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Re: Setting up problems



On Friday, Oct 10, 2003, John S. Denker wrote:
. . . .
That 'aha' moment only arrives through struggle.

I disagree. Saying that's the "only" way is a
tremendous overstatement, to say the least.

To borrow a metaphor from Pólya, that would be
analogous to saying that the "only" way to learn
to swim is to jump into the water and splash
around until you become a skillful swimmer. Maybe
some people learn to swim that way, but I took
swimming lessons, and so did most of my friends. . . .

I often tell how I learned to swim. It was by pretending.
With one leg still jumping along the ground I was using
the other leg to splash the water behind. My hands were
in usual swimming motion. One day I discovered that
I was really swimming.

What does this old story has to do with this thread?
Not much, except it confirms that there are many
ways to learn. In learning physics students often try
to act as teachers, authors and scientists. Then some
of them become better than most of us.

Many years later, as a graduate student, I was facing
a real physics problem. A mass spectrometer was
producing double peaks (a minimum at the top of each
peak). Thinking about what can possibly cause this I
guessed that the sweeping magnetic field might have
slow fluctuations superimposed on it. We replaced a
power supply and the minima disappeared. At that
moment I felt the same way as when I discovered
that I was swimming (instead of pretending).
Ludwik Kowalski