Reaction to Chapter 6 of Beyond the
Third Dimension
Andrew Miller
Reactions
I found Dali's conception and construction of the 30
kilometer long horse to be clever and fascinating. The idea behind the
art piece reminded me of several instances in my life where perspective
deceived me. Peculiar lighting cast on certain objects seen from a certain
point can lead one to a false mental representation of the object. Only,
in curiosity, when one investigates the unusual perspective further from
other points, can the true shape of the object be understood. It is interesting
to me how the brain creates three dimensional images from sometimes limited
virtually two dimensional perspectives. Through experience with common
objects, we can integrate color, shading, texture and contour to create
amazingly accurate representations. This biological ability is probably
linked to our need for rapid identification of objects in our environment,
which is necessary to survival. This phenomenon also explains why we sometimes
mistake unfamiliar shapes, such as a shadow cast in a dark room, for more
familiar ones, such as an animate figure. Dali exploits this evolvolutionary
trait in his art piece of the horse.
I am also intrigued by the use of perspective in art
in general, such as Dali's piece and the trompe l'oeil paintings.
I enjoy three dimensional art that provides multiple and complex representations
when seen from different perspectives. Dali's piece suggests that we can
deceive ourselves by operating under an incorrect conception generated
by a illusory perspective. We would gain a more an accurate picture by
examined multiple facets of ouselves, others or the world. The trompe
l'oeil paintings cause a similar deception that is resolved when we
examine one from several positions.
The seven views of the Clifford torus are beautiful,
but somewhat confusing to me. What exactly occurs between the fourth and
fifth picture? It appears that this is the critical shift in which the
horizontal bands become vertical, but because the shapes exands into infinity,
this is difficult to ascertain. The fifth picture seems an awkward representation.
Would it have been clearer to have shown it from a greater distance and
from a point towards which the bands did not pass?
What type of computer software is used in the generation
of 1) central projections, and 2) polygonal animation, such as in The
Hypercube: Projections and Slicing? Is the software commercial or designed
specifically for various projects within academia? It seems that contemporary
mathematics is becoming more and more dominated by the use of computers.
To what extent have mathematicians had to learn how to use computers in
order to stay updated and involved in current research? To what extent
has the development of more powerful computers facilitated a better understanding
of concepts?