[nfbwatlk] Math, Art, and Railroad Tracks

[PUBLIC RADIO 113]

MATH, ART, AND RAILROAD TRACKS:

Art Class:

When I attended Clark Community College there was a requirement for
music majors also to take art appreciation.  For a person with only
light perception in one eye and hand movement at 4 feet in the other,
the class was too challenging, so I was transferred to Mr. Stensrude’s
elementary drawing class.  Our medium was charcoal.  Technique:  I
placed one hand on an object such as a cup, an old iron with a
cloth-covered cord, or some interesting piece of hardware.  I would
then draw what it felt like with my charcoal in the other hand.  This
worked out fairly well.

One day Mr. Stensrude asked me to draw railroad tracks.  Since I have
often taken trains and have walked along railroad tracks this was an
easy thing to do.  I took a ruler and drew parallel lines and marked
between them to represent the ties and bumps.  I even drew stick
figure trees along the side of the tracks.

When Mr. Stensrude came by to check he seemed puzzled.  “This looks
like an aerial view of railroad tracks with the trees lying down,” he
mused. “The railroad tracks have to gradually get closer together as
they go away from you.”  I knew art people were a bit strange, so I
explained to him that the tracks could not get gradually closer
together because the damn train would fall off, which would be a big
drag for everybody.  Try as he might, he could not get through to me
the concept of what we call perspective. Objects that are far away
look smaller than objects up close.  Parallel lines (edges of a road
or railroad tracks, for example) appear to get closer together as they
extend out away from you until they disappear at the horizon.  “It’s a
visual concept and it’s kind of complicated,” he reassured me.

Perspective / Comparative Distance:

Another decade would pass before the concept would become clear. A
blind mathematics and physics professor at the University of Toronto
teaches a class in perspective.  We chanced to meet at a convention we
were both attending so naturally I asked him about this railroad track
thing. He explained perspective not in visual terms, but as a
geometric formula.  Simply, it is the matter of comparative distance
or relative distance.  Here is how it works:

Imagine you are standing between two trees, one on the right, one on
the left.  You and the trees are 3 points that will become a triangle.
 If you reach out and touch the trees your arms will be out straight.
As you back away from the trees, arms still extended but pointing
toward the trees, your hands will go closer together.  As you back
away from the trees the comparative distance between you and them
becomes greater, but the distance between those two trees remains the
same. As you back away your triangle goes from fat and flat to long
and narrow making the trees appear to be closer together compared to
your distance from them.    .   .

Math/Music/Art:

J. S. Bach was not only the world’s greatest composer, he gave us the
equal tempered scale.  Architects, engineers, and scientists are not
the only people who should have math in their curriculum.  Who would
have thought that a blind math professor would have been the one to
shed light on those railroad tracks.