"Shadows and Structures"
Like Michelle Imber suggested last week, I'm going to skip the book report deal and just get to the point(s).
First of all, I have a nitpicky question about counting (for exmaple) the number of edges on a square. The author says that each corner has two edges. so two edges times four corners equals 8. Divide that by two (because each side is counted twice this way) and you get the correct number (4). Fancy this: a square has four corners of different colors (red, blue, green, yellow). Now, for every point on the square, color it the same color as the nearest vertex. There will be two red half-edges, two blue half-edges, two yellow half-edges, and two green half-edges. Then you could say that each vertex is connected to two half edges, which total to one edge per corner. One edge/vertex * four vertexes = 4 edges. Maybe this is silly, but I think it's a better way of thinking about it.
OK, let me get this straight: if a three dimensional sun cast light on a hypercube, we would see a cube; and if a four-dimensional sun cast light on a hypercube, we would see a figure with 32 edges? Is this right. It's kind of a confusing point. I'd like to hear more about the relationship between slices and shadows. what are their similarities? What are their differences?
The data visualization section is very interesting. A good exercise would be to take a set of given data, and graph the data using several different slices in order to come to a better understanding of the data. Wow, that was vague. Hopefully, I will edit this later tonight and be a little more specific...