***It's hard for me to visualize what kind of limitation this would be. Would that mean that God could be all powerful, all knowing, etc but these darn limitations keep getting in the way?***
I think the limitation should be seen, not as a loss of some capability, but the condition of never having had the capability in the first place.
I think the biggest error that religions have foisted on people is the notion that God is infinite, perfect, omnipotent, and all the rest. It is easy to see where this came from, though. The My-God-is-more-powerful-than-your-god contests that have been waged or imagined throughout history have naturally led to the view of an almighty god.
If we start with that view, then any limitation of god seems to be a loss and therefore unacceptable. If, on the other hand, you view god as a learning, growing entity, then the limitations are a natural aspect of not being perfect or all-powerful.
It also makes more cosmological sense. If we acknowledge a god and then ask how he got to be so powerful, the traditional view has to make what seem to be preposterous claims: that he has had all this power from the very beginning and yet he creates obviously imperfect universes. In my view, god got to be as powerful as he is through a natural process of experiencing, learning, and growing.
As for "visualiz[ing] what kind of limitation this would be", I think it is very easy. Part of it would be the type of limitation you impose on yourself when you decide to follow the rules of some game, or to adopt a certain set of axioms.
Another part would be simply not knowing things that you haven't learned yet.
*** But, if there is this limitation which prevents him from synthesizing and being cognizant of all the events, actions, and thoughts occuring in nature, then what can God really know about what is going on?***
Let me explain with an analogy. You are limited in that you are prevented from synthesizing and being cognizant of all the events and actions that occur in your car while you are driving it. So, what can you really know about what is going on in your car?
Well, while you are driving it, you can know about its macro behavior. You can know how it handles, how it accelerates, corners, rides, and so on. But if I asked you how many times a particular spark plug fired during a certain trip, you wouldn't know that. With the car dismantled in a garage and a mechanic explaining some things to you, you can know a lot about what goes on under the hood. But you can't be driving it in that circumstance.
The point is that there are different modes and perspectives of knowing. I suspect that god has many more such modes and perspectives with respect to us than we do with respect to our cars. But because of that complementarity idea I suggested earlier, I claim that god can't know everything about everything all the time.
***Would he for example know who we are?***
Under my scheme, the answer is easy. Yes, absolutely he knows who we are in particular circumstances. For example, at the particular point in space-time when Paul is typing this sentence, god knows who Paul is and is very much aware of what he is doing and thinking. Similarly, at the particular point in space-time when Harv happens to be reading this sentence, god knows who Harv is and exactly what he is doing and thinking. God knows what each of us is doing by way of the medium of our senses feeding information to our brain which in turn forwards that information to god. Very easy to comprehend.
***Or, are we some dim glow of incoming sense impressions that he can vaguely make out. I'm thinking that he doesn't distinguish one person from another, or even a human from a chimpanzee. Is that how you see it?***
Sure. I think that there are "times" when god is not out driving organisms when he is looking from a much higher perspective and maybe isn't aware of any finer resolution than seeing a single galaxy.
I put "times" in quotes to make sure you realize that I believe that god operates in temporal dimensions that are completely separate and distinct from our earthly temporal dimension.
***My concept of this is that the universe. . .***
Thank you for explaining your concept of the universe. Of course you realize that you used a whole bunch of words that are not well defined. But, so must anyone who tries to describe their concept of the universe.
I think that if you either removed or cleared up any ambiguity or misunderstanding in our descriptions of our concepts of the universe, that you and Alan and I and probably everyone else would pretty much agree. The fact is that we would all have to acknowledge some great mystery that we couldn't even articulate much less solve.
When I think of Alan's explanation of the three-cornered game, connecting the dots, etc. and then I think of my explanation of a primordial mind thinking of numbers and playing mental games with them to the point of producing the illusion that there are conscious beings inhabiting a physical universe, and then I think of your explanation of God starting out following a minimal path toward some goal involving symmetry transformations thus producing the natural history of the world, I get the distinct feeling that we are all trying to describe the same concept. We just use different words and different mental models that seem to make sense to us but they make less sense to the others. I don't think we are very far apart, except in our use of language.