From: dph1jg%tuda@newcastle.ac.uk (J.P.Gardner)
Subject: Re: Pair-allel Universes
Organization: Yale CS Mail/News Gateway
Date: Sat, 12 Dec 1992 16:58:41 GMT

From: lower-tony@cs.yale.edu (Tony Lower)
>  Manx signals Mike for a ginger ale, and wanders off into the corner.
>There ensues the sound of wood on wood, and some grunts.  Pretty soon,
>he is back, pushing a twenty foot tall stack of soap-boxes.  He sets
>it in the middle of the floor, takes a ladder, and climbs to the top.
>
>  "OK... just my standard dig on parallel universes as portrayed by
>SF authors... and it goes like this:
>
>    AN INFINITE SET DOES _NOT_ NECESSARILY CONTAIN EVERYTHING!
>
>  "It's much easier to see with numbers.  The even numbers (those
>divisible by 2) form an infinite set.  According to the way SF
>writers deal with universes, we can therefore prove that every
>conceivable number is a member of that set, thus showing that
>1,3,5, etc., are even.
>
>  "Therefore, it is a fallacy to say that in an infinite number
>of universes, ANYTHING must have a representation.  It is quite
>reasonable to assume that there are some constants: the laws of
>physics, perhaps.

The Space Cadet says, "Well it is true enough that an infinite
set does not _necessarily_ contain everything, but it _can_ contain
everything. An infinite set of objects distributed according to
some probability distribution will contain everything that is
possible, no matter how improbable, not only once, but an infinite
number of times. Thus, to use jargon to give an example, an 
infinite set with a gaussian distribution with sigma of 1.0 will
contain an infinite number of 1000's, and an infinite number of
1000.1's etc., even though any finite subsample of the set 
is very unlikely to contain a 1000."

"Something similar to the SF multi-verse convention was proposed by
Ludwig Boltzmann in the 1850s as a theory of cosmology. Boltzmann is
the father of the science of thermodynamics, which deals with
probability distributions. An infinite universe containing particles in
thermodynamic equilibrium (a state of maximal entropy) will contain
"patches" of order (where entropy is temporarily low, but increasing).
He proposed that we happen to be living in such a "patch."

"This was before the discovery of the expansion of the universe, and
even before it was known that the "spiral nebulae" were galaxies
external to, and much like our own. In addition, an infinite, static
universe causes problems in general relativity, although it is possible
with the addition of a "cosmological constant", which corresponds
physically to a negative energy field holding things apart from
gravitational collapse."

"In any case, Boltzmannian cosmology is very unsatisfactory as an
explanation for the universe -- by Occam's razor we have _much_ better
ones, like the Big Bang. The SF convention, of course, deals with other
universes being separated from ours not by simple three dimensional
distance, as they would be in Boltzmann's universe, but by distance in
a fourth dimension."

>  Manx looks down and gets a sudden case of acrophobia.  He clutches
>the suddenly teetering pile of boxes.  "Now HOW am I going to get
>down?"

The Space Cadet ignites his rocket backpack, flies up and helps Manx
back to the ground. On the way down, the exhaust burns up the soap
boxes.

"While I have a lot of respect for SF writers who acknowledge the
consequences of the laws of physics regarding such things as FTL
travel, I can forgive them for using the standard conventions in order
to tell a good story. It only bothers me when there are people out
there that actually _believe_ that FTL just takes new technology, and
not a fundamental restructuring of our understanding of the universe."

"Completely changing the subject, there is nothing like a deadline to
help you get something done. Yesterday I mailed off a paper to the
Astrophysical Journal. If it is accepted, it will be my first real
professional publication. I'm leaving tonight for two weeks in the
US for Christmas vacation. Happy holidays, everyone. See you next
year."

With that, the Space Cadet heads out the door into the snow.

--The Space Cadet
Jon Gardner, University of Durham, Physics Dept.
dph1jg@tuda.ncl.ac.uk

Newsgroups: alt.callahans