...is not working out that badly, it turns out.
So some weeks back, my mom asks, when do you want to come home? Because she has to buy the plane tickets. I, finding life outside of classes rather dull, said, I don't know, as soon as it ends. (Meaning, to yank you back into the present momentarily, this coming Saturday.)
...what about time to clean up, to pack? Yeah, I wasn't thinking about that. Oh, and what about, you know, that paper I'm supposed to write and will presumably be furiously working on in the last few days? I definitely wasn't thinking about that. I finally realized this a few weeks ago, and asked if it could be changed, but no, those plane tickets are non-refundable.
The paper which, I of course, basically ignored the entire time. I mean, I certainly wasn't thinking about it the first two weeks. And then came YSP, and I certainly wasn't thinking about it. And then there's the last two weeks - oh yeah, the paper!
OK, so I had met with my mentor-people once or twice. Jim asked me the first time, what are you interested in? And I said, I don't know... finite group theory? (Just to throw something out there.) And so we started talking, and somehow we ended up on the topic of finite projective planes. And so that sort of became my topic by default. And he sent me some names of books, and I went to Eckhart and I checked them out, and also found another one, An Introduction to Finite Projective planes, and I spent a week reading through it (this was fifth week, I believe), and then I got sick of it and put away for a week. And then came seventh week and I realized I had better start doing something. And, I came up with a good idea - a natural question that came up reading this book, which probably wouldn't be too hard to answer. Somehow I just didn't get around to doing it, though.
Now I should note, even though we're nominally here for "research", most of the papers people write are not anything new. Often it's compilatory work. I think Steve Balady[0] last year took Selberg's elementary proof of the prime number theorem and filled in all the missing steps (which were, apparently, not so obvious). But you can get away with much less; Sayer tells me, when he was here, he just did a few problems from an algebra book. And I don't think it's at all uncommon to take something known and just write it up, because, uh... you can. This isn't what they're paying us for.[4]
But somehow the apartment just isn't conducive to doing work. Or maybe that's just me being lazy. Of course I procrastinated and it came to a head last night. Because when I did do work, it was on the exercises from class. This was Wednesday night and I hadn't started writing anything. Hell, I hadn't even worked on any of those easy questions I had come up with. So first I did that - I got some answers, or at least some answers under the assumption of linearity. Then... I did nothing. I did many hours of nothing. (Well, not nothing, obviously. In actuality I spent many hours here. This wiki ate up hours of my time when I first discovered it a year or two ago. Then I forgot about it, rediscovered it, and found it eating up my time again - especially now that I'm actually writing some stuff in it. Much more of a timesink than Wikipedia.) In order that I might get my actual work done, I decided to stop working on the exercises from class - which just meant I got nothing done.
Anyway, I figured first things first - one thing I don't really know in TeX is all the framing stuff. So I downloaded the template Peter May had put up. Then I decided, I had better check, exactly when is this due? Search email for Peter May. Ah, here it is! Friday, August 17... wait, what?! *Phew* I have a whole nother week to do it! Of course, I'll be at home... where I might find it easier to work. Of course, I have to return my books to the library tomorrow. Well, I'll make copies of what I actually used. *shrug*
So going home early has caused a lot of trouble. (Due to sleeping through the day today, and the people giving their talks, I didn't even get to do my laundry[3], and will have to do it tomorrow.) What's the upside? OK, maybe I'll have an easier time working, and I'll have more consistent internet, but I think the big one is getting some good food. 8 weeks of having to feed myself has not been good to me. Only 3 times have I worked up the energy and patience to cook anything, and only one of those times did it really come out right. (Though only one of those times did it really come out bad, for that matter.) Otherwise I've been surviving on Chef Boyardee, Easy Mac, breakfast cereal, and sandwiches. Sandwiches being by far the majority. Two slices of bread, a bit of meat, and possibly some mustard. I have to say I don't think I ever appreciated mustard quite so much before. So I get home and finally get to eat well again, right?
Well, not quite. Turns out the family's going on vacation nearly as soon as I get back. I always find these vacations miserable so I'm staying home. Which means another two weeks of feeding myself, when I could have just stayed for another two weeks anyway (that's when my sublease ends).
