Re: Request for a glossary of acronyms
Jesse Mazer wrote: 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. But I would expect this consistency to be a matter of degree, because sharing memories with other observer-moments also seems to be a matter of degree. Normally we use the word memories to refer to discrete episodic memories, but this is actually a fairly restricted use of the term, episodic memories are based on particular specialized brain structures (like the hippocampus, which if damaged can produce an inability to form new episodic memories like the main character in the movie 'Memento') and it is possible to imagine conscious beings which don't have them. The more general kind of memory is the kind we see in a basic neural network, basically just conditioned associations. So if a theory of consciousness determined similarity of observer-moments in terms of a very general notion of memory like this, there'd be a small degree to which my memories match those of any other person on earth, so I'd expect a nonzero (but hopefully tiny) probability of my next experience being that of a totally different person. Therefore all one needs to show is that the absolute measure assigns a low probability to observer-moments that contain inconsistent observer-moments. But if observer-moments don't contain past ones in discrete way, but just have some sort of fuzzy degree of similarity with possible past observer-moments, then you could only talk about some sort of probability distribution on possible pasts, one which might be concentrated on observer-moments a lot like my current one but assign some tiny but nonzero probability to very different ones. In any case, surely my current observer-moment is not complex enough to contain every bit of information about all observer-moments I've experienced in the past, right? If you agree, then what do you mean when you say my current one contains past ones? 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. Yes, it depends on whether one believes there is some theory that would give an objective truth about first-person conditional probabilities. But even if one does assume such an objective truth about conditional probabilities, quantum immortality need not *necessarily* be true--perhaps for a given observer-moment, this theory would assign probabilities to various possible future observer-moments, but would also include a nonzero probability that this observer-moment would be a terminal one, with no successors. However, I do have some arguments for why an objective conditional probability distribution would at least strongly suggest the quantum immortality idea, which I outlined in a post at http://www.escribe.com/science/theory/m4805.html 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)
Re: Request for a glossary of acronyms
Bruno Marchal wrote: At 20:17 03/02/04 -0500, Jesse Mazer wrote: Personally, I would prefer to assign a deeper significance to the notion of absolute probability, since for me the fact that I find myself to be a human rather than one of the vastly more numerous but less intelligent other animals seems like an observation that cries out for some kind of explanation. I am not sure about that. Suppose a teacher has 10^1000 students. Today he says to the students that he will, tomorrow, interrogate one student of the class and he will chooses it randomly. Each student thinks that there is only 1/(10^1000) chance that he will be interrogated. That's quite negligible, and (assuming that all student are lazy) none of the students prepare the interrogation. But then the day after the teacher says: Smith, come on to the board, I will interrogate you. I hope you agree there has been no miracle here, even if for the student, being the one interrogated is a sort of (1-person) miracle. No doubt that this student could cry out for an explanation, but we know there is no explanations... Suppose the teacher and the student are immortal and the teacher interrogates one student each day. Eternity is very long, and there will be arbitrarily large period where poor student Smith will be interrogated each days of that period. Obviously Smith will believe that the teacher has something special against him/her. But still we know it is not the case ... So I don't think apparent low probability forces us to search for an explanation especially in an everything context, only the relative probability of continuation could make sense, or ab initio absolute probabilities could perhaps be given for the entire histories. But your example assumes we already know the probabilities. If Smith has two different hypotheses that a priori both seem subjectively plausible to him--for example, the teacher will pick fairly, therefore my probability of being picked is 1 in 10^1000 vs. I know my father is the teacher's arch-nemesis, therefore to punish my family I expect he will fake the random draw and unfairly single me out with probability 1, then if Smith actually is picked, he can use Bayesian reasoning to now conclude the second hypothesis is more likely (unless he considered its a priori subjective likelihood to be less than 10^-1000 that of the first hypothesis). This is a better analogy to the situation of finding myself to be a human and not one of the much larger number of other conscious animals (even if we restrict ourselves to mammals and birds, who most would agree are genuinely conscious, the number of mammals/birds that have ever lived is surely much larger than the number of humans that have ever lived--just think of how many rodents have been born throughout the last 65 million years!) Even if I a priori favor the idea that I should consider any observer-moment equally likely, unless I am virtually certain that the probabilities are not biased in favor of observer-moments with human-level complexity, then finding myself to actually be experiencing such an observer-moment should lead me to shift my subjective probability estimate in favor of this second sort of hypothesis. Of course, both hypotheses assume it is meaningful to talk about the absolute probability of being different observer-moments, an assumption you may not share (but in that case the Smith/teacher analogy should not be a good one from your perspective). Another possible argument I thought of for having absolute probabilities as well as conditional probabilities. If one had a theory that only involved conditional probabilities, this might in some way be able to explain why I see the laws of physics work a certain way from one moment to the next, by describing it in terms of the probability that my next experience will be Y if my current one is X. But how would it explain why, when I examine records of events that happened in the past, even records of events before my subjective stream of consciousness began, I still see that everything obeyed those same laws back then as well? Could you explain that without talking about the absolute probability of what type of universe a typical observer-moment is likely to percieve himself being in, including memories and external records of the past? Jesse _ Create your own personal Web page with the info you use most, at My MSN. http://click.atdmt.com/AVE/go/onm00200364ave/direct/01/
Re: Request for a glossary of acronyms
At 20:17 03/02/04 -0500, Jesse Mazer wrote: Personally, I would prefer to assign a deeper significance to the notion of absolute probability, since for me the fact that I find myself to be a human rather than one of the vastly more numerous but less intelligent other animals seems like an observation that cries out for some kind of explanation. I am not sure about that. Suppose a teacher has 10^1000 students. Today he says to the students that he will, tomorrow, interrogate one student of the class and he will chooses it randomly. Each student thinks that there is only 1/(10^1000) chance that he will be interrogated. That's quite negligible, and (assuming that all student are lazy) none of the students prepare the interrogation. But then the day after the teacher says: Smith, come on to the board, I will interrogate you. I hope you agree there has been no miracle here, even if for the student, being the one interrogated is a sort of (1-person) miracle. No doubt that this student could cry out for an explanation, but we know there is no explanations... Suppose the teacher and the student are immortal and the teacher interrogates one student each day. Eternity is very long, and there will be arbitrarily large period where poor student Smith will be interrogated each days of that period. Obviously Smith will believe that the teacher has something special against him/her. But still we know it is not the case ... So I don't think apparent low probability forces us to search for an explanation especially in an everything context, only the relative probability of continuation could make sense, or ab initio absolute probabilities could perhaps be given for the entire histories. But I think this is more of a philosophical difference, so that even if an ultimate TOE was discovered that gave unique absolute and conditional probabilities to each observer-moment, people could still differ on the interpretation of those absolute probabilities. I am not yet sure I can make sense of them. I think also that your view on RSSA is not only compatible with the sort of approach I have developed, but is coherent with Saibal Mitra backtracking, which, at first I have taken as wishful thinking. What is the backtracking idea you're referring to here? That if you put the probabilities on the infinite stories, any finite story will