I took Betty on a little walk hoping that we would travel maybe 100 yards at most and that she would sniff stuff for 30 minutes or so while I stood around and did nothing, but Betty wasn’t about to let me get away with slouching off during a walk. Betty wandered ahead slowly at first, but I took too long to catch up. She looked back at me with annoyance and decided that it was time for role reversal. She zoomed forward to the limit of the leash intent on dragging me out of complacency. I pleaded my case saying, “C’mon Betty, can’t I just take it easy and look around at the sky and the trees and the leaves?” but my feeble plea was rejected. This walk was going to be a run.
Betty yanked me along the usual route spending only nanoseconds sniffing the familiar spots. Resting and lingering weren’t happening, and Betty wasn’t going to be fooled by my little trick of turning around and pretending that she was going the wrong way. The whole walk was done at the basset hound gallop pace. The lesson was clear, but I’m not sure if I learned it.
Our entire yard is enclosed by a fence. The fence around the front and side yards is about 3 feet high, and the fence around the backyard is around 7 feet high. I took Betty outside and I was sitting in a chair in the backyard when I heard a loud voice coming from the neighbors’ yard saying: “I heard you have an adorable basset.” I turned to look and there was someone I’d never seen before bending over the side yard fence twisting her torso to barely see me sitting in the chair. Who is this person? Where does she live?
How does she know about Betty?
Betty, of course, was eager to please this adoring new fan. She ran over and performed her standard act for greeting fans. Her fans love it. But as Betty’s co-manager (Carol is the other), I could only lament the failure to gain some revenue from the event. I’ve tried to explain to Betty that 5% of 0 is still 0, but she just brushes me off as wanting to exploit her talents for personal profit. Betty, after all, is an artist, and she certainly can’t be concerned about mundane things like finances.
I took Betty out to the backyard to chill and eat some breakfast. She was fine as long as the Pop-Tarts lasted, but she became very annoyed after we finished eating them because I then just sat in a chair and thought about calculus. Betty’s point is why think about calculus when a cool fall breeze is blowing, leaves are falling, and the now is calling? Really, says Betty, why are you wasting life on the abstract that definitely cannot be sniffed?
Betty might be right, but letting go of the abstract realm of mathematics is beyond my abilities. Calculus is so wonderfully addictive. I like to think about its history and how long it took to provide it with a rigorous foundation. Yes, calculus is the ultimate tool for understanding the physical universe, but I’ve always disliked including physical applications when I teach it. Leave the physical applications to the physicists and engineers who know more about them than I do. I want to teach calculus as a beautiful subject outside of the physical.
I don’t teach calculus much anymore—I teach cryptography instead. This pleases me. Cryptography is something all of us use many times each day, and yet it is pure mathematics. All modern cryptography can be understood in the mind—no apparatus is necessary. I can safely stay in the abstract when I teach cryptography without worrying that students won’t be able to use it.