Re: 'plug & chug' problems

["John S. Denker" <jsd@MONMOUTH.COM>]

On Thu, 25 Jul 2002, Roger Haar wrote:
> >    I know this may sound strange,  but I think one
> > big reason that students should take physics ( and
> > why many college degree programs require it) is so
> > that those students have at least some problem
> > solving and some operational algebra skills.  Do I
> > care if my doctor understands Maxwell's equations
> > or even Gauss's law?  NO.  Do I care if he can do
> > a proportionality to determine a dosage?  YES.

Bravo!  Well said!  That doesn't sound strange to me!

Einstein said an education is that which remains when
one has forgotten everything learned in school.  I
think Roger is saying the same thing, in a little
more detail.

Joseph Bellina wrote:
> Interesting comment, in particular the call for proportional reasoning.
> How many people actually attend to that...how many textbooks work on it
> explicitly?  I suspect few.

Probably few.  But there are counterexamples.  I've
been blessed with tremendous educational opportunities,
the likes of which most people can hardly imagine.  I
was most certainly taught proportionality, scaling laws,
and qualitative reasoning in general.


1) For example, about the second week of class, freshman
year, we were assigned problem B-14 from Leighton, Vogt
_Exercises in Introductory Physics_, to wit:

In the truss shown,
  http://www.monmouth.com/~jsd/physics/gif48/bridge.gif
all diagonal struts are of length 5 units and all
horizontal ones are of length 6 units.  All joints are
freely hinged, and the weight of the truss is negligible.
  a) Which of the members could be replaced with flexible
     cables, for the load position shown?
  b) Calculate the forces in struts BD and DE.

=====

I'll give you a big hint:  There are two ways of doing the
problem:
 -- The clever way, and
 -- the plug&chug way, which takes about 100 times longer.

The professors were quite blunt about it:  they went over
the problem in class and explained that it was intended to
be an unforgettable lesson that being clever pays off.

Most of the class got the message.

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

2) We were told that 350 years ago some guy wrote a book
called "Discourses on Two New Sciences".  One of the new
sciences was the laws of motion.  What was the other one?
Scaling laws!  I don't recall ever doing a "unit" on scaling
laws, but scaling-law arguments were just part and parcel
of everything we did.

3) A certain eccentric physicist conducted an off-the-record
(almost clandestine) course called "Physics X" which covered
such things as bongo-playing, the true meaning of quantum
mechanics, perpetual motion machines, symmetries, conservation
laws, qualitative reasoning, how to do hard math problems in
your head, and basically anything else we could think to ask
him.  You wouldn't expect a no-credit course to have homework,
but this one did, and we spent hours and hours on it.

4) Much later and far away, when I was in grad school, we
invited Viki Weisskopf to give a colloquium on scaling laws
and qualitative reasoning.  Quite a tour de force.  We also
had classes from Michael Fisher, Ben Widom, and Ken Wilson,
who knew a thing or two about scaling laws.....
  http://www.nobel.se/physics/laureates/1982/wilson-lecture.html

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

To address Joseph's other question:  I have no clue where to
find a textbook discussion of this.  I've just flipped through
the indices in my (rather spotty) collection of textbooks and
have come up with nothing very useful.  David Goodstein _States of
Matter_ has a dozen pages on "scaling laws" at the end, but it's
neither elementary nor up-to-date (it's pre-renormalizaton-group).