The Search for Wisdom
Dr. Maureen Hunter | TLT President's Report September 2014
What happens when a Calculus class takes a left turn at Philosophy 101?
The Pythagorean Theorem is not about a chalkboard triangle. It’s about the perfect, intelligible, eternal triangle.
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I HAVE TWO KIDS IN COLLEGE and sometimes wish I could once again experience the thrill of those long-ago days. Last semester, I had that chance. Well, sort of.
One evening I was sitting at the kitchen table trying to write my first presidential column for TLT. My two older kids were both home for the weekend. They were in the basement, and the conversation was getting loud.
“What’s going on down there?” I called out. No one answered.
My husband walked into the kitchen from the TV room saying, “Sounds like a typical late night post-pizza party bull session. The kind you and your friends used to have in grad school.” We’d had pizza for dinner.
Then he sat down at the table next to me, and we listened…
My daughter Laura, who’s not much of a math person, was studying for the final exam in her Calculus I class. “I don’t get it,” she lamented to Chris. “Sine waves confuse me. I can mumble ‘SOH CAH TOA.’ I can draw lines within triangles. But what does it all mean?”
“Laura, Laura, Laura,” Chris repeated. “You’re going about it all wrong. You need to see it with your mind’s eye.”
“What does that mean?” she asked frustrated.
“Well, do you really want to understand it or just learn it to get a good grade?”
“Chris, I want to understand it
and get a good grade. Why else would I be studying so hard for this test,” she answered with disgust.
“Okay. Remember in high school when you were learning about triangles and you learned the Pythagorean Theorem?”
“I guess.”
“You did that proof for a
2 + b
2 = c
2. Well, that proof wasn’t about the chalk triangle on the board.”
“Then what did I waste my time for?” Laura commented sarcastically.
“The triangle on the board was just a reminder of the real triangle. You’ll never see the real triangle with your eyes. You’ll never even imagine the triangle that the proof was about.”
“I don’t get it. You’re just confusing me more.”
“Exactly. At first you don’t get it. So you think as hard as you can about that proof, but it’s just not coming, you’re trying to understand, you don’t see it, you get confused, you work at it and then all of a sudden—aha! You understand! You got it! Now you see! We’ve all had that aha moment. That is seeing with the mind’s eye. The triangle that you understand with your mind’s eye is more real than a chalk triangle that can easily be erased.”
“O-kay,” Laura remarked, skepticism dripping from her word.
“The Pythagorean Theorem is not about a triangle on the chalkboard. It’s about the perfect, intelligible, eternal triangle that gives form to the chalk triangle. The chalk triangle can never be perfect, but the triangle that the Pythagorean Theorem is about is perfect, and it’s eternal. It was never created, always existed and will never pass out of existence. It’s unchanging. It will always be true.”
“Really.”
“It is only the intelligibility of the eternal triangle that allows us to know the drawing on the chalkboard
is a triangle. Don’t you ever hunger for that experience of understanding? Long to feel that aha moment?” Chris asked.
“Never about math.”
“It doesn’t have to be about math. It could be anything—the human body, courage, justice, anything.”
“Like the perfect, eternal form of a dog or a chair or truth or humility?”
“You got it. That glimpse of understanding is seeing with the mind’s eye. Shouldn’t that drive your whole mode of being? Isn’t that what we’re all really looking for in college and in life in general?”
“The—search—for—wisdom,” Laura said slowly. After a short silence, she spoke again, “I think you’ve taken too many philosophy classes. I have a Calculus test to pass.”
Immediately, the discussion shifted to chatter about sine waves.
“He’s climbed out of the cave,” my husband remarked wide-eyed.
“Yes,” I nodded my head. “And Plato would be proud.”
Maureen Hunter is the technical service manager for King Industries, Inc., in Norwalk, Conn. You can reach her at mhunter@kingindustries.com.