18th
Man, I work a lot less these days.
It’s pretty sweet! And pretty necessary, because I’m going to Real Grownup Grad School next year and want to take my breaks while I can.
Mathematically, I’m really into braids right now; doodling them in class and braiding a friend’s hair during the department’s weekly lunch talks. I’m discovering that lots of braids that look good on paper don’t look good in hair because of the way the strands slide around each other.
I’m not totally sure how to define a braid. I assume there’s a mathematical consensus on this that I could look up, but I want to decide first what I think is braid-y. One characteristic I’m sure of is that it involves some number of strands which cross over and under each other. And this is equivalent to having some number of closed loops that cross over and under each other, since you could just glue the two loose ends of each strand together outside of the braid.
I’m also sure I want a braid (at least my mathematical braids, for now; hair braiding is more of a mystery) to necessarily have each strand alternate going over and under other strands—I mean that no strand can go over two other strands without going under some strand in between them.
The third property I could go either way on, so far. Something you might not know about your everyday 3-stranded braid—something I didn’t know until the past few years—is that no two of the strands are wrapped around each other. If you pulled out any one strand, the other two would lie next to each other or one on top of the other, never twisted. I think I never noticed this because hair braids are usually all one color, but try it with three colored ribbons or strings and you’ll see it’s true. The standard, perfectly symmetrical ways that I learned at summer camp to make many-stranded braids all have this property, too, but other ways I’ve braided hair or can imagine braiding hair don’t.
