Algebra appreciation

We take algebra for granted, at least those who still remember it. But it’s not as obvious as we think (as those who don’t remember it can attest.) Consider Boolean algebra: it’s very similar to ordinary algebra yet we find it highly surprising (Boolean algebra is basically just algebra for logic). Boring old algebra is similarly surprising when you think about it.

To be precise, I’m using algebra here to refer to elementary algebra. It’s the one we’re all familiar with: solving an equation for a variable (x).

Algebra lets us solve problems that would be extremely difficult without. Easy equations can be solved trivially in your head: for example, say you have $8 and you give $3 to your son and the rest to your daughter. Obviously, you gave her $5, but you could also write out the equation and solve it: Subtracting 3 from both sides we get

But when it gets more complicated, it’s much more convenient to use the rules of algebra to manipulate the equation to isolate x: for example, say you’re at an amusement park and the pricing is as follows. $12 to get in and $3 per ride. You have $30 and a 50% off coupon. How many rides can you afford? You could count it out, or write out the equation and solve it using algebra: This is tedious to solve without algebra. But it’s very easy to solve with algebra: multiply through by 2, then subtract 12, and divide by 3, yielding x=16.

As you can imagine, when the equations get more complicated it becomes practically impossible to solve them without using algebra. Algebra provides a set of tools to systematically solve equations. We can even program computers with these rules so that they can solve equations for us algorithmically.

Manipulating equations to solve them is extremely useful, and not intuitively obvious. Without algebra, we would be greatly inconvenienced.

University Hack

First year university courses suck. Chances are you’re in a huge class with at least 100 other students and the lecturer is a grad student whose English is hard to understand. These classes are pointless: you could just as easily watch a video of the lecture, or better yet just read the lesson and skip the lecture. Lectures are a terribly inefficient way of sharing information. Lecturing is a tradition that dates to the middle ages, before the invention of the printing press, when the best way to share information was to lecture to a class of students who would take notes. Nowadays, this method is horribly inefficient: the instructor reads his notes while the student attempts to both listen and write down what he says. Needless to say, much is lost in transmission. Sadly, while the rest of the world enters the information age, university courses are still taught with the ancient lecture method. The university still hasn’t fully adapted to the printing press, never mind the computer or the internet.

So what is one to do? Simple: take distance courses. Online or independent study. It probably won’t save you much money, but it can save you a load of time and effort. First, if you’re a fast learner you aren’t wasting any time in lectures aimed at slower students. Second, you completely avoid lectures and note-taking, and you’ll learn that much better. Third, you can work around your own schedule and if you can get all your courses by distance, you can completely avoid living on campus or commuting.

You’ll need to be self-motivated and disciplined, because it’s all too easy to neglect your coursework. If you’re a strong student, you’ll love it.

Vivaldi Concerto RV 443 on Recorder

This is an amazing performance, Antonini is on fire! It’s also kind of humorous how animated he is!

For more wonderful Vivaldi music, get this torrent.