Doing Math
David L. Heiserman
I didn't actually dislike math through the primary and secondary grades. It's
more like I was passive about it. I completed the work, usually paid attention
in class, and got decent gradesnot really great grades, but a bit above
average. The passive nature of my early math education is reflected by an
incident in a high school plane geometry class. The teacher was an older,
nearretirement guy whose vision was getting really bad. So one day, around six
or eight of us decided to have a party during class. We each brought a bottle of
Coke (still in the greenish bottles in the late 1950s), and a handful of
peanuts. Luckily, someone thought to bring a bottle opener. Yes, we opened our
Cokes, passed the peanuts around, and enjoyed a party while that faithful old
math teacher droned on about the areas of triangles or some such thing. I had joined the Navy immediately after graduation from high school. It was
during that time that I completed correspondence courses in college algebra and
trigonometry. Why? I had gotten a serious opportunity for a fullride college
scholarship, and thought I might be able to get a bit ahead by passing some
proficiency exams in math, and going straight to calculus. My plan worked, at
least the startup part. The problem was that I was
taking engineering physics at the same time. Too much for someone who was clueless about
good study habits. So I switch my major to psychology. I was doing okay with the psych courses, and didn't need any more math except
one semester of statistics. And I flunked it! Now, that's just wrong! So I had
to repeat the stat course ... and I flunked again. So much for college. I
gathered up my stuff and simply walked away from school and my full scholarship. I have never made amends with statistics. I've had to mess around with mean,
median, mode, and the bell curve from absolute necessity. And just last week, I
finally got an intuitive grasp of the standard deviation. It seems that the
whole world that interests me is embracing more concepts requiring statistical
analysis. So I will probably have to get my head straight and get with the
program. Maybe I should write a book about it. My first postcollege job was managing and teaching basic electronics at a
franchise radio and TV repair school. It was fun and I learned a lot about
electronicsabout one day ahead of my classes. But the math bug made a nest in
my soul about that time. Whereas I'd spent most of my life with a passive
attitude toward math, I became intensely interested in the derivation of some
equations for the transport of ions across semipermeable membranes. It was a
recent development in biophysics; but more important for me, it demonstrated the
mindset that drives mathematiciansapplied mathematicians, in this case. The
discovery was already done, and the guy got a Nobel Prize for it. I was just
driven to go through the process of deriving that equation from what was known
about ions and semipermeable membranes. It is a fantastic feeling to see a problem that needs to be solved, knowing it
is just a bit beyond your grasp at the moment. Doing math, theoretical and
applied, is quite inexpensive and no one cares how many degrees you are using
for wallpaper. It's the results that matter. Perfect freedom. I eventually solved the problem. A year or so later, I was back at my
university, but as a lab technician in pharmacology. One of the profs was
conducting graduatelevel courses in nerve cell conduction; and, being more of a
pharmacologist than biophysicist, he needed help with explaining ion transport.
So he offered me several hours of graduate credit to take his classes and
actively participate when the topic of the week was ion transport. So I flunk
out of undergraduate school, but accumulate some 4.0 GPA graduate work. Go
figure. My next step in my math life was to take a parttime position teaching
trigonometry at a private business college. That was fun! I was back into
teaching and learning a lot of cool new things about trigonometry. I did not
have proper credentials for teaching at an accredited college, even a private
one. But it seems there was a shortage of collegelevel math teachers in the
area, so the requirements were waived. I enjoyed teaching and apparently the
students enjoyed my classes. Someone must have been impressed because I
eventually conducted courses in analytic geometry and calculus. I had taught myself the fascinating subject of analytic geometry, as it was
called in those days. I think they call it something like algebraic geometry
these days and have lumped it into something called precalculus. But no matter
what they want to call it, combining trig, geometry, elementary calculus, and
perhaps some ... whatever. It's fun to learn, fun to play with, and fun to
teach. One day I got an offer I couldn't refuseteaching ordinary differential
equations at a state college. This was just three nights a week, but I would do
about anything to teach ODE. It was an amazing and fulfilling experience. I got
there with no formal credentials, but with experience, a network of people who
knew my work, a love for math, and a knack for teaching. (Incidentally, I was
teaching myself the material about a week ahead of the class. So I was acutely
aware of what was going on in the minds of my students who were likewise facing
the material for the first time. It was a very productive synergy.). After leaving classroom teaching altogether and forever, I had more time for my
freelance writing. I did one rather unusual math book, Experiments in Four
Dimensions. It was basically about geometric translations in four dimensions.
Now that isn't a strange thing these daystranslations in four dimensions is a
required skill for game developers. Anyway, I am proud of the topic and the
algorithm I developed for viewing 4dimensional objects in 2dimensional space
(on a sheet of paper). However, I am embarrassed with the way I implemented it.
Maybe I will revise it someday, leaving out all of the unnecessary solution
procedures and assuming the reader has access to a computer.
Note: It occurred to me just a moment agowhile finishing the previous
paragraphthat it would be so much fun to do coordinates for 3D projections and
construct ballandstick models of fourdimensional objects as they would appear
in threedimensional space. The moral that story here that the best ideas usually come when actively
engaged in the subject ... and not from formal brainstorming sessions. Don't get
all wrapped up and led astray by popular attempts to systamize creativity.
That's like trying to milk the grass before feeding it to the cow.
