Two and a half months later...

Nothing New Under the Sun

You can consider this a wrap-up post for my academic career. I don't mean that I intend to stop learning, or even stop attending classes, but I've been going to school since I can remember, and in three weeks I won't be going to school anymore. I'm finally graduating from college, and at this point in my life I'd like to take a break--by which I mean I intend to enter the working world, rather than continue on to graduate school. It's only fitting that I should be reminded, now, about something I've noticed more and more frequently as I accumulated knowledge.

Don't take the title too literally--I am certain that there are things yet to be discovered. But as history piles up behind us, there seems to be less and less to discover. Humanity certainly knows more now than any single human could figure out on his own, even over an entire lifetime. As a result, a person's level of knowledge is more a measure of how exhaustively he has gathered up the lessons that others have learned. This isn't directly linked to years of formal education, of course... but it's not far off, either.

I speak from experience. Many times in the past, I have discovered something clever or insightful (often about philosophy, psychology, or the human condition), only to find out, sometimes years later, that it had already been discovered centuries ago, and written down for everyone to know. I'm not opposed to sharing knowledge... but the results of it can be disenchanting, sometimes.

I haven't mentioned it before because I could never recall a specific example. But in this case, it happened moments ago. I'm pretty sure I just figured out the Sieve of Eratosthenes.

There I was, moments ago, sitting around thinking about primes. (Not my usual occupation, I can assure you.) I started thinking about the quest for a pattern behind primes--a way to predict them. It occurred to me that there was a pattern, but it wasn't a pattern of primes. It was a pattern of factors. Imagine a number line of integers, with a line (like a sine wave) going along it, passing through 2, 4, 6, 8, etc. The integers it passes through are even numbers, and the gaps are not. The next number that occurs in a gap has another line starting at it, and recurring at 6, 9, 12, etc. There are now some overlaps (which may have significance, but not at the moment), but fewer gaps. Now repeat. It becomes a cornucopia of interwoven patterns, and the patterns are all very simple... but their interaction is not. No matter how many lines there are, there are always gaps. And as thick as the nest becomes, there's always another line arising from the prime in the gap, to add its pattern to the rest.

Which is a much better visual than the GIF in that Wikipedia page (just imagine all the primes glowing... and maybe the lines start out thick and taper as they go... isn't that pretty?). But I'm still kind of disappointed that someone else thought of it first. Rational or not... I feel as if I've arrived at a party thousands of years late, and all the beer's gone.

Was It All Worth It?

I got a letter from the government today. I've been getting them for a while, but this one has special significance. Just recently I confirmed that despite all odds, each one of the six remaining classes I need to graduate is offered next semester, and with very little time overlap as well. I still have to take the GWPE (Graduate Writing Proficiency Exam), and of course I still have to take each course and worry about keeping up my GPA, but passing them is not a concern. I now have no reason to be concerned that I might not graduate in May. This brings with it a huge list of concerns, but it's also very heartening, and I'm quite relieved. I'm particularly enjoying the thought of no longer having to fill out a FAFSA (Free Application for Federal Student Aid). (Basically it's a form where you have to prove how much money you have, so they know how little to loan you.)

The letter I got today was just a statement of how much money I owe in federal loans. I'm not going to take any more loans, so this is it--essentially, this is the bill for five years of college. It comes out to just about $20,000.

I don't really have a framework to understand that amount. It's not horribly much, I suppose... in fact I think it's about average. It could have been more. I guess I won't really know until I find a job, and discover just how much I can expect to pay per month, and how much I'll be making. It's good to have an amount, though. And it'll be even better to have a degree. It's all coming to a close.

Theis Schmesis

For about a year now I've been actively contemplating graduate school. I'm getting my Bachelor's degree (barring misfortune) in just two more semesters. After that, the rules go away. Oh, they've been fading for a while, and college has been a great way to gradually transition into the concept of actual responsibility. But up to now I've always had a pretty well-defined "roadmap" for success. Every year a new class, every week a new assignment, every summer a few grades and a long vacation. This pattern has structured my years for literally my entire life--I can't remember a time when I wasn't in school. And it's been something of a crutch, too, at least for me. I crave structure. I fear making decisions. And although I've had to make a few vague choices about my future when applying to college, choosing my major, and taking classes, in one year I'm about to fall out of the structured, comfortable, predictable, guaranteed, reliable system, and into... what? Whatever it is, the transition isn't going to be structured, and it isn't guaranteed to be smooth.

So for about a year I've been contemplating the steep cliff in front of me. And I can see two options: get a job (career?), or go to graduate school. (I can't help but notice here that I've implicitly defined failure as "not an option". I wonder if I'll be chuckling about this in 12 months...) And I'm really not very familiar with either of them. I'm afraid that at some level the primary reason I want to go to graduate school is just to stay within a structured system--if true, I would consider that a "wrong reason", perhaps even a character flaw. But I can't tell if it's true. What I can say is that the thing that frightens me most about graduate school is the concept of the Thesis. And despite the two rambling introductory paragraphs, that's actually what I started this post intending to talk about.

You see, the Thesis scares me. But it just occurred to me that I don't know why. I hardly even know what it is! I suspect that all this "thinking about my future" that I've been doing has been nothing more than rehashing the precious little I know about what my future could be, rather than going out and actually researching what it would be like. My concept of a Thesis was only vaguely defined as being something along the lines of a 100+ page paper. I doubt anyone really enjoys writing papers, and in many cases it's been nothing more than drudgery. What's more, the drudgery has been directly linked to the length of the paper. Strangely enough, it only just occurred to me to look behind the mere stimulus-response of this learned aversion to paper writing, and figure out what was causing it. It's not all that surprising when looked at carefully: When taking six classes a semester, there's only so much time/effort/interest one can put into each class. And the greater the amount of work that an individual professor assigns, the more strained that already-small amount of time/effort/interet becomes. The result is often a whole lot of disingenuous boilerplate, which can quickly sour the entire paper-writing process.

But is a thesis different? I never asked myself that question before, but I think the answer is yes. I love to learn, and I'm gradually coming to the conclusion that having only one thing to learn at once, instead of seven, might make a huge difference in my motivation level. So far, in the last few weeks, I've been working on this code almost nonstop--partially because I don't have anything else to do with my free time, but also because I really am interested in improving it. I think this is a good sign, because hopefully this will be similar to what I could be employed to do... but something tells me that I might be better served by staying in a university setting, where I'd have more freedom to choose a topic to learn about, and spend my time producing knowledge, rather than being heavily focused on producing a product. Maybe the thesis is just an extension of this concept--I could learn and learn to my heart's content, and the "proof" of that learning, in the form of expounding on the topic at length in a paper (and in a verbal defense), would come naturally.

This gives me hope. But I have to make sure I'm not forgetting any key details... like teaching classes. Is that an inherent part of graduate school? I'll have to do some more research...

(Word to the wise: In case you couldn't tell, the verbosity of this post (both in length of individual words and number of words written) is a dead giveaway that I'm writing this post at or around midnight, frantically typing out a half-formed idea before I fall asleep and forget it entirely. I suspect that's the entire point of blogging, but I just thought I should warn you nonetheless. Hmm. Maybe I should just put that in my profile and save time.)