Defining causal isomorphism

Those are basically the two questions I want answers to. In the thread I originally posted in, Eliezer refers to "pointwise causal isomorphism":

Given an extremely-high-resolution em with verified pointwise causal isomorphism (that is, it has been verified >that emulated synaptic compartments are behaving like biological synaptic compartments to the limits of >detection) and verified surface correspondence (the person emulated says they can't internally detect any >difference) then my probability of consciousness is essentially "top", i.e. I would not bother to think about >alternative hypotheses because the probability would be low enough to fall off the radar of things I should think >about. Do you spend a lot of time worrying that maybe a brain made out of gold would be conscious even >though your biological brain isn't?

We could similarly define a pointwise isomorphism between computations A and B. I think I could come up with a formal definition, but what I want to know is: under what conditions is computation A simulated by computation B, so that if computation A is emulating a brain and we all agree that it contains a consciousness, we can be sure that B does as well.

Actually, I started thinking about computations containing people (in this context) because I was interested in the idea of one computation simulating another, not the other way around. Specifically, I started thinking about this while reading Scott Aaronson's review of Stephen Wolfram's book. In it, he makes a claim something like: the rule 110 cellular automata hasn't been proved to be turing complete because the simulation has an exponential slowdown. I'm not sure if the claim was that strong, but definitely it was claimed later by others that turing completeness hadn't been proved for that reason. I felt this was wrong, and justified my feeling by the thought experiment: suppose we had an intelligence that was contained in a computer program and we simulated this program in rule 110, with the exponential slowdown. Assuming the original program contained a consciousness, would the simulation also? And I felt strongly, and still do, that it would.

It was later shown, If i'm remembering right, that there was a simulation with only polynomial slowdown, but I still think it's a useful question to ask, although the notion it captures, if it does so at all, seems to me to be a slippery one.