From: Simon Gordon (sim_dizzy@yahoo.com)
Date: Sat Apr 26 2003 - 18:13:11 MDT
--- "Perry E. Metzger" <perry@piermont.com> wrote:
>
> the number of Level IV universes is
> countable.
You try counting all the level IV universes, lol.
Seriously if you can provide me with a link to a proof
that the set of all formal systems is countable i'd be
more than happy but in any case i think the level IV
is much broader than the ensemble of all formal
systems. Having not read the Tegmark level
classification paper yet i cannot yet be sure.
Either way i see no problem with equating sets to
universes though. A set is after all just a many which
can thought of as a whole under some property or
arrangement. Spacetime is indeed such a entity, a
collection, a many which is united, and can be thought
of as whole under the arrangment of physics.
Similiarly the elements of a set (be it a set of
anything you like) can be thought of as making up a
space comprised of those elements, they may or may not
be rules which allow those elements to interact or
demonstrate a relationship with each other, but the
point is that you have a space and so you might as
well call it a universe in its own right.
So if every set is a universe and visa versa, only set
theory can tell you how big the ensemble of
universes/sets is and the answer seems to be: as big
as it gets i.e. infinite in the absolute sense, beyond
all the transfinites.
Just because we are in a nice orderly universe which
seems to have the richness of a simple organisational
underlying structure like a formal systerm, just
because we are in *that* particular part of the
metaspace, doesnt mean that all the rest of the
universes are like that. It is clear to me that there
are some horrendously complicated and abstract
universes out there!
Keep it real.
Simon.
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