The Nature of Math

3/9/08 – 3/16/08
by C. Zaitz

I’ve done many different things to make a living, but I never thought I’d be teaching math to anyone. Frankly, I wasn’t a big fan of math classes in school, though I’ve taken my share of them to get to the “good stuff” in physics and astronomy. I found some math teachers to be in a “mathy” tower, using a “mathy” language that was hard to understand. But I needed the tools of math, like poets need a language to do their art. Without math, physics and astronomy are only descriptive. Without it, we would never have been able to pin down the age of the universe, much less balance our checking accounts. So we have to do math.

I’m teaching it only temporarily, but already I have a new appreciation for the language of mathematics. Math never wanted to be in a tower, and never wanted to be a separate language. Math permeates everything. Nature has a deep friendship with math- it uses it to design itself. Leaves, seashells, flowers and pinecones all reflect specific mathematical relationships.

Not only did nature use math in its designs, mathematical relationships have allowed us to unlock the mystery behind why the planets orbit they way they do, to understand the relationship between a star’s distance and brightness, and even to figure out how fast we are moving on the surface of our planet, earth.

I’m not saying the language of math is always easy, but it’s not always hard either. Kepler’s laws tell us that the period of a planet is related only to its distance from the sun. That’s beautiful, but it requires finding squares and cubes of numbers. Thank goodness for calculators. To figure out how bright a star is, you can use the inverse-square law. That sounds complicated, but nature says the further you are from a source of light, it gets dimmer faster than you’d think. If you are twice as far away from a star as your neighboring alien, you will experience only a quarter as much light. The cool thing is that the law works for other things, like gravity and magnetism! The math is fairly simple, but it has far reaching import.

To find our speed standing still on the surface of the earth, we need to know how fast the earth is spinning. 2 pi divided by 24 hours times the radius of the earth yields around 1,000 mph! That’s how fast the ground under our feet is moving (at the equator.) And so are we. But it takes physics to explain why we aren’t flying off the planet if we’re traveling so fast. We call it inertia- we’ve all been going that fast since we were born, and the only way we’d feel it is if the earth sped up or slowed down abruptly. Math coupled with science is the most powerful tool we humans have.

For me, the beauty of math has been about how useful it is. But the Golden Ratio is a famous relationship between ratios, and its proportions are pleasing to us. Artists have used it throughout history in famous paintings. There have been philosophers who suggest that numbers have been our connection to the eternal. But I’m not that ambitious with math. If I can just get my students to figure out how high a flagpole is by measuring its shadow and using trigonometry, I’ll be happy.

Until next week, my friends, enjoy the view.