Returning again to Washington, D.C., a wonderful place to study dimensionality, there is an optical illusion on a wall near Union Station. I can't for the life of me figure out what the building itself is for, it seems to be just a big grey wall. Near the top there is a large painting that makes it look like you are seeing blue sky on the other side. Of course, if it's raining you can tell that it is just a painting, but if the sky is blue, it is an incredible effect. It throws me off every time I see it.
I don't know a lot of magic, but I understand that it relies on optical illusions at least in part. There is a page in the book with an optical illusion of a line with two pointy brackets pointing in at either end. The next line is the same length, but because the pointy brackets now face out, it looks longer. That and the visual effects of animation are amazing to me. It would be neat to make a little book with an image of a rotating hypercube, though I'm sure a computer could shade it in better, and convey the motion more smoothly.
I have heard that if film runs too quickly, as in the number of still frames per second, that people get nauseated. Vision is a big topic, and Michelle Imber is very into it. (She did her thesis on how people view translational, or moving, plaid.) I would be interested to know if there are any color blind people in the class, and if so, can they visualize a hpercube at all? We've been doing a lot with shading and color, and I wonder if color blindness would be a set-back, or a moot point.
I really like the pictures on pages 128-9. The bottom right most one reminds me of a slinky, or an expanded coil of ribbon. The other figures remind me of a car tire, which looks like it's being stressed in different places as it rotates. The top right most picture also reminds me of a tornado. I was in a tornado once, and dimensionality definitely took on a whole new meaning. Things were getting twisted and turned inside out like you would not believe until you've seen it. The interesting thing was that things that were perfectly safe (and not sharp) were made into dangerous things. Trees became long, sharp splinters, and curved pieces of metal were twisted and made pointy. Having had that experience makes it easier to visualize a lot of these shapes unfolded or turned inside out.
Find examples of animation and/ or perspective art in your surroundings. Pick a simply shaped object, such as a cup or a box, and draw it complete with perspective, shadow, and shading. Try to take on one of those three aspects at a time, and see how it changes your perception of the object as realistic. Try to create one of the Schlegel diagrams (start with the tetrahedron or the cube) in three space by folding paper, or create another origami shape of your own and note the geometric qualities.