So after I was asleep for fourteen hours, I went to the bathroom to pee.

…and then I crawled back into bed to sleep some more.

What is up with incredibly hot girls who smoke around our beloved city?

I think girls like this have an societal obligation not to smoke — along with their other obligations, such as wearing curve-fitting jeans, skirts, dresses, and the occasional low-cut blouse.

That way, I can feel free to stare all I like without getting turned off.

Because, man, when I see a pretty girl who smokes, it’s such a disconnected feeling. Like eating one of those ‘display-only’ cakes, which look great, but tastes like cardboard.

Not that I’ve done that.

I’ve been on the verge of stress induced attacks nearly every day these past few weeks — and I don’t think they’re about to stop anytime soon. There’s just so many different things I’m worried about. The threat of scholarships and graduate applications are (more or less) over, but this has only been replaced by more and more work.

The biggest problem is of course my thesis, which largely remains unwritten and is technically due in two weeks — though unofficially, I have about a month plus a few days — assuming I’d be okay with pissing off a few members of the committee (I am). The classwork itself is unrelenting, with assignments piling up, (one) midterm left, and final projects due near exam period.

And then there’s the TAship — which by itself isn’t too bad. I’d say about 9 hours a week are spent here, which isn’t exorbitant, but it piles up quickly. This includes office hours, tutorial centre hours, marking, giving tutorials, tutorial preparation, and so on.

Finally, there’s the personal problems — which for better or worse, remain personal.

Watching The O.C. way back in high school was sort of the thing to do.

Everybody watched it. Everybody talked about it. And sometimes even the teachers got in on the action. It was sort of our Generation Y’s version of Beverly Hills 90210. You know, melodramatic teen (and not quite so teen) angst. High school kids who look like 25 year old fashion models. 45 year old mothers with 25 year old boobs. Brooding men punching each other. That sort of thing.

It was announced early this year that The O.C. would air it’s final episode on Thursday, February 22, 2007.

And it really shows. The soon-to-end forth season has been really strong, the big difference being that the writers and producers finally have a game plan — knowing that they have to wrap it all up by today.

I’ve really been enjoying this light-hearted season (Taylor Townsend (Autumn Reese) is so hawt), and I’m totally stoked about watching one last final, melancholic episode of The O.C. tonight

P.S. I hope Ryan punches someone.

Over the course of the next few days week, we’re going to derive this sucker:

What is it, exactly? An equation of course. But for what? The area of a triangle? A measure of how cool the author is? The erratic behaviour of your new girlfriend? An explanation of why men are such dogs?

Better. That equation — or more specifically — the set of three equations (there are actually three hidden in there) are collectively known as the Navier Stokes Equations — the fundamental equations governing the motion of practically all fluids (liquids and gases).

Unfortunately, although we can write out the equations pretty quickly and even derive them, solving them is a whole new can of worms. In their general form, they’re virtually impossible to solve analytically (on paper and pencil) and solving the equations using a computer is no walk in the park either — being the central focus of research in Computational Fluid Dynamics.

In fact, the Clay Mathematical Institute has long offered $1,000,000.00 to the first person who can answer a few basic, fundamental questions about these equations. Oh, and there is the small reward of appearing on the front page of every newspaper in the world, as well as gaining a good chunk of academic immortality.

Oh, and think of all the chicks you can pick up, too. This is the sort of thing babes go crazy over.

Trust me.

Unfortunately, unlike my previous excursions into the mathematical battlefield, I won’t be able to steer this towards everyone. There’s a fair amount of background material you’ll need to have in hand, and it would be a big mistake for me to try and write a self-contained series.

Here’s sort of an outline of the prerequisites:

1. Grade 12 Physics: Newton’s laws, vector arithmetic, and force diagrams.

2. Elementary Calculus: Differentiation, integration, differentials.

3. Vector and Multivariate Calculus: Partial derivatives, surface integrals, volume integrals, divergence

Basically, if you’re in Math, Physics, or Engineering, you should be fine. If you’re in Biology, Chemistry, Computer Science, or similar fields, you might need to Wikipedia some terms. If you’re in the Social Sciences or the Arts, you may…well, you may want to consider a career change (zing!).

I’m kidding. Really. Please, don’t hurt me.

Crates and Fluid Blobs

Let’s take a moment and reminisce about that stuffy old physics classroom you spent so much time in during high school. It’s June, stifling hot, there’s only one crappy fan in the class, and the dorky guy next to you won’t shut up (Hi Mom).

You were learning about Newton’s three laws, and the teacher would give a question about pushing crates.

There was always a crate, you know. Even if your teacher was sympathetic and drew in a toboggan to pull or a pile of textbooks to push, you knew it was really about a crate.

Yeeesh.

To analyze the motion of the crate, you applied Newton’s laws to balance certain equations involving the different forces involved — the applied force, the normal force, and the gravitational force. Sometimes, you’d use conservation of energy or conservation of momentum arguments to also find a balance between the different quantities.

For the most part, our analysis of fluids will be similar. But instead of looking at crates, we’ll be examining fluid elements — blobs of water if you will. We’ll apply conservation laws to these blobs of water, and just as we developed equations to describe the motion of crates being pushed, we’ll develop equations to describe the flow of a certain fluid.

Oh man, how wicked is that?