[ExI] a doubt concerning the h+ future
Lee Corbin
lcorbin at rawbw.com
Sun Jun 3 21:24:53 UTC 2007
John Clark writes
> Stathis Papaioannou Wrote:
>
>> There are vastly fewer copies of me typing in which the keyboard turns
>> into a teapot than there are copies of me typing in which the keyboard
>> stays a keyboard
>
> If there are indeed an infinite, and not just very large, number of
> universes and if the probability of your keyboard turning into a teapot is
> greater than zero (and it is) then what you say is incorrect, there is an
> equal number of both things happening.
It is true that the concept of *cardinality* in mathematics answers
the question "how many".
But "how many" is not the appropriate concept to use when discussing
slices of the Everett metaverse, or the sizes of plane figures, and so
on. For example, there is a one-to-one correspondence between
the number of points in a small circle and the number of points in
a large circle, and so their cardinality (how many points) is the same
But their *measure* is not!
We therefore discard cardinality ("how many") in most cases dealing
with infinite sets in this kind of discussion. Instead, we adopt the
language of measure theory.
We say that the measure of universes in which your keyboard remains
a keyboard is vastly greater than the measure of universes in which it
turns into a teapot.
Lee
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