Re: [Phys-l] ill-posed problems

["John Clement" <clement@hal-pc.org>]

If you really want to know about the pedagogy of "rich context" problems
read the papers by the Hellers at Michigan, and also look at some of the
work done by the U.Mass PER group, Amherst.

John M. Clement
Houston, TX


In the context of a Su Doku puzzle,
On 03/15/2010 07:07 AM, chuck britton wrote:

> Does this in fact relate to the CT image generation?

Yes.

It also relates to seismology and a ton of other things.
All of these can be formulated as _deconvolution_ problems.

> 	(JD's example below is four-fold degenerate?)

Yes.  Constructed to be so.

=========

Why did I bring this up?  Because we need more pedagogical
examples of ill-posed problems.

Real-world problems are usually ill-posed.  For example,
in the classroom, when was the last time a student came
up to you and said "I'm confused, and here's exactly
what I'm confused about....."  In any non-menial job,
the job description itself is ill-posed.

Outside the workplace, the situation is the same.  The
question of what shoes to buy is ill-posed ... not to
mention the question of whom to vote for.

Yet in almost all the textbooks, the end-of-chapter
problems are all well-posed.  There is precious little
discussion of
 -- how to recognize problems that are overspecified
  or underspecified
 -- systematic procedures for dealing with such problems.

In this forum, the recent discussion of what happens
when you push on a gas with a piston went on for *days*
before John M. sorted out all the ways in which the
question was ill-posed.

I really like yesterday's load-sharing problem.  It is 
an easy-to-state 100% genuine problem.  The physics is
easy, so it is easy to have a discussion of ill-posedness
without having to dig through any arcane physics to get
there.

The Su Doku problem doesn't require any physics at all,
but I had to tell a long story to connect it to real-world
applications.

It would be nice to have a collection of good pedagogical
examples of ill-posed problems.  If anybody knows of such
a collection ... or who has a favorite example to share 
... I'd very much appreciate hearing about it.
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