From: Ben Goertzel (ben@goertzel.org)
Date: Sun Apr 27 2003 - 17:44:46 MDT
> > OK, but any two processes that contain me up to this point, and that
> > are indistinguishable by any experiment I could do in the future, are
> > effectively equivalent from my point of view. They don't have
> > separate, independent existence.
>
> No, my point was that many different processes which contain you
> *up until
> this point* may diverge *in the future*.
yes, that is true, of course
> > So, considering the hypothetical aliens outside my light cone -- if
> > universes with & without them are not distinguishable by any future
> > experiments I could do, then the universes with & without them are
> > equivalent to me.
> >
> > Now, we may invoke Occam's Razor ;) If I'm given an equivalence class
> > C of universes, all of which are pragmatically indistinguishable to me,
> > I'm going to assess the plausibility of a universe in C in terms of its
> > simplicity. Simpler universes in C are more plausible. The universes
> > with the hypothetical aliens in it are going to be rated relatively
> > implausible, because the aliens fail the Occam's razor test -- they are
> > extra elements, which make the hypothetical universe more complex
> > without adding any new testable properties.
>
> On the contrary, as Tegmark points out, they make the universe more
> simple. The integer 398,745,842,209,487,873,767 contains more
> information
> than the set of all integers.
Well, that depends on your definition of "information"
If you define "information content" as "Kolmogorov complexity" you may be
right...
But I think that is a flawed definition...
If you define "information content" as "total amount of pattern present"
then the set of all integers has more information content than any
particular integer, as it has (formally speaking) a shitload of patterns in
it...
Anyway, I think it's OK to maintain all these hypothetical universes, but
one needs to maintain a probability distribution over them, and one then has
a question of the "prior distribution". Is the a priori probability of a
universe calculated using the solomonoff-levin measure?
> The many-worlds interpretation of the
> Schrodinger equation is the simplest because it contains no collapse
> postulate.
Hmmm... this is a side argument, but I'd argue that the statistical
interpretation (Asher Peres, Abner Shimony, etc.) is simpler still because
it contains no collapse postulate and no "extra" universes!
> "(As an historical aside it is worth noting that Ockham's razor was also
> falsely used to argue in favour of the older heliocentric theories
> *against* Galileo's notion of the vastness of the cosmos. The notion
> of vast empty interstellar spaces was too uneconomical to be believable
> to the Medieval mind. Again they were confusing the notion of vastness
> with complexity.)"
> - http://kuoi.asui.uidaho.edu/~kamikaze/documents/many-worlds-faq.html
Actually, I tend to like the MWI, but I feel it's incomplete -- a good
thought but not quite good enough ;)
I have long wondered what happens if you take the path integrals in quantum
field theory or quantum gravity, and use an algorithmic information based
measure inside them (to weight possible universes). Maybe some
long-standing divergent integral problems are solved... who knows ;)
-- ben g
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