Re: physics/pedagogy of coffee-mixing

[Maurice Barnhill <mvb@UDEL.EDU>]

One of the interesting things (to me, at least) about this problem is
that if you relax the assumption that the same amount of liquid is
transferred in both directions, you get a different but equally
symmetric answer.  The magnitude of the difference between the amount of
coffee in one cup and the amount of tea in the other is exactly half the
magnitude of the difference between the total amount of liquid in the
first and second cups.  This result is easy to get algebraically,
especially after working the simpler case.  I think that you can work
out the result qualitatively by thinking backwards: if the difference
between the amount of tea in one cup and the amount of coffee in the
other is  m , what is the difference in the total amount of liquid in
the two cups?  I haven't completely the qualitative argument, however.

Another point, after reading Stefan Jeglinski's post.  The natural
language of physics is mathematics.  To explain physics to a layman
means translating the mathematics into English, or whatever.  That this
is really true is suggested to me by the many different ways we would do
this translation depending on the background of our layman, and the
different ways the same physics has been translated from one period in
history to another depending on what people were familiar with at the
time.  There is no reason to expect that translation to be any easier
than it would be to teach the subtleties of (say) French literature in
English to someone who knows little or no French.

John Denker wrote:
> At 02:28 PM 6/25/00 -0500, brian whatcott wrote:
>
> > Hehehe....John is providing an amusing illustration of the dangers of using
> >  simplifying assumptions, another favorite device of physicists....
> >
> > And that is how I show that his incisive qualititative analysis is wrong.
>
> I stand by the correctness of my analysis.
>
> > His misdirection here, is in taking "a spoonful" to mean a fixed number
> >  of molecules of tea or coffee.
>
> This was not intended to be a misdirection.  I was trying to make a point
> about physics and pedagogy.  My point does not require playing word
> games.  The solution I gave follows from the question I gave, by following
> the directions and giving each word its most ordinary natural meaning.
>
> If Brian's point is that nothing in the world is exactly perfect, OK, fine,
> I agree with that.  If his point is that no matter what you are doing, you
> can always do it drastically wrong, OK, fine, I agree with that, too.  But
> my solution holds to an arbitrarily high degree of approximation, and the
> more carefully you follow the directions the more accurately it holds.
>
> In Ludwik's model of discrete balls, my solution holds exactly.

--
Maurice Barnhill (mvb@udel.edu)
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716