Re: serializing the facts

[John Denker <jsd@MONMOUTH.COM>]

At 08:54 PM 8/19/00 -0400, Ludwik Kowalski wrote:
> Quoting Hugh Haskell:
>
> > >>we say that physics is no more a pile of facts than
> > >>a house is a pile of stones
>
> I also like this, and the phrase before it:
>
> >>They [students] need to understand that physics is a serial topic
> >>where each level is built on the previous one and that there is a
> >> logical thread that holds it all together.

I like the first statement much more than the second.

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.