Imaginary numbers with real consequences
My college degree is in mathematics. (Please withhold the math-major jokes in the comments; I’ve heard them all!)
During senior year, math majors had to take a class called Functions of an Imaginary Variable. Yes, imaginary! That’s what mathematicians call numbers that, when squared, are negative. If you remember anything about the fourth grade, you know that any time you square a number (multiply it by itself), the result is positive. The ancient Greeks discovered these seemingly impossible numbers; they backed into them, really. They couldn’t work certain equations without them, so they decided they must exist, reason be damned. Mathematicians kept studying them, and they were well understood and described by the 1500s. Imaginary numbers, and the complex equations that involve them, have concrete and essential uses today in disciplines such as electromagnetism, fluid dynamics, and quantum mechanics.
And so for ten weeks I studied i, which is the letter assigned to imaginary numbers. And it was utterly fascinating! Well, actually, the crusty old professor just rattled on about theorems and proofs, his chalk clacking hard against the board as he illustrated his points with equations. But it was poetry to me, and I sat through every class in awe and wonder.
But oh, did I struggle with the homework. I understood the concepts and could have held my own in any discussion with the professor. I just couldn’t work the problems. They were seriously hard.
So my test scores were in the toilet. “There will be four tests and a final exam,” the professor grunted on the class’s first day. I failed all four tests, and not by a little bit. My highest score was something like 42%. I scored 16% on one test! As we approached the final exam, I was failing with prejudice.
The course would not be offered again until the next school year. If I failed it, I’d have to come back the next year to take the class again. My buddies used to call that, “the extended dance remix of college.” I could hear my father’s voice in my mind. “Jimbo,” he said, “I can barely afford four years of this. So four years is all you get. If you need more time, you have to pay for it entirely yourself.” And here I was in danger of not graduating because of these fantasy numbers!
In high-school English class I learned about deus ex machina, a literary device in which an improbable, contrived intervention solves an intractable problem. It may be a weak way to end a story, but when it happened to me in this situation relief washed over me and I nearly cried and danced at the same time. A week before the final, the professor held up a sheet of paper dense with text. “This is a list of all the concepts we studied in these ten weeks,” he said. “I’m going to give you a choice of finals. One will be composed of problems like you’ve worked on all the tests so far. The other final will show ten concepts off this list. You will define and prove each one. Who is interested in this alternative final?”
My hand shot up; I was the only taker. The professor gave me his sheet of paper. At home, I wrote definitions and proofs for every concept and memorized them. On the day of the final, I regurgitated the ten requested answers. I got a 99% – which was enough to raise my grade to a D-.
I graduated on time!
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My alma mater’s campus is beautiful.
Check this photo I took one spring morning.