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I think Joe's analysis here is bang on. And I don't see a great
disagreement with what I said. The lesson we should take from this is
that we ought to try to teach science the way it is done, which
implies that guided discovery and constructivist ideas should be our
guidelines. If we had the time. The problem is that we have to
condense up to 300 years of discovery learning into about a year or
two, or less, so we simply cannot do it all by discovery. Deductive
methods are one way to speed this process up. Of course working
scientists use deductive methods as well. Once a theoretical
explanation has been proposed, deductive methods are often used to
make the predications that will be used to test the theory.
But I have a few other caveats. New science is usually not well
understood. Sometimes it takes decades or longer before the new
concepts are properly interpreted. The lack of a fundamental theory
of superconductivity didn't keep condensed matter physicists from
learning a lot about the phenomenon in the fifty years between its
discovery and the explanatory theory. But the scientists working with
those concepts press on in spite of their lack of understanding. They
have developed methods of coping with the problems they deal with
that I have called algorithmic, although I presume Jack would want to
use a different term. It seems to me that one of the ways we learn at
any level is by what I have called algorithms. They let us make
progress while the ideas take root and mature. And when the insight
of understanding comes, we are ready to take advantage of it.
Of course, if we could just do something about the way physics is--
taught (all in one year), and give the students the 6 or 7 years of
physics instruction in school, we could do a lot more discovery stuff
and have to rely a lot less on the pure deductive methods.
Hugh