Completely unrelatedly, hooray for BGG! A guy offered to trade me a copy of Nexus Ops for my copy of Ingenious, and I accepted. Since I'm coming home in a few days, I had him send it there. So when I get home, I will have a new copy of Nexus Ops! What's up with that, anyway - people trading away things still new in shrink? Why would you trade something away before you'd even played it? Maybe someone got it for you as a present, and you already had one, or had already played it and knew you didn't like it? Or maybe you bought it, never opened it, and then played it elsewhere and decided you didn't like it? I find it kind of hard to believe that people would buy games just to trade them. I mean it's not like Magic cards, you know what you're getting.
Also! Cool theorem from Babai's class that I just felt like mentioning. So you take two random graphs on n vertices, n finite, what's the probability they're isomorphic? It's ≤n!/2^(n choose 2), which rapidly goes to 0. Now take two random graphs on ℵ0 vertices, what's the probability they're isomorphic? It's 1! Of course, this means (and this is how you prove it) that there is a single countably infinite graph such that any random countably infinite graph is isomorphic to it, with probability 1. There are continuum-many isomorphism types of countably infinite graphs, but pick one at random and you'll almost certainly pick this one. So we can just call it "the random graph". It's characterized among countable graphs by the property (and again, this is how you prove it) that for any two finite subsets of its vertices S and T, there's some vertex v which is adjacent to everything in S but nonadjacent to everything in T. So this also means that every countable graph occurs as an induced subgraph of the random graph.
...I think that ends this entry. I should probably get to packing or something. Meanwhile I still need a vacuum so I can clean up the cereal and something that cleans glass so I can clean off the desk, and I don't have much time to find it in.
-Harry
[0]I'm going to stop referring to him as "Big-Haired Steve" here, because the only people I know who call him that are those who knew him from when he was in Tufts. As I know him generally from the context of math stuff, I'm going to call him how he's known in that context, "Steve Balady". (Also, the name always sounded strange to me because he's not that big-haired. Presumably it was in comparison to another Steve.) I'll call him "Big-Haired Steve" when speaking in the context of Tufts.
[3]Our laundry room closes late at night.
[4]Kind of funny: Today was the first round of presentations, for those students who were giving them. One, Sarah Constantin, was talking about a problem she had actually found a new lower bound for. Maybe I'm just a braggart[5], but it was kind of funny how she blazed through that bit compared to the other stuff she talked about. Maybe because it was actually the easiest bit to demonstrate, and she only had so much time. :P
[5]Remember how excited I was just because I proved something Babai didn't know?
So some weeks back, my mom asks, when do you want to come home? Because she has to buy the plane tickets. I, finding life outside of classes rather dull, said, I don't know, as soon as it ends. (Meaning, to yank you back into the present momentarily, this coming Saturday.)
...what about time to clean up, to pack? Yeah, I wasn't thinking about that. Oh, and what about, you know, that paper I'm supposed to write and will presumably be furiously working on in the last few days? I definitely wasn't thinking about that. I finally realized this a few weeks ago, and asked if it could be changed, but no, those plane tickets are non-refundable.
The paper which, I of course, basically ignored the entire time. I mean, I certainly wasn't thinking about it the first two weeks. And then came YSP, and I certainly wasn't thinking about it. And then there's the last two weeks - oh yeah, the paper!
OK, so I had met with my mentor-people once or twice. Jim asked me the first time, what are you interested in? And I said, I don't know... finite group theory? (Just to throw something out there.) And so we started talking, and somehow we ended up on the topic of finite projective planes. And so that sort of became my topic by default. And he sent me some names of books, and I went to Eckhart and I checked them out, and also found another one, An Introduction to Finite Projective planes, and I spent a week reading through it (this was fifth week, I believe), and then I got sick of it and put away for a week. And then came seventh week and I realized I had better start doing something. And, I came up with a good idea - a natural question that came up reading this book, which probably wouldn't be too hard to answer. Somehow I just didn't get around to doing it, though.
Now I should note, even though we're nominally here for "research", most of the papers people write are not anything new. Often it's compilatory work. I think Steve Balady[0] last year took Selberg's elementary proof of the prime number theorem and filled in all the missing steps (which were, apparently, not so obvious). But you can get away with much less; Sayer tells me, when he was here, he just did a few problems from an algebra book. And I don't think it's at all uncommon to take something known and just write it up, because, uh... you can. This isn't what they're paying us for.[4]
But somehow the apartment just isn't conducive to doing work. Or maybe that's just me being lazy. Of course I procrastinated and it came to a head last night. Because when I did do work, it was on the exercises from class. This was Wednesday night and I hadn't started writing anything. Hell, I hadn't even worked on any of those easy questions I had come up with. So first I did that - I got some answers, or at least some answers under the assumption of linearity. Then... I did nothing. I did many hours of nothing. (Well, not nothing, obviously. In actuality I spent many hours here. This wiki ate up hours of my time when I first discovered it a year or two ago. Then I forgot about it, rediscovered it, and found it eating up my time again - especially now that I'm actually writing some stuff in it. Much more of a timesink than Wikipedia.) In order that I might get my actual work done, I decided to stop working on the exercises from class - which just meant I got nothing done.