be of measure null, so that if an accident happens to you, and make you dead (in some absolute sense), you will never live that accident, nor the events leading to that accident: from a 3-person pov it is like there has been some backtracking, but it's seems linear from a 1-pov. (pov = point of view) OK you make me feel COMP could be a little less frightening I'm use to think. Well, if I've spared you some sleepless nights I'm glad! ;) Thanks. Concerning consciousness theory and its use to isolate a similarity relation on the computational histories---as seen from some first person point of view, I will try to answer asap in a common answer to Stephen and Stathis (and you) who asked very related questions. Alas I have not really the time now---I would also like to find a way to explain the consciousness theory without relying too much on mathematical logic, but the similarity between 1-histories *has* been derived technically in the part of the theory which is the most counter-intuitive ... mmh I will try soon ... Yes, I definitely hope to understand the details of your theory someday, I think I will need to learn some more math to really follow it well though. My current self-study project is to try to learn the basic mathematical details of quantum computation and the many-worlds interpretation, It seems a good plan. but after that maybe I'll try to study up a bit on mathematical logic and recursive function theory. And even if I do, there's the little problem of my not knowing French, but I'll cross that bridge when I come to it... Nice, you will be able to read the long version of my thesis ... It's almost self-contained. In logic it is only the beginning which is hard, really. Nevertheless I will try to explain the consciousness theory and the minimal amount of logic needed. The fact is that it is easy to be wrong with self-applied probability, and using logic, it is possible to derive the logic of [probability one] quasi-directly from the (counter-intuitive) godelian logic of self-reference. There are already evidence that we get sort of quantum logic for those probability one. I'm really searching how to justify the wavy aspect of nature. Bruno
Re: Request for a glossary of acronyms
- 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
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-uspage=byoa/premST=1
Re: Request for a glossary of acronyms
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
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. 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). 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. 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. 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). It would work if you instead used 1/N * (P(S)/P(S')), where N is the total number of distinct possible observer-moments, but obviously that won't work if the number of distinct possible observer-moments is infinite. And as I said, this condition should not *uniquely* imply a certain set of conditional probabilities given the absolute probabilities, so even with a finite N this wouldn't be the only way to satisfy the condition. Jesse _ Scope out the new MSN Plus Internet Software optimizes dial-up to the max! http://join.msn.com/?pgmarket=en-uspage=byoa/plusST=1
Re: Request for a glossary of acronyms
Jesse Mazer wrote: George Levy wrote: You assume that you could get your hands on the absolute probability distribution. You must assume when you observe a physical system is that you are an observer. The existence of (objective) absolute reality is another assumption that may not be necessary. Assuming the existence of an absolute probability distribution is like assuming the existence of an absolute frame of reference in space. No, I don't assume I know the absolute probability distribution to begin with. As I explained in earlier posts, I assume that there is some sort of theory that would be able to tell me the conditional probabilities *if* I already knew the absolute probability distribution, and likewise that this theory could tell me the absolute probability distribution *if* I already knew the all the conditional probabilities. But I don't know either one to begin with--the idea is that the two mutually constrain each other in such a way as to provide a unique solution to both, like solving a set of N simultaneous equations with N variables. Or: 1. Conditional probability of observer-moment A having observer-moment B as its next experience = some function F of the form F(formal properties of A, formal properties of B, P(B)) [by 'formal properties' I am suggesting something like the 'similarity' between the two observer-moments which I talked about earlier, which is why I think this would need to be based on a theory of consciousness] 2. Absolute probability of observer-moment B = P(B) = some function G of the form G(the set of conditional probabilities between B and every other observer-moment) The idea is that the theory of consciousness could tell me the exact form of the functions F and G, but the actual values of all the absolute probabilities and conditional probabilities are unknown. But since each function depends on the other in this way, it is conceivable they would mutually constrain each other in such a way that you could solve for all the absolute probabilities and conditional probabilities, although of course this is just my own pet theory. You say that the values of the absolute and conditional probabilities are unknown. In my opinion, I have a very good idea of what their values are. The absolute probability of any given observer moment is infinitesimal given the extremely large, possibly infinite, number of observer moments states in the plenitude, and also given the much larger non-observer moment states in the plenitude. Non-conscious observers states greatly outnumber conscious observer states. The only way to talk meaningfully about absolute probability is to "normalize" it, effectively converting it to a conditional probability. The conditional probability of any given observer moment A transitioning to observer moment B given that he is in observer B is one. The conditional probability of any given observer moment A transitioning to observer moment B given that he is in observer A is infinitesimal. There are many more ways for our physical state to transition (randomly decay) into a non-conscious observer moments than to transition to a conscious observer moment. Any state in the plenitude could be a target of this transition. The ASSA requires one additional assumption: the existence of an objective reality. Yes, but in a way doesn't a belief in an "objective" truth about conditional probabilities assume this too? A truly subjective approach would be one like Wei Dai's, where observers can make any assumptions about probabilities that they like. Who says truth has to be objective? or even if there is such a thing an objective truth? And I don't agree with Wei. Ultimately the assumptions that an observer makes about probabilities must be grounded in his own status as observer. Assuming the observer is the only assumption that needs to be made. Imho there can be an emergent reality purely based on the observer states without the need for any objective entity. The observer himself is an emergent phenomenon reflected on / reflecting the observer himself. George
Re: Request for a glossary of acronyms
Thank you Jesse for your clear answer. Your comparison
of your use of both ASSA and RSSA with Google ranking system
has been quite useful.
This does not mean I am totally convince because ASSA raises the
problem of the basic frame: I don't think there is any sense to compare
the probability of being a human or being a bacteria ..., but your
RSSA use of ASSA does not *necessarily* give a meaning to such
strong form of absolute Self Sampling Assumption, or does it?
I think also that your view on RSSA is not only compatible with
the sort of approach I have developed, but is coherent with
Saibal Mitra backtracking, which, at first I have taken
as wishful thinking. OK you make me feel COMP could be a little less
frightening I'm use to think.
Concerning consciousness theory and its use to isolate a similarity
relation on the computational histories---as seen from some first person
point of view, I will try to answer asap in a common answer to
Stephen and Stathis (and you) who asked very related questions.
Alas I have not really the time now---I would also like to find a way to
explain
the consciousness theory without relying too much on mathematical logic,
but the similarity between 1-histories *has* been derived technically in
the part
of the theory which is the most counter-intuitive ... mmh I will try soon ...
Bruno
At 00:02 01/02/04 -0500, Jesse Mazer wrote:
From: Bruno Marchal [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Request for a glossary of acronyms
Date: Sat, 31 Jan 2004 16:11:39 +0100
Here is an interesting post by Jesse. Curiously I have not been able to
find it
in the archive, but luckily I find it in my computer memory.
Is that normal? I will try again later.
Thanks for reviving this post, it's in the archives here:
http://www.escribe.com/science/theory/m4882.html
It was part of this thread:
http://www.escribe.com/science/theory/index.html?by=OneThreadt=Request%20for%20a%20glossary%20of%20acronyms
Jesse's TOE pet is very similar to the type of TOE compatible with the comp
hyp, I guess everyone can see that.
Jesse, imo, that post deserves to be developed. The way you manage to save
partially the ASSA (Absolute Self-Sampling Assumption) is not very clear
to me.
