I just finished my calculus midterm.
What I like most about take-home exams is that while taking the test you can listen to OCR songs and play games of chess and scrabble at the same time. Plus, if you get stuck on a problem, you can always sleep on it and try again the following day. I think that whenever I finally get a job teaching mathematics, I'm going to primarily give take-home exams. It just seems better to me.
Y'know, it's a very scary thought to think of me teaching. Not two years ago, I was what CHL called a Rand-head, though I denied it at the time. And it is only in the past week that I have started reading things like Russell and Whitehead's Principia Mathematica. (Interestingly, the Wikipedia entry on this book is only a paragraph long... Perhaps I should try getting off my ass and actually doing something constructive for once by writing about it.) I know that perhaps it seems strange to others that I would comment on this, but it is a big deal to me. I am not well trained, and it bothers me.
Now I know that others will probably groan at this point. I know that Russ would say: "What do you want to be trained for? Training is brain-washing." Just the other day, I spoke of philosophers needing to know the now almost universally defunct Aristotle in front of Matt, and his immediate knee-jerk reaction was wonder at why anyone should study a historical philosophy that has little relevance to what is commonly believed in today. So why should I worry about my training? After all, I am at least somewhat adequate at argument, and I know enough in my own fields to be moderately aware of what is going on.
But... It's just not enough.
It seems like most everything I've done in my life has been pretty damned half-assed. I dropped out of school, opting instead for a GED. I never worked in any job for longer than a few months at the most. Every essay I've written has been decidedly subpar, and every argument I've been in has resulted in little-to-no difference in the minds of those I argued against.
It's not that I'm not intelligent; I've seen the world around me, and I realize my own proficiency when it comes to mathematics, physics, or philosophy. But... I'm just not... reliable.
This semester, I signed up for an English class that looked interesting, just as an elective course. But I've missed five classes so far, and missed reading two of the books on the syllabus for the class. Even in my most advanced math class, I recently got a note from my professor telling me that I had already missed one class, and that if I was absent again, he would have to drop me. His statement hit pretty hard, since I am, after all, his favorite student -- but he's right: I need to be responsible.
About a year ago, I wrote a primer on the MTGN forums concerning the virtue of skeptical thinking. I cited Carl Sagan's Demon Haunted World and Robert Carroll's Skeptic's Dictionary as references, but... ::sigh:: I've always felt particularly crappy about the primer I wrote. As I was writing it, I kept thinking to myself over and over again: "Why am I bothering to write this? There are literally dozens of essays on exactly this same topic, the best two of which I'm citing here, but why bother writing an essay when I could just link to these better writers instead?"
Now, when I look back on it, I shudder. The essay is badly written and hard to follow. Those aren't exactly the best qualities for a primer to have. It is by no means concise, let alone elegant. I used bad word choices. I used "e.g." where I should have put "i.e.". I added no new information that Sagan, Carroll, et al had already spoken adequately on. It was a worthless, useless essay, unless it might have caused someone to see the citations given and actually follow up on them. (Yeah, right.)
But I still remember the day I wrote it. I was browsing the forums, watching my peers write the most disturbing and horribly thought out posts and actually trying to pass off the incoherence as argument. And I just happened to have come across Sagan's Demon Haunted World earlier that day by Dr. Allin, and I decided to try and get out Sagan's message to my fellow forum readers.
It seems virtuous enough when I put it like that, except I left out one thing. When I wrote the essay, I did so thinking that I was doing a service, since surely none of the others had read the book before. Only the next day, I come to find out that CHL and others had already read the book, and it hit me: I know virtually nothing that others do not know more of.
It's enough to make one feel rather worthless.
None of this would really be that big a deal, except these are the fields that I am actually intent upon knowing about. Just the other day, David asked me some random question on Lorentz fields, fully expecting that I would know the answer right away -- and I certainly should have! -- but I could not even remember where the name Lorentz came from. I could not place the name of a Nobel-prize winning theoretical physicist, who got his prize for correctly predicting the electron! For someone who insists that one of his fields is physics, this kind of thing should be a piece of cake, but instead I had to do a google search in order to answer David's question.
To accomplish nothing substantive is extremely disappointing to me. I still remember the old middle school days when Emp and I 'proved' 2=1, though we divided by zero, and when we 'proved' all triangles were isosceles, though we misused the visual geometry when we should have looked to the actual axioms instead. But these are extreme examples. I can remember when I first read Euclid's Elements, proving on my own the propositions before reading Euclid's proof. Or when I worked on raw data from particle interactions to see if I could reproduce some of the old Fermilab results. Doing stuff back then was enjoyable, even if only because it felt like I was actually doing something. I think the main cause of my depression between middle school and my college years was my lack of doing anything at all. ::sigh:: So many years wasted...
I would like to actually do something substantive. I feel like I'm on a roll after finishing this calculus midterm; I think I'm actually going to try and write a Wikipedia article on Russell and Whitehead's Principia Mathematica. And I'm not going to do this half-assed, either. I'm going to do the research necessary to write a well thought out article, covering as many aspects as possible on the topic.
Wish me luck.