[nfbwatlk] FW: Math, Art, and Railroad Tracks

Mary Ellen gabias at telus.net
Fri Aug 28 20:00:31 UTC 2009

Here's more information on the topic of perspective from Paul. Some of his
research deals with the way blind people represent perspective in raised
line drawings. It's interesting stuff.

-----Original Message-----
From: Paul Gabias [mailto:pgabias at gabiaswellness.com] 
Sent: August 27, 2009 11:23 PM
To: 'Mary Ellen'
Subject: RE: [nfbwatlk] Math, Art, and Railroad Tracks

Hello Everybody,

I teach this in my psychology of touch course.  This kind of perspective
also works in the vertical dimension.  If you are close to a building, and
you are asked to point to a bird on top and a mouse on the ground, your arm
will have to point straight up or straight down.  As you move away from the
building, if you still point straight up or straight down, you will missed
the bird or the mouse.  As you move away from the building, you have to move
your arm down to point to the bird, and up to point to the mouse.  With
sufficient distance away from the building, your arm will be pointing
straight ahead, whether you are pointing to the mouse or the bird.  This is
what can be called the tactual horizon, which is equivalent to the visual
horizon That's why you can see farther away, the higher you are in the air.
I credit the mouse and bird example to John Kennedy, my Ph.D. adviser.  He
also came up with the tree example.  He did some experiments with blind
children, asking them to point to imaginary trees with increases in
distance, and they performed just like the sighted children.

All The Best


-----Original Message-----
From: Mary Ellen [mailto:gabias at telus.net] 
Sent: Thursday, August 27, 2009 10:51 PM
To: pgabias at gabiaswellness.com
Subject: FW: [nfbwatlk] Math, Art, and Railroad Tracks

-----Original Message-----
From: nfbwatlk-bounces at nfbnet.org [mailto:nfbwatlk-bounces at nfbnet.org] On
Behalf Of PUBLIC RADIO 113
Sent: August 26, 2009 12:57 AM
To: nfbwatlk at nfbnet.org
Subject: [nfbwatlk] 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.    .   .


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.

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