Today I woke up to a group text from Kelly, my proctor. She was telling us the clue for a tiny pink lamp hidden somewhere around the campus (whoever found it would earn points for their House). The clue this morning was "I pine to be found," which clearly meant it was in or by a pine tree somewhere (Kelly said that they wanted the first clue to be findable, so they made the clue easy).
In Knot Theory, we first learned a little about sets, then she talked about the history of Knot Theory (because someone had asked the other day). It's actually a very new branch of mathematics, less than a century old, but the basic ideas for it go all the way back to Gauss, around 1800. Halfway through this lesson, we all heard a sudden loud hissing noise. When we looked out the window, we saw that a fire hydrant on the sidewalk had broken and was spraying massive amounts of water fifty yards onto the lawn. Soon enough some workers had fixed it, and we got back to lesson. We only had time to learn about equivalence relations before lunch. I also did my quick presentation on truth tables and put up an example. It was only about a five minute presentation, so it was no big deal.
|These are all tricolorable knots.|
After lunch, we went to the computer lab to play with a knotting program called KnotPlot. Honestly, I prefer drawing my knots by hand. Even if it takes longer and requires more thinking, it seems much more intuitive to me. We went back to the classroom for the last hour to learn about link invariants--properties of link diagrams that remain the same for a link no matter how you deform them with Reidemeister moves. A simple one, the only one we had time for today, is tricolorability. If a link is tricolorable, that means that you can make each strand a color using exactly three colors so that at each crossing, either the three strands that meet there are all the same color, or they're all different colors. We tried some examples in class: for example the unknot (a simple loop) is not tricolorable because there's only one strand, so you can only use one color, not three.
At the beginning of the TA-led session, we all heard some thunder, then a few seconds later there was a huge, sudden whoosh, and it was pouring rain. I'm used to rain that builds slowly over the course of a day and starts at a trickle for at least an hour, not this. This was a sudden opening of floodgates. During the worst of it, the air was literally white everywhere that was further than about thirty feet, and branches were being blown off trees and into the windows. I was staring out the window in rapture while this was going on, and one of the boys in my class asked, "Have you never seen rain before? Like, why is this impressive?" (Oh, you have no idea.) And then, five minutes later, it stopped just as suddenly as it had started. (So strange...)
In my Arete class today, I learned passing! I could only really do it with the teacher, because the two other people who know how to juggle don't have really regular timing, but it was incredibly fun! It's so much more interesting to juggle when you also have to think about someone else throwing balls at you, and throwing balls back at them with perfect timing. It really leaves much less leeway, which I think makes it more challenging and exciting. (In the area of clubs, I've progressed to practicing two clubs at once, but I really need to work on getting the spin right--my right hand always gives more spin than my left. Also, juggling clubs is really hard on your back muscles, because they're heavy.)
After Arete was forty minutes of free time, so I took the chance to start searching through pine trees. It took me about twenty minutes, and ten or fifteen failed pine trees, before I finally found the right one. There were lots of tall grasses around its base, and I had to dig through them before I caught the glimpse of neon pink that told me I'd found it. The lamp will be re-hidden every morning after it's found, so I'll have another chance to find it again tomorrow. Wish me luck!