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.
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