Bruno
Well, the idea I discussed was somewhat vague, I think to develop it I'd
need to have better ideas about what a theory of consciousness should look
like, and I don't know where to begin with that. But as for how the ASSA
is incorporated, I'll try to summarize again and maybe make it a little
clearer. Basically my idea was that there would be two types of measures
on observer-moments: a relative measure, which gives you answers to
questions like if I am currently experiencing observer-moment A, what is
the probability that my next experience will be of observer-moment B?,
and an absolute measure, which is sort of like the probability that my
current observer-moment will be A in the first place. This idea of
absolute measure might seem meaningless since whatever observer-moment I'm
experiencing right now, from my point of view the probability is 1 that
I'm experiencing that one and not some other, but probably the best way to
think of it is in terms of the self-sampling assumption, where reasoning
*as if* I'm randomly sampled from some group (for example, 'all humans
ever born' in the doomsday argument) can lead to useful conclusions, even
if I don't actually believe that God used a random-number generator to
decide which body my preexisting soul would be placed in.
So, once you have the idea of both a relative measure
('probability-of-becoming') and an absolute measure
('probability-of-being') on observer-moments, my idea is that the two
measures could be interrelated, like this:
1. My probability-of-becoming some possible future observer-moment is
based both on something like the 'similarity' between that observer-moment
and my current one (so my next experience is unlikely to be that of George
W. Bush sitting in the White House, for example, because his memories and
personality are so different from my current ones) but also on the
absolute probability of that observer-moment (so that I am unlikely to
find myself having the experience of talking to an intelligent white
rabbit, because even if that future observer-moment is fairly similar to
my current one in terms of personality, memories, etc., white-rabbit
observer-moments are objectively improbable). I don't know how to quantify
similarity though, or exactly how both similarity and absolute
probabilities would be used to calculate the relative measure between two
observer-moments...this is where some sort of theory of consciousness
would be needed.
2. Meanwhile, the absolute measure is itself dependent on the relative
measure, in the sense that an observer-moment A will have higher absolute
measure if a lot of other observer-moments that themselves have high
absolute measure see A as a likely next experience or a likely
Re: Request for a glossary of acronyms
Bruno Marchal wrote: Thank you Jesse for your clear answer. Your comparison of your use of both ASSA and RSSA with Google ranking system has been quite useful. This does not mean I am totally convince because ASSA raises the problem of the basic frame: I don't think there is any sense to compare the probability of being a human or being a bacteria ..., but your RSSA use of ASSA does not *necessarily* give a meaning to such strong form of absolute Self Sampling Assumption, or does it? No, I don't think it's *necessary* to think that way. Nick Bostrom gives a good example of the use something like the absolute self-sampling assumption in the FAQ of anthropic-principle.com, where two batches of humans would be created, the first batch containing 3 members of one sex, the second batch containing 5000 members of the opposite sex. If I know I am the outcome of this experiment but I don't know which of the two batches I am a part of, I can see that I am a male, and use Bostrom's version of the self-sampling assumption to conclude there's a 5000:3 probability that the larger batch is male (assuming the prior probability of either batch being male was 50:50). One way to look at this is that if the larger batch is male, I have a 5000/5003 chance of being male and a 3/5003 chance of of being female--but presumably since you don't think it makes sense to talk about the probability of being a bacteria vs. a human, you also wouldn't think it makes sense to talk about the probability of being a male vs. being a female. So, another way to think of this would just be as a sort of abstract mathematical assumption you must make in order to calculate the conditional probability that, when I go and ask the creators of the experiment whether the larger batch is male or female, I will have the experience of hearing them tell me it was male. This mathematical assumption tells you to reason *as if* you were randomly sampled from all humans in the experiment, but it's not strictly necessary to attach any metaphysical significance to this assumption, it can just be considered as a step in the calculation of probabilities that I will later learn various things about my place in the universe. In a similar way, one could accept both an absolute probability distribution on observer-moments and a conditional probability distribution from each observer-moment to any other, but one could view the absolute probability distribution as just a sort of abstract step in the calculation of conditional probabilities. For example, consider the two-step duplication experiment again. Say we have an observer A who will later be copied, resulting in two diverging observers B and C. A little later, C will be copied again four times, while B will be left alone, so the end result will be five observers, B, C1, C2, C3, and C4, who all remember being A in the past. Assuming the probable future of these 5 is about the same, each one would be likely to have about the same absolute probability. But according to the Google-like process of assigning absolute probability I mentioned earlier, this means that later observer-moments of C1, C2, C3 and C4 will together reinforce the first observer-moment of C immediately after the split more than later observer-moments of B will reinforce the first observer-moment of B immediately after the split, so the first observer-moment of C will be assigned a higher absolute probability than that of B. This in turn means that A should expect a higher conditional probability of becoming C than B. So again, you can say that this final answer about A's conditional probabilities is what's really important, that the consideration of the absolute probability of all those future observer-moments was just a step in getting this answer, and that absolute probabilites have no meaning apart from their role in calculating conditional probabilities. I can't think of a way to justify the conclusion that A is more likely to experiencing becoming C in this situation without introducing a step like this, though. Personally, I would prefer to assign a deeper significance to the notion of absolute probability, since for me the fact that I find myself to be a human rather than one of the vastly more numerous but less intelligent other animals seems like an observation that cries out for some kind of explanation. But I think this is more of a philosophical difference, so that even if an ultimate TOE was discovered that gave unique absolute and conditional probabilities to each observer-moment, people could still differ on the interpretation of those absolute probabilities. I think also that your view on RSSA is not only compatible with the sort of approach I have developed, but is coherent with Saibal Mitra backtracking, which, at first I have taken as wishful thinking. What is the backtracking idea you're referring to here? OK you make me feel COMP could be a little less frightening I'm
Re: Request for a glossary of acronyms
Here is an interesting post by Jesse. Curiously I have not been able to find it in the archive, but luckily I find it in my computer memory. Is that normal? I will try again later. Jesse's TOE pet is very similar to the type of TOE compatible with the comp hyp, I guess everyone can see that. Jesse, imo, that post deserves to be developed. The way you manage to save partially the ASSA (Absolute Self-Sampling Assumption) is not very clear to me. Bruno At 04:43 14/11/03 -0500, Jesse Mazer wrote: Hal Finney wrote: Jesse Mazer writes: In your definition of the ASSA, why do you define it in terms of your next observer moment? The ASSA and the RSSA were historically defined as competing views. I am not 100% sure that I have the ASSA right, in that it doesn't seem too different from the SSSA. (BTW I have kept the definitions at the end of this email.) (BTW, BTW means By The Way.) But I am pretty sure about the RSSA being in terms of the next moment, so I defined the ASSA the same way, to better illustrate its complementary relationship to the RSSA. The real difference between these views was not addressed in my glossary, which is that the RSSA is supposed to justify the QTI, the quantum theory of immortality, while the ASSA is supposed to refute it. That is, if you only experience universes where your identity continues, as the RSSA implies, then it would seem that you will never die. But if your life-moments are ruled by statistics based on physical law as the ASSA says, then the chance that you will ever experience being extremely old is infinitesimal. Personally I think the ASSA as I have it is somewhat incoherent, speaking of a next observer moment in a framework where there really isn't any such notion. But as I said it has been considered as the alternative to the RSSA. I invite suggestions for improved wording. I think that proponents of the type of ASSA youre talking about would say that the experience of consciousness passing through multiple observer-moments is simply an illusion, and that I am nothing more than my current observer-moment. Therefore they would not believe in quantum immortality, and they also would not define the ASSA in terms of the next observer-moment, only the current observer-moment. I think youd be hard-pressed to find any supporters of the ASSA who would define it in the way you have. But as I say below, I think it is possible to have a different interpretation of the ASSA in which consciousness-over-time is not an illusion, and in which it can be compatible with the RSSA, not opposed to it. Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? That seems contradictory. You have one distribution for the current observer-moment (sampled from all of them), and another distribution for the next observer-moment (sampled from those that are continuous with the same identity). But the current observer-moment is also a next observer-moment (relative to the previous observer-moment). So you can't use the ASSA for current OM's and the RSSA for next OM's, because every next is a current, and vice versa. (By OM I mean observer-moment.) Well, any theory involving splitting/merging consciousness is naturally going to privilege the current observer-moment, because its the only thing you can be really sure of a la I think therefore I am when talking about the past or the future, there will be multiple pasts and multiple futures compatible with your present OM, so you can only talk about a sort of probabilistic spread. That said, although some might argue theres a sort of philosophical contradiction there, I think it is possible to conceive of a mathematical theory of consciousness which incorporates both the ASSA and the RSSA without leading to any formal/mathematical contradictions. There could even be a sort of complementarity between the two aspects of the theory, so that OMs with the highest absolute probability-of-being would also be the ones that have the most other high-absolute-probability OMs that see them as a likely successor in terms of relative probability-of-becoming. In fact, an elegant solution for determining a given OMs absolute probability-of-being might be to simply do a sum over the probability of becoming that OM relative to all the other OMs in the multiverse, weighted by their own probability-of-being. Heres a simple model for how this could work. Say you have some large set of all the OMs in the multiverse, possibly finite if there is some upper limit on the complexity of an OMs, but probably infinite. You have some theory of consciousness that quantifies the similarity S between any two given OMs, which deals with how well they fit as the same mind at different moments, how many of the same memories
Re: Request for a glossary of acronyms
From: Bruno Marchal [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Request for a glossary of acronyms
Date: Sat, 31 Jan 2004 16:11:39 +0100
Here is an interesting post by Jesse. Curiously I have not been able to
find it
in the archive, but luckily I find it in my computer memory.
