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.

Jumping to Conclusions

Just a moment ago I was kind of frazzled. I was handing in the first assignment in Calculus, and it was almost painfully easy--just a single problem, that required nothing more complicated than an application of the Pythagorean theorem. In fact as I was writing it, the math teachers from my past were chiding me in my head that I wasn't "showing my work". The paper looked awfully bare... but there was nothing to show, really. There was no work involved. But the professor rejected the assignment as I was handing it in, saying that I should have written out the question (it was a word problem, by the way, three or four sentences of text describing a single equation), and I shouldn't have written it in pen, and that she would give me a low grade for that reason if I handed it in as-is.

As I was walking out of class, I was feeling kind of upset by this, and briefly considered writing a three-page essay with nested footnotes describing in all possible detail (and then some) the thought processes that went on behind the solving of this problem. In the end all I did was write a blog post about professors who value style over substance--or perhaps are unable to appreciate substance without the proper style. And as I was typing away on my laptop, the professor walked up to me out of the blue, and apologized. She said that she was just trying to set an example, more for the other students than for me (because she had been my precalc teacher and she knew that I wasn't at the same level as most of the other students), and that what seems silly now is necessary to get coherent assignments back from the class when the problems started getting harder.

Needless to say I was mollified, and as I thought about it more I realized that I had noticed that earlier in class the professor was kind of put-off by the questions that other students asked, and the deep lack of understanding thereby revealed. Her response as I tried to turn in the assignment was likely colored by some amount of frustration, and frankly the paper looked pretty desolate. So, once again, I'm simply trying to get through the day, and I nevertheless find myself thrown on an emotional rollercoaster, and learning a valuable lesson besides. And there's a little synchronicity thrown in to take the point home.

The post I started writing was titled "little tyrants". I thought that I remembered the phrase from somewhere, and I decided to look it up to give proper credit, or at least not mangle the original intent of the phrase. I never found out where it came from, but the first Google search that came up was a conservative echo chamber. Please read the post--it's short, and your eyes won't melt a whole lot. Here's the key phrase:

"I am not willing to assume the presence of facts not in evidence that would have recast their behavior in an acceptable light."

This phrase struck a chord with me, because I've known for a long time that this position is thoroughly inadvisable. This particular event was just one in a long string of experiences which taught me the importance of reserving judgement. It's very easy to hear about a situation, or even be in one, and think you know all the facts. If you look at the other side of an issue, there is almost always more information that you weren't aware of. It's very easy to be convinced of something if you're entirely unaware of the facts of the other side. And once you're convinced of something, it's just one small step away from rejecting contradictory evidence, and then you have a feedback loop.

Open your mind from the start, and do your darndest to keep it that way. It needs the fresh air.