One day, I hope that a musical will bust out in my class. Given the title, can you guess the song I would like to hear? To dream the impossible dream—From Man of LaMancha. I am a romantic in that regard. I admit sometimes as a teacher I give assignments that are too much for them; sometimes this is not well thought out as an assignment on my part and giving achievable challenges would be a better strategy. However, I still want to reserve the right to challenge students in ways that that overwhelm them completely.
Why would I want to do this? Well it is part of how I learned. Let me tell you about my 9th grade geometry teacher, Fran Lassiter. I was an eager student in 9th grade—eager to dodge any work I could. So when the teacher offered the chance of an A for the class and no work for the rest of the year, my ears perked up. We were told that if anyone could trisect an angle using only a compass and a straight edge, that person would get an A and a free pass to do nothing further in the class. Even though I was eager to avoid work, I was not lazy; so I began to get busy. I learned how to bisect angles, copy angles and a whole host of others skills that I would need to accomplish the trisection. I worked and worked—but to no avail. One strategy was to bisect my bisected angles and continue on until I got a way to combine the bisections into a multiple of three. (If I had remembered algebra, I would have realized this was impossible—but I was busy working.) Finally I realized that trisection, using the tools I was given, was geometrically impossible. It wasn’t a lack of ingenuity on my part—it was just impossible.
Mr. Lassiter could have told me it was impossible—but now I knew it and I knew it on my own. This is part of the beauty of geometry for me—some necessities are independent of social constructs. (I think this is why Plato had written in gold letters above the entrance to the grove of trees in his academy—“let no one who has not studied geometry enter here”).
One more example of an impossible assignment—when I was applying for a teaching job at Hopkinsville Community College I was told to give a teaching demonstration on Plato’s allegory of the cave. OK, sounds reasonable. Then came the crushing blow—do it in 15 minutes. I think an appropriate analog in the sciences would be something like: teach the muscle, ligament and bone structure of the human body in detail in 15 minutes. I was well prepared for the assignment and had been teaching Plato for many years. I prepped and prepped—but the more I prepped the more complicated the presentation became and the more it sprawled beyond the time limit. The presentation grew from a simple introduction to an in-depth consideration of a near infinite number of problems associated with human knowledge. Either I could present a sprawling talk and go over the time limit or I would have to talk so fast that no one could keep up. Finally, I realized they have given me an impossible task.
My strategy then was to redefine the assignment. I re-tooled, threw out all my lengthy notes and created a board game—called Escape from Plato’s Cave. I made the game virtually unwinnable. When playing time came many of the people on the committee were going around and around on a circular track or being sent back to square one. The point—escaping the cultural limitations of our ideas and sense of reality is virtually impossible. As we played, the group decided to break the rules of the game and cheat a little so that we could see what beating the cave would entail. So I met the impossible task of presenting Plato’s theory of the cave with giving the committee an impossible task of beating a virtually unbeatable game. (I think part of my motivation was to get revenge.)
What was learned? I think that even in the demonstration class/ job interview we learned something about possibilities and limits. Sometimes our world confronts us with impossibilities or near impossibilities. What do we do in the face of them? We can recognize some genuine impossibilities (as I did in the geometry class) and learn a kind of humility. Bumping against impossibilities is frustrating, but stepping back and looking at them promotes a kind of learning that is pleasurable—not in any conventional sense, but in learning unpleasant limits. It is the pure pleasure of knowing.
Coming up against these unachievable limits is a necessary part of an education and that is why I want to offer a praise of unachievable challenges. There is too much to do, not enough time, not enough knowledge about what we need to know to make decisions, and the list goes on. Yes, we can and sometimes do manage—but there is an overwhelming-ness to life. Learning about unachievable challenges is part of life. Introducing philosophy to students opens a daunting can of worms; each question spawns another, every answer spawns several objections and soon there is a huge tangled mess to sort. It is an unachievable challenge. But there I am in the class and there the students are expecting to learn—it’s just like life.
pleasureteam note: Dr. Ken Casey is Chair of the Liberal Arts and Social Sciences Division of Hopkinsville Community College, where students and colleagues alike benefit from his knowledge of philosophy and world cultures. We deeply appreciate his support of this project.
If trisecting angles tickles your fancy, you may want to surf over to wolfram.com.