I guess I wasnÕt the only one whose favorite chapter so far was NOT #4. It was just so.....dry. IÕm not sure why. Shadows are nifty, after all. So are structures, if weÕre going to get technical about these matters. Perhaps my tired brain was allergic to the forb and pine pollen.
The one aspect of this chapter which completely pleased me was the demonstration of the drawing of a hypercube based on its shadows. This was such a neat way to get that ever-more-familiar structure down onto a sheet of paper. I also liked the stuff about coloring simplexes. How many smaller figures in the big figure can be a pretty interesting question, and I hope to work at least a bit more with this idea to get to understand it more fully.
I found something about the simplexes confusing, though--I didnÕt see much of a progression between the various dimensions. I mean, of course I canÕt SEE beyond the first 3 Ds, but with the shadow-hypercube at least I can conceive of its being looked at several different ways; it really looks like the shadow of something higher-dimensional. With the 4- and 5-simplexes, though, perhaps because we are only choosing one point not in line with the preceding ones to connect them to, the complexity of the figures seems to grow much more slowly. Is this just because triangles have 3 sides,while squares have four? Prisms and pyramids seem to me about equally confusing in their higher-dimensional projections, so why are simplexes so--uh, simple? (Not that IÕm claiming to be an expert in their field.......)
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