Day-Dream
I'm not going to fret about making this a good literary piece; I'm just going to describe it.
It started, I think, while we were taking about problem 3 in section 5 of chapter 14. The problem involves proving that every finite group can be the Galois group of some field extension. I remember staring at the problem as people were discussing it, mostly following what was being said but not entirely because I was distracted by the overwhelming feeling that this problem was familiar, deeply familiar, that the whole situation was familiar but I couldn't figure out exactly why...I think the photographer was still there at that point, and that played into it, this problem, the fact that every group was a subgroup of a symmetric group, the feeling that I was the only person in the class who wasn't in any of the pictures...all of it tied together and I knew that either this had happened before, or that I'd somehow foreseen or had a vision of it before it was happening...but it was distracting me because I couldn't understand the memories, they didn't make sense or tie to anything that I could understand logically. These was just this disorienting certainty that something was weird because I remembered all of this, from some time that couldn't have existed because it didn't make sense. Like deja vu, only prolonged, not just a flash of familiarity that you can shake away, but a prolonged barrage of memories and associations that I couldn't make sense of, but that were very immediate and powerful. I wish I could remember the exact thoughts...the problem related somehow, I think, to some memory of a car or an ambulence or going somewhere along some road...but I'm not certain, I don't remember it concretely now. At the time, I knew I was in math class and should be paying attention, which was hard since I was busy trying to interpret these intense surreal memories. I gradually became more and more aware that something was really strange, that these memories weren't normal, and I remember worrying about losing reality entirely somehow, so I focused on things I knew were real and true and stable, like the students I could see out the window walking to Kohlberg, and I remember thinking "those are Swarthmore students, they're waking toward Kohlberg," as a way of making sure I remembered what was real even as I was confused by all these dream-like associations. I remember thinking that there was a sip of water left in the bottle in my backpack, and that maybe doing something, an action, like drinking water, would stop this strange state and help me regain control of my mind. I reached into my backpack, got the bottle, opened the top, and took a small sip. I remember looking at the bottle--my memory of the whole water-drinking event is much stronger than my memory of anything said by anyone else in class during this time, although I know that I could understand the words, if not follow all of the implications. I put the bottle back in my backpack, knowing it hadn't helped. I remember making myself think about Andrew, as if thinking of something outside of math class and outside of my academic life, something important and prominant, would help me remember what was real; I wrote his name on the top of my paper, on an impulse, and then squiggled it out, with some sort of thought that the people next to me might be able to see and might think it was weird. At that point, I think, although I'm not sure, the barrage of dream-memories had stopped, or become weaker, but I still had a disoriented feeling that I wasn't processing what was going on around me and that I had some sort of lessened control over my thoughts, less ability to organize and make sense of them and understand things coherently. I'm not sure whether I'd describe anything I felt as sort of disembodiment...only in the sense that, at least in my memories of it, I felt like thoughts were rushing inside my consciousness that were somewhat disconnected from my embodied situation, sitting in math class, and I felt ungrounded in reality--hence why I kept purposefully trying to ground myself. The whole time, I had inside my head both the intense feelings of deja vu and of everything being from some strong memory that I couldn't pinpoint, and all the connections and associations that I didn't understand...and also a consciousness that realized that my state wasn't normal, that I had lost some control, that I couldn't bring myself back from these dream-like floods of memory the way I would expect to be able to. I remember wondering for a moment whether I could, or should, leave class, say I wasn't feeling well, and go lie down. Interestingly, I don't remember a feeling of anxiety...not in the sense of intense, fast-breathing, shaky, upset anxiety. I was aware that something wasn't normal about my thoughts, and I was making efforts to pull myself back, and I remember thoughts like "something is wrong", "what's happening to my thoughts?"...so I guess there was part of me that was worried, but it didn't feel panicky, which surprises me in retrospect since I would expect, if I found myself in such a confused, disoriented state for several minutes, that I would pretty much freak out. It seems like the confusion sort of overrode any panic reaction, or something. Also, at least as I remember it, my sense of time was odd. After class, I told Kristy I'd been feeling weird for "ten or fifteen minutes." As I think about it now, I would guess it wasn't more than two or three minutes, just because of how much content was covered in the class while I was feeling this. However, since I don't remember clearly exactly what was covered during that time, I'm not sure how long it was, really. But I think it must have felt subjectively longer that it was, or at least my immediate memory of it estimated it as longer than it was. When we moved on to section 8, problem 5, I must have raised my hand to volunteer. I think I remember knowing that I'd gotten that problem and that I'd sort of planned before class to volunteer for it, and vaguely wondering as I raised my hand whether I could un-confuse myself enough to