What are people's ideas about the problem of a global measure on "everything?" It seems to me that a lot of the TOE's I've seen make an assumption like "one structure, one vote." For example, if one assumes that "everything" is the set of all computations, then one strategy might be to look at the behavior of an average large turing machine and see what the computation might look like "from the inside", treating it as a simulation of a universe of some kind. But the notion of "average" seems to assume that each possible turing machine is given equal weight...how do we know they shouldn't be weighed by kolmogorov complexity or something else? Similarly, Max Tegmark's TOE involves looking at all possible mathematical structures, dividing them into equivalence classes, and then seeing what kind of universe the majority of self-aware observers will find themselves in. But again, this assumes that if one possible mathematical structure contains 10 observers and another contains 100, then an observer is ten times more likely to find himself in the second structure than the first...but why should this necessarily be the case? Are we assuming that the land of Platonic forms contains exactly one "copy" of each distinct structure? Again, isn't it possible that some other measure would make sense?
The main appeal of TOE's is that they reduce the amount of arbitrariness in our basic assumptions about reality. If all possible universes are real to observers inside them (or all possible observer-moments are real, to cut out the middleman), then we can escape the problem of "why these laws of physics and not some others?" But I think we do need some kind of global measure on the set of "everything", since everything obviously includes worlds (or observer-moments) that seem to be identical to this one up to a certain point but in which the laws suddenly break down, and we want to be able to say that this is less probable somehow (I've never been sure what people were talking about when they referred to 'white rabbits' but I think it's another version of this problem...isn't white actually a pretty common color for rabbits though? Is it an Alice in Wonderland reference?) The problem is that in introducing a global measure we run the risk of bringing back exactly the same arbitrariness that we had before--"why this global measure and not some other?" It seems to me that this is really the central problem in divising a good TOE. One solution is to say there is no global measure...this is what James Higgo believes, if I understand him correctly, and possibly Hans Moravec as well. James Higgo's picture of reality is a pretty honest look at what "no global measure" implies--basically we can't talk about the probabilities of any future events at all, and our knowledge is limited to the particular things we're experiencing in this observer-moment and the statement "all possible thoughts exist." Another solution is the "one distinct structure, one vote" idea that Max Tegmark seems to use, and possibly some others as well. A third solution might be to try to show that given some other more basic assumptions, there is only one possible measure consistent with the assumptions--this is the one I'm in favor of, and I have a rough idea about how a kind of formalized version of anthropic reasoning might provide the necessary constraints. The last solution I can think of would be to treat the many-worlds theory as a measure on the set of all computations (assuming that all computations actually end up being instantiated in some branch or another) and then work backwards to see what the properties of this measure are...perhaps it will be elegant enough that we can think of some kind of philosophical "justification" for it. A lot of people have a lot of different ideas about TOE's on this list, so maybe the global measure issue could help clarify where we all stand in relation to each other...do people have specific proposals about this? I guess the other relevant question is, what is the set of "everything" that you're putting the measure on...all computations? All mathematical structures? All observer-moments? Let me know what you think... Jesse _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com
