Russell, list, [Ben]>> The "dovetailer" keeps sounding like a powerful idea. I do remember that it has often been mentioned here, but somehow I failed to pick up a sense of what it was really about. Was there a message to the Everything-List in which it was explained so that non-experts can understand it? I'm not asking you to track that message (or series of messages) down, but if you or somebody remembers around which month it was, that should be enough for me to find it. Or is there a link to a Webpage with such an exposition?
[Russell]> Do a Google search, or a search on the everything list archives eg Google "everything list dovetailer". I know that the phrase has been used in very many posts, I thought it might take me a long time. Anyway, Bruno has narrowed it down. [Ben]>> Level III varies across quantum branchings. Level II varies across times and places along a single quantum branch in such a way that its features come out the same as Level III's features. [Russell]> This is not my reading. Level II universes vary their fundamental physical constants, eg G, alpha and so on. [Russell]> Level I universes merely vary in time and space, but sufficiently separated as to be causally independent. That's exactly what I meant. I think the terminology has gotten me into trouble here. G, alpha, etc. vary across Level II, across its various inflationary bubbles. Level II's features are the same as Level III's features. Level III embodies a variation-across-quantum-branchings of constants, initial conditions, etc., variations which Level II has across the various Level I universes or Level I multiverses (I did think that my using the word "universe" instead would get me into trouble!) which Level II "contains" along a single quantum branch. Or maybe talking about "different Level I multiverses" still implies that I'm speaking only of Level I variation, not Level II variation. Anyway, I mean variation of constants, etc. With regard to quantum branching, this kind of variation is quite like the kind of variation exhibited by hits in a repeated experiment within a single Level I multiverse, with one big difference: the pattern of a sufficiently repeated experiment's hits is s! ufficient to tell us the probability distribution for the particle in that experiment in that Level I multiverse, but is not an adequate sample of variation across a Level II multiverse, since it does not reflect variation of fundamental constants, initial conditions insofar as these might affect the constants, etc. A pattern of "hits" representing only Level II variation is just the pattern which we can't observe -- it's the pattern made across various inflationary bubbles -- they are such "hits." Anyway, given a mathematical structure distinguishable topologically or perhaps infinite-graph-theoretically, there are still variations of constants, initial conditions insofar as these might affect the constants, etc., which are reflected in variations of probability distribution for a given experiment's result across a Level III multiverse's quantum branchings of the genesis of an inflationary bubble and across a Level II multiverse's various inflationary bubbles along a sing! le quantum branch. Maybe we could approximate some such variat! ion by v arying the experimental conditions, I'm unsure how to think about that. Would it be bad for Tegmark if there were no probability distribution for a multiverse's having one mathematical structure instead of another? Maybe that's where variational or optimizational principles would come in. [Ben>> But I haven't noticed anybody here talking about variational principles or optimizational equations in any connection, much less in relation to Level IV. (While there is an obvious echo of optimization in applying Occam's Razor to Level IV's mathematical structures, this doesn't seem to involve any application of mathematical extremization, variations, Morse Theory, etc., so it seems not really the same thing. It's certainly not the only echo between a mode of inference (present instance: surmise, simplest explanation) and a mathematical formalism (extremization, shortest paths, etc.).) [Russell]> Extremum principles come up mostly in Roy Frieden's work. No-one has managed to integrate Frieden's stuff into the usual framework of this list, so little mention has been made of it, but I do mention it in my book. The hope is that some connection can be forged. I'll try looking into him. Best, Ben Udell
