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[Phys-L] ill-posed questions



As several people have pointed out, you can't have a
static, uniformly charged metal disk.

This is what we call an /ill posed/ question. Such
things are extremely common in the real world. As
a general rule, well-posed problems get solved long
before they land on my desk.

In a typical textbook, the end-of-chapter problems
are intended to be well posed; there is exactly
enough information to permit a solution. There is
only one right answer ... and probably only one
feasible method of solution.

There are of course some ill-posed questions in
the book, but only by accident. What's worse,
there is no attempt to train students how to
handle ill-posed questions.

This is so unlike the real world that it makes my
hair stand on end. In the real world, you typically
have lots of extra information. That is to say,
the problem is over-determined. some of the extra
information needs to be ignored, but some of it is
super-useful. It permits more than one method of
solution, which means you can CHECK THE WORK. If the
various solutions are consistent, it increases your
confidence in the result. If they are not consistent,
it gives you a way to catch the mistake.

Sometimes the problem is ill-posed in the other
direction, i.e. under-determined. In that case
you get to go hunt up additional information.
Sometimes there are multiple answers, all of which
make sense. Underdetermined is not necessarily bad.

If the problem is over-determined or under-determined,
in most cases you can negotiate with the guy who asked
the question. This is unlike the all-too-typical
high-stakes testing situation.

Seriously, when was the last time a student walked
up to you and said "I'm confused. Here are the four
possible things that could be causing the problem.
Pick one."

For additional discussion and some possibly-constructive
suggestions for how to teach people to handle ill-posed
questions, see
https://www.av8n.com/physics/ill-posed.htm
or equivalently (with less security)
http://www.av8n.com/physics/ill-posed.htm