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From: ntt@dciem.UUCP (Mark Brader)
Newsgroups: net.sf-lovers
Subject: Re: numbering alternate universes
Message-ID: <324@dciem.UUCP>
Date: Thu, 25-Aug-83 18:01:52 EDT
Article-I.D.: dciem.324
Posted: Thu Aug 25 18:01:52 1983
Date-Received: Fri, 26-Aug-83 11:15:20 EDT
References: <4486@sri-arpa.UUCP>
Organization: NTT Systems Inc., Toronto, Canada
Lines: 44


    Jon McCombie writes:
    
    A  friend  of  mine, Mike Davis, proposes the following method of numbering
    multiple universes.  I submit it for our collective consideration. 
    
    "At virtually every point in time, some event is  occurring  which  can  be
    represented  as a binary decision.  Every time such a decision is made, new
    universes are made, one for each possible outcome of the decision. 
       ....
    
    "Each  universe,  then,  can  be  described  by the unique bit stream which
    describes the yes/no decisions which went into making the universe."
    
    Unfortunately, that  makes  for  universe  whose  descriptive  numbers  are
    infinitely  long.   Then again, this is a necessity in this description, in
    which there are an infinite number of alternate universes. 

You cannot assume that all decisions are binary.  The various constants of
nature had to be chosen (by God, or whomever), for instance, and they are
in general irrational numbers.  The entire irrational number would have to
be included in the universe-description, but that requires an infinite number
of bits, so you can never get to the part that represents the next decision.

(This result is related to Cantor's theorem that shows the real numbers, and
hence the irrationals, to be more numerous than the rationals.  If anybody
didn't know that theorem and is interested, consult math books at about the
first-year-university level or better yet read Douglas Hofstadter's "Godel,
Escher, Bach: an Eternal Golden Braid".  Look under Cantor.)

Perhaps it would be sufficient to "number" each universe with a FUNCTION
mapping real numbers to real numbers; I believe these are more numerous
than real numbers.  But I would hate to define the mapping.

Incidentally, a novel I found very good which is precisely concerned with
parallel universes with differing constants of nature (specifically the
constant describing the strength of the "strong nuclear force") is Isaac
Asimov's "The Gods Themselves".  According to his autobiography, he started
it after hearing another writer (who wanted to make some example concrete)
speak of plutonium-186; Asimov remarked to him, "You know there's no such
isotope, but just to show you what a real SF writer can do, I'll write a
story about plutonium-186."

Mark Brader (M. Math), NTT Systems Inc., Toronto