[nSLUG] Calculus (Was: APL (was: On programming))

Mike Spencer mspencer at tallships.ca
Thu Oct 23 02:30:11 ADT 2003


peter> I went to university to get an education and learn more about
peter> stuff I was interested in, not just to make money.

Hear, hear!  <AOL>  But then, I haven't made any money. :-)

I've always though that one went to university to learn how to think.
Trouble is, you can't learn how to think unless you have something to
think *about*, Edward deBono notwithstanding.

A year or two of Calculus is a course in learning to think -- to
analyze problems, make mental models and do gedanken experiments -- in
a certain way that is disciplined and narrowly constrained.
Biochemistry and physiology (say) teach you to think in a somewhat
different way, especially about your own body, sickness, health, drugs
etc.

If you start as a hard science major and wander over to the Classics
Dept. and take a course on (say) St. Augustine, you will encounter a
shockingly different way of thinking about the world [1], of analyzing
problems, of modeling the world and about what to dismiss as
inconsequential before you make your mental model.

Regrettably, many professors lose sight of this objective (if they
ever saw it at all).  They may become bored with undergrads and teach
by rote; they may teach as if the only students that matter are those
who will become specialists in their discipline; may teach as if there
were only one cognitive style (theirs).  There is actually a whole bunch
of mathematicians who think, "If you can visualize it, it isn't
mathematics", despite the fact that there are many people who are
intrigued by math but can only grasp stuff that they can visualize in
some way.

peter> I finished high school in 1997...

Er, um, 1959 for me.  How come we agree on anything? :-)

jamie> You can pick up the knowledge after in "the real world" where
jamie> you have instruction manuals, calculators and no managers going
jamie> "Quick, if I left the office to go to a sales meeting
jamie> 13.2349824km away, and I travelled at 57.4km/h, would I arrive
jamie> before our competitor who has to travel 14.6172313km but
jamie> travels at 58.1km/h?  Take into account wind resistance and the
jamie> average pot hole distribution along the respective routes."

So no "normal person" ever encounters a problem for which a cookbook
solution or a computer app doesn't exist and which might be solved by
application of calculus?  So just how useful is calculus if you're not
in physics or engineering?  I'm an artist blacksmith (or an ornamental
metalwork designer, depending on whose jargon you like.)  I've hit a
couple of problems for which calculus seemed to be the right tool:

   How do you lay out and determine measurements for an elliptical
   spiral staircase?

   What's the motion of a power hammer head (essentially, to
   over-simplify, a weight on a spring connected to an otherwise rigid
   object moving sinusoidally along a vertical path) with a given
   mass, spring constant, retarding force, amplitude and frequency?

Both of these turned out to be too hard for my level of sophistication
in calculus -- eliptical integrals and Laplace transforms.  I have a
notion that I could solve both to an adequate degree of precision with
discrete math if only [Ob. Linux] I would beat up svgalib so I could
draw pictures of the results, then twiddle the code til the results
looked right.  But I would have the model-making skills from calculus
in the back of my mind to help me along.z

Or maybe I should install Maple? :-)

(Interestingly enough, I have used analytic geometry to generate the
curves for a some metal arches which classically would have been made
using segments of circles.  Circlar curves would have looked clunky in
my case.  Did it with a pocket calculator and graph paper but later
gave the equations to the Mathmatica booth guy at Siggraph and he
produced the the whole family of curves on the screen in short time.)


- Mike


[1] ...shockingly different way of thinking...

    A Dal classics prof once asked me, "What is this 'chaos' stuff I
    keep hearing about?"  I gave him my best thumbnail sketch,
    mostly based on Hofstadter's long SciAm piece and Glieck's book.
    His dismissive reply was, "Oh, that's just providence."


-- 
Michael Spencer                  Nova Scotia, Canada       .~. 
                                                           /V\ 
mspencer at tallships.ca                                     /( )\
http://home.tallships.ca/mspencer/                        ^^-^^

-- 





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