Re: [Phys-l] "Unlearning"

[John Denker <jsd@av8n.com>]

On 09/10/2010 03:12 AM, Dan L. MacIsaac wrote in part:

> - the incomplete nature of scientific knowledge (and what "wrong"
> means in what context)
>
> - the incomplete nature of individual learning (and what it means to
> learn something "right" in what context)
>
> - the use of idealized models to approximate natural phenomena under
> restricted domains and ranges (more nature of science; all models are
> "wrong" out of context)
>
> - the learning of developmentally appropriate models ......

That's all true, and that raises an important point, more
important than the main point of my previous note.

Ww all agree that approximations are necessary.  There are
at least three levels on which this could be discussed:
 a) Sometimes we must make tradeoffs, as when model A is 
  simpler and more convenient, but model B is more accurate.  
  I don't consider this a problem;  it's just part of the 
  job.  It's not easy, but it's just part of the job of 
  living in the world.
 b) Item (a) gets to be a problem when it is done badly,
  e.g. using bad approximations when simpler-and-better 
  approximations are readily available (as previously 
  discussed).
 c) Much, much more serious problems arise from pretending 
  that something is The Truth when in fact it's only a 
  rough approximation.

Some texts suffer from problem (c) much less than others.
For example:

 ++ When Feynman introduces the idea of energy, using the 
  parable of Dennis and the blocks, he also discusses 
  several ways in which the blocks are *not* an apt model.

 ++ Similarly, when he introduces the notion of electric 
  and magnetic field lines, he also discusses several ways
  in which the lines are *not* an apt model.

Other positive examples abound.  This is how things should
be done.  In addition to whatever domain-specific knowledge
is being learned, there is a much more important lesson in 
general-purpose _thinking_ skills, namely that it is important 
to be upfront about the strengths /and weaknesses/ of the
models one is using.

By way of contrast:

 -- I have a book here that states in Chapter 1 that
  "you must round off the value to the correct number of
  significant figures" ... and then goes on to reiterate
  this point throughout the text, without reservation,
  without any caveats or provisos.

This book's handling of this topic wins the trifecta in 
the race to the bottom:
 1) Simpler methods are available.  (This is a minor
   criticism of sig figs in particular.)
 2) The simpler methods work /better/, so there is
  not even a tradeoff involved.  (This is another
  minor criticism of sig figs in particular.)
 3) There is a _major problem_ with the presentation,
  passing off a lousy approximation as if it were
  The Rule.

Some of these problems arise from ignorance, which is 
sometimes excusable ... but sometimes not.  I'm not 
asking for perfection;  I'm just asking for a basic 
level of professionalism and due diligence.  I don't 
want to complain about minor mistakes, because those 
are inevitable.  Instead, I am complaining about cases
where even modest levels of diligence and critical
thinking would have raised red flags.

> - whether anything can be "unlearned" at all 

Habits can be changed.  For example, when people travel 
from Britain to the US, we expect them to learn to drive
on the right side of the road.  Some of them struggle
with it more than others.

The point of this note is that in my experience, students
can unlearn (or modify) an old idea more easily if they
were warned -- from the very beginning -- about the
limitations of the idea, so that they never become
unduly attached to it.