energy etc. +- precise language

[John Denker <jsd@MONMOUTH.COM>]

At 10:17 AM 8/10/99 +0100, Ludwik Kowalski wrote:
> I agree with Jim. What about the "magnitude of energy" instead
> of "level of energy"?  Yes, to say "the amount of energy" is a
> trap promoting the "substance-like" interpretations.

Ahemmmm.

In in a real physics lab, people talk about
 *) The amount of water in a sponge;
 *) The amount of energy in a flywheel;
 *) The amount of entropy in an adiabatic demagnetization refrigeration stage;
 *) The amount of space in the trunk of my car;
 *) et cetera.

Indeed I have often explained the demag stage as being like a sponge:  we
use a big magnet to squeeze the entropy out of the spin system.  This makes
the lattice get hot.  We pump away the heat.  Finally, when we demagnetize,
the spin system sponges up entropy from the lattice and the lattice gets
very, very cold.

So there you have it.  It's an analogy.  Is the demag stage *exactly* like
a sponge?  No. Is entropy *exactly* like water?  Of course not.  But it's
an analogy that was well-suited to what I was doing.

One of the principles of pedagogy is that "learning proceeds from the known
to the unknown".  People walk into our lab knowing something about sponges.
 If I can proceed from there to teach them something about what my
colleagues and I are doing, I will do so, and the world will be better for it.

Apparently a few phys-l-folks have run across students so literal-minded
that any such analogy would leave the impression that physicists harvest
sponges from the South Seas in order to make their cryostats.  To that I
say, focus on the real problem.  The real problem is a manifest inability
to know what is a precise equality and what is a qualitative analogy.

In physics and in every other branch of life, we use English and similar
natural languages to express qualitative thoughts, analogies, and
metaphors.  If and when we need to make a really precise statement, we have
a language for that, too, namely the language of mathematics.

Trying to use English so precisely that you expect your students to
distinguish "amount of energy" versus "magnitude of energy" versus "level
of energy" is absurd.  That is a distinction that your students have never
made in the past and will never make in the future. If learning proceeds
from the known to the unknown, that distinction is neither a usable
starting place, nor a desirable ending place.  It's not even a sensible
step along the way.

Clear thinking is good.  Clear communication is good.  Loading up your
language with prissy nonstandard nuances does nobody any good.

=====

You say that energy is not a substance.  So what?  Empty space is not a
substance either, but 99.9999% of the population knows what I mean when I
talk about the amount of space in the trunk of my car.

By the same token, if a student is confused by hearing the word "amount"
applied to energy, the problem was not caused by vocabulary and will not be
cured by vocabulary.

================

Analogies and metaphors have enormous pedagogic value, but they also have
limitations.  Consider the following contrast:

(a) As Feynman said on many occasions,
    "The same equations have the same solutions."

(b) In contrast, note that there is no continuity in the space of all
possible theorems;  that is,
    "Roughly similar equations need not have roughly similar solutions."

Therefore it is crucial that your students be able to use analogies *and*
be able to use equations -- and to know the difference, and to know when
one or the other is appropriate.

=================

Suppose your students go out and get jobs that require them to use what
you've taught them.  They will virtually never receive tasks neatly
packaged as equations.  Indeed they will rarely receive tasks stated with
any great level of precision in any language.  Suppose the boss asks
"please find out the springiness of X".
  a) Should your alumnus refuse to solve the problem because it wasn't
stated using canonical language?  I know somebody who tended to do that,
and guess what?  She had to get a new job.  The new job pays about half of
what the old job did.
  b) Or should our hero ask the boss whether springiness refers to Young's
modulus, or isothermal compressibility, or coefficient of restitution, or
whatever?  The boss doesn't know!
  *) The job -- the *real* job -- is to go find out what "springiness"
means in this particular case, to document whatever assumptions are
necessary, to restate the question in unambiguous (probably mathematical)
terms, and then (finally!) to answer the restated question.

==================================

So.....
  Can we agree that it is more interesting to talk about what energy is,
rather than what it isn't?
  Can we agree that even imperfect sentences often convey plenty of useful
meaning?