From Fish to Infinity

Yesterday, my eight-year-old said, “I don’t like math, but I’m good at it.”

This is a huge improvement from the math-related tug-of-wars we’ve encountered almost daily for the past year and a half. Yesterday, she also finished a “Star Wars Math” game, where the idea is to play a Trivial Pursuits style game, spaced-out versions of blackjack, and other games where you have a better chance of winning if you do the math.

Until recently, Carolyn would simply guess at the various answers, and make no real effort to learn the math. But for some reason, yesterday something clicked, and in one sitting she earned the last $10,000 she needed in order to buy a $25,000 hyperdrive engine to get off of Tatooine and win the game.  (Winning the game came after she announced she was good at math, by the way.)

A former roommate of mine (a math major) just posted a link to the first of a series of math-related essays in the New York Times. I’m looking forward to learning more about this discipline.

[Numbers] apparently exist in some sort of Platonic realm, a level above reality. In that respect they are more like other lofty concepts (e.g., truth and justice), and less like the ordinary objects of daily life. Upon further reflection, their philosophical status becomes even murkier. Where exactly do numbers come from? Did humanity invent them? Or discover them?

A further subtlety is that numbers (and all mathematical ideas, for that matter) have lives of their own. We can’t control them. Even though they exist in our minds, once we decide what we mean by them we have no say in how they behave. They obey certain laws and have certain properties, personalities, and ways of combining with one another, and there’s nothing we can do about it except watch and try to understand. In that sense they are eerily reminiscent of atoms and stars, the things of this world, which are likewise subject to laws beyond our control … except that those things exist outside our heads.

This dual aspect of numbers — as part- heaven, and part- earth — is perhaps the most paradoxical thing about them, and the feature that makes them so useful. It is what the physicist Eugene Wigner had in mind when he wrote of “the unreasonable effectiveness of mathematics in the natural sciences.” –Steven Strogatz, New York Times