Every cup I reach for falls over, ever fork slips out of my hand, every idea fades as soon as it's been formed - emails are sent with typos and even my whiteboard won't stay on the wall. And since this is my physical and mental environment, you can imagine how I am reacting to everyone around me today: specifically, I feel like slapping everybody in the face, hunching my shoulders, and going to take a nap for the rest of the day. But it's okay. As soon as I realized that today was just going to be like that no matter what I did, it got a bit easier, and I could giggle a bit at just how ornery I was and how uncooperative the rest of my immediate universe was.
And so now I'm home, I've managed to carve out some headspace for math with some beverage that I have not yet spilled and I think I'll be able to concentrate a bit. I wanted to tell you first, though, about something that happens sometimes in Algebraic Topology. So, Algebraic Topology (ALT for short) is every Tuesday and Thursday from 12-2, that mystical time of day when everyone is either lost in thought because they are daydreaming about lunch, or falling asleep because they just had lunch, or bothering everyone by eating lunch right there and then in class. In general, the rule in Hungary is to start the class actually at a quarter after whichever hour was on the schedule, and then at the halfway mark to take a fifteen minute break. Quite civilized. So, we get started around 12:15. The gears start turning in a woefully slow manner, we brush off the dust of the weekend and start to think about higher-dimensional donuts and loops and other mind-boggling things. By the time the break rolls around, the professor has usually revealed something so similar to what can only be described of as a thought-twister (akin to the familiar tongue-twisters) and has promised us a proof after the break that will resolve our worries and pain in comprehension of the topic at hand.
We shuffle out to the hallway, the open window, the bathroom, or the coffee machine in a daze. We all show up back in the classroom before the break is over - little lost sheep, don't know where else to go. And usually, some kind of deep discussion ensues for the last five minutes of the break before we actually do more math. Today, it started this way - a comment from a friend of mine who sits in the back row and waits for the math to impress him, but in a somehow charming way. "Professor," he says, lounging in the corner. "What if I just... don't believe you?"
I turn around at the question. And I see that instead of the typical sassiness on his face, he actually looks a bit like he just lost a battle for the comprehension of the last topic. (Let me just say that that last concept involved assuming that one can visualize a cube in n dimensions and then hold that in mind while you do weird morphy math to it and glue it somehow to an n+1 - dimensional cube...) "Believe me about what?" The professor asks. This professor is about 34, named Boldizsar (effing badass mathematician name, if you ask me), and seems like he breathes this infinite-dimensional business and could read our ALT textbook the way I do Calvin and Hobbes.
My friend in the back row continues. "Just -- everything. What if I think you're making this all up??" His utter confusion is so plain on his face that this question echoes and skitters around the room and we all laugh, including Boldizsar. For the next ten minutes, we follow along this slightly meta route and talk about mathematics and the larger world, how some it relates to physics, how it's all just a model anyway, how some mathematicians can't even talk to any other mathematicians because their particular area of study is so specific that it doesn't relate to anything else.
And even though I'm about to go and labor over the technical and rigorous definitions we don't do in class but that I need for understanding ("That's the worst and most boring part of mathematics." - quote Boldizsar, when we asked him why we don't do these technical things in class), and even though it hurts and I don't really want to do it on some level - at the end of class, I had another moment when I remembered why I do this. A concept was presented that was so mind-bogglingly abstract for me -- well, let me first briefly clarify. (Am I just avoiding researching the definitions by writing this? I'll let you decide. ) Some/most of what we do in ALT is mind-bogglingly abstract by any normal standards. But when you don't really understand something that is abstract, it doesn't really seem all that insane. That not knowing, that confusion, fits rather easily in my head. For example, I don't know what a black hole is, and when I think about black holes, I think about how I don't understand them, and that's about it. But if someone were to talk to me about what a black hole is really like in terms that I understand, the more I understand what goes into that concept, the harder it is to really think about because the idea is becoming more well-formed.
So today, among all the n-dimensional cubes and infinitesimally knotted pieces of 1-dimensional rope, one concept came up where I knew all of the bits that came into the definition of this new thing, but I never knew they could be put together in that way before. I felt like my jaw actually hit the desk when the idea crashed into my brain. (I write with my face so close to my notebook paper that this is actually quite possible - confirm with old classmates of mine). I understood each of the pieces so well and put them together and it felt like having the idea fully formed was stretching the inside of my brain. That's what math does to my head. It's kinda fun.
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