present. But by that point, I think the deja-vu stuff had gone, and I was just feeling sort of dazed and spacey. I remember standing up and writing the problem number up on the board. The problem involved finding the degree of some sums of powers of the primitive thirteenth root of unity. I had done the problem by using a theorem that says that the degree of an element of a Galois extension is the order of its orbit under action by the Galois group. Using the extension of the rationals adjoined with the thirteenth root of unity, it's easy to identify all elements of the Galois group, so it's easy to find the orbits of sums of powers of the root. I don't think that I ever really forgot this or didn't know what I had done or why. But I remember feeling helpless about how to begin explaining it, or justifying it, and I felt a sudden nervousness that what I had done might just be completely wrong and crazy and make no sense--after all, my thoughts during the past few minutes hadn't made any sense. So I guess my confidence in my mind to have done something rational--even though I'd done the problem the previous night and I did, at some level, know it was right--wavered then, and I remember staring at my notebook and feeling self-conscious and trying to gather my thoughts to explain, knowing I was supposed to be talking...I said something about having looked at the orbits, and I think I said something like "that's what I did but I don't remember why..." Which wasn't true, I think. I remembered why, I just couldn't access it or articulate it or have faith in it. I looked through the book for the proposition that supported what I had done, with the vague thought that if I could read it from the book then it would make sense, and I found it and read it. I remember looking at Professor Shimamoto, who was nodding as though he thought I'd done the right thing, which gave me confidence. I began to write up what I'd done for part (a), and talk through it, and as I did I felt more confident and less confused, and I went through the whole problem, focusing on the math, which I became able to talk about again. Professor Shimamoto walked me through a slightly easier way to calculate and visualize what I had done (by listing the orbit of zeta (the root) under action by a generator for the Galois group, the automorphism taking zeta to zeta-squared), and I understood what he was getting at and by that point I felt focused again. I sat back down, at this point wondering what had happened to me, but still not panicking at all, and I think still feeling a little bit dazed, but after that I could engage in the class and pay attention and focus on the math we were doing, and I didn't feel like I was in a dream anymore.
So that's what I remember at this point. I wish I knew more about what those memories and associations that were so powerful were...although I would guess that they wouldn't admit to articulation as real sentences, exactly, even if I remembered them.
Okay that's all for this entry. I'm off to figure out what to ask Suda-sensei tomorrow...
It started, I think, while we were taking about problem 3 in section 5 of chapter 14. The problem involves proving that every finite group can be the Galois group of some field extension. I remember staring at the problem as people were discussing it, mostly following what was being said but not entirely because I was distracted by the overwhelming feeling that this problem was familiar, deeply familiar, that the whole situation was familiar but I couldn't figure out exactly why...I think the photographer was still there at that point, and that played into it, this problem, the fact that every group was a subgroup of a symmetric group, the feeling that I was the only person in the class who wasn't in any of the pictures...all of it tied together and I knew that either this had happened before, or that I'd somehow foreseen or had a vision of it before it was happening...but it was distracting me because I couldn't understand the memories, they didn't make sense or tie to anything that I could understand logically. These was just this disorienting certainty that something was weird because I remembered all of this, from some time that couldn't have existed because it didn't make sense. Like deja vu, only prolonged, not just a flash of familiarity that you can shake away, but a prolonged barrage of memories and associations that I couldn't make sense of, but that were very immediate and powerful. I wish I could remember the exact thoughts...the problem related somehow, I think, to some memory of a car or an ambulence or going somewhere along some road...but I'm not certain, I don't remember it concretely now. At the time, I knew I was in math class and should be paying attention, which was hard since I was busy trying to interpret these intense surreal memories. I gradually became more and more aware that something was really strange, that these memories weren't normal, and I remember worrying about losing reality entirely somehow, so I focused on things I knew were real and true and stable, like the students I could see out the window walking to Kohlberg, and I remember thinking "those are Swarthmore students, they're waking toward Kohlberg," as a way of making sure I remembered what was real even as I was confused by all these dream-like associations. I remember thinking that there was a sip of water left in the bottle in my backpack, and that maybe doing something, an action, like drinking water, would stop this strange state and help me regain control of my mind. I reached into my backpack, got the bottle, opened the top, and took a small sip. I remember looking at the bottle--my memory of the whole water-drinking event is much stronger than my memory of anything said by anyone else in class during this time, although I know that I could understand the words, if not follow all of the implications. I put the bottle back in my backpack, knowing it hadn't helped. I remember making myself think about Andrew, as if thinking of something outside of math class and outside of my academic life, something important