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modeling

Humans are used to predicting things by "thinking through" them. Intuition says my claim that you can't predict anything except by observing it is absurd: we do it every day. But this kind of prediction has two problems: it's very superficial, and it's very short-term. God can't settle for "thinking through", He should KNOW. To know means to model, with 100% certainty.

I'll make an analogy with human relationships. You have a friend. You know him because you can predict, with reasonable certainty, what he will do. You can do this because inside your brain you have a model of your friend's behaviour. It is not perfect, but it is good enough to work most of the time. Consider, if you will, that this model is like a little copy of your friend's brain, with fewer neurons, and hence not an exact model. If we gradually improve this model, it will approach the point where it is 100% accurate: namely, it is an exact copy of your friend's brain inside your head. Now realize that you ARE your friend. And notice also, that your predictive ability has been eliminated, because it takes exactly as long for your "model brain" to predict what it will do as it does for it to do it.

Aside: I'm realizing there are some problems with this theory of models. I assume that the only requirement of models is that they execute faster than their real counterparts. That's actually not necessary at all. To predict something using the model, all you really have to do is set the model to some known state, and then be able to assume that the real counterpart, when in the corresponding state, will behave the same way. That's determinism. To be able to "set" the model implies that there exists a system outside the model. So my theory can be stated more directly so:

It is impossible to create a mapping between states of a subset of a system and states of a system. That is, the cardinality of states of the subset must be less than that of states of the set. Therefore, it is impossible to completely model a system with a subset of that system.

Furthermore, it is impossible to model a system faster than the system itself. Because the speed of state transitions is determined by the context of the model, which must be the same as the context of the original. (That is, both the model and the original exist in the same bigger system.)

Furthermore, a system modeling itself is indistinguishable from itself.

In our example, the system was your brain, which can run your pseudo-friend-brain-model. And, if your brain was really big, you could even run a 100%-accurate model of your friend's brain without being your friend. I claimed you couldn't because I was viewing all brains as part of a single system; that is, each possible brain is a state of the system. So your brain and your friend's brain are both states of the same system, so modelling your friends brain or any other is no different than modelling your own in that the system is modelling itself, IS itself.

What I'm getting at is there is no such thing as an abstract; every model must exist in concrete form, even if that concrete form is a collection of neurons in our brain. Or, directly, that the proposition is the experience because there is no other way to state a proposition. (It only seems otherwise because we are used to resorting to grossly inaccurate approximations.) I would say that God is similarly restricted; we might consider ourselves, in fact, to be just a model in God's brain. :)

(A further thought; if the universe is a model in God's brain, and the model is the original... God is the universe. A very easy explanation for how he can be all-knowing. Although there's still that first-cause problem...)