What's up? Late night post is what's up. So, I don't want this to just become my brog (this is a term I just made up for brag-blog), but I should probably mention that I was awarded, or at least informed that I would soon be awarded, another teaching assistant award, this time a department-exclusive one. So that's kind of nice and will probably result in some more money coming my way. So, real topics:
My research is actually going pretty well. I am just finishing up a problem that I have been working on for basically ever involving homotopy categories of modules, blah blah, nobody really knows what that means. At least I think I am in the home stretch. There is some sort of connecting material which I am not totally clear on, but I think it is just classical results that I can adapt if need be. It's odd that most of the time I have spent seems to be on simply understanding what the problem even was, and the second most time I spent was trying to decode the particularly French way that some stuff is encoded. The French style can be, from what I can tell, generally summed up succinctly as "obfuscation."
I don't know if I have ever posted about this stuff before, but I probably did at least mention that based on my admittedly small (n=1) sample size, being in grad school has a weird sort of specialization effect to it, where people on the outside just see you and your peers as "doing math (or whatever you do)," but you each see what the other people do as completely foreign. Maybe it is more exclusive to math, but I actually have the feeling that it is even
less pronounced in math than in other fields, but as mathematicians, we don't really see outside of our own bubble. Actually, a tree is probably a better model than a bubble, but I digress. I only learned relatively recently that the number of, say, biologists doing research today is something like 10 times the number of mathematicians doing the same, so it is even more disparate. I don't actually know if that is true; it's just what I heard. Ultimately, I don't care that much if it is true, but it would be sort of interesting if it were.
The whole point of that last paragraph was that I got into some totally non-serious argument weeks ago with another student about how I act like my math is harder than other people's math, but it's really not. I don't really think that's fair, because I usually preface talking about my stuff with "it's actually very easy," or "anyone could do this," or "it's just composing linear maps" if I am feeling fancy. I do get to name drop a bunch of crazy sounding things like "total derived functors" and "supercommutative algebras associative up to homotopy" and "quasi-coherent sheaves of modules," for example, but this is just the benefit/curse of doing anything algebraic. The field necessitates a bunch of terminology, which makes it very front-end heavy when learning. That's compounded by the fact that a lot of the difficulty comes in actually understanding
what result you are trying to get, as opposed to
how to get there. I can't really explain it without getting into more detail, which I don't want to do, but oftentimes the actual computational work is relatively simple, without analysis-like complicated inequalities, or crazy functions like ! or Gamma or zeta or anything because that's not
algebraic by it's very nature. Also, people tend to turn off if they don't immediately know the thing you are talking about because they (understandably) don't want to spend all their time wading through definitions they'll probably never use.
Just to contrast, the argument came up because I said sometimes I was jealous of her (she does combinatorics) because often you can just pick up a paper and read the intro or the initial definitions and say to yourself "ah, I see what you would like to count; that's a reasonable type of object," even if the actual work in getting the result is painstaking and, well, sort of awful to do. It's just kind of nice not have to stop after the first sentence to chase down the ridiculous set of axioms that define a "triangulated category" or something. She didn't really read what I was saying as that, but it all worked out, and, anyway, my other friend, who also does combinatorics-like stuff, totally understood what I was saying. I think he only understands it better after slogging through ten weeks of algebraic geometry to get to the realization that it's mostly things like zeroes of polynomials. Ha ha.
Ok, so I guess there's not much going on in my life outside of school? I saw three,
three, woodchucks in rapid succession on Monday. They were definitely all different woodchucks, too. I thought it was pretty impressive. When I told my friend (the first one, above) about it, she said "do you mean groundhogs?" I said, "yes, they are the same animal," and she said, "yes, but you are here, and here they are called groundhogs." So maybe it's a regional thing? I mean, I definitely have heard both, but I prefer the name woodchuck.
Oh, yeah, and another note about math. My advisor once told me I was "kind of a weirdo for this school because you're the only one that likes algebra." He also said in class that algebraic geometry was kind of a "crappy field to go into, because everyone else will be publishing papers and you'll still be trying to figure out what's going on" or something to that effect. I just thought that was kind of funny.
That gate there is the entrance to the shrine, and that thing spitting out water is, well, a thing spitting out water. It is for washing your hands before entering the shrine proper. You can sort of make out on the sign, which was where our path finally crossed with another one. To the left is the way to the top, 1.2 km up, to the right, the way down, 1.6 km, and you can barely see it, but the way we came was 2.3 km, I think. This was all done in just sneakers because we hadn't planned on actually climbing the mountain. There were tons of people going up and down the mountain with all their gear, which was kind of hilarious. It's not like you can't do it without gear, though. There's no scaling a rock face or anything, just kind of hiking uphill.
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