This chapter I felt was helpful, but, like chapter two, it limits your audience with its mathematical aspects. IÕm really beginning to get the hang of the analogy game, which is a lot of the time the only way to grasp these ideas. I would even say that the analogies have become implanted at this point; they form automatically. For instance, I had a much easier time than I would have before the course understanding the hyperplane slicing, mainly because of the story I wrote earlier on.
As I go along in these chapters, I write in my notebook any thoughts that pop into my head, and then later go back and see if any of them seem to make sense and are worth discussing. Most of my thoughts this week were quite off the subject of the chapter, but I feel that as long as the chapter in some bizarre way got me to think about these things, the it served a good purpose, though perhaps not the intended purpose. I began wondering if there was any mathematics that was possible in the fourth dimension, that is not possible here. But I guess you wouldn't know, nor would anyone in our universe. But, something more practical and along the same lines is a question of 4D technology. Is there anything that would be of use on earth that would need to be constructed in the fourth dimension? Are there any failed or abandoned experiments/inventions that have taken place that needed a fourth dimension to build in?
Also, in 4 space, is the relationship with five space have the same limitations as our relations with 4 space. For instance, our images of 4 space intersect themselves. Would five dimensional figures projected down into four space intersect themselves in an analogous fashion?
Finally, in three space, our four dimensions (three spatial, one time) keep us from intersecting. For instance, I do not bump into someone who was sitting in this same chair an hour ago because his time coordinate has changed. How would one understand individuality in four space? The analogy that I came up with was imagining a flatlanderÕs view of the stacking up spheres on top of one anther with centers along the same line which runs perpendicular to Flatland. A flatlander would imagine them all all intersecting if their centers were all at the same point. Does this hold for four dimensions? Would the fifth dimension on four-space, also be time?