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Saturday, 9 November 2013

If I could be born again...

I woke up to a very odd dream on Thursday morning. In my dream I'd somehow cut off/otherwise removed my right thumb. It had been re-attached on my right arm, some 20cm or so away from my pinkie. Except I remember later having six fingers on my right hand, with just the awkward extra thumb just sticking out where I just mentioned. That wasn't all, though. I'd somehow hurt myself and I had this big of sagging skin around my elbow where a little fluid had collected. When I felt around this flap of skin I could feel solid bits, what I imagined were bits of broken bone. Upon realising my arm was broken I asked for my sister's assistance helping me bandage it to immobilise it. When I first called for her help she was busy and my call upset her. She still came to me and we duct taped my arm as best we could (which was not very well). I remember trying very hard not to move my arm much, but forgetting about it and then stretching it anyway. When I woke up, my parents, my sister and I were in a dark room, on the bed with Jenny, Victor and three cats (female, in my dream). I was petting one of them. It's odd then I should have found a solid bit of I know not what on my right arm on Thursday morning. It's some 12-15cm away from my wrist, on the side closest to the visible veins. Touching it reveals it's some kind of growth, less than 5mm wide) attached to the muscle, as I can easily pull my skin over it but can't get it to move. I'll have to get it checked out.

I hopefully didn't do too badly on the exam I had on Thursday. Which I shamelessly crammed for because I only realised the exam was on Thursday when the professor's late night e-mail arrived on Wednesday. This one's a bit worse than before because I wrote it down in my notebook. I had the right date jotted down. I'd written the date for the exam on the same page I was looking at to do the project I turned in on Tuesday. Against my stubbornness, I might have to follow the therapist's advice and buy (and try to use with some degree of discipline) a planner.

Thursday during class I finished solving the problem of the month I found in the maths club website. When I was done solving it I felt a bit silly for taking so long but I felt accomplished (it's been a long time since the last time that happened). As is usual in me, if you know me, I started a very complicated and long-winded attempt that led nowhere first, even though I'd sort of contemplated the solution I ended up using... it's just that it didn't "feel" like it was the right answer and I didn't follow through with it. The problem at hand is this:

Prove that the following equation has no solution in the set of positive integers.

x² + y² + z² + w² = 2xyzw

Admittedly, the original formulation of the problem used u instead of w but, as I remember it, we usually went for w as a fourth variable, leaving u and v to denote vectors. Maybe it's just me. I nevertheless finished out my sketch of the proof on an index card and felt very pleased with myself as I walked over to my appointment. That night I actually went as far as typing up the solution in LaTeX, polishing my rusty LaTeX coding skills and downloading both an editor and the libraries on the new computer (I hadn't bothered until then). All so I could send my solution. Not that I expect to win the prize. I sent my solution a full week into the month, time by which I imagine anyone else more clever than me would have come up with a solution a lot sooner. I also don't think highly enough of myself to even allow thoughts that my solution might be the best one (which, according to the website, is the one that gets the prize.)


SPOILER ALERT (I'm about to hint at the solution): I initially thought that since we were dealing with integers and the number on the right is even I could just toy with what the numbers on the left could be. Then I noticed that the left hand side looked a lot like a norm squared and I wasted quite a bit of time going over inequalities (Cauchy-Schwarz, triangle, what have you) trying to find upper and lower limits that cut the 2xyzw somewhere before and/or after the nearest integer (proving that the answer then couldn't be an integer). One late night when I thought of giving it another shot I thought I had it, with inequalities where I could cancel out terms so that the numbers didn't quite work out to be integers and called it a night thinking I'd solved it at last. It didn't work out very well. Turns out I forgot to square one side. Then I went back to the whole even numbers formulation, split it up into cases, and it worked out very nicely. Though I reckon I should have had it a bit earlier. I can't help but wonder if there's a nicer, direct, proof that doesn't rely on contradiction.


You know what my first thoughts were when I solved it? I wished I could tell SmTn. I made up my mind then and there. I won't give up on maths completely, occasionally indulging in solving such problems and attending seminars and colloquia when possible: to make him proud. Not that he'd care much, with me not telling him about it and all, but I like to imagine, like I imagine he's keeping me company when he's online, that he'd be proud of me if he knew I took time out of my days to work on real maths problems and went to maths related events. I had every intention to go to the maths club seminar on Friday at 2pm (it was supposed to be centred around mystical mathematicians, if we can call them that) but the work that was supposed to start at 9am actually started at 10:30am and then we weren't done until 3pm. It's quite all right though. It was all the push I needed to find out if there aren't other seminars or colloquia and it turns out there are, so I'm attending those whenever I can. I can get an excuse to go to university on Fridays (I may not even need one). 

