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From: Platt%UPenn@UDel-Relay@sri-unix.UUCP
Newsgroups: net.sf-lovers
Subject: (un)countable universes
Message-ID: <4551@sri-arpa.UUCP>
Date: Thu, 25-Aug-83 14:01:00 EDT
Article-I.D.: sri-arpa.4551
Posted: Thu Aug 25 14:01:00 1983
Date-Received: Mon, 29-Aug-83 03:07:39 EDT
Lines: 48

From:  Steve Platt <Platt%UPenn@UDel-Relay>

Hypothesis: there are more universes than can be counted.

Assumptions: there is more than one universe; all this talk of "multiple
    decision-universes" makes sense.  Every "decision" made by every 
    particle is discrete (binary, n-ary, etc.  Same thing.)

1.  The person who proposed this said there are an infinite number of
    decisions.  Hence, by Cantor's diagonal argument, it is possible to
    show that the number of universes is not countable.  Number each
    universe as an n-vector <d1 d2 d3 .. d[infinity]>.  It should be
    noted that this places the count of universes in 1:1 correspondance
    with the integers -- a countable infinity.
      Now construct a new universe as follows: d1 is different than d1 of
    universe 1, d2 is different than d2 of universe 2, etc.  When done,
    we have (conceptually) constructed a new universe, one beyond the
    "infinite" number we have just dealt with.  Therefore, the number
    of universes is not countable, presuming there are an infinite number
    of decisions in each.

Of course, the last sentence is the kicker; it presumes an infinite (though 
countable) number of decisions for each.  If this seems unsatisfactory to
you, 

Assumptions:  Particles may be discrete, but time and space aren't.

2.  This means that while all "decisions" of particles such as "do I decay
    now or not" may be representable in a finite or countably infinite
    manner, decisions of the form "when do I decay", or in the case of
    particle-antiparticle creations, "when, where, at what angle and velocity
    do I appear" do not form into a neat countable model.  In fact, the last
    problem is uncountable 11 times over (R x R x R x ... x R x R x R x R)! 
    (xyz coordinates, time, xyzs velocity, xyz angle vector).

-----

Personally, I am part of the one-universe school of thought:  if it can ever
reach us or contact us in any manner (or vice versa), it is part of our
universe.

Should we save some of this for ConStellation?

Yours more in math than physics,

 -steve

platt.upenn@udel-relay