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[Phys-l] ivory windmills



I was struck by the following:

A certain exercise ...
... is right out of Resnick & Halliday, chapter 20 on Sound Waves
(problem #6 at the end of the chapter). So, sound is a given.

I don't want to pick on that particular exercise, but it is
symptomatic of a larger pattern, and we need to pay attention
to the pattern.

Many (albeit not all) textbooks play by the same rules as Resnick
& Halliday, namely the the ivory-tower busywork rules. That is,
the exercises at the end of chapter 20 are to be worked using the
methods of chapter 20, period. In other words, if we studied
hammers this week, almost all of the exercises will consist of
pounding nails.

If everybody knows the rules and plays by the rules, I can't
complain too much ... but I can complain some. Here goes:

I don't like these rules!

I don't like these rules, because IMHO they tend to defeat the
purpose of the educational system.

In the real world, except maybe if you are working at a McJob,
you can't assume whatever learned this week is sufficient to
solve this week's problems. Instead, you have to rack your
brain to figure out which (if any) of the various things you
have learned over the years might be helpful.

I do understand the value of the building-block approach, i.e.
taking apart a complicated concept and learning the elements
one by one (and then putting them all together) ... but we don't
want too much of a good thing: If all the exercises are narrowly
focused, it defeats the purpose of the educational system as a
whole. That's because the busywork rules have a nasty converse:
Students know the stuff they "learned" this week will never be
used again, once this week's homework is done.

To say the same thing another way, the busywork rules train the
students to look for keys under the lamp-post. That works just
fine so long as you are sure that somebody stashed all the keys
under the lamp-post.

My point remains: In the real world, in my experience, the keys
that are worth having are not stashed under the lamp-post. They
are hidden far, far away from the nearest lamp.

As another line of reasoning that leads to the same conclusion,
I disapprove of assignments where the more you know, the *less*
likely you are to get the "desired" answer. The stone-in-well
exercise is by no means the worse offender, but it does fall into
this category, because the problem is straightforward so long as
you don't know about air resistance. The exercise as stated
doesn't /say/ we should neglect air resistance, and there is no
good physical reason why we should neglect it ... especially if
we are including other small corrections ... yet the desired
answer assumes we will neglect it.

Not all texts play by the same rules. A famous counterexample
is the Misner, Thorne, Wheeler _Gravitation_ book. Consider
exercise 1.2, which calls for calculating the height of the
spring tide and the neap tide. The first time I read that, I
was completely mystified, because I couldn't find anything in
chapter 1 that explained how to do such a calculation.

Eventually I realized the question did not say "Using the methods
of chapter 1, calculate the height ...." It just said "Calculate
the height ...." You are supposed to use _everything you know_
as input to calculation. MTW plays by real-world grown-up rules,
not nursery-school busywork rules.

If you apply for a job at Google, the job interview will include
some off-the-wall questions that call for outside-the-box thinking.
If you respond by saying "we didn't cover that in class" then the
interview is over, and not in a good way. More than a few other
employers play by the same rules. For more on this, see e.g.
http://www.guardian.co.uk/technology/2012/mar/23/google-interviews-job-search-giant

IMHO we need to be asking ourselves: What is the overall purpose
of the educational system? Is it to prepare students to pass some
multiple-choice test ... or is it to prepare them to do well in
the real world?

See also
http://www.av8n.com/physics/ill-posed.htm
http://www.av8n.com/physics/thinking.htm
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