and prominant, would help me remember what was real; I wrote his name on the top of my paper, on an impulse, and then squiggled it out, with some sort of thought that the people next to me might be able to see and might think it was weird. At that point, I think, although I'm not sure, the barrage of dream-memories had stopped, or become weaker, but I still had a disoriented feeling that I wasn't processing what was going on around me and that I had some sort of lessened control over my thoughts, less ability to organize and make sense of them and understand things coherently. I'm not sure whether I'd describe anything I felt as sort of disembodiment...only in the sense that, at least in my memories of it, I felt like thoughts were rushing inside my consciousness that were somewhat disconnected from my embodied situation, sitting in math class, and I felt ungrounded in reality--hence why I kept purposefully trying to ground myself. The whole time, I had inside my head both the intense feelings of deja vu and of everything being from some strong memory that I couldn't pinpoint, and all the connections and associations that I didn't understand...and also a consciousness that realized that my state wasn't normal, that I had lost some control, that I couldn't bring myself back from these dream-like floods of memory the way I would expect to be able to. I remember wondering for a moment whether I could, or should, leave class, say I wasn't feeling well, and go lie down. Interestingly, I don't remember a feeling of anxiety...not in the sense of intense, fast-breathing, shaky, upset anxiety. I was aware that something wasn't normal about my thoughts, and I was making efforts to pull myself back, and I remember thoughts like "something is wrong", "what's happening to my thoughts?"...so I guess there was part of me that was worried, but it didn't feel panicky, which surprises me in retrospect since I would expect, if I found myself in such a confused, disoriented state for several minutes, that I would pretty much freak out. It seems like the confusion sort of overrode any panic reaction, or something. Also, at least as I remember it, my sense of time was odd. After class, I told Kristy I'd been feeling weird for "ten or fifteen minutes." As I think about it now, I would guess it wasn't more than two or three minutes, just because of how much content was covered in the class while I was feeling this. However, since I don't remember clearly exactly what was covered during that time, I'm not sure how long it was, really. But I think it must have felt subjectively longer that it was, or at least my immediate memory of it estimated it as longer than it was. When we moved on to section 8, problem 5, I must have raised my hand to volunteer. I think I remember knowing that I'd gotten that problem and that I'd sort of planned before class to volunteer for it, and vaguely wondering as I raised my hand whether I could un-confuse myself enough to present. But by that point, I think the deja-vu stuff had gone, and I was just feeling sort of dazed and spacey. I remember standing up and writing the problem number up on the board. The problem involved finding the degree of some sums of powers of the primitive thirteenth root of unity. I had done the problem by using a theorem that says that the degree of an element of a Galois extension is the order of its orbit under action by the Galois group. Using the extension of the rationals adjoined with the thirteenth root of unity, it's easy to identify all elements of the Galois group, so it's easy to find the orbits of sums of powers of the root. I don't think that I ever really forgot this or didn't know what I had done or why. But I remember feeling helpless about how to begin explaining it, or justifying it, and I felt a sudden nervousness that what I had done might just be completely wrong and crazy and make no sense--after all, my thoughts during the past few minutes hadn't made any sense. So I guess my confidence in my mind to have done something rational--even though I'd done the problem the previous night and I did, at some level, know it was right--wavered then, and I remember staring at my notebook and feeling self-conscious and trying to gather my thoughts to explain, knowing I was supposed to be talking...I said something about having looked at the orbits, and I think I said something like "that's what I did but I don't remember why..." Which wasn't true, I think. I remembered why, I just couldn't access it or articulate it or have faith in it. I looked through the book for the proposition that supported what I had done, with the vague thought that if I could read it from the book then it would make sense, and I found it and read it. I remember looking at Professor Shimamoto, who was nodding as though he thought I'd done the right thing, which gave me confidence. I began to write up what I'd done for part (a), and talk through it, and as I did I felt more confident and less confused, and I went through the whole problem, focusing on the math, which I became able to talk about again. Professor Shimamoto walked me through a slightly easier way to calculate and visualize what I had done (by listing the orbit of zeta (the root) under action by a generator for the Galois group, the automorphism taking zeta to zeta-squared), and I understood what he was getting at and by that point I felt focused again. I sat back down, at this point wondering what had happened to me, but still not panicking at all, and I think still feeling a little bit dazed, but after that I could engage in the class and pay attention and focus on the math we were doing, and I didn't feel like I was in a dream anymore.
So that's what I remember at this point. I wish I knew more about what those memories and associations that were so powerful were...although I would guess that they wouldn't admit to articulation as real sentences, exactly, even if I remembered them.
Okay that's all for this entry. I'm off to figure out what to ask Suda-sensei tomorrow...
posted by Ashila at 11:00 PM
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