The discussion of uncertainty reminds me of a story about Piaget that
struck a chord with me.
Apparently, when Piaget was but a pup, he had the job of scoring tests
given to kids. His job was to count the correct answers, but he started
getting interested in the wrong answers. When he mentioned to his
bosses that the wrong answers looked really interesting in their
wrongness, they got made at him and pointed out that wrong was just
wrong, and all they were interested in was how to make the kids get more
right answers.
At that point, P had a revelation: looking at right answers told him
nothing about the children, whereas all the information about what they
were really thinking was buried in the wrong answers. So he dumped his
dead-end job and became Jean Piaget, Famous Psychologist instead.
When I read the story I had a similar feeling of Aha! Thinking isn't
about a lot of Right Thinking sprinkled with the occasional annoying
Mistake. Thinking is actually a seething cauldron of Mistakes, some of
which get less egregious over time and become Not-Quite-So-Bad Mistakes,
which we call rational thinking.
I think this attitude to how the mind works, though it is painted in
bright colors, is more healthy than the attitude that thinking is about
reasoning modulated by uncertainty.
(Perhaps this is what irritates me so much about the people who call
themselves Bayesians: people so desperate to believe that they are
perfect that they have made a religion out of telling each other that
they think perfectly, when in fact they are just as irrational as any
other religious fanatic). ;-)
Richard Loosemore.
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