Is that normal? I will try again later.
Thanks for reviving this post, it's in the archives here:
http://www.escribe.com/science/theory/m4882.html
It was part of this thread:
http://www.escribe.com/science/theory/index.html?by=OneThreadt=Request%20for%20a%20glossary%20of%20acronyms
Jesse's TOE pet is very similar to the type of TOE compatible with the comp
hyp, I guess everyone can see that.
Jesse, imo, that post deserves to be developed. The way you manage to save
partially the ASSA (Absolute Self-Sampling Assumption) is not very clear to
me.
Bruno
Well, the idea I discussed was somewhat vague, I think to develop it I'd
need to have better ideas about what a theory of consciousness should look
like, and I don't know where to begin with that. But as for how the ASSA is
incorporated, I'll try to summarize again and maybe make it a little
clearer. Basically my idea was that there would be two types of measures on
observer-moments: a relative measure, which gives you answers to questions
like if I am currently experiencing observer-moment A, what is the
probability that my next experience will be of observer-moment B?, and an
absolute measure, which is sort of like the probability that my current
observer-moment will be A in the first place. This idea of absolute measure
might seem meaningless since whatever observer-moment I'm experiencing right
now, from my point of view the probability is 1 that I'm experiencing that
one and not some other, but probably the best way to think of it is in terms
of the self-sampling assumption, where reasoning *as if* I'm randomly
sampled from some group (for example, 'all humans ever born' in the doomsday
argument) can lead to useful conclusions, even if I don't actually believe
that God used a random-number generator to decide which body my preexisting
soul would be placed in.
So, once you have the idea of both a relative measure
('probability-of-becoming') and an absolute measure ('probability-of-being')
on observer-moments, my idea is that the two measures could be interrelated,
like this:
1. My probability-of-becoming some possible future observer-moment is based
both on something like the 'similarity' between that observer-moment and my
current one (so my next experience is unlikely to be that of George W. Bush
sitting in the White House, for example, because his memories and
personality are so different from my current ones) but also on the absolute
probability of that observer-moment (so that I am unlikely to find myself
having the experience of talking to an intelligent white rabbit, because
even if that future observer-moment is fairly similar to my current one in
terms of personality, memories, etc., white-rabbit observer-moments are
objectively improbable). I don't know how to quantify similarity though,
or exactly how both similarity and absolute probabilities would be used to
calculate the relative measure between two observer-moments...this is where
some sort of theory of consciousness would be needed.
2. Meanwhile, the absolute measure is itself dependent on the relative
measure, in the sense that an observer-moment A will have higher absolute
measure if a lot of other observer-moments that themselves have high
absolute measure see A as a likely next experience or a likely past
experience (ie there's a high relative measure between them). This idea is
based partly on that thought experiment where two copies of a person are
made, then one copy is itself later copied many more times, the idea being
that the copy that is destined to be copied more in the future has a higher
absolute measure because there are more future observer-moments
reinforcing it (see http://www.escribe.com/science/theory/m4841.html for
more on this thought-experiment). I think of this whole idea in analogy to
the way Google's ranking system works: pages are ranked as more popular if
they are linked to by a lot of other pages that are themselves highly
ranked. So, the popularity of a particular page is sort of like the absolute
probability of being a particular observer-moment, while a link from one
page to another is like a high relative probability from one observer-moment
to another (to make the analogy better you'd have to use weighted links, and
you'd have to assume the weight of the link between page A and page B itself
depends partly on B's popularity).
