Friday, February 17, 2006

What is the Value of Algebra?

A column by that title appeared in the Washington Post.

The columnist, Richard Cohen, describes the case of a girl who dropped out of high school in her senior year after flunking algebra six times. Algebra was a graduation requirement.

Richard Cohen himself flunked algebra once, apparently, and barely passed the second time. He says it was a miracle he made it through geometry, and that to this day, although he can do basic arithmetic, he struggles with percentages. And yet he has had a successful career - his own column in the Washington Post! The lesson he draws is that algebra is completely unnecessary. He has never used it, and never regretted not being able to use it.

What's more, he doesn't believe that alegebra teaches reasoning. He says that writing is the highest form of reasoning - you know, rhetoric, debate, the stuff that lawyers do.

Okay, I'm not going to write the blistering critique that this undoubtedly deserves: P.Z. Myers already did. You should read his post, because he's right. But, as usual, he makes good points in a way that makes me want to disagree with him.

See, I struggled with algebra too. I think I got a C, actually. Around the same time, I was getting 50th percentile on standardized math tests. And although those events were around age 14, I also chose more recently, to take the new writing-reasoning section on the Graduate Record Exam instead of the old analytical section: "Amy sits across from Bobby and Carla sits two places down from David. Where were Emily and Frank sitting?"

Not a single math class ever came easily to me, but I learned it, and learned more, and I'm glad I did.

What I've learned is that algebra isn't just for solving homework problems. I took a formal logic class from the philosophy department, and learned that statements, as well as numbers, can be represented symbolically. I used algebra for any chain of reasoning longer than a simple syllogism. I honestly believe that lawyers and Washington Post writers would perpetrate fewer logical fallacies if they all had to take that class.

That's the class where I first learned about truth-tables, a technique I went on to use in my electronics course, where I learned how to build simple digital logic circuits. Richard Cohen may not do a lot of algebra, but I bet he uses a lot of digital logic circuits. I used algebra in computer programming -- I bet he uses a lot of computer programs. He can claim it's not necessary for him to know algebra, but he can't claim algebra isn't useful to him, because it makes a lot of the things that he uses possible.

But those are just utilitarian arguments. He probably thinks that the world worked just fine before all of these things were discovered. Cars are useful too, but we are not all required to learn auto-repair in high school. He probably sees math as a vocational skill. He seems to think that the engineers who built these things were "whizzes at math but did not know a thing about history and could not write a readable English sentence." (He mentions a girl from high school who couldn't locate the Sahara desert on a map. Never mind that according to National Geographic a third of Americans age 18 to 24 can't find the Pacific Ocean on a map.) To Richard, math is like money. Flashy modern electronics may require a lot of it, but it is a shallow subject.

He's rather think deep thoughts about the nature of the world we live in.

But guess what, Richard? At every level, the world we live in obeys mathematical laws. You are worried about injustice? Find me the statistics to tell me who is starving and how much food they need. There is no way you are ever going to solve the problem without quantifying it. You want people to know geography, Richard? Without algebra, sailors would never have been able to navigate beyond their own coasts. Are you at all interested in the fundamental questions about the nature of reality, about time and free will and what those lights in the sky might be? The answers are in physics, Richard. The stars and the planets and we ourselves are all subject to the same immutable algebraic laws. How can you be so incurious that you don't even care to know what they are?

P.Z. Myers is right. Algebra is useful to society if not to Washington Post columnists, and it opens doors to those who learn it. But it is more than just useful. It is the language in which the universe is written. Even if you don't like it for its own sake (I never did), you must learn it to even begin understand the world in which you live.


Anonymous said...


From Pyracantha

Mary said...

Yeah, I seem to make that typo almost every time I write the word... Figures I'd make myself look illiterate in the title of a post about innumeracy...