes, divide by zero and get infinity as a legitimate result. So what’s the problem?

To me, the notion that God exists outside of time is like saying God exists outside of space. No one seems to have a problem with the second one, after all, omnipresence is one of God’s attributes. This is an idea we can use.

I’m sure we’re all familiar with the concept of 3-space, or $\mathbb R^3$, which is how we describe the three physical dimensions of space and all. So God’s omnipresence in 3-space would just mean that he’s present in every point in $\mathbb R^3$.

But mathematicians aren’t satisfied with stopping at $\mathbb R^3$. We like to generalize, which is where we get into things like $\mathbb R^n$ for some integer $n$. Or how about even $\mathbb C^n$? So now we’ve got $n$-dimensional space to deal with. That’s hard to wrap your head around if you try to think of it in analogous physical terms (because there aren’t any). Anyhow, we don’t even have to stop at finite-dimensional spaces, we can extend things to infinite-dimensional spaces.

Whether or not these things actually physically exist isn’t that important. We’re just concerned with this: how does God’s omnipresence translate when we extend space to however many dimensions? It’s simple, he’s still present at every point in space.

So what if we take one of those dimensions to be time? I mean, a lot of people often like to think of time as the fourth dimension.

Then God is present at every point in time as well. For me, thinking about it this way actually answers a question I did have for a while: what is meant by God’s unchanging nature? This is one of those questions that the outside of time thing was meant to “answer” but it doesn’t actually answer anything, since it really just handwaves it away. But with the dimensionality angle, we can say that God is the same entity at every point in time.

I’m sure there are plenty of other questions that arise from thinking about it like this, but, at least for me, the advantage in this approach is that it’s analogous to ideas we’re already comfortable with, namely God’s omnipresence in $\mathbb R^3$. It explains why God can change his mind and direct things at multiple points in time if he wanted to.

So this thought experiment led an interesting question on prayer. One component of prayer is that Christians often petition God to act in some way, in the present or future. But if God is all-powerful and ever-present, does it make sense to pray for things that occurred in the past?