Principia Mathematica

I've just come from a physics class that was 50 minutes of unadulterated mathematical wanking. (any physicists who read this, please do not get angry at me. I have a better grasp of the concepts than I generally like to admit.) Basically what we did was take a nice tidy equation like this:

F= q*E + q*v*B

and turn it into a nine-headed beast that looked something like this:

f = (grad dot E)*E + 1/2 (E*del)^2+ (grad dot B)*B + 1/2 (B*del)^2 plus some more terms times some constants.

Not to mention that what we've done is take an innocuous little equation involving, at most, some multiplication and some trig, and decided it would be nicer to have it involve operators, which are nasty byproducts of quantum mechanics, and are sometimes written like this:

|operator>

which is called Dirac notation after the man who invented it/understood it. Ostensibly it makes things easier. What it really does is take old, baffling concepts (I don't know where things are? Of course I know where things are! They're...right here.) and puts them into new, baffling notation. (the hell is this arrow thing?)

Anyway, in class, we defined a new thing as a whole lot of ugly, dumped all the ugly from the nasty monster equation into it, and ended up with another tidy equation:

F = T*volume + S*surface

Which is all well and good, and we're told it's useful. Great.

This illustrates the central problem of teaching physics: do you show the derivations of these new, useful equations, and put everyone right off them because the derivations are ugly, or do you just throw the equations at the kids and just wait for the one prat who sits in the corner to say "but what's the justification for this?"

There's usually a justification. I like to imagine the evolution of chaos theory/fractals: one person sitting in his office fiddling with math and making ridiculously pretty graphs. When people ask him what he's doing, he tells them that any shape they can draw has an essentially infinite perimeter bounding a finite area. He's obviously nuts, right?

This is a demonstration that works much better with pictures, but I'll try to be brief. Imagine you have an island. You take a walk around the island (it's a small island) and conclude that its perimeter is about 500 paces. Okay. But then some pedantic government berk comes out with a set of calipers and concludes that your island's perimeter is actually 18963527 caliper-steps, which is more than 500 paces, because the calipers go in and out and around places that you just stepped over. Then imagine someone with a teeny piece of yarn. Etc.

That's all well and good, but what use is it, other than telling us why people like Jackson Pollock paintings? Well, fractals in nature give rise to this idea that there's order in disorder. And that's another concept that seems like more computational masturbation. An example: Let's say you have a group of friends, and you're walking down the sidewalk. Each of you keeps your own pace, yet there are times when you're all in step, even though you're not a marching band. Useless, right?

Yeah, unless you own a multi-purpose chaotic pendulum (who could come up with one purpose for a chaotic pendulum? The point of pendulums is that they are the same.)

Or if you're a meteorologist, ecologist, or play the stock market. Or a physicist or mathematician. Or if you like differential equations.

I guess my point is, I really like chaos theory. I think it's fantastically inappropriately named, I love the idea that if you shake anything that's disordered long enough and plot the data just so, you'll end up with order, and I like Jackson Pollock. What I don't like are stress tensors. They are rather appropriately named. And that's about enough math talk.