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Anya Weber

After reading a couple of really interesting responses to this chapter (8), especially Andrew's and Lisa Hicks's, I feel like I understand it somewhat better. The Golden Mean is certainly a very appealing and seductive idea; I would be interested to hear more debate about how much of a role it actually plays in nature. The visual examples that Andrew linked to are pretty compelling.

I kept on thinking about computers while looking at this chapter. The fact that computers, as the text puts it, dont know what dimension theyre in, is what enables them to make fourth- and higher-dimensional images for us. Does it take a kind of blindness to the able to make such projections? Or is it just an open-mindedness? One of the biggest themes in the chapter and in the book is that you can use two- and three-dimensional approaches to higher-dimensional figures. But what disquiets me is the notion that it takes a certain blind faith to do this--a denial of important limitations, like which dimension were actually IN. I dont know why it doesn't bother me to see an algebraic equation with a "to-the-fourth'" in it, but a 3-D figure representing a 4-D one throws my brain out of whack.

I guess computers are more open-minded than people, or at least than I am, in the sense that they make their best effort to compute what you tell them to without making judgments about it. But its our judgmental-ness ("Hey wait, arent we in the THIRD dimension here?") that helps us figure out where were located, and gives us the necessary perspective (see ch. 9) so that we can create ourselves a clear picture of the universe. BUT, it's also our judgemental-ness that holds us down, keeps us from using our intuition to explore the possibility that our universe may not be all there is. Interesting contradiction.

I think another issue in this chapter and in the course is the division between algebra and geometry. Are they two sides of the same coin? Is geometry the visualization of algebra, and algebra the structural explanation of geometry, kind of a blueprint for it? I never thought about that before, but Im sure other people have. Is it something that's debated, or is it pretty cut and dry?

I thought this chapter was really dense but very cool.

Prof. Banchoff's response.

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