The final part of my pet theory is that by having the two measures
interrelated in this way, you'd end up with a unique self-consistent
solution to what each measure would look like, like what happens when you
have a bunch of simultaneous equations specifying how different variables
relate
Re: Request for a glossary of acronyms
Hal Finney wrote: Jesse Mazer writes: In your definition of the ASSA, why do you define it in terms of your next observer moment? The ASSA and the RSSA were historically defined as competing views. I am not 100% sure that I have the ASSA right, in that it doesn't seem too different from the SSSA. (BTW I have kept the definitions at the end of this email.) (BTW, BTW means By The Way.) But I am pretty sure about the RSSA being in terms of the next moment, so I defined the ASSA the same way, to better illustrate its complementary relationship to the RSSA. The real difference between these views was not addressed in my glossary, which is that the RSSA is supposed to justify the QTI, the quantum theory of immortality, while the ASSA is supposed to refute it. That is, if you only experience universes where your identity continues, as the RSSA implies, then it would seem that you will never die. But if your life-moments are ruled by statistics based on physical law as the ASSA says, then the chance that you will ever experience being extremely old is infinitesimal. Personally I think the ASSA as I have it is somewhat incoherent, speaking of a next observer moment in a framework where there really isn't any such notion. But as I said it has been considered as the alternative to the RSSA. I invite suggestions for improved wording. I think that proponents of the type of ASSA youre talking about would say that the experience of consciousness passing through multiple observer-moments is simply an illusion, and that I am nothing more than my current observer-moment. Therefore they would not believe in quantum immortality, and they also would not define the ASSA in terms of the next observer-moment, only the current observer-moment. I think youd be hard-pressed to find any supporters of the ASSA who would define it in the way you have. But as I say below, I think it is possible to have a different interpretation of the ASSA in which consciousness-over-time is not an illusion, and in which it can be compatible with the RSSA, not opposed to it. Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? That seems contradictory. You have one distribution for the current observer-moment (sampled from all of them), and another distribution for the next observer-moment (sampled from those that are continuous with the same identity). But the current observer-moment is also a next observer-moment (relative to the previous observer-moment). So you can't use the ASSA for current OM's and the RSSA for next OM's, because every next is a current, and vice versa. (By OM I mean observer-moment.) Well, any theory involving splitting/merging consciousness is naturally going to privilege the current observer-moment, because its the only thing you can be really sure of a la I think therefore I am when talking about the past or the future, there will be multiple pasts and multiple futures compatible with your present OM, so you can only talk about a sort of probabilistic spread. That said, although some might argue theres a sort of philosophical contradiction there, I think it is possible to conceive of a mathematical theory of consciousness which incorporates both the ASSA and the RSSA without leading to any formal/mathematical contradictions. There could even be a sort of complementarity between the two aspects of the theory, so that OMs with the highest absolute probability-of-being would also be the ones that have the most other high-absolute-probability OMs that see them as a likely successor in terms of relative probability-of-becoming. In fact, an elegant solution for determining a given OMs absolute probability-of-being might be to simply do a sum over the probability of becoming that OM relative to all the other OMs in the multiverse, weighted by their own probability-of-being. Heres a simple model for how this could work. Say you have some large set of all the OMs in the multiverse, possibly finite if there is some upper limit on the complexity of an OMs, but probably infinite. You have some theory of consciousness that quantifies the similarity S between any two given OMs, which deals with how well they fit as the same mind at different moments, how many of the same memories they share in common, how similar are their causal patterns, and so on. You also have some absolute measure on all the OMs, a probability-of-being B assigned to each onethis is basically just my idea that the self-sampling assumption could be weighted somehow, so that the ideal way to use the ASSA is to assume that your current OM is randomly sampled from the set of all possible observer-moments, weighted by their own probability-of-being B. Then, to determine the relative
Re: Request for a glossary of acronyms
My message 6/11 to Alberto Gómez seems not to have gone through. I send it again. Apology for those who did receive it. B. At 09:24 06/11/03 +0100, Alberto Gómez wrote: For me there is no bigger step between to wonder about how conscience arises from a universe made by atoms in a Newtonian universe, particles in a quantum universe, quarks in a quantum relativistic universe and finally, superstring/n-branes in a 11 dimensional universe for one side and, on the other side, to wonder about how SAS in a complex enough mathematical structure can have a sense of conscience. BM: I agree. It is a genuine point. [SNIP] AG:That must be true either in our physical world or the world of a geometrical figure in a n-dimensional spacetime, or in a computer simulation defined by a complex enough algorithm (These three alternative ways of describing universes may be isomorphic, being the first a particular case or not. The computability of our universe doesn't matter for this question). BM:I disagree, because if you take the comp. hyp. seriously enough the physical should emerge as some precise modality from an inside view of Arithmetical Truth. See UDA ref in Hal Finney's post. AG:So the mathematical existence, when SAS are possible inside the mathematical formulation, implies existence (the _expression_ physical existence may be a redundancy) BM:Same remark. What you say is not only true, but with comp it is quasi-constructively true so that you can extract the logic and probability physical rules in computer science (even in computer's computer science). making the comp. hyp. popper-falsifiable. AG:But, for these mathematical descriptions to exist, it is necessary the existence of being with a higher dimensionality and intelligence that formulate these mathematical descriptions? That is: every mathematical object does exist outside of any conscience? The issue is not to question that mathematical existence (with SAS) implies physical existence, (according with the above arguments it is equivalent). The question is the mathematical existence itself. BM:Now, it is a fact, the failure of logicism, that you cannot define integers without implicitely postulating them. So Arithmetical existence is a quasi necessary departure reality. It is big and not unifiable by any axiomatisable theory (by Godel). (axiomatizable theory = theory such that you can verify algorithmically the proofs of the theorems) I refer often to Arithmetical Realism AR; and it constitutes 1/3 of the computationalist hypothesis, alias the comp. hyp., alias COMP: COMP = AR + CT + YD (Yes, more acronyms, sorry!) AR = Arithmetical Realism (cf also the Hardy post) CT = Church Thesis YD = (I propose) the Yes Doctor, It is the belief that you can be decomposed into part such that you don't experience anything when those parts are substituted by functionnaly equivalent digital parts. It makes possible to give sense saying yes to a surgeon who propose you some artificial substitution of your body. With COMP you can justify why this needs an irreductible act of faith (the consistency of COMP entails the consistency of the negation of COMP, this is akin to Godel's second incompleteness theorem. It has nothing to do with the hypothesis that there is a physical universe which would be either the running or the output of a computer program. Hal, with COMP the identity problem is tackled by the venerable old computer science/logic approach to self-reference (with the result by Godel, Lob, Solovay, build on Kleene, Turing, Post etc...). Bruno
Re: Request for a glossary of acronyms
Also, what about a weighted version of the ASSA? I believe other animals are conscious and thus would qualify as observers/observer-moments, which would suggest I am extraordinarily lucky to find myself as an observer-moment of what seems like the most intelligent species on the planet...but could there be an element of the anthropic principle here? Perhaps some kind of theory of consciousness would assign something like a mental complexity to different observer-moments, and the self-sampling assumption could be biased in favor of more complex minds. I think the anthropic principle could be used quite well to account for that, since if you were an animal other than a human being, you could not be asking that question. But I don't see the need nor the basis to assign any sort of weight to the 'selection' of different observers, just as there is no weight (other than the anthropic principle) to account for the fact that we live in this particular universe which allows for human beings. -Eric.
