Let me just say, first of all, that I had a great bike ride today, and although I may have worked so hard I’ll still be tired on Saturday when I race next, I don’t really care. I wouldn’t want to not have done this ride today. Really, great training rides are SO much more fun than races. Sometimes I feel like my racing gets in the way of my riding.
Anyway, I rode with Hobgoblin and two other friends with whom we’ve got a semi-regular Thursday ride going. We rode for three hours, although we were out closer to four when you count the stop at the coffee shop, the stop to fix a flat, and the stops to regroup. It was a fast ride, something over 18 mph (fast for me), covering 56 miles. We rode down to the Long Island Sound and back, and the weather was beautiful — in the 70s and dry. We couldn’t have asked for a better summer day.
But now on to books. I’m really enjoying Keith Devlin’s The Math Gene and am about half way through it. I like math a lot and wish I knew more about it. I haven’t studied it since high school, since I got far enough there to test out of my college requirements. It didn’t occur to me then to study it just for fun, although it occurs to me now; someday I’ll take math classes at my school, since I can do it for free.
But even if you don’t enjoy math or think you aren’t good at it, you can still read and get something out of Devlin’s book. He’s very good at writing for non-math people, and, in fact, large portions of his book are devoted to the question of why some people just can’t seem to do math — or think they can’t. You won’t be surprised to learn that he doesn’t buy the idea that some people simply can’t do math; he argues that those people haven’t been taught to understand what math is all about — they don’t get it because they don’t understand the meaning behind it. They were taught rules but have no idea what the rules mean or why they matter. This makes me appreciate my high school calculus teacher who took great pains to teach us just what calculus is useful for and how it began.
My favorite part so far is where he gets into some actual math instead of talking about it more generally; he has a section of a chapter where he explains group theory and gives the equations that explain some of the relevant concepts. He introduces this section by saying that it’s okay to skip it if the math becomes too hard, although skipping it will mean you won’t understand all of his later points fully. Of course this laid down a fun challenge, and although I struggled a bit, I made sure I understood what was going on with those equations. But I also like the way he takes care to reassure the reader that not getting it is okay. He’s a very kind and understanding author that way.
The book is also fun because it explains things like why lots of people count on their fingers, why parts of the multiplication tables can be so hard to remember (why many people, including me, have to think a bit about problems like 8×7, 8×6, and 9×6), and why Chinese and Japanese students tend to do better at math in school than Americans. This is not entirely explained by the relative quality of education, but it also has do with language: numbers are easier to learn in Chinese and Japanese because the words for numbers are easier. One study shows that most Chinese and Japanese children can count to 40 by age 4, while it takes American children one year longer to reach this point. We know this difference is due to language because, interestingly, there are no differences among these children when it comes to learning numbers 1-12, numbers that are easy to learn in English as well as Asian languages. It’s the numbers 13 and beyond that trip American children up because of the complicated way they are formed.
Devlin is excellent at explaining things — at using clear examples and telling interesting stories. If you aren’t a “math person,” but are at all tempted by this, be reassured that he makes the subject accessible and interesting. I’m looking forward to the book’s second half!