Last night, Shields tower lounge. As I mentioned before, Rosenberg had been talking about fundamental groups in geometry, and we were talking about fundamental groups - Chris recalls someone asked him what π1 was - and Chris referred to π1 as a function. What follows is pretty much accurate, though I may have missed something.
Fergie: It's not a function, it's a set of equivalence classes of functions; it's a group.
Me: No, it's a function taking topological spaces to groups.
Chris: One might even call it a functor...
Fergie: Motherfunctor!
Ila: *That* was the other dirty-sounding math word - "ergodic theory" and "functor"!
[Just at that moment, Bernie enters]
Bernie: Did somebody just say functor?!
[We all point out Ila]
Bernie: Ila, I love you!
[I may have omitted something at this point]
Ila: Can I bribe you with my zeta problem set?
Bernie: Bribe me *not* to talk about functors?!
Chris: I think I can take the blame for this one. I said π1 was a functor taking topological spaces to groups.
Bernie: Chris, give me a hug! [He walks over and pats Chris on the shoulder] You couldn't be more right! [He then launches into incomprehensible category-theoretic stuff related to π1.]
Other random quotes from yesterday: Ila misspoke "Really mad at Bob" as "Really bad at mob". There was a "Rational Points on Conics" mini-course which I didn't go to; apparently Andy went up to the board and replaced "Conics" with "Connie". Fergie responded, "Wait, Connie has rational points?"
Today we entered Stone B50 to find someone fiddling with a video camera. Apparently, someone was recording this lecture - putting a microphone on Glenn and all - for, well, something or other. I asked Chris, "Do you think this will make Infinity-boy speak up more or less?" "Less," he replied.
Well, today was, as Chris put it, a new low. Today was Glenn's "Do we think this system has UPF? What about this system?" lecture. No matter what system was put up, ∞-boy voted "No". "He probably thinks UPF is unique to the integers, like WOP," I commented to Chris. Later, of course, he claimed he had proven UPF in Z[i] - by proving that the norm has a UPF! Ugh... Even worse was when he defined "prime" as "no divisors except itself and 1" (ignoring that this doesn't even work in Z), and then when Glenn factored a prime in some system as a unit times one of the prime's associates, he said that doesn't make it composite, because that's a unit! Gah! I mean, yes, it's good that he recognized the correct definition, but you can't just go changing your definitions like that! If he's going to make that complaint, the first thing you should do is acknowledge that your earlier definition was bad![0]
In good things, Glenn got to do his Z[x] thing. Nobody suggested adding "There are no integers between 0 and 1" as an axiom (instead of WOP) this year - not in class, anyway - so he never got to demonstrate that Z[x] also satisfied all those properties. In Z, we used WOP to prove UFT - can we do this in Z[i]? Does it have some equivalent of WOP? No, because it can't even be ordered. How about in Z[x]? Can we do it there? And Jason Bland raises his hand and says that if you take the set of positives to be those with positive leading coefficient, that orders it. And so Glenn now demonstrates that indeed, this does order it, but it doesn't satisfy WOP - although, he points out at the end, somewhat out of context, there are no polynomials between 0 and 1.
Of course, something had to go wrong. When Glenn asked the class if this does indeed satisfy trichotomy, Jason Pollock raised his hand and said, "Doesn't that depend on what x is?" Yay for people not understanding what [x] means! :P :-/ Worse yet, before Glenn pointed out that Z[x] doesn't have WOP, when it had been verified that it could be ordered, he raised his hand and asked if that made it indistinguishable from Z! Totally forgetting about WOP, which is, after all, the one that's really characteristic of Z.
Oy oy oy...
The cameraman actually left about halfway through, though for what reason exactly, I don't know.
-Sniffnoy
[0]To anyone newly reading this who replies to this with a comment about the distinction between "prime" and "irreducible": here at PROMYS we just call "irreducible" "prime", and don't have a special word for "prime". It's easier for the first-years, and we don't ever really have to refer to non-irreducible primes.
Fergie: It's not a function, it's a set of equivalence classes of functions; it's a group.
Me: No, it's a function taking topological spaces to groups.
Chris: One might even call it a functor...
Fergie: Motherfunctor!
Ila: *That* was the other dirty-sounding math word - "ergodic theory" and "functor"!
[Just at that moment, Bernie enters]
Bernie: Did somebody just say functor?!
[We all point out Ila]
Bernie: Ila, I love you!
[I may have omitted something at this point]
Ila: Can I bribe you with my zeta problem set?
Bernie: Bribe me *not* to talk about functors?!
Chris: I think I can take the blame for this one. I said π1 was a functor taking topological spaces to groups.
Bernie: Chris, give me a hug! [He walks over and pats Chris on the shoulder] You couldn't be more right! [He then launches into incomprehensible category-theoretic stuff related to π1.]
Other random quotes from yesterday: Ila misspoke "Really mad at Bob" as "Really bad at mob". There was a "Rational Points on Conics" mini-course which I didn't go to; apparently Andy went up to the board and replaced "Conics" with "Connie". Fergie responded, "Wait, Connie has rational points?"
Today we entered Stone B50 to find someone fiddling with a video camera. Apparently, someone was recording this lecture - putting a microphone on Glenn and all - for, well, something or other. I asked Chris, "Do you think this will make Infinity-boy speak up more or less?" "Less," he replied.
Well, today was, as Chris put it, a new low. Today was Glenn's "Do we think this system has UPF? What about this system?" lecture. No matter what system was put up, ∞-boy voted "No". "He probably thinks UPF is unique to the integers, like WOP," I commented to Chris. Later, of course, he claimed he had proven UPF in Z[i] - by proving that the norm has a UPF! Ugh... Even worse was when he defined "prime" as "no divisors except itself and 1" (ignoring that this doesn't even work in Z), and then when Glenn factored a prime in some system as a unit times one of the prime's associates, he said that doesn't make it composite, because that's a unit! Gah! I mean, yes, it's good that he recognized the correct definition, but you can't just go changing your definitions like that! If he's going to make that complaint, the first thing you should do is acknowledge that your earlier definition was bad![0]
In good things, Glenn got to do his Z[x] thing. Nobody suggested adding "There are no integers between 0 and 1" as an axiom (instead of WOP) this year - not in class, anyway - so he never got to demonstrate that Z[x] also satisfied all those properties. In Z, we used WOP to prove UFT - can we do this in Z[i]? Does it have some equivalent of WOP? No, because it can't even be ordered. How about in Z[x]? Can we do it there? And Jason Bland raises his hand and says that if you take the set of positives to be those with positive leading coefficient, that orders it. And so Glenn now demonstrates that indeed, this does order it, but it doesn't satisfy WOP - although, he points out at the end, somewhat out of context, there are no polynomials between 0 and 1.
Of course, something had to go wrong. When Glenn asked the class if this does indeed satisfy trichotomy, Jason Pollock raised his hand and said, "Doesn't that depend on what x is?" Yay for people not understanding what [x] means! :P :-/ Worse yet, before Glenn pointed out that Z[x] doesn't have WOP, when it had been verified that it could be ordered, he raised his hand and asked if that made it indistinguishable from Z! Totally forgetting about WOP, which is, after all, the one that's really characteristic of Z.
Oy oy oy...
The cameraman actually left about halfway through, though for what reason exactly, I don't know.
-Sniffnoy
[0]To anyone newly reading this who replies to this with a comment about the distinction between "prime" and "irreducible": here at PROMYS we just call "irreducible" "prime", and don't have a special word for "prime". It's easier for the first-years, and we don't ever really have to refer to non-irreducible primes.
