This means that the relative measure is completely fixed by the absolute measure. Also the relative measure is no longer defined when probabilities are not conserved (e.g. when the observer may not survive an experiment as in quantum suicide). I don't see why you need a theory of consciousness.
Let P(S) denote the probability that an observer finds itself in state S. Now S has to contain everything that the observer knows, including who he is and all previous observations he remembers making. The ''conditional'' probability that ''this'' observer will finds himself in state S' given that he was in state S an hour ago is simply P(S')/P(S). Note that S' has to contain the information that an hour ago he remembers being in state S. The concept of the conditional probability is only an approximate one, and has no meaning e.g. when simulating a person directly in state S' or in cases where there are no states S' that remember being in S (e.g. S is the state an observer is in just before certain death). Ignoring these effects, it is easy to see that P(S')/P(S) has the properties you would expect. E.g. the sum over all S' compatible with S yields 1. Saibal ----- Original Message ----- From: Jesse Mazer <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, February 04, 2004 10:58 AM Subject: Re: Request for a glossary of acronyms > 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. > > Jesse > > _________________________________________________________________ > Let the new MSN Premium Internet Software make the most of your high-speed > experience. http://join.msn.com/?pgmarket=en-us&page=byoa/prem&ST=1
