Today's title comes from Bob Connelly's talk, "Globally Rigid Symmetric Tensegrity Structures," which is an amusing title in itself, if only because it gives me a hard-on and a headache in equal proportions. The lecture itself wasn't so fascinating, unless you have a serious matrix fetish, but it does bring me to the interesting relation between math and sex. By this I don't refer to any of those seriously weak mathematics purity test, or lame one-liners like "Mathematics: The Best Contraceptive," "Markov was into chains," or even, "Functor? I don't even know her." I simply mean that in the everday study of math, one regularly encounters objects which would give any strict Freudian a heart attack. For instance, I have long held that mathematicians study sine waves partly because they are a fundamental trig function, and partly because they look a lot like hooters. It's simple logic: if five billion breasts can't be wrong, do not an infinite number of breasts approach the divine Good in the asymptotic limit?
Related to the question of mathematics and sex is the conflict between mathematics and religion. Throughout history, many of the prominent critics of mathematics (St. Augustine, Bishop Berkeley) have been of the religious type, while mathematics has been a hot bed of atheism since even before Bertrand Russell (Don Asimov, the nephew of another famous 20th century atheist, is here at the RGI.) I guess the conflict arises because both fields have traditionally made claims to absolute truth, and just like there can only be one Absolut vodka, there can only be one absolute truth. Those figures like Plato who have tried to merge the two camps generally end up being laughed at by both. For some reason, the division between religion and math seems particular intense among the french. French thinkers are typically classified into those following Descarte and those following Pascal. A particularly poignant instance of this is the brother and sister pair of Andre and Simone Weil, who were respectively, the best mathematician and best theologian of their day; their letters make fascinating reading.
I spent a large part of today bonding with the various undergraduates at the RGI. They gave a talk at 11:30 on their two research projects for the summer: finding bounds on the energy of knots and on the surface areas of constant volume space tilings. Latter on we played Ultimate frisbee, and proved that I was slightly out of shape. Funny thing about frisbee is, though, the worse you are the better you appear; if you make enough easy catches look hard by diving for them and barely catching 'em, you just might convince someone that didn't know any better that you were really pretty good. Anyway, the undergraduates are a good bunch of kids, and more importantly, they've already been here for a month, so they know what's happening around town on weekends.
Stan Wagon -- author, Mathematica guru, problem-meister, and all around good guy -- arrived today and gave a talk. In what is rapidly becoming an RGI tradition, he embarassed me by gratitously citing some old research of mine. Then again, I did give him some preprints of my newer stuff after his talk over dinner, so I guess it's just my own damn fault if it happens again. Stan's talk was about rolling square wheels -- you can actually get them to roll smoothly if the surface you are rolling them has bumps in the right places, and for the rest of the summer I think I'm going to refer to squares as "Wagon's wheels." Stan will be giving a lecture tomorrow morning to convert the folks here to Mathematica; I have no idea how much Wolfram Research is paying him.
Laura Anderson, a friend and fellow MIT grad student, finished off the day with a simply beautiful talk on "Oriented Matroids and Differential Manifolds." An oriented matroid is what a combinatorist thinks a bunch of vectors is, and a combinatorial differential manifold is a triangulated manifold with all of the tangent spaces replaced by oriented matroids. Turns out that you can use most of the differential manifold tools with combinatorial differential manifolds, and they all work much more elegantly in that setting. Laura has been doing a lot of really cool work in this field, and her talk was justly attended by a lot of the professors (who, in general have been ignoring the grad student talks.)
Tomorrow I'm ignoring the morning talks and sleeping in.