On Saturday morning, while I was getting ready to go to my son's baseball game, I was thinking about how completely incapable I am of ever being anything like God. Whenever I think, "I've made some progress from where I used to be," I then realize, "there's no way I can ever get to where I need to be."
Anyway, this got me wondering about the nature of God. I wondered how, if God has a tangible, physical body of finite dimensions, and so has a finite number of brain cells and synapses, He can have infinite knowledge. I mean, assuming a byte of information requires a unique combination of synapses, with a finite number of synapses there will be a finite number of permutations available. "Maybe He doesn't have a finite number of synapses, smart guy!" But if His brain has defined dimensions and a synapse takes up any amount of positive space, the number of synapses has a limit. (Looking, failing Real Analysis was actually good for something!)
Then I thought, well, maybe God doesn't have infinite knowledge, but He has perfect knowledge of the rules of the Universe, and with that knowledge of those rules, He can deduce all knowledge. But then I wondered if rules function the same ways as permutations of synapses, that a finite brain can only know a finite number of rules which can only support a finite number of facts.
By this time, we were driving to the baseball game, so I was puzzling this aloud with Jerome, when I realized that the rules of mathematics allow for a finite rule to support infinite facts. For instance, the rule of addition allows me to add any two numbers from an infinite set. The permutations are infinite, but a single rule allows me to know them all. So God's finite brain can hold a finite number of rules but can use those rules to know infinite knowledge.