Re: Request for a glossary of acronyms
At 09:24 06/11/03 +0100, Alberto Gómez wrote: For me there is no bigger step between to wonder about how conscience arises from a universe made by atoms in a Newtonian universe, particles in a quantum universe, quarks in a quantum relativistic universe and finally, superstring/n-branes in a 11 dimensional universe for one side and, on the other side, to wonder about how SAS in a complex enough mathematical structure can have a sense of conscience. I agree. It is a genuine point. [SNIP] That must be true either in our physical world or the world of a geometrical figure in a n-dimensional spacetime, or in a computer simulation defined by a complex enough algorithm (These three alternative ways of describing universes may be isomorphic, being the first a particular case or not. The computability of our universe doesn't matter for this question). I disagree, because if you take the comp. hyp. seriously enough the physical should emerge as some precise modality from an inside view of Arithmetical Truth. See UDA ref in Hal Finney's post. So the mathematical existence, when SAS are possible inside the mathematical formulation, implies existence (the expression physical existence may be a redundancy) Same remark. What you say is not only true, but with comp it is quasi-constructively true so that you can extract the logic and probability physical rules in computer science (even in computer's computer science). making the comp. hyp. popper-falsifiable. But, for these mathematical descriptions to exist, it is necessary the existence of being with a higher dimensionality and intelligence that formulate these mathematical descriptions? That is: every mathematical object does exist outside of any conscience? The issue is not to question that mathematical existence (with SAS) implies physical existence, (according with the above arguments it is equivalent). The question is the mathematical existence itself. Now, it is fact, the failure of logicism, that you cannot define integers without implicitely postulating them. So Arithmetical existence is a quasi necessary departure reality. It is big and not unifiable by any axiomatisable theory (by Godel). (axiomatizable theory = theory such that you can verify algorithmically the proofs of the theorems) I refer often to Arithmetical Realism AR; and it constitutes 1/3 of the computationalist hypothesis, alias the comp. hyp., alias COMP: COMP = AR + CT + YD(Yes, more acronyms, sorry!) AR = Arithmetical Realism (cf also the Hardy post) CT = Church Thesis YD = (I propose) the Yes Doctor, It is the belief that you can be decomposed into part such that you don't experience anything when those parts are substituted by functionnaly equivalent digital parts. It makes possible to give sense saying yes to a surgeon who propose you some artificial substitution of your body. With COMP you can justify why this needs an irreductible act of faith (the consistency of COMP entails the consistency of the negation of COMP, this is akin to Godel's second incompleteness theorem. It has nothing to do with the hypothesis that there is a physical universe which would be either the running or the output of a computer program. Hal, with COMP the identity problem is tackled by the venerable old computer science/logic approach to self-reference (with the result by Godel, Lob, Solovay, build on Kleene, Turing, Post etc...). I will comment Jesse's post later, because I must go now. Bruno
Re: Request for a glossary of acronyms
At 16:54 05/11/03 -0500, Jesse Mazer wrote: Hal Finney wrote: One correction, in the descriptions below I should have said multiverse for all of them instead of universe. The distinction between the SSA and the SSSA is not multiverse vs universe, it is observers vs observer- moments. I'll send out an updated copy when I get some more links and/or corrections and new definitions. Hal SSA - The Self-Sampling Assumption, which says that you should consider yourself as a randomly sampled observer from among all observers in the multiverse. SSSA - The Strong Self-Sampling Assumption, which says that you should consider this particular observer-moment you are experiencing as being randomly sampled from among all observer-moments in the universe. ASSA - The Absolute Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments in the universe. RSSA - The Relative Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments which come immediately after your current observer-moment and belong to the same observer. In your definition of the ASSA, why do you define it in terms of your next observer moment? Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? Also, what about a weighted version of the ASSA? I believe other animals are conscious and thus would qualify as observers/observer-moments, which would suggest I am extraordinarily lucky to find myself as an observer-moment of what seems like the most intelligent species on the planet...but could there be an element of the anthropic principle here? Perhaps some kind of theory of consciousness would assign something like a mental complexity to different observer-moments, and the self-sampling assumption could be biased in favor of more complex minds. Likewise, one might use a graded version of the RSSA to deal with degrees of similarity, instead of having it be a simple either-or whether a future observer-moment belongs to the same observer or not as you suggest in your definition. There could be some small probability that my next observer-moment will be of a completely different person, but in most cases it would be more likely that my next observer-moment would be basically similar to my current one. But one might also have to take into account the absolute measure on all-observer moments that I suggest above, so that if there is a very low absolute probability of a brain that can suggest a future observer-moment which is very similar to my current one (because, say, I am standing at ground zero of a nuclear explosion) then the relative probability of my next observer-moment being completely different would be higher. Again, one would need something like a theory of consciousness to quantify stuff like degrees of similarity and the details of how the tradeoff between relative probability and absolute probability would work. In my opinion, and if I understand Jesse Mazer properly, he is right. Now, with the comp. hyp. you have (obviously) constraints coming from computer science (itself related to number theory including universal one not depending of any particular implementation). A theory of consciousness which suits well both the traditional thought experiment (self-duplicability) and self-referential discourse can be extracted from what a machine can, in general, correctly bet on its possible consistent computational extensions. That moves corresponds to comp-immortality, we just don't take into account the cul-de-sac worlds, (which corresponds to the world with no more accessible worlds in the Kripke semantics of the logic of self-reference). It is the move going from the logic of machine-provability to the logic of machine provability consistency, or the move from []p to a *new* box defined by []p-[]-p. From this (when p is restricted on the DU accessible proposition), (the $\Sigma_1 proposition for the logicians), you get A quantum logic, from which you get, I think, the similarity relations you are searching. (This because from the yes/no quantum logic you can derive an angle of PI/2 radians, and from that angle you can derive all the angles, well if THAT quantum logic behaves sufficiently well, and that's not yet clear at this point. Of course at this point things are rather technical. Just to make a link with what Hal Finney said, I have provide indeed an argument showing that if we (I) are machine then physics comes from computer science, but I have also provide the more technically involved arithmetical translation of that argument in the language of a mean self-referentially consistent universal Turing machine (from which I
Re: Request for a glossary of acronyms
I agree with Eric Hawthorne. Much of what's said here is unintelligible to me. I think that most of the contributors to this list are outstanding intellects that want to enlighten, not obfuscate, and have some fascinating ideas. I'd like to be able to decipher what you're saying. Norman - Original Message - From: Eric Hawthorne [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Wednesday, November 05, 2003 9:47 AM Subject: Request for a glossary of acronyms UD, ASSA, Level 1 world, RSSA, Pilot Wave, ... MW, Is anyone willing to post a glossary of the acronyms used on this list, preferably with a very short summary of each, and a reference to the full papers that best explicate them? The glossary could also include the major contending theories (with their variations), listed in a hierarchy to show their place wrt each other. When using acronyms, please remember that the readership is diverse in educational background. I'm sure you wouldn't appreciate it if I started talking about how we could use the RUP or XP combined with a LINDA based RBES based on an RMI P2P grid to investigate these issues. Would be much appreciated.
