Eric's comments made me think about these two articles: http://arxiv.org/abs/math-ph/0008018

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Change, time and information geometry Authors: Ariel Caticha ''Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we show that once we define what we are talking about, namely, the system, its states and a criterion to distinguish among them, there is a single, unique, and natural dynamical law for irreversible processes that is compatible with the principle of maximum entropy. In this alternative dynamics changes are described relative to an internal, ``intrinsic'' time which is a derived, statistical concept defined and measured by change itself. Time is quantified change.'' And: http://arxiv.org/abs/gr-qc/0109068 Entropic Dynamics Authors: Ariel Caticha ''I explore the possibility that the laws of physics might be laws of inference rather than laws of nature. What sort of dynamics can one derive from well-established rules of inference? Specifically, I ask: Given relevant information codified in the initial and the final states, what trajectory is the system expected to follow? The answer follows from a principle of inference, the principle of maximum entropy, and not from a principle of physics. The entropic dynamics derived this way exhibits some remarkable formal similarities with other generally covariant theories such as general relativity.'' Instead of identifying an observer moment with the exact information stored in the ''brain'' of an observer, one could identify it with a probability distribution over such precisely defined states. This seems more realistic to me. No observer can be aware of all the information stored in his brain. When I think about who I am, I am actually performing a measurement of some average of the state my brain is in. After this measurement the probability distribution will be updated. To apply Caticha's ideas, one has to identify the measurements with taking averages over an ensemble of observers described by the same probability distribution. In general this cannot be true, but like in statistical mechanics, under certain conditions one is allowed to replace actual averages involving only one system with averages over a (hypothetical) ensemble. Saibal ----- Original Message ----- From: Eric Hawthorne To: [EMAIL PROTECTED] Sent: Saturday, February 07, 2004 5:26 AM Subject: Re: measure and observer moments Given temporal proximity of two states (e.g. observer-moments), increasing difference between the states will lead to dramatically lower measure/probability for the co-occurrence as observer-moments of the same observer (or co-occurrence in the same universe, is that maybe equivalent?) . When I say two states S1, S4 are more different from each other whereas states S1,S2 are less different from each other, I mean that a complete (and yet fully abstracted i.e. fully informationally compressed) informational representation of the state (e.g. RS1) shares more identical (equivalent) information with RS2 than it does with RS4. This tells us something about what time IS. It's a dimension in which more (non-time) difference between co-universe-inhabiting states can occur with a particular probability (absolute measure) as the states get further from each other in the time of their occurrence. Things (states) which were (nearly) the same can only become more different from each other (or their follow-on most-similar states can anyway) with the passage of time (OR with lower probability in a shorter time.) Maybe? Eric Saibal Mitra wrote: ----- Original Message ----- From: Jesse Mazer <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Thursday, February 05, 2004 12:19 AM Subject: Re: Request for a glossary of acronyms Saibal Mitra wrote: 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. The theory of consciousness is needed because I think the conditional probability of observer-moment A experiencing observer-moment B next should be based on something like the "similarity" of the two, along with the absolute probability of B. This would provide reason to expect that my next moment will probably have most of the same memories, personality, etc. as my current one, instead of having my subjective experience flit about between radically different observer-moments. Such questions can also be addressed using only an absolute measure. So, why doesn't my subjective experience ''flit about between radically different observer-moments''? Could I tell if it did? No! All I can know about are memories stored in my brain about my ''previous'' experiences. Those memories of ''previous'' experiences are part of the current experience. An observer-moment thus contains other ''previous'' observer moments that are consistent with it. Therefore all one needs to show is that the absolute measure assigns a low probability to observer-moments that contain inconsistent observer-moments. As for probabilities not being conserved, what do you mean by that? I am assuming that the sum of all the conditional probabilities between A and all possible "next" observer-moments is 1, which is based on the quantum immortality idea that my experience will never completely end, that I will always have some kind of next experience (although there is some small probability it will be very different from my current one). I don't believe in the quantum immortality idea. In fact, this idea arises if one assumes a fundamental conditional probability. I believe that everything should follow from an absolute measure. From this quantity one should derive an effective conditional probability. This probability will no longer be well defined in some extreme cases, like in case of quantum suicide experiments. By probabilities being conserved, I mean your condition that ''the sum of all the conditional probabilities between A and all possible "next" observer-moments is 1'' should hold for the effective conditional probability. In case of quantum suicide or amnesia (see below) this does not hold. Finally, as for your statement that "the relative measure is completely fixed by the absolute measure" I think you're wrong on that, or maybe you were misunderstanding the condition I was describing in that post. I agree with you. I was wrong to say that it is completely fixed. There is some freedom left to define it. However, in a theory in which everything follows from the absolute measure, I would say that it can't be anything else than P(S'|S)=P(S')/P(S) Imagine the multiverse contained only three distinct possible observer-moments, A, B, and C. Let's represent the absolute probability of A as P(A), and the conditional probability of A's next experience being B as P(B|A). In that case, the condition I was describing would amount to the following: P(A|A)*P(A) + P(A|B)*P(B) + P(A|C)*P(C) = P(A) P(B|A)*P(A) + P(B|B)*P(B) + P(B|C)*P(C) = P(B) P(C|A)*P(A) + P(C|B)*P(B) + P(C|C)*P(C) = P(C) And of course, since these are supposed to be probabilities we should also have the condition P(A) + P(B) + P(C) = 1, P(A|A) + P(B|A) + P(C|A) = 1 (A must have *some* next experience with probability 1), P(A|B) + P(B|B) + P(C|B) = 1 (same goes for B), P(A|C) + P(B|C) + P(C|C) = 1 (same goes for C). These last 3 conditions allow you to reduce the number of unknown conditional probabilities (for example, P(A|A) can be replaced by (1 - P(B|A) - P(C|A)), but you're still left with only three equations and six distinct conditional probabilities which are unknown, so knowing the values of the absolute probabilities should not uniquely determine the conditional probabilities. Agreed. The reverse is true. From the above equations, interpreting the conditional probabilities P(i|j) as a matrix, the absolute probability is the right eigenvector corresponding to eigenvalue 1. 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). This won't work--plugging into the first equation above, you'd get (P(A)/P(A)) * P(A) + (P(B)/P(A)) * P(B) + P(P(C)/P(A)) * P(C), which is not equal to P(A). You meant to say: ''P(A)/P(A)) * P(A) + (P(A)/P(B)) * P(B) + P(A)/P(C) * P(C), which is not equal to P(A).'' This shows that in general, the conditional probability cannot be defined in this way. In P(S')/P(S), S' should be consistent with only one S. Otherwise you are considering the effects of amnesia. In such cases, you would expect the probability to increase. Saibal