Thu, 23 Feb 2006top
This is stupidity at its finest. Richard Cohen decries the necessity of the existence of algebra and uses the old argument that people shouldn't need to learn what they don't want to.
When I think of how far behind the U.S. is when compared to the rest of the world in science and math, it astounds me and indeed pains me grieviously. This gap in itself, unless changed, will probably eventually spell the end of American cultural and economic dominance and hegemony. Nevermind the technological breakthroughs that make our lives unrecognizable not only from the lives of Americans a hundred years ago, but from the lives of Americans just a generation back, the breakthroughs that are the backbone of our prosperity and wealth. Ultimately, what do you think allows us to create weapons of mass destruction that allow us to rule us to world as we see fit? That's right. Science and math. Even designing a gun that won't blow up in your hands requires sophisticated science and math that just probably requires some understanding of algebra. Once America becomes a nation of fat idiots who have to buy their weapons from the French, it's all pretty much over, and that's the trajectory that we're plotting out right now.
Cohen brings up the strawman argument: "It teaches reasoning," said in the same tone of voice one says "It builds character," which everyone knows is code for "this will make your life miserable and won't bring about any material gain for you, but do it anyway and just suck it up." Yes, algebra can cause misery. My introductory Physics class, designed for premeds and biologists, which taught me Classical Mechanics without requiring me to use calculus (go ahead and laugh, all you real physicists, mathematicians, and engineers) was basically just algebra dressed up in vaguely physical terms. (You know, falling in a vacuum, or moving about on frictionless surfaces.) This class once caused me to go on a book-ripping, pencil-breaking, screaming-and-yelling rampage and (along with the subsequent semester of Electromagnetism, again without calculus) caused me to realize my intellectual limitations. Yes, algebra teaches reasoning. But it teaches a very specific and, to my mind, exquisitely useful form of reasoning that helps me in more mundane everyday tasks like, oh, figuring out how much to tip, or how much money I'll end up paying the banks for all the debts that I've incurred, or how much I'm going to have to pay in taxes. I bet you that even you folks who thought algebra really sucked and was completely worthless can do these essential tasks (essential at least in a capitalist society) Well guess what, you're probably using some algebra and you didn't even know it. (Or maybe you're not. Maybe you're just going through life spending money you don't really have. Maybe you're wondering how the hell your accountant came up with such a ridiculously small or absurdly large sum. Well, folks, maybe this might be why your credit rating stinks and why the banks won't let you buy a house.)
But I'm not going to go into how algebra makes balancing your check book, creating a budget, calculating compound interest, or figuring out how much money you saved at the department store sale a hell of a lot easier. Even if you use Quicken or Excel and think that the computer is doing all the thinking, it's really not. I'm going to talk about something more esoteric: the concept of the Unknown Quantity.
Computers don't really know how to deal with the Unknown Quantity. The only reason why it seems like they do is because most of us can do basic algebraic operations without realizing that that's what we're doing, and this allows us to pose the question to the computer in a form it can answer. But again, I'm not really going to go into that.
Everybody probably remembers good old x. This was pretty much the avatar of the Unknown Quantity. And what good is the Unknown Quantity? It lets us solve problems even when we don't have all the information at hand. This is an extremely powerful tool, and while most of us use it on a practical basis without necessarily writing out the algebraic equations, this is basically what algebra is.
I don't know. Maybe there really are people out there who can't deal with the Unknown Quantity. Religious fundamentalists and diehard ultraconservatists come to mind. But I can't really understand what this would be like. To need to have every bit of information at hand before you can act. To not be able to conceive that there may very well be something we don't know lurking out there, which can either be a boon or a deadly hazard. The concept of x allows us to go about our lives while taking the vast uncertainties of our lives into account. To not understand the Unknown Quantity is a supreme failure of the imagination.
OK, maybe I over-simplify. You need at least algebra and the concept of limits.
I remember the first time I saw this, I thought it was magical: lim x→∞ 1/x = 0
Basically there are tricks you can use to make uncertainty perturb your vision only slightly, or maybe even cancel out completely. But I digress.