Re: Request for a glossary of acronyms
[This is a repost, I didn't see it come out before. I have a sinking feeling that the first URL contains the magic letters s - c - r - i - b - e and that is triggering some kind of filter! If so that is rather inconvenient given that this is one of the main list archive sites. Hopefully this header will move it down far enough that the filter will ignore it. Extra line. Extra line2. Extra line3. Extra line4. That should be enough!] Here is a start at a glossary: UD - The Universal Dovetailer, a hypothetical system for running all possible computer programs. See UDA. UDA - The Universal Dovetailer Argument of Bruno Marchal, which concludes that we must derive the laws of physics from computer science. See http://www.escribe.com/science/theory/m3044.html. Level 1, 2, 3, 4 multiverses - These are based on Max Tegmark's hierarchy, described at http://www.hep.upenn.edu/~max/multiverse1.html. Briefly, the level 1 multiverse consists of regions of space within our universe that are beyond our observation horizon. Level 2 is the multiple bubbles of space predicted by inflation theory. Level 3 is the Many-Worlds Interpretation of Quantum Mechanics (MWI). Level 4 is the hypothesis that all mathematical structures exist and that some of them can be though of as universes. MWI - The Many-Worlds Interpretation of Quantum Mechanics, which holds that at every quantum event the universe splits into parallel worlds. See http://www.hep.upenn.edu/~max/everett.html for Tegmark's version. Also see the level 3 multiverse reference for more links. For the following, I don't have links, and my definitions may not be quite right, so I invite corrections and links to definitions. SSA - The Self-Sampling Assumption, which says that you should consider yourself as a randomly sampled observer from among all observers in the multiverse. SSSA - The Strong Self-Sampling Assumption, which says that you should consider this particular observer-moment you are experiencing as being randomly sampled from among all observer-moments in the universe. ASSA - The Absolute Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments in the universe. RSSA - The Relative Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments which come immediately after your current observer-moment and belong to the same observer. Hal
Re: Request for a glossary of acronyms
Here is a start at a glossary: UD - The Universal Dovetailer, a hypothetical system for running all possible computer programs. See UDA. UDA - The Universal Dovetailer Argument of Bruno Marchal, which concludes that we must derive the laws of physics from computer science. See http://www.escribe.com/science/theory/m3044.html. Level 1, 2, 3, 4 multiverses - These are based on Max Tegmark's hierarchy, described at http://www.hep.upenn.edu/~max/multiverse1.html. Briefly, the level 1 multiverse consists of regions of space within our universe that are beyond our observation horizon. Level 2 is the multiple bubbles of space predicted by inflation theory. Level 3 is the Many-Worlds Interpretation of Quantum Mechanics (MWI). Level 4 is the hypothesis that all mathematical structures exist and that some of them can be though of as universes. MWI - The Many-Worlds Interpretation of Quantum Mechanics, which holds that at every quantum event the universe splits into parallel worlds. See http://www.hep.upenn.edu/~max/everett.html for Tegmark's version. Also see the level 3 multiverse reference for more links. For the following, I don't have links, and my definitions may not be quite right, so I invite corrections and links to definitions. SSA - The Self-Sampling Assumption, which says that you should consider yourself as a randomly sampled observer from among all observers in the multiverse. SSSA - The Strong Self-Sampling Assumption, which says that you should consider this particular observer-moment you are experiencing as being randomly sampled from among all observer-moments in the universe. ASSA - The Absolute Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments in the universe. RSSA - The Relative Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments which come immediately after your current observer-moment and belong to the same observer. Hal
Re: Request for a glossary of acronyms
One correction, in the descriptions below I should have said multiverse for all of them instead of universe. The distinction between the SSA and the SSSA is not multiverse vs universe, it is observers vs observer- moments. I'll send out an updated copy when I get some more links and/or corrections and new definitions. Hal SSA - The Self-Sampling Assumption, which says that you should consider yourself as a randomly sampled observer from among all observers in the multiverse. SSSA - The Strong Self-Sampling Assumption, which says that you should consider this particular observer-moment you are experiencing as being randomly sampled from among all observer-moments in the universe. ASSA - The Absolute Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments in the universe. RSSA - The Relative Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments which come immediately after your current observer-moment and belong to the same observer.
Re: Request for a glossary of acronyms
Hal Finney wrote: One correction, in the descriptions below I should have said multiverse for all of them instead of universe. The distinction between the SSA and the SSSA is not multiverse vs universe, it is observers vs observer- moments. I'll send out an updated copy when I get some more links and/or corrections and new definitions. Hal SSA - The Self-Sampling Assumption, which says that you should consider yourself as a randomly sampled observer from among all observers in the multiverse. SSSA - The Strong Self-Sampling Assumption, which says that you should consider this particular observer-moment you are experiencing as being randomly sampled from among all observer-moments in the universe. ASSA - The Absolute Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments in the universe. RSSA - The Relative Self-Sampling Assumption, which says that you should consider your next observer-moment to be randomly sampled from among all observer-moments which come immediately after your current observer-moment and belong to the same observer. In your definition of the ASSA, why do you define it in terms of your next observer moment? Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? Also, what about a weighted version of the ASSA? I believe other animals are conscious and thus would qualify as observers/observer-moments, which would suggest I am extraordinarily lucky to find myself as an observer-moment of what seems like the most intelligent species on the planet...but could there be an element of the anthropic principle here? Perhaps some kind of theory of consciousness would assign something like a mental complexity to different observer-moments, and the self-sampling assumption could be biased in favor of more complex minds. Likewise, one might use a graded version of the RSSA to deal with degrees of similarity, instead of having it be a simple either-or whether a future observer-moment belongs to the same observer or not as you suggest in your definition. There could be some small probability that my next observer-moment will be of a completely different person, but in most cases it would be more likely that my next observer-moment would be basically similar to my current one. But one might also have to take into account the absolute measure on all-observer moments that I suggest above, so that if there is a very low absolute probability of a brain that can suggest a future observer-moment which is very similar to my current one (because, say, I am standing at ground zero of a nuclear explosion) then the relative probability of my next observer-moment being completely different would be higher. Again, one would need something like a theory of consciousness to quantify stuff like degrees of similarity and the details of how the tradeoff between relative probability and absolute probability would work. Jesse _ Concerned that messages may bounce because your Hotmail account is over limit? Get Hotmail Extra Storage! http://join.msn.com/?PAGE=features/es
Re: Request for a glossary of acronyms
By the way, for anyone who wants to learn more about the whole issue of the self-sampling assumption in general, I recommend this website: http://www.anthropic-principle.com/ The author of the site, Nick Bostrom, (who I think is a member of this list, or used to be) also wrote a whole book on the subject titled Anthropic Bias: Observation Selection Effects in Science and Philosophy. I haven't picked it up yet because of the steep price, but I'm gonna have to get it one of these days. Jesse _ MSN Messenger with backgrounds, emoticons and more. http://www.msnmessenger-download.com/tracking/cdp_customize
Re: Request for a glossary of acronyms
But one might also have to take into account the absolute measure on all-observer moments that I suggest above, so that if there is a very low absolute probability of a brain that can suggest a future observer-moment which is very similar to my current one Sorry, meant to say a very low absolute probability of a brain that can *support* a future observer-moment... _ Is your computer infected with a virus? Find out with a FREE computer virus scan from McAfee. Take the FreeScan now! http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963
Re: Request for a glossary of acronyms
