I don't know if in the hypothesis of simulation, the conflict of Countable
and Uncountable has been considered.
When we're talking about a machine with an infinite power of computation,
we're considering a TM which has a countable number of states, even if it's
running an undecidable problem to produce the infinite possible outputs and
even we're considering time to be infinitely compressed to allow for the
infinity of the power of our machine, at the end the possible states of a TM
is Countably infinite.
But as one might notice we have some continuous and therefore Uncountable
parameters in our universe, like the measures of distance which are not
reducible to countable ones even considering the concept of precision. They
are naturally Uncountable.
Now the question is: can that kind of infinitely powerful machine simulate
this infinite reality?
Am I missing a point?
--
Mohsen Ravanbakhsh,
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Received on Mon Mar 05 2007 - 04:33:45 PST