On Sun, 9 Nov 1997 Hal Finney <hal@rain.org> Wrote:
>Believing otherwise is tantamount to believing in Penrose's
>mysticism regarding the non-algorithmic capabilities of minds.
Penrose's argument is that if people are algorithmic like a Turing machine
then we couldn't jump out of the system, look at ourselves and find the
inadequacies in the system as Godel seemed to do it his proof. I think at the
very lowest level we are the equivalent of Turing machines, however the
axioms are numerous but ridiculously simple at that level, "If you're in
state A and see a 0, change it to a 1, go to state B, and move one square to
the left". I don't think we can jump out of THAT system and change the basic
operating principles that Turing found 60 years ago, but that very low level
can't be the level the conscious mind operates. Something must be running on
top of that machinery, something that has few if any axioms and so is not a
formal system.
Minds are problem solvers and I don't think non-algorithmic problem solving
is necessarily mystical. I doubt if we use axioms like "if A and B then C"
very much, more important are billions of heuristics like "if A and B then
usually something close to C".
Good advice is also important like "If something happened many times in the
past it will probable happen again" or " If you have several possible
solutions to a problem but not enough information to prove that any of them
will work then try the simplest one first" or "if a rule of thumb seemed
like a good idea but is not solving anything, then dump that rule and look
for a better one". We can jump out of THAT system.
If the mind is not a formal system, at least at the highest conscious level,
then Godel does not apply to us or to a intelligent program running on a
computer.
>To the extent that some randomness is needed, then an algorithmic
>pseudo random number generator ought to be good enough.
I agree, if a pseudo random number generator is not good enough then
something very weird must be going on.
John K Clark johnkc@well.com
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