X-Message-Number: 11268
Date: Mon, 15 Feb 1999 01:40:33 -0700
From: Mike Perry <>
Subject: Re: CryoNet #11264

Thomas Donaldson writes,

...>With an uncountable set of other
>universes (uncountable in the math sense, just as the real numbers are
>uncountable) then there is no difficulty with repetition of someone who
>can only be described using real numbers rather than (ultimately)
>integers (as a digital person would be). If I understand the original
>ideas behind the notion of multiple universes, there is nothing in quantum
>theory preventing them from being uncountable (again, in the mathematical
>sense).  
>
True, as far as I know. Actually, digital universes, if we consider their
behavior over infinite time and space, could be uncountable, but would have
(at most) the cardinal number of the continuum. In a reasonable sense, the
space of all these universes would have a countable dense subset, each
element of which could be represented by a finite body of information, i.e.
digitally. In the same way the real numbers have a countable dense subset,
the rationals, that can be represented digitally. NOW, there is nothing in
quantum theory (as far as I know) that rules out the idea that your space of
universes could have *no* countable dense subset yet everything (persons,
etc.) is repeated. This would be a non-digital reality, where other
properties one would like still hold. But to me this seems a real stab in
the dark. I think the digital model, in its full generality, is reasonably
well attested by the evidence, and I feel confident in advocating it, though
it could always be wrong, but you can say that about many other things too.

>Moreover, even the presence of multiple universes does not imply anything
>about whether or not those universes may be characterized by rational
>numbers --- as the notion of characterizing them DIGITALLY seems to imply.
>So far as I can see, the two ideas bear no relationship to one another.
>
I think the digital model is more general than that, see above. A real
number, for instance, can be characterized by a (countable) sequence of
rationals, which falls within the digital paradigm as I understand it. (A
Turing machine with infinitely inscribed tape would still be "digital" for
example.)
>
>For that matter, it is an assumption (perhaps or perhaps not well founded
>from what we now know) that these multiple universes will produce copies
>of us. 

I go into this issue at some length in my book. Many-worlds, as far as I can
see,
guarantees that copies of us will be produced. If you doubt many-worlds,
there are still other mechanisms that could accomplish it. In all, the
likelihood seemed
better than a tossup, "a good, fighting chance" I concluded, when you consider
that we are here, i.e. there was enough "multiplicity" to put us here,
without apparently any conscious planning. (It's interesting that, if we are
alone in our universe, it strengthens the case for large multiplicity, given
that our presence
is basically an accident.)
...
>
>That is why I do not feel personally interested in unreachable versions of
>myself which may survive when I do not. 
>
To me there are no truly "unreachable" versions. This relates to my
principle of Interchangeability. "You" extend over all identical (or
equivalently functioning) copies of you in the multiverse, regardless of the
more usual causal boundaries. These copies, of course, are continually
diverging so that "you" fission into versions that are no longer in "touch".
However, in any one universe in which immortality is possible (ours?) I
expect that, over infinite time, emulations of all possible sentient beings
will be carried out, because, properly done, it's the good and right thing
to do, as wise immortals ought to be able to see. So, you will encounter
(instantiations of) even the "unreachable" beings of other, inaccessible
universes.

In spite of all this, it's better to be frozen (I argue, again in the book),
than depend on future advanced beings to resurrect you from noise.

Mike Perry

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