List of things to do before next semester:

 - Figure out which classes I need to register for
 - Figure out if I have a job for next semester
 - Sort out the health insurance issues
 - Ask for permission to go on vacation
 - Find out which maths classes I'd be interested in auditing

Hopefully, I'll be able to make myself busy that way. I don't know how much of a hassle it will be to register for another three credit hours. I'll sort that out when I know if I have a job or not. *sigh* These are all things I don't look forward to doing. It feels like a chore. Kind of like bioelectricity, except that working with the professor who teaches it has given me a new kind of respect for him that makes me feel awful about not being a good enough student. 

Can we talk about chores? Let me talk about chores here. Thursday's session could have been about anything, but I ended up venting about passive aggressive aunt A, not being able to sleep and I-need-to-get-the-fuck-out-of-here-...-FUCK. I'm a little annoyed she suggested I approach the unspoken subject of expectations and say I'll compromise to chores (doing the dishes, laundry, etc.) every so often on certain days and then stick to it. I can see numerous ways for it to not work out because aunt A can always be counted on to find lies to suit her whims. While I appreciate the therapist's efforts and can't even say her idea is a bad one, or that it's certain to fail, I don't think she appreciated how fed up I am with the situation and who unwilling it makes me to try and solve it through rational means when the people I live with are far from reasonable. That probably set the pace for what followed. I mentioned I'd been to group therapy and she asked how it had been. I maybe overemphasised the cartoonish nature of it all and called psychology a sham.

Let me explain. I don't know the first thing about psychology. Not real psychology, at any rate. The way I understand it (and I reckon I'm not too far off the mark), psychology studies behaviour, good and bad. Then, having broken them down into steps/bite-size pieces, bad behaviour is corrected by recognising its pieces and replacing them, as well as can be managed, by their counterparts in good behaviour. If I'm absolutely horrible at hearing people tell me about their troubles, I can correct "rolling my eyes," "offering advice no one asked for" and "not giving a flying fuck" by first realising what I'm doing, stopping myself short of doing it and replacing those actions for "listening and pretending to care," "finding a kernel of truth I can agree with and show empathy for" and "say reassuring/comforting things." Something like that, if not that exactly. When you're indulging in a behaviour that's harmful/counter-productive, you're supposed to realise that it starts with a thought that leads to a feeling and it's the feeling that leads to actions. Different actions have different outcomes, and seeing how the thoughts and feelings are mostly all in your head (and nowhere else, like when you bring yourself down telling yourself the things you imagine people saying behind your back), you're supposed to decide what the best outcome is, choose the right action that leads to it and realise that the automatic thoughts and feelings are kind of invalid. Doesn't it all sound very reasonable? It actually is. It's just so hard to actually tell yourself what to feel and do.

As I see it, feelings are automatic processes. They're natural and irrational. It just so happens some feel good and others not so much. While I can see why it makes sense to rationalise them, it seems wrong to do so. I'm all too aware of the fact that I'm trying to emulate what comes naturally to others by breaking it down into artificial steps. Key word: artificial. Sure, I could practise saying gracious "Thank you"s to every compliment I get, but I would be aware of how I was trying extra-hard to be nice and any feelings generated through this phony process would feel less legitimate than the automatic ones. It's basically me being unwilling to change operating systems and being stubborn about it. I should probably apologise to the therapist and explain that the whole reason I'm in therapy is because I realise talking to someone who can offer a fresh perspective is important. 

She told me about a book she's passionate about (she didn't say it, but I could see her copy was well-loved and well-read). It's Outliers, by Malcolm Gladwell. I made a point out of reading it even though I disagreed with its premise as it was explained to me by the therapist. She brought up the book in the context of ... I actually have no idea. My brain doesn't work the way it once did. The point is that she said I could be as smart as I wanted to be and even train myself to be some kind of genius if I just put enough time into it. She debated anyone's innate ability to do anything as something that can be explained by their background and upbringing. I pointed out that, to me, there's a big difference between someone who's just practised playing the piano a lot and a true virtuoso. She argued that you can get good at anything if you just do it enough and mentioned the book.

I hate to say it in so many words but I don't think she understood the book. Or maybe I'm a bit too sceptical/cynical. You see, the book centres on successful people and how they got where they are. Successful people, as is assumed by the author, are almost invariably rich, in a job that feels fulfilling, and in a higher tier of society. Doctors, lawyers, Bill Gates, Steve Jobs, successful sports players, you know the ones. The whole book could be summarised by that quote mentioned in that Brittany Murphy film (if you don't mind, I'll paraphrase because I don't feel like looking it up) "Good luck is what happens when preparation meets opportunity." Sheer dumb luck is useless. Wait, let me actually look it up. I can't remember if it's "good luck" or "success" and I realise now it's kind of important. It seems I got it right. It's "Luck." 

