Le 29-oct.-05, à 00:57, Hal Finney a écrit :
> I would suggest that the multiverse concept is better thought of in
> somewhat different terms. It's goal is not really to explain where the
> universe comes from. (In fact, that question does not even make sense
> to me.)
I think we should not confuse the problem of the selection of a
(apparant) universe/history from the assumption of a multiverse (like
the quantum hypothesis) with the question of explaining the appearances
of a multiverse itself. Godelian self-reference can explain both from
numbers and their nameable and unameable relations.
BTW, although I knew this from the beginning I think I got the tools
for making this more precise. What? That my reasoning goes though ...
without comp!
Comp makes it just more "simple".
But, actually comp is just Sigma_1 comp, and comp can be generalized to
any degrees of unsolvability, but also by relativizing it to almost any
"well chosen" mathematical structure.
The nice thinks is that the modal logics of self-reference remains
sound and complete for many of those "alpha"-comp, when "alpha" is not
a too much non constructive object. But if "alpha" is non constructive,
G and G* remains sound (and different, so the theaetetic variants THEAE
still makes sense!). And G can be apparently extended as Solovay did
already show.
So my proof does not only give a test for testing comp. It gives a tool
for measuring our degree of non-computationality. In case of non-comp.
Mathematically it is a functor from some category of consistent "
alpha-computer sciences" (note the plural) into a category of possible
"physical sciences".
Technically remember comp-phys (the physics extracted by comp) is equal
to the composition of three modal transformations SOL ° THEAE ° COMP to
the logic G.
If the "real physics" (still unknown but probably LOOP GRAVITY or M
THEORY, or some other quantum theory) appears only when the functor SOL
° THEAE ° COMP is applied to an extension of G, then we would have an
empirical case for non-comp!
Hope I'm not to technical. I do think that if QM is the science of our
apparent multiverse then Modal Logic is really the sciences of the
multiverses in general. A physical theory is a set of rules which
remains invariant for the transformations allowed in a multiverse. And
comp or its generalization makes our apparent multiverse the result of
the interference of the possible (with respect the the comp hyp chosen)
multiverses.
This is just the Everett move, done in mathematics.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Tue Nov 01 2005 - 06:59:13 PST