Changing the subject slightly: the optimal use of probabilities is
NOT always the best foundation for action.
I say this because of a news report I heard a few months back (on
NPR: sorry, I can't remember the reference), about a math student
who was very bright, and whose professor decided to play a trick on
him, because he was fed up with the student doing his assignements
in no time flat. The professor quietly inserted an 'impossible'
math problem in the guy's next assignment. The problem was
'impossible' because it had been attacked repeatedly by many
brilliant mathematicians, for (IIRC) centuries, with little or no
progress. The student then took an extraordinary length of time to
complete the assigment, but handed it in eventually, with comments
about the "trouble he had with problem 6".
As you might have guessed, he solved the problem. His comment
afterwards was that he was glad that his professor did not tell him
about the reputation that this problem had, because if he had
known, he would never have believed in himself enough to try to
solve it.
In this case, better knowledge of the probability of success would
(probably) have been detrimental to his goal.
But that is because if he had known the problem was an unsolved
problem, he would have incorrectly UNDERestimated his probability of
solving it in the allotted time....
So, yeah, if you make one mistake, sometimes making another mistake
can partly fix the problem. Two wrongs sometimes really do make a
right.
This is actually a relevant point for mind design: If a mind is going
to make probabilistic errors (which is necessary given complex goals
and limited resources), it's better if some of these errors cancel
out like this clever student's did ;-) .... In this case, big errors
regarding smaller things may partly cancel out leaving smaller errors
regarding bigger things. Novamente definitely tries to make us of
this principle..
-- Ben
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