It Seems We Have a Problem

He got frustrated with it. Don't let him get frustrated with you.

Today started off slowly, or at least sluggishly, as I dragged myself out of bed at 7:45. I had a small breakfast, then walked over to Knot Theory with the rest of my class. We continued what we were doing on Saturday, which was learning about the Jones polynomial. We tried to prove it was a link invariant, but instead found that it wasn't actually an invariant. Our teacher said that this intermediate step was called the bracket polynomial, and we'd learn the full Jones polynomial after lunch. Josh, who sits next to me, was trying to solve a four-by-four Rubik's cube, which wasn't really working for him.

Because today was a preview day for potential Vanderbilt students, the dining hall was making all of the best food. I had four-cheese grilled cheese with amazing tomato soup and mashed potatoes that were just wonderful and perfect. I sat with some people from my class, and we got sidetracked into an interesting philosophical discussion. Then one of the girls who was there said that thinking about that made her head hurt and she wanted to talk about something else. (This was disappointing to me, because I thought we were having a fascinating debate.)

This was what she wrote when the equation wasn't working out.

In class, she gave us the equation that combined the bracket polynomial with the writhe of a knot--another property that wasn't invariant in the same way that the bracket polynomial wasn't, so when combined in the right equation they sort of cancel out and become invariant. The equation is: X(L)=((-A^3)^-w(L))[L] where X(L) is the Jones polynomial of the knot L, w(L) is the writhe of the knot, and [L] is the bracket polynomial. It's a rather complicated equation, so when she asked us to use it we weren't all that surprised that our answers were wrong. However, upon double- and triple-checking my algebra, I became convinced that it was the equation that was wrong somehow. When I showed her my work, she looked at it for a while and then agreed that the equation should be working, but wasn't. She made quite a few revisions to the premises to try to fix it, but I pointed out that when she did that she was using two different knot crossings in the different parts of the equation, and so it was invalid. She stared at the equations on the board for a while, then said, "Looks like it's about time for a ten-minute break!" She promised to figure out what was going wrong during our break. When we came back in she seemed to have fixed it, but then I saw that she was using positive orientations of crossing with negative ones when she shouldn't be. Eventually, we found out that what had gone wrong was in the very beginning, when she had defined positive and negative crossings for us. She'd switched them, and so when she switched the positive and negative definitions back to what they should have been, everything worked perfectly. Then afterwards, she came up to me and thanked me for arguing with her when I saw something that didn't make sense, because otherwise the whole class would have been completely wrong about everything for the next two weeks. That was nice, because many teachers don't appreciate students arguing with them or correcting them.

Today was also the first day of my new Arete class, Improv. We played a lot of theatre games, which was fun, and I'm glad Miranda's there, because she's really the only one there who I know and talk to (though hopefully that'll change as I get to know people). Also, I'm told that this week, starting tomorrow, there will be a dinosaur egg hunt, similar to the lamp hunt last week. I'm looking forward to that.