Here is my response to Bruno's UDA argument as described in the links from http://www.escribe.com/science/theory/m3044.html.
I agree with the general idea, that if we assume that a UDA program exists in some sense (Platonic or otherwise), then each observer moment is instantiated multiple times (probably a countably infinite number of times) throughout the structure generated by the UDA. In that case we have to accept that our mental experiences are not unique to some universe (by "universe" I mean the output of one program being simulated by the UDA) but are present in infinitely many of them. However there are a few places where I would expand upon the steps, and take issue with some of them. First, as far as the basic idea of COMP, I do agree that functional substitution is enough for consciousness indistinguishable from my own. I would expand on this to explain that the reason for this belief is not due to philosophy, but to biology. The way the brain works appears to be a matter of processing information via electrochemical signals transmitted by neural cells. Each such cell is acting as an information processor. The collection of these cells in the brain takes in information on incoming nerves, and sends out commands on outgoing nerves. Everything is information. So it seems to me that replacing this system with something that can process information in a functionally equivalent way would produce an equivalent system. If I didn't know that the brain worked in this way, I would probably not accept COMP. However, based on some arguments which Wei Dai gave (and which I'm not sure if he accepts), I believe there are some aspects of consciousness which are not fully captured by a purely functional substitution. Specifically, as we get into the questions about duplications, I believe that some details of the functional substitution may affect the first-person likelihood of experiencing that implementation. Issues such as the speed, size and degree of redundancy of an implementation may affect how much "measure" it has, that is, how much of a contribution it makes to the space of all my first-person experiences. If we jump to the end of Bruno's argument, step 10 or 11, and accept that we are instantiated in multiple forms, it is obvious that not all ways we could be instantiated are equally probable. Otherwise the universe we observe would be chaotic. So somehow it must be the case that implementations which exist in simple and lawful universes are more probable (in the first person sense) than those in random universes. Given that we accept the reality of different measures for different implementation states, I think we need to consider the possibility that not all functional substitutions have equal measure (i.e. first-person probability). I won't go into the details here, but I think a detailed argument shows that different sizes and speeds of the functional substitution must make a difference in measure. Several of Bruno's questions raise the idea of quantifying the first person probability of various duplication scenarios. In the comment preceding question 7 in http://www.escribe.com/science/theory/m2992.html, he writes: > The way to quantify the indeterminacy is the unknown. Although we can > argue that the {W, M} duplication gives a sort of perfect 1-coin, simple > probabilty reasoning leads quickly to hard problems. I think Bruno agrees here that you can't just say that if you have 2 duplicates made, you therefore have a 50% first-person probability of experiencing each of them. We have discussed various paradoxes and problems that arise with this kind of reasoning. Nevertheless he asks in questions 7 and 8, *if* we accept a 50% probability in one experiment, will we also see it in another? I am not sure how to answer these, because I don't have a good understanding of how to begin to quantify the probabilities. So I cannot answer in the affirmative, but I can't deny the possibility either. I have to answer that I need to get a better understanding of what aspects are relevant in understanding probabilities. Likewise in question 10, where we assume a UDA is actually implemented in the physical universe, I believe it is possible that the measure of the implementations in the UDA may be smaller than the measure of biological physical implementations. So while the UDA machine will produce copies of my mental state, it might turn out that they make an insignificant contribution in terms of first-person probability, compared to the contributions from the physical universe. (For the purposes of question 10, we assume that the physical universe exists.) To sum up, I agree with Bruno (I think) on the following points: - Functional substitution is adequate to maintain consciousness - Mental states must be (in some sense) shared across all equivalent functional implementations - The UDA program produces multiple functional equivalents of all possible observers - If we accept a certain view of Platonic reality of mathematics, then the UDA exists even if it is not implemented in our reality - In that case our current mental states can be viewed as being created by a UDA or some similar program I may disagree on some points: - Not all functional substitutions have equal measure - Universes are well defined: each universe is the output of one of the programs which are simulated in "dovetailed" fashion by the UDA - Each observer-moment spans a specific set of universes - that is, those specific programs which functionally implement it And my very tentative theory for measure, which was first proposed by Wei Dai: - The measure of an observer-moment is proportional to the fraction of programs that implement it, and proportional to the fraction of each programs' trace that it occupies. That is, observer moments have higher measure if they are implemented by more programs, and also if they use up more of the "resources" of the universe created by each of these programs. Hal Finney
