Because most philosophies that frown on reproduction don't survive.

Thursday, August 24, 2006

Time to buy another book...

Darwin, on his quest to brush up his mathematics, checked out Unknown Quantity by John Derbyshire, a new book on the history of algebra. Unfortunately, the library's two-week period for new books has coincided with an overload of work for him, so he hasn't had time to read more than the first few pages. And as it was sitting about, I picked it up and have been working through it.

I'm no math whiz. Algebra and higher mathematics are a long-forgotten memory from my distant past. I don't know if I didn't take well to numbers because I have no natural aptitude or because I never encountered that teacher who had a passion for the subject and could unlock the secrets of math. But reading Unknown Quantity, from the perspective of an adult with no deadlines looming (except for the due date, of course) and a desire to become informed, I've developed a respect for algebra and for mathematicians. I haven't finished reading it yet -- it's a bit of a hard slog for me because I'm trying to work out some of the basic equations presented and I can't do it quickly. For example, Derbyshire talks about removing the term x to the second power from a cubic equation. I have grainy black and white memories of reading about this in Saxon Algebra, and even of performing the operation. But for the life of me I can't remember how it was done, and the example he provides isn't jogging my memory much.

Still, I'm starting to see why this is interesting to many people. Reading him explain about the different kinds of numbers and the different ways to solve equations, it strikes me that working out a complex equation might be a bit like writing a story. The author might know how the story ends up, but he has to work out the plot to achieve that solution. He could use the equivalent of natural numbers, and make the plot as simple and straightforward as possible. Or he could add a few twists -- how 'bout them integers? Didn't expect negative numbers, did you? -- keeping in mind the rule of signs, of course. But what if the story is some kind of Tim Powers-esque romp, with ghosts and djinn and the Cold War and time travel? Then you need the real numbers, like the square root of two. It exists, but you can't see it. It's real, but not rational!

Perhaps some real matheticians will show up and slap me around and say, "Actually, it's nothing like that at all!" But it pleases me to think that if I could just see it the right way, I could enjoy math as much as reading a well-constructed story or directing a play.

NOTE: Patrick sensibly points out that of course you can see the square root of 2 if you draw a 1x1 square and measure the diagonal. And the calculator confirms this and gives me a figure of 1.414213562. Now I feel rather silly (no fault of Patrick's, of course) and rather less insightful than previously. You know what they say about a fool opening her mouth...


Patrick said...

(fails to restrain self)

But the square root of two is a perfectly good number! You can see it! Draw a 1x1 square; the diagonal measures √2!

Now imaginary numbers, those are more mystical.

I'm really glad you're seeing it as interesting. I think it's just amazing how complicated the working out of simple rules can become. It really reminds me of the way that, even though God is philosophically simple, one never exhausts His depths, never runs out of new and staggering understandings of Him, never completes the knowledge of Him.

mrsdarwin said...

I was about to question you intensely about the square root of two, but suddenly I had a flash of insight: multiplication is not addition! This is elementary to you and to everyone else, but it just clicked with me. I wish I had someone more knowledgeable to walk me through this stuff and to shake me out of my lazy thinking.