Classical theism, with its identification of God with infinity, has developed a reputation for emphasizing divine transcendence to the point of making God nearly unknowable. The problem with this judgment is that infinity—as in, God is infinitely unknowable—does not admit to degrees. An infinite God is not like an unimaginably large number that we could count to if only we had enough time. Nor is an infinite God like the largest possible number we know, or at least know well enough to use in any practical way. That would be, according to the Guinness Book of World Records, Graham’s number, which has to do with the theoretical dimensions of the geometric shape known as a hypercube. Paradoxically, Graham’s number is at least as mysterious as the idea of infinity, since it exists only as a function of an extremely complex mathematical proof, and infinity, though hotly debated, is a fairly fixed idea—even if it is really nothing more than the idea of that which is unimaginable.
So which is harder to grasp: Graham’s number or the infinity of God? Graham’s number is so great that if each digit occupied a Planck volume (a unit too small for empirical use), the entire universe would not be big enough to contain it. Theologians in the tradition of classical theism claim that God is also greater than the known universe, but can they propose a rational way of demonstrating that God is greater than Graham’s number? We can know Graham’s number by describing how it functions (although really we are left with trusting that some very specialized mathematicians can describe this number to each other), but we can never know what that number actually is. If God is infinitely greater than that, then it seems like God is more like a random number picked from a range similar to Graham’s number. That number would be impossible to describe as well as to notate. That number, we could say, would be infinite all the way down. It would also be infinitely irrational, since it would be impossible to use it in any useful way.
Read Full Article »