A friend just sent me a video of Tony Orrico, whose Penwald series seems to be gaining some steam in certain art/dance circles. Here’s a sample:

Essentially, we have an artist who devotes his body to an algorithm. He takes several simple moves, and repeats them in some kind of pattern. You could feed a computer a few lines of code and generate these designs almost instantly. Of course, they wouldn’t be quite the same, since Orrico is human, and there has to be some imperfection in his execution. I think there must be some thrill for people in seeing how computer-like a person can be, and also feeling the deviations from exactness that give his work some sense of humanness.

I’ve written about algorithmic art here before, and while the field as a whole is fascinating to me, there’s a way that Orrico makes me uncomfortable (Katherine thought he was hiliarous). Why should a human being replicate a computer’s function, especially in such an uncomfortable way? He’s an endurance artist, a highbrow cousin of the circus. (I’m reminded of Kafka’s *A Hunger Artist*, a story that never fails to bring me to tears.)

This is the argument of the pro-computer crowd in math education of course. Sometimes, I find myself with them. But on the anti-computer side, people say: doesn’t Orrico get a deeper understanding of the algorithm and its implications than anyone who just clicks a button? And I have to say, I’m sympathetic to that point of view as well. When I wanted to think about a laser bouncing around a circle for a recent talk (which will be available here soon, I hope), I had two options available to me: Wolfram Alpha Demonstrations and drawing it out by hand. By hand was simpler.

It started with a single light beam shot 3/8 of the way around a circle and

ended 8 bounces later with the beam returning to the top of the circle, to repeat the same route again forever.

Meanwhile, Wolfram Demonstrations let me go further than I ever could have gone by hand.

Which is the better way?

The good news is, we don’t really have to choose one way, and throw the other away. Doing work by hand helps me see the underlying structure are work here (the beam of light went 3/8 of the way around, and it had to bounce 8 times, hitting every eighth… maybe I can use whatever fraction the light first hits to predict how many bounces it will take to get back to start… and what if it doesn’t hit a fraction at all?)

On the other hand, there’s something fun about the Wolfram Demos, and many of them let me grasp things that might be much more difficult to see and feel otherwise. For example, I can see immediately that there’s something like a circle in the middle of the larger circle that the light never enters. Playing with the Demo gives me an instant sense of intuition for why that is, and how big that empty circle will be. Other demonstrations, like this one about reflective chaos, would be virtually impossible to grok without the help of a computer.

Maybe this is just a matter of personality. I have a decently high threshold of patience for long calculations, but nowhere near Orrico’s. When I need to solve a quadratic equation, I’ll do it by hand. When I need to solve a cubic, I reach for a computer. Finding the right blend of computer vs. human when it comes to calculations is a subtle question, but in most contexts, I think a tuned in teacher has a sense about what a decent balance looks like. The danger, as with all things systemic, is that the choice gets made once and for all so far away from the classroom that by the time it filters in there’s only one right way to do things, and it doesn’t make sense for that class, or for that teacher, or for those students. I tend not to use calculators when I’m teaching because I think they tend to become a shortcut for students before they’ve understood the territory. I’ve seen them lead to mental laziness, with high schoolers dividing 3 by 2 to get 1.5, rather than just knowing that 3 divided by 2 is three halves, which is one and a half. But is it possible to teach well with calculators? Absolutely. Done right, there are some real advantages to it. It spares our children from having to become little Orricos against their will, for one thing.

And I end up at the same place I always do: if you’ve got the love, if something about what you’re doing calls to you, then it’s worth doing. Orrico is following his own questions and his own passion; that’s why (some) people like to see him perform, and want his art. It’s not about being pro- or anti-calculator. The question is, what are you driven to understand, and what tools do you need to get where you want to go?

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