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Re: serializing the facts



John Denker wrote:

Science is not serial. It is a very high-dimensional tangled latticework
of facts. There is no natural ordering of the facts.

Example: Suppose you've just covered the simple harmonic
oscillator. Where do you go next? The anharmonic oscillator? The damped
harmonic oscillator? Coupled harmonic oscillators? The quantum harmonic
oscillator? At every moment in the classroom there are innumerable
perfectly plausible directions you could pursue. A big part of the job is
deciding what not to pursue.

Example: Imagine "sorting" the articles in the encyclopedia into an
ordered list such that "related" articles are near each other.

Teaching is serial. Learning is serial. The trick to cover a
high-dimensional topic using a one-dimensional (i.e. serial) communication
channel. There is a theorem that says you can't change dimensions in a way
that is one-to-one and continuous (the flower-pressing theorem). This is
one of the reasons why teaching is hard work and always will be.

I have to agree with you. However, I will quibble with your use of
the word "facts." I think I would have preferred "concepts" which, as
I see it, includes "facts" but much more. From your first example:
SHM isn't a "fact" so much as it is a concept, and concepts lead to
other concepts (often many others at the same time as you so well
point out).

When I said what I said, I was trying to find a quip, and I didn't
think through the implication of what I said. What I should have said
was that physics is linked, with each topic connected to at least
several others, with a logical thread connecting them all. By serial,
I wanted to give the idea that one could progress from one topic to
another and through each topic in a logical manner. I was intending
to juxtapose that with the way science is *done.* But you said it
much better. I may steal that.



Hugh
--

Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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