On Mon, Aug 13, 2012 at 8:09 PM, William R. Buckley
> Consider that the Turing machine is computational omniscient[...]
Turing's entire reason for inventing what we now call a Turing Machine was
to prove that computational omniscience is NOT possible. He rigorously
proved that no Turing Machine, that is to say no computer, can determine in
advance if any given computer program will eventually stop.
For example, it would be very easy to write a program to look for the first
even number greater than 2 that is not the sum of two prime numbers and
then stop. But will the machine ever stop? The Turing Machine doesn't know,
I don't know, you don't know, nobody knows. Maybe it will stop in the next
5 seconds, maybe it will stop in 5 billion years, maybe it will never stop.
If you want to know what the machine will do you just have to watch it and
see, and even the machine doesn't know what it will do until it does it.
John K Clark
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