jmccombi@BBN-UNIX@sri-unix.UUCP (08/24/83)
From: Jon McCombie <jmccombi@BBN-UNIX> 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. "For example (though this particular one need not necessarily have occurred), when God/Creator/Supreme Being was deciding to make humans, S/He could have made them in His/Her image, or the image of His/Her brother Fred. One universe (or set of universes, perhaps) has humans in God's image, the other in the image of Fred. "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. Enjoy, Jon
ntt@dciem.UUCP (Mark Brader) (08/26/83)
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., Torontoandrew@tekecs.UUCP (Andrew Klossner) (08/27/83)
"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."
A single bit stream can still be used, as long as there are only a
countable number of such irrational numbers. You simply interleave the
bit stream representations of those irrationals with the rest of the
information describing the universe. Of course, your bit stream is now
infinitely long, and so problems such as comparing two universes become
rather hard.
-- Andrew Klossner (decvax!tektronix!tekecs!andrew) [UUCP]
(andrew.tektronix@rand-relay) [ARPA]ntt@dciem.UUCP (Mark Brader) (08/30/83)
"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."
A single bit stream can still be used, as long as there are only a
countable number of such irrational numbers. You simply interleave the
bit stream representations of those irrationals with the rest of the
information describing the universe. Of course, your bit stream is now
infinitely long, and so problems such as comparing two universes become
rather hard.
Can you map a countable number of irrationals onto one bit stream? I thought
it had to be a finite number, and I don't think we can assume that a finite
number will do for all possible universes. If I'm wrong, please tell me
how to do it (by mail). --Anyway, can we not conceive on a universe that
has an analog of the Uncertainty Principle but in which physics is NOT
quantized? I would think that such a universe would generate uncountable
infinities of irrationals.
Mark Brader, NTT Systems Inc., decvax!utzoo!dciem!nttntt@dciem.UUCP (Mark Brader) (08/30/83)
Ouch, I should have read Steve Platt (Platt%UPenn@UDel-Relay)'s item before submitting. He correctly points out that bitstreams will not number universes, for a reason much simpler than mine. Mark Brader
israel@umcp-cs.UUCP (08/31/83)
Can you map a countable number of irrationals onto one bit
stream? I thought it had to be a finite number, and I don't
think we can assume that a finite number will do for all
possible universes. If I'm wrong, please tell me how to do it
(by mail). --Anyway, can we not conceive on a universe that
has an analog of the Uncertainty Principle but in which physics
is NOT quantized? I would think that such a universe would
generate uncountable infinities of irrationals.
Sure, you can map a countable number of irrationals onto one infinite
bit stream given that you can map a single irrational onto an infinite
bit stream. You just do it by dovetailing. For example, first you list
all the bit streams in order:
bit-stream for Irrational[1] b[1,1] b[1,2] b[1,3] b[1,4] ...
bit-stream for Irrational[2] b[2,1] b[2,2] b[2,3] b[2,4] ...
bit-stream for Irrational[3] b[3,1] b[3,2] b[3,3] b[3,4] ...
. . .
Then you just start at the corner and dovetail out to create the list:
i.e.,
1 2 6 7 15 16
3 5 8 14 .
4 9 13 .
10 12 .
11
to create:
b[1,1] b[1,2] b[2,1] b[3,1] b[2,2] b[1,3] b[1,4] ...
Also, I wanted to address the person who said that you can't use a
bit-mapped numbering scheme representing the decisions because one
choice of decision A may make decision B non-existent in one framework
and existent in the other. It doesn't matter that B is non-existent
in one since the places are not tied to a specific decision, but
instead to and order of decisions (in other words, the 'n' bits
preceding it should uniquely determine the decision that that bit
represents).
--
~~~ Bruce
Computer Science Dept., University of Maryland
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