CHAPTER 6 began with the highly ordered picture of the Taj Mahal. Even the water in the foreground of the picture was perfectly calm allowing the viewer an almost exact reflection. Because the surface of the water is horizontal to the foundations of the building, the reflected image lies semetrically opposite. If the water was in fact a big mirror that could be shifted to alter its angle, one could achieve different reflections of the building. If one was to attempt to draw this picture, including the reflections in the 'mirror', it would become very complicated when one altered the angle of the 'mirror.' For example where would you put the vanishing points and the horizon line. If you were to take this one step further and reflect the building (or perhaps something a little less complicated) a second time you would be faced with further complication as to the wherabouts of the horizon line and the new vanishing point. This could be made into an exercise. An exercise might be if the reader were to use the fixed mirror in a bathroom and a portable one and then attempted to draw what was seen through them both. This would ask the reader to deal directly with the problems of distortion, reflection and placement of vanishing points.
The other interesting sub-chapter was "Animating the Hypercube" this begun with Eadweard Muybridge's animated pictures. Here we notice, periodical slices of Muybridge walking up hill. He certainly pioneered the concept of film making but, what is really interesting is; he was the first man to prove that a horse in full gallop does not have any hooves touching the ground. Before his time slices were invented, it was suggested that; a horse did at some point in its stride have no hooves on the ground. What was baffling was the notion that the weight of the horse could be held off the ground intermittently during a gallop. But, when you think about it when we run we spend a large proportion of our time in the air. Perhaps in the land of the fourth dimension upon the advent of a time slicing machine, similar breakthrough's were made.
Prof. Banchoff's Response