HALT!

A quick addition to last entry. Only, it's actually a separate entry.

So today (just now, actually) Rebecca gave her second lecture on computability, this time on Turing machines.

ADan: So these Turing machines, they actually exist?
Rebecca: ADan, does anything with an infinite tape exist?
ADan: Your mom!

At one point she used "HALT_TM" to represent a certain language, and I suggested she should shout "HALT!" whenever she wrote this, but she didn't. So I shouted it once.

...yeah, that's really it. Now to actually get to work on my psets.

-Sniffnoy

Prime prime and omega cockroach

So today in Number Theory Glenn wrote down the correct definition of prime on the board - almost. (It may not have been him who suggested it; I arrived a bit late and it was already up when I got there.) It was that π is prime iff ∀ α,β, with αβ=π, α or β is a unit. Of course, eventually someone pointed out that their definition doesn't exclude units. So Glenn says, Is 1 prime by this definition? Yes! But we agreed earlier that we *don't* want 1 to be prime. "Your mother would be very unhappy if she found out we were teaching mathematics like that."

So of course today Glenn, going along with this, also introduced an alternate definition of "prime" - i.e. the standard one - and, since it was an alternate definition, he put a little prime mark next to it - so it was read as "prime prime". Yay! And he said how what we were defining as prime would normally be called irreducible, but oh well, we'll just go ahead and call it prime anyway.

So yesterday Issao gave a mini-course on generating functions, and before it, Tan Dan had written on the very top back board, "Your MOTHER was a generating function!" And somehow, this had not gotten erased before today, and so Glenn ended up revealing it during lecture and it took him quite a while to realize what was so funny. Also, someone had added "-Connie" to the end, and he actually went and asked, "Connie, did you do this?"

So today in Zeta, Rohrlich introduced the p-adic Hurwitz zeta function - although he gave absolutely no explanation of why it was defined that way (the definition looks nothing at all like the complex Hurwitz zeta). Presumably we'll get to that next time. After class he compared the ω function (maps p-adics of norm 1 to the root of unity congruent to it mod p (mod 4 in the case p=2)) that appears in the zeta function to a cockroach - "You can't get rid of it; you open a cabinet, there it is. You close the cabinet, open a drawer, there it is."

...yeah, that's really all.

-Sniffnoy