Calculus is Fun!

Yesterday I came to the disturbing realization that I enjoy calculus.

Why disturbing? Because when I went to college the first time, I did not enjoy calculus. In fact I hated, hated, hated it. Especially Calc II, the class I’m now taking again. The one I’m enjoying.

For twenty years I believed that I hated calculus. Now, suddenly, I don’t.

Who am I, anyway? (And who is it that asks?)

I gave this question some thought, and it’s pretty simple. On my last go-round with calculus, I was focused on computers. Calculus was not going to help me learn to program in that new-fangled C language. In fact, since I had learned about Simpson’s Approximation and other techniques, I knew that it was possible to use a simple algorithm to get a numerical answer to a calculus problem to any degree of accuracy, without needing to memorize a bunch of cryptic integration forms. Who needs more than that? The simplest understanding of derivatives and integrals, and any programmable calculator, can answer any real-world calculus question. Why was I being forced to waste my time on this crap?
Pretty clear. Shallow and arrogant, but clear.

So what’s different today?

I’m taking calculus today in order to get an aerospace engineering degree, which, unlike programming, requires calculus. I really want this degree because I really want to help create a spacefaring civilization, preferably by helping to design and build spaceships.

Since I’ve seen this material before, it’s a lot easier this time around. That helps a lot.

Also, I recently reread Neal Stephenson‘s Baroque Cycle trilogy, which takes place around the time of Newton’s and/or Leibniz’s discovery of calculus, and does an excellent job of explaining what a big deal this was in Mankind’s ability to understand and explain the universe. For example, we had all this astronomical data showing that heavenly bodies all move along conic sections. Also, we knew enough about the moon and the earth to see that whatever force keeps the moon in its orbit happens to obey an inverse square law. Now, here comes calculus, and suddenly we can prove that a particle in an inverse square field always moves along a conic section, and that an body behaves as if all its mass is concentrated at its center of mass i.e. it behaves like a particle. Suddenly we were able to explain how gravity, which we once believed to be a purely local property of Earth, is producing the motions of all the rest of the bodies in the universe.

Calculus isn’t a pointless, sadistic tool for torturing undergraduates, it’s an astoundingly powerful tool for understanding the universe! Why didn’t I see that before?

My wife, the life coach, tells me that my beliefs about calculus changed, so now this huge change in my character became effortless – in fact it happened without me even noticing. Cool. I’m getting an A in Calculus!

Now how can I change my beliefs about cleaning toilets?