Very well, then. As Gladwell explained, it takes quite a bit to be successful: you have to be among the smarter people, be hard-working, have happened to be born in the right time period and the right culture and the planets themselves have to align so that you get your golden opportunity at a time when you can grasp it. It's not enough with being talented/hard-working/smart: you need to have been born at the right time for the arbitrary deadlines to work in your favour, you need to have been practising for thousands of hours to have become good at what you want to do, you need the kind of cultural background that puts you in the right mindset and have exactly the abilities that are in demand a given time. In the book, a man with an IQ of 195 who never managed to get a college degree because life sucks when you're poor and your family isn't the most supportive/helpful is a bloody failure. Especially next to the man who attempted to poison his tutor and then went on to come up with the atomic bomb. Because Oppenheimer had people skills, apparently. Being the smartest of the smart, as Gladwell tries to prove, is pointless because once you're smart enough (above some threshold) everyone does equally well (i.e. they get about the same pay). I don't have a mind for such a definition of success or for how he dismisses clearly intelligent people as not worth his attention just because they couldn't use their high IQs to get the right kind of job and recognition. His message, pretty much, was "You don't need to be like them, just work hard and work smart, it's all the same." If you will, he's just saying that it's not worth it being smarter, because you won't be more successful. So you can even lie and make it mean you can be just like a genius if you just work hard enough. You won't be genius-smart, but society will never know the difference.

I'm sorry. Whether he'd ever admit to it or not, there's a difference. I think all he said in the book that even remotely hints at evidence for true innate talent is the fact that after 10,000 hours of working at something everyone's "good enough" there's no way to account for why some people get more out of their hours. I don't need an explanation for it. I know it exists and I don't like such talent being looked down on. The fact that Chris Langan can't get anyone respectable to referee or publish his work doesn't make it any less good. For all I know, he could be making breakthroughs and I don't have a mind for the kind of society that deems a college degree so important that not having one can make you dismiss the likely clever writings of a clearly intelligent man. I don't think it's bad that he's living the simple life. I think it's bad that the world failed to see his genius and I'll be damned if I ever try to blame his lack of "success" on not having the right people skills or family background. The man is most likely brilliant and deserves my respect and awe. It sucks that I'm not as brilliant as him or others, but I won't delude myself into thinking that if I just clock in enough hours I'll get there. I most certainly won't try to tell myself I can "succeed more" than the rest of them smarter folks if I just follow some set of steps they didn't think to follow. It's the difference between Julie Andrews and virtually any other theatre singer/actress ever: no amount of practice can make up for such levels of raw talent.

In the case of maths, you may get good at high school maths and even linear algebra and calculus through practise, but you cannot clock in enough hours to make you the kind of person who can come up with elegant solutions to problems. That kind of insight is something you can't train for. Some people have it built into them and some don't. The fact that it's rare makes it precious and beautiful. Kind of like SmTn's way to talk. I may have been writing in this blog for a long time now, clocking in quite a lot of hours, but I assure you it doesn't make me good enough to be truly worth reading. It still won't be worth reading ten years from now. Not unless you like what I have to say or the way I say things. Those won't be changing all that much in whatever time I've got left. 

I can sort of see the therapist's point, don't get me wrong. I'm not completely obtuse. I can see my circumstances keeping me from reaching full potential and I've wondered it aloud myself. Perhaps even in this blog. I do wonder if I wouldn't perhaps do better if I could dedicate less brain function to worrying about money and being unhappy living with crazies. The thing is... I can't see very far ahead into how to overcome this. The book doesn't shed much light on it either. To the right person and seemingly-right-but-not-quite circumstances the author offered no advice. It was just bad luck he was born in the wrong time, to the wrong parents, in the wrong country. What do you do then, besides act as a stepping stone for your children who will undoubtedly be successful?


Because the thought is in my head anyway and I can't chase it off, I'll write it down: if I could choose when and where to be born, to what parents, if I could choose the "right" circumstances.... I have wondered if I wouldn't have made it so that I'd met SmTn before he met his girlfriend/wife. Maybe all it would have taken was going to summer school two years earlier. I don't know.



I'm still in a La Oreja de Van Gogh mood: "La Playa" is the song I most often turn to. 

I can't help but find it odd, you know. I don't think I'd listened to so many songs in Spanish since I was... what, 15?

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