Jesse Mazer writes: In your definition of the ASSA, why do you define it in terms of your next observer moment? The ASSA and the RSSA were historically defined as competing views. I am not 100% sure that I have the ASSA right, in that it doesn't seem too different from the SSSA. (BTW I have kept the definitions at the end of this email.) (BTW, BTW means By The Way.) But I am pretty sure about the RSSA being in terms of the next moment, so I defined the ASSA the same way, to better illustrate its complementary relationship to the RSSA. The real difference between these views was not addressed in my glossary, which is that the RSSA is supposed to justify the QTI, the quantum theory of immortality, while the ASSA is supposed to refute it. That is, if you only experience universes where your identity continues, as the RSSA implies, then it would seem that you will never die. But if your life-moments are ruled by statistics based on physical law as the ASSA says, then the chance that you will ever experience being extremely old is infinitesimal. Personally I think the ASSA as I have it is somewhat incoherent, speaking of a next observer moment in a framework where there really isn't any such notion. But as I said it has been considered as the alternative to the RSSA. I invite suggestions for improved wording. Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? That seems contradictory. You have one distribution for the current observer-moment (sampled from all of them), and another distribution for the next observer-moment (sampled from those that are continuous with the same identity). But the current observer-moment is also a next observer-moment (relative to the previous observer-moment). So you can't use the ASSA for current OM's and the RSSA for next OM's, because every next is a current, and vice versa. (By OM I mean observer-moment.) Also, what about a weighted version of the ASSA? I believe other animals are conscious and thus would qualify as observers/observer-moments, which would suggest I am extraordinarily lucky to find myself as an observer-moment of what seems like the most intelligent species on the planet...but could there be an element of the anthropic principle here? Perhaps some kind of theory of consciousness would assign something like a mental complexity to different observer-moments, and the self-sampling assumption could be biased in favor of more complex minds. Yes, I think the possibility of weighting OM's is implicit in these definitions. We often use the term measure to indicate that some OM's carry more weight and more probability than others. For example, one theory is that OM's which take a larger program to output would have lower measure than ones which are described by a short program. By this definition we might think that less complex minds would have more measure, the opposite of your idea. I haven't heard of anyone suggesting that complex minds would inherently have higher measure. Instead, it seems that most people use a somewhat arbitrary cutoff for complexity which is necessary to qualify as an observer. In the anthropic literature this general issue is discussed as the problem of the reference class. I'm not that familiar with all the ideas which have been proposed. Your idea, and my alternative about less complex minds having more measure, have the problem that it seems that much more and less complex minds should exist in the multiverse, and as you note we obviously have evidence of less-complex minds existing in abundance right here on Earth. So if more complexity is better, why aren't we super-intelligent aliens? Likewise, one might use a graded version of the RSSA to deal with degrees of similarity, instead of having it be a simple either-or whether a future observer-moment belongs to the same observer or not as you suggest in your definition. There could be some small probability that my next observer-moment will be of a completely different person, but in most cases it would be more likely that my next observer-moment would be basically similar to my current one. But one might also have to take into account the absolute measure on all-observer moments that I suggest above, so that if there is a very low absolute probability of a brain that can suggest a future observer-moment which is very similar to my current one (because, say, I am standing at ground zero of a nuclear explosion) then the relative probability of my next observer-moment being completely different would be higher. Again, one would need something like a theory of consciousness to quantify stuff like degrees of similarity and the details of how the tradeoff between relative probability and absolute probability
Re: Request for a glossary of acronyms
Hal, Waht about a definition of Observer-Moment? That would surely help me... Thanks, -Joao Hal Finney wrote: Jesse Mazer writes: In your definition of the ASSA, why do you define it in terms of your next observer moment? The ASSA and the RSSA were historically defined as competing views. I am not 100% sure that I have the ASSA right, in that it doesn't seem too different from the SSSA. (BTW I have kept the definitions at the end of this email.) (BTW, BTW means By The Way.) But I am pretty sure about the RSSA being in terms of the next moment, so I defined the ASSA the same way, to better illustrate its complementary relationship to the RSSA. The real difference between these views was not addressed in my glossary, which is that the RSSA is supposed to justify the QTI, the quantum theory of immortality, while the ASSA is supposed to refute it. That is, if you only experience universes where your identity continues, as the RSSA implies, then it would seem that you will never die. But if your life-moments are ruled by statistics based on physical law as the ASSA says, then the chance that you will ever experience being extremely old is infinitesimal. Personally I think the ASSA as I have it is somewhat incoherent, speaking of a next observer moment in a framework where there really isn't any such notion. But as I said it has been considered as the alternative to the RSSA. I invite suggestions for improved wording. Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? That seems contradictory. You have one distribution for the current observer-moment (sampled from all of them), and another distribution for the next observer-moment (sampled from those that are continuous with the same identity). But the current observer-moment is also a next observer-moment (relative to the previous observer-moment). So you can't use the ASSA for current OM's and the RSSA for next OM's, because every next is a current, and vice versa. (By OM I mean observer-moment.) Also, what about a weighted version of the ASSA? I believe other animals are conscious and thus would qualify as observers/observer-moments, which would suggest I am extraordinarily lucky to find myself as an observer-moment of what seems like the most intelligent species on the planet...but could there be an element of the anthropic principle here? Perhaps some kind of theory of consciousness would assign something like a mental complexity to different observer-moments, and the self-sampling assumption could be biased in favor of more complex minds. Yes, I think the possibility of weighting OM's is implicit in these definitions. We often use the term measure to indicate that some OM's carry more weight and more probability than others. For example, one theory is that OM's which take a larger program to output would have lower measure than ones which are described by a short program. By this definition we might think that less complex minds would have more measure, the opposite of your idea. I haven't heard of anyone suggesting that complex minds would inherently have higher measure. Instead, it seems that most people use a somewhat arbitrary cutoff for complexity which is necessary to qualify as an observer. In the anthropic literature this general issue is discussed as the problem of the reference class. I'm not that familiar with all the ideas which have been proposed. Your idea, and my alternative about less complex minds having more measure, have the problem that it seems that much more and less complex minds should exist in the multiverse, and as you note we obviously have evidence of less-complex minds existing in abundance right here on Earth. So if more complexity is better, why aren't we super-intelligent aliens? Likewise, one might use a graded version of the RSSA to deal with degrees of similarity, instead of having it be a simple either-or whether a future observer-moment belongs to the same observer or not as you suggest in your definition. There could be some small probability that my next observer-moment will be of a completely different person, but in most cases it would be more likely that my next observer-moment would be basically similar to my current one. But one might also have to take into account the absolute measure on all-observer moments that I suggest above, so that if there is a very low absolute probability of a brain that can suggest a future observer-moment which is very similar to my current one (because, say, I am standing at ground zero of a nuclear explosion) then the relative probability of my next observer-moment being completely different would be higher. Again, one would need something like a
Re: Request for a glossary of acronyms
Here are some more: QM - Quantum Mechanics, our best current theory for the physics of the small. GR - General Relativity, our best current theory for the physics of the large. TM - Turing Machine, a formal model of computation. UTM - Universal Turing Machine, a type of Turing Machine that can emulate any other TM. QTI - Quantum Theory of Immortality, the notion that the existence of the multiverse implies that every observer will live forever since his existence continues in some worlds. QS - Quantum Suicide, the extension of the QTI theory into a proposal that by setting up a suicide machine to be triggered by negative events, one can increase the probability of experiencing favorable events. SIA - The Self-Indication Assumption, which says his own existence gives an observer evidence that other observers probably exist. Due to Nick Bostrom, who has much related material available at http://www.anthropic-principle.com. FOR - The Fabric of Reality mailing list, based on David Deutsch's book of the same name. Archived at http://groups.yahoo.com/group/Fabric-of-Reality/. AUP - All Universe Principle. See AUH. AUH - All Universe Hypothesis. One of many names for the idea that all universes exist. Others include the Principle of Plenitude and the All Universe Principle. AP - Anthropic Principle, the idea that we can only observe that which is consistent with the existence of an observer. TOE - Theory of Everything, the hypothetical physical theory that will fully describe our universe. It would have to encompass or extend Quantum Mechanics and General Relativity. CA - Cellular Automaton (singular) or Cellular Automata (plural). This is a computational model based on cells arranged in some kind of array or pattern which perform (usually) simple calculations based on their internal state and the state of their neighbors. Stephen Wolfram has a book proposing that systems similar to CAs may underly many natural phenomena, http://www.wolframscience.com/. SAS - Self Aware Subsystem, an observer when considered as part of a mathematical structure. Hal
Re: Request for a glossary of acronyms
Hal, Waht about a definition of Observer-Moment? That would surely help me... Thanks, -Joao I was mostly sticking to acronyms, otherwise it becomes a FAQ. Doing observer-moment also requires defining observer. Here is a try at it: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. Hal
