A Puzzlement
Nov. 27th, 2012 09:19 pmHas it ever been determined whether Superman's X-ray vision can penetrate his own eyelids? (Question prompted by the latest JL8 comic.)
The Wrong Butler
Nov. 28th, 2011 09:12 amSome typos have more serious consequences than others. It'll be interesting to see how they get out of this one.
"Costume" Is the Word
Sep. 17th, 2011 10:52 amNormally I don't have much truck with beauty pageants, but this display of Miss Universe 2011 National Costumes is just mind-boggling. (Hat tip to ![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
nancylebov, who describes it, accurately, as a competition between Las Vegas and the Mummers Parade.)
nancylebov, who describes it, accurately, as a competition between Las Vegas and the Mummers Parade.)Our weekly geometry seminar meets on Monday afternoons. Currently, we're discussing closed geodesics on polyhedra - that is, paths that end where they began, with the property that you can't shorten them by making small changes. This past Monday, Prof. T had an idea for physically modelling the question.
She brought in a small cube with a rubber band wrapped around it, following the path of a geodesic. (There are three kinds of closed geodesic on the cube; two are fairly easy to find, and one is a bit more exotic. This was the exotic one.) She suggested the following: if you wrap a rubber band around a polyhedron in a path that isn't a geodesic, the tendency of the rubber band to contract ought to shift it in the direction of a geodesic (or else make it pop off the polyhedron altogether). T worried a bit about friction; Prof. W grandly replied, "There is no friction!" (This isn't quite a "spherical cow" moment; since we're using a physical model to represent a mathematical concept - rather than the other way around - it makes sense to ignore unnecessary complications.)
While T and W discussed this, I started fiddling with the cube, and noticed something that seemed to support her idea. "Aha!", I said, and stood up to show it to them. They gently pointed out that what I'd seen had a completely different cause, nothing to do with her idea. Feeling rather foolish, I raised my hands histrionically to the heavens, then leaned forward to gently thump my forehead on the tabletop. Then I began to sit back down.
I had been sitting on an office chair, the kind with wheels. Very well lubricated wheels. When I leaned forward, the backs of my thighs bumped the seat of the chair. As a result, when I started to sit again, the chair was no longer there.
What followed happened in slow motion, since my arms were still on the table, providing me with a bit of traction. This, I believe, is what my colleagues saw from across the table. First, half my torso vanished from view as my hands clutched at the tabletop. Then my right arm slid off the table and I pivoted around to the left. Next, the rest of my torso and my head dropped out of sight, accompanied by a soft thump. [This was my butt, hitting the floor. Unfortunately, thanks to the pivot, it was no longer directly under me.] Finally, my left arm flipped up into the air and vanished floorward, with a second thump [me, landing on my back].
After a moment's silence, W asked, "Are you all right?" From the floor, I called back, "I'm all right!", and started giggling. He came around the table and helped me to my feet. This done, he started to say something about people falling out of their chairs in excitement. I interrupted: "It wasn't excitement!" Pointing at the errant chair: "It was lack of friction!" He turned back to T and, smiling, said, "What'd I tell you?"
She brought in a small cube with a rubber band wrapped around it, following the path of a geodesic. (There are three kinds of closed geodesic on the cube; two are fairly easy to find, and one is a bit more exotic. This was the exotic one.) She suggested the following: if you wrap a rubber band around a polyhedron in a path that isn't a geodesic, the tendency of the rubber band to contract ought to shift it in the direction of a geodesic (or else make it pop off the polyhedron altogether). T worried a bit about friction; Prof. W grandly replied, "There is no friction!" (This isn't quite a "spherical cow" moment; since we're using a physical model to represent a mathematical concept - rather than the other way around - it makes sense to ignore unnecessary complications.)
While T and W discussed this, I started fiddling with the cube, and noticed something that seemed to support her idea. "Aha!", I said, and stood up to show it to them. They gently pointed out that what I'd seen had a completely different cause, nothing to do with her idea. Feeling rather foolish, I raised my hands histrionically to the heavens, then leaned forward to gently thump my forehead on the tabletop. Then I began to sit back down.
I had been sitting on an office chair, the kind with wheels. Very well lubricated wheels. When I leaned forward, the backs of my thighs bumped the seat of the chair. As a result, when I started to sit again, the chair was no longer there.
What followed happened in slow motion, since my arms were still on the table, providing me with a bit of traction. This, I believe, is what my colleagues saw from across the table. First, half my torso vanished from view as my hands clutched at the tabletop. Then my right arm slid off the table and I pivoted around to the left. Next, the rest of my torso and my head dropped out of sight, accompanied by a soft thump. [This was my butt, hitting the floor. Unfortunately, thanks to the pivot, it was no longer directly under me.] Finally, my left arm flipped up into the air and vanished floorward, with a second thump [me, landing on my back].
After a moment's silence, W asked, "Are you all right?" From the floor, I called back, "I'm all right!", and started giggling. He came around the table and helped me to my feet. This done, he started to say something about people falling out of their chairs in excitement. I interrupted: "It wasn't excitement!" Pointing at the errant chair: "It was lack of friction!" He turned back to T and, smiling, said, "What'd I tell you?"
