[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