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. ---------------------------------------------------------------------------- Questions * 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? ---------------------------------------------------------------------------- Links * Several photographs of trompe l'oeil painting by contemporary decorative artists for commercial and residential interiors * Examples of computer rendered art and animation * Mail the author, Andrew Miller