Non-Euclidean Geometry

Warning: not proofread.

I was milling over the fact that I have written very little of substance in this blog over the past 9 months. Readership has dwindled, and I've felt very uncreative and not thoughtful at all. How unfortunate indeed! Anyway, I've decided that since I have fairly consistent and complete access to a computer here, I'm going to write down my observations with some more regularity and insight than I have been doing recently. It has occurred to me that I am witnessing a very interesting social situation in my stay in New Mexico. Namely, I am witnessing the formation of a complete "social order" of sorts. Typically, when looking at any group of people, one observes that people have differentiated themselves into semi-independent groups. It is the natural course of things. But rarely is one given the chance to observe the formation of these groups. One might suppose that a group of nerds would be less discriminating and less apt to allow these divisions to form than the population as a whole. This indisputably true. The people here are quite intelligent and the social divisions that are formed are not entirely exclusive or concrete, but they still exist. It seems to be an indisputable fact of human nature to form groups of accquaintance that act to somehow exclude other people. Even I find myself drawn in with a particular semi-exclusive group.

Another observation that fascinates me is the demographics of the people here. We see the predictably large proportion of Asians (about 35% or so) and a few foreigners from Korea, Russia, and Italy. More interesting though is the distribution of people from public and private schools. At least half of the people are from private schools, many of them from those obnoxious east-coast boarding schools like Andover, Saint Andrews, etc. It's odd because there is a definite stigma against the public schools, some people seeming to doubt that anything of academic merit could come from a normal public school. I had a particularly interesting conversation at lunch this morning. As it turns out, I've always thought that I was really bad at chess because I inevitably lose to nearly all of my friends at school. Here, I'm probably the second or third best player. I guess my distortion comes from the fact that our school has an outstanding chess team and most of my friends who play chess are on it. So, whenever I play with my friends, I always get slaughtered. We were talking about chess, so I was explaining this situation to someone, and when he heard that my friends were quite good at chess, he immediately said, "I take it you go to a private school?" I replied "no," so he continued, "Oh, so you go to a magnet school then?" When I replied "no" to that, there seemed to be this odd period of misunderstanding in which the notion of my enrollment in a public school was as confounding as n-dimensional geometry to this person. It was quite awkward, but I think it epitomized the impression of the American public education system by many people. To a large degree, it is an accurate picture, but not entirely accurate. It's very interesting because the people here aren't really any "smarter" than most of my friends. The failure of public education comes in fully converting this intellectual potential into actual accomplishment, especially for the top bracket of students. There is no question that many of the people here, even those that are not particularly insightful, are quite accomplished. Most of them attend private schools. It's quite remarkable.

Anyway, I have one last thing to discuss before I finish. We were at the New Mexico Museum of Natural History yesterday afternoon, and I saw this huge old metal sign with two big metal bars positioned in an x between the corners of the square. Later that night I was waiting for my time slot at the observatory. It was around midnight and I didn't have much to do, so I fashioned this nifty geometric proof. Consider a regular n-sided polygon. Draw line segments from the center to each of the vertices. Now, each of the interior angles of the polygon will have a measure of x = (180*(n-2))/n. The angle between each of the segments will be y = 360/n. If you translate each of the line segments to the other end of the adjacent segment, the interior angle formed will be y = 180-(360/n). Rearraging a little gives y = (180*(n-2))/n, which is exactly the same as angle x. So x = y. Since all of the line segments are of equal magnitude, translating the interior line segments in the fashion just described will produce a regular n-sided polygon similar to the original. Utterly useless, but kind of nifty. Oh, and I just thought of something. I think the new polygon will be of such a size to circumscribe the old polygon with each of the vertices located at the midpoint of each of the sides. I don't really want to prove that in ASCII text. Talk about utterly useless, but kind of nifty all the same.