[Phys-L] computation +- math skills

[jsd at AV8N.COM (John Denker)]

Ludwik Kowalski wrote:
...
> 2) What effect does commercial mathematical software tools have on
> motivation to develop mathematical skills?

That's quite an interesting question.  As I see it, it's a two-edged
sword.  There are strong arguments in two different directions.  I
guess the executive summary is that (a) the rich are getting richer
and (b) the poor are getting poorer.

a) Mathematics has benefitted greatly from computation.  The most
obvious examples are things like the four-color proof, which could
not have been done without a computer
   http://www.google.com/search?q=haken+appel
but less-obvious effects are pervasive.  Math (of the sort that
mathematcians do) is all about proofs ... and the standard of
proof involved in /proving/ the correctness of computer programs is
dramatically higher than the old-style standards of the mathematics
community.

a') Conversely, computing has benefitted greatly from mathematics.
The algorithms you need for doing things on a computer are oftentimes
different in detail from the algorithms you need for doing things with
pencil and paper ... but only in detail.  The general thought-processes
that go into designing a fiendishly clever algorithm are fundamentally
the same.

==========

b) At the other end of the spectrum, as computers and technology in
general become more sophisticated, the more they look like magic to
the casual user.

Belief in magic is extremely corrosive to rational thought.  In a
democracy, this is a very very serious problem.

On a smaller scale, but still a topic of concern, I don't like the
fact that a lot of mass-market software tells the user what to do,
not vice versa.  The nightmare scenario of the sorcerer's apprentice
goes back ~2000 years ... not to mention Faust and probably 100
science-fiction dystopia stories per year for the last 100 years.
I want to be telling my machines what to do, not vice versa!

This makes contact with Michael E's lament that students tend to assume
the powerpoint format must be the right report format, and the excel
"chart" format must be the right "chart" format.  It is crucial to
teach the students that they are in charge ... and they have personal
responsibility for the final product.

I see this in my student pilots.  The ones that can afford fancy
electronics (GPS moving map etc.) would -- if I let them -- come to
rely on that stuff too much.  I counter this initally by asking lots
of hypothetical but pointed questions about what they would do if
this-or-that instrument failed.  Later I make the lesson entirely
non-hypothetical by turning off all the fancy stuff when they least
expect it, giving them the "opportunity" to get us home using basic
stick-and-rudder skills.  Sometimes they are initially irate about
this, but a couple days later they call me up and say "let's go do
that again".  It is easy for the flight instructor to motivate the
students, because these are clearly life-and-death issues.  It is
harder to achieve the same level of motivation in intro physics class.