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| Authored by: Anonymous on Thursday, May 16 2013 @ 09:08 AM EDT |
First anon here. Not to necro, but there are still only a
finite number of states. It's a finite set of states. We
have no idea what state it will end up in, but there are
still only a finite (but VERY large) number of states it CAN
end up in.
I believe you're trying to talk about the probability that
it will end up in any one state. Even then, there are no
infinities unless you impose some arbitrary process on it.
For example, you could imagine the selection of one of those
end states as (for all our purposes) the universe generating
a random number between 0 and 1, and then using a
predetermined mapping from the infinite set [0,1) to end
states.
But that seems rather contrived. In reality, we don't know
anything, and one end state occurs. Even though we have no
idea which end state will occur, we can (in theory)
enumerate all the possible end states that can occur,
because the number of possible states is limited by the
combination of all the possible states of all the particles
in the machine. Granted, we would certainly not be able to
do so in any useful time frame and most probably not even in
the lifetime of humanity. But it is possible, given enough
time. And that's how you know it's finite.[ Reply to This | Parent | # ]
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