By the way, after writing my message the other day about the question of what it means for the RSSA and ASSA to be compatible or incompatible, I thought of another condition that should be met if you want to have both an absolute probability distribution on observer-moments and a conditional one from any one observer-moment to another. Suppose I pick an observer-moment B from the set of all observer-moments according to the following procedure:

1. First, randomly select an observer-moment A from the set of all observer-moments, using the absolute probability distribution.
2. Then, select a "next" observer-moment B to follow A from the set of all observer-moments, using the conditional probability distribution from A to all others.

What will be the probability of getting a particular observer-moment for your B if you use this procedure? I would say that in order for the RSSA and ASSA to be compatible, it should always be the *same* probability as that of getting that particular observer-moment if you just use the absolute probability distribution alone. If this wasn't true, if the two probability distributions differed, then I don't see how you could justify using one or the other in the ASSA--after all, my "current" observer-moment is also just the "next" moment from my previous observer-moment's point of view, and a moment from now I will experience a different observer-moment which is the successor of my current one. I shouldn't get different conclusions if I look at a given observer-moment from different but equally valid perspectives, or else there is something fundamentally wrong with the theory.

I think there'd be an analogy for this in statistical mechanics, in a case where you have a probabilistic rule for deciding the path through phase space...if the system is at equilibrium, then the probabilities of the system being in different states should not change over time, so if I find the probability the system will be in the state B at time t+1 by first finding the probability of all possible states at time t and then multiplying by the conditional probability of each one evolving to B at time t+1, then summing all these products, I should get the same answer as if I just looked at the probability I would find it in state B at time t. I'm not sure what the general conditions are that need to be met in order for an absolute probability distribution and a set of conditional probability distributions to have this property though. In the case of absolute and conditional probability distributions on observer-moments, hopefully this property would just emerge naturally once you found the correct theory of consciousness and wrote the equations for how the absolute and relative distributions must relate to one another.

One final weird thought I had a while ago on this type of TOE. What if, in finding the correct theory of consciousness, there turned out to a sort of self-similarity between the way individual observer-moments work and the way the probability distributions on the set of all observer-moments work? In other words, perhaps the theory of consciousness would describe an individual observer-moment in terms of some set of sub-components which are each assigned a different absolute weight (perhaps corresponding to the amount of 'attention' I am giving to different elements of my current experience), along with weighted links between these elements (which could correspond to the percieved relationships between these different elements, like in a neural net). This kind of self-similarity might justify a sort of pantheist interpretation of the theory, or an "absolute idealist" one maybe, in which the multiverse as a whole could be seen as a kind of infinite observer-moment, the only possible self-consistent one (assuming the absolute and conditional probability distributions constrain each other in such a way as to lead to a unique solution, as I suggested earlier). Of course there's no reason to think a theory of consciousness will necessarily describe observer-moments in this way, but it doesn't seem completely implausible that it would, so it's interesting to think about.


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