I apologize for not saying much about the Banach-Tarski talk yesterday. One of the most amusing things he discussed was scissors congruence and magic scissors congruence.
Theorem: If A is scissors congruent to B, then A is magic scissors congruent to B.
Proof: This has to be true because magic scissors are better than normal scissors. However, scissors do something very mysterious: you take a closed set and turn it into two closed set. When I was a little kid, I would cut up lots of pieces of paper and try to find the little strip that was missing because I didn’t believe this.
Amusing professors are good.
Three students showed up for Putnam practice today. That was something of a letdown after eight showed up on Monday. I don’t think we ever had more than eight. We had really hard problems today that no one could solve. Let’s hope they don’t show up on the Putnam. I want to get problems right. The difficult problems and sketchy and fast-moving solutions resulted in the following conversation:
Ryavec: You’re all smart.
I: Except for me.
Ryavec: You’re catching up.
After Putnam, I came back and found that my key no longer worked. What’s wrong with these people? We’re allowed to stay here until 10AM tomorrow, so why did they do evil tricks with the locks so soon? Anyway, now I’m in, but I doubt I can leave since I’ll probably be locked out for good. I don’t approve.
I’m less sick now. I decided to get even more sleep, and apparently 8.5 or 9 hours was enough to make me feel almost better.
I’m going home tomorrow. I wonder if anyone will recognize me. I wonder if I’ll recognize them. (With probability 1-epsilon for almost any epsilon>0, the answer will be “yes” to both of these wonders.)