Anyway, I figured first things first - one thing I don't really know in TeX is all the framing stuff. So I downloaded the template Peter May had put up. Then I decided, I had better check, exactly when is this due? Search email for Peter May. Ah, here it is! Friday, August 17... wait, what?! *Phew* I have a whole nother week to do it! Of course, I'll be at home... where I might find it easier to work. Of course, I have to return my books to the library tomorrow. Well, I'll make copies of what I actually used. *shrug*
So going home early has caused a lot of trouble. (Due to sleeping through the day today, and the people giving their talks, I didn't even get to do my laundry[3], and will have to do it tomorrow.) What's the upside? OK, maybe I'll have an easier time working, and I'll have more consistent internet, but I think the big one is getting some good food. 8 weeks of having to feed myself has not been good to me. Only 3 times have I worked up the energy and patience to cook anything, and only one of those times did it really come out right. (Though only one of those times did it really come out bad, for that matter.) Otherwise I've been surviving on Chef Boyardee, Easy Mac, breakfast cereal, and sandwiches. Sandwiches being by far the majority. Two slices of bread, a bit of meat, and possibly some mustard. I have to say I don't think I ever appreciated mustard quite so much before. So I get home and finally get to eat well again, right?
Well, not quite. Turns out the family's going on vacation nearly as soon as I get back. I always find these vacations miserable so I'm staying home. Which means another two weeks of feeding myself, when I could have just stayed for another two weeks anyway (that's when my sublease ends).
Completely unrelatedly, hooray for BGG! A guy offered to trade me a copy of Nexus Ops for my copy of Ingenious, and I accepted. Since I'm coming home in a few days, I had him send it there. So when I get home, I will have a new copy of Nexus Ops! What's up with that, anyway - people trading away things still new in shrink? Why would you trade something away before you'd even played it? Maybe someone got it for you as a present, and you already had one, or had already played it and knew you didn't like it? Or maybe you bought it, never opened it, and then played it elsewhere and decided you didn't like it? I find it kind of hard to believe that people would buy games just to trade them. I mean it's not like Magic cards, you know what you're getting.
Also! Cool theorem from Babai's class that I just felt like mentioning. So you take two random graphs on n vertices, n finite, what's the probability they're isomorphic? It's ≤n!/2^(n choose 2), which rapidly goes to 0. Now take two random graphs on ℵ0 vertices, what's the probability they're isomorphic? It's 1! Of course, this means (and this is how you prove it) that there is a single countably infinite graph such that any random countably infinite graph is isomorphic to it, with probability 1. There are continuum-many isomorphism types of countably infinite graphs, but pick one at random and you'll almost certainly pick this one. So we can just call it "the random graph". It's characterized among countable graphs by the property (and again, this is how you prove it) that for any two finite subsets of its vertices S and T, there's some vertex v which is adjacent to everything in S but nonadjacent to everything in T. So this also means that every countable graph occurs as an induced subgraph of the random graph.
...I think that ends this entry. I should probably get to packing or something. Meanwhile I still need a vacuum so I can clean up the cereal and something that cleans glass so I can clean off the desk, and I don't have much time to find it in.
-Harry
[0]I'm going to stop referring to him as "Big-Haired Steve" here, because the only people I know who call him that are those who knew him from when he was in Tufts. As I know him generally from the context of math stuff, I'm going to call him how he's known in that context, "Steve Balady". (Also, the name always sounded strange to me because he's not that big-haired. Presumably it was in comparison to another Steve.) I'll call him "Big-Haired Steve" when speaking in the context of Tufts.
[3]Our laundry room closes late at night.
[4]Kind of funny: Today was the first round of presentations, for those students who were giving them. One, Sarah Constantin, was talking about a problem she had actually found a new lower bound for. Maybe I'm just a braggart[5], but it was kind of funny how she blazed through that bit compared to the other stuff she talked about. Maybe because it was actually the easiest bit to demonstrate, and she only had so much time. :P
[5]Remember how excited I was just because I proved something Babai didn't know?
