Photographs and stories by Jim Grey

Since 2007

# 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-.

Do you have a close-scrape story to share? Tell it in the comments, or on your own blog (with a link back here)!

My alma mater’s campus is beautiful. Check this photo I took one spring morning.

### 21 responses to “Imaginary numbers with real consequences”

1. Oh, I remember that nail-biting anxiety before big tests in college. Granted I didn’t even try to take math classes. English major all the way. Regular math with regular old numbers was confusing enough for me!

1. I had a kind of a Zen attitude towards tests in general — it would be what it would be. But heading into the final in this class with an average hovering around 40% had my stomach tied in a Gordian knot!

2. I can balance my check book, read a tape measure in 1/8ths, and calculate a 15% tip in my head. That’s about the extent of my math. If there were any “close calls” in my scholastic career I’ve put a mental block on them. I don’t work well under pressure.

1. I do, but I don’t like it. Actually, without pressure I tend not to get anything done.

1. I find that a good cup of coffee works.

1. I’d mainline coffee if I could.

2. Michael

There should be a like button for that comment, but it was Mountain Dew at Rose.

3. Beautiful story. I think you had an answer to prayer, even if you did not verbalize it.
Close scrapes? Which one to choose? So many; so many.

1. I wasn’t a believer back in college, but my college days were characterized by a constant stream of prayer anyway, because Rose was a very tough school and my continued scholarship was frequently in doubt!

4. In the first year of my undergrad studies I failed a course called ‘philosophy of logic’. Over 20 years later, I still haven’t lived it down :)

1. Don’t feel bad. My sophomore year I failed Disco. That was what we all called a course called Discrete and Combinatorial Mathematics.

5. On the other end of the spectrum, I was a journalism major, and I had to take only one math class, and my advisory steered me toward a class that might as well have been called “Math for Poets,” taught by a middle-school math teacher, who treated us the same as she should a middle-schooler. When we were taking tests, she’d stroll the aisles and look over our shoulder and say things like, “Is that how we do No. 8?” On her next pass, if we still had it wrong, she’d say thing like, “Don’t we move the 7 over here?” Long story short, I got an A. My parents and everyone who knew me were stunned.

1. Wow. I never got so lucky in engineering school.

I padded my GPA by taking German, which always came easily to me.

6. Although math was always a close scrape for me, my biggest problem with college graduation came when my advisor accidentally left me three credits short of graduating. Not realizing this until late in the semester, I decided to take a job anyway and left school without a degree. I banged out my final coursework on an electric typewriter sent in fat envelopes to UF for several months while anchoring at a TV station in Binghamton, NY. I found correspondence classes were graded much easier than the real thing. Creative Writing and Nutrition.

1. Binghamton?! My condolences! :-)

7. I dragged my husband in on this – he’s the mathematician in our family. I loved maths at school, and algebra always fascinated me. Unfortunately, family circumstances meant I couldn’t carry on with my studies.

1. It was a lot of fun to study it in college, but the truth was that I wasn’t very good at it and got a C average!

8. Michael

I didn’t recall that you scraped by so close. I wasn’t so fortunate. I failed the course I was taking in place of Lit & Writ last term because I turned in a paper a couple days late. Pissed me off. The positive side was having to take an equivalent course at ISU, which I got more from than 4 years of Honors English and that Rose course. Who would have thought???

1. You needed a 2.0 in your major to graduate; I had a 2.019! I loved math; I just wasn’t very good at it.

9. Lone Primate

Thanks for building us a soap box, Jim. :) Ahem…

When I was in third year university, one of the English courses I was taking was Chaucer. I can remember coming into class one morning and our professor, a chirpy, middle aged woman I quite liked, said, “Okay, essays up at the front. You have till four this afternoon to hand them in.”

Essay?

Essay?? What essay? Oh, the essay worth a third of the course. That essay. To this day, I don’t understand how I managed to miss what must have been a half dozen in-class mentions of this essay, not to mention completely ignoring the topic sheet, but somehow I did. Academically, I think it’s the most scared I’ve ever been. Still dream about it sometimes.

If you’ve ever seen the movie Lock, Stock, and Two Smoking Barrels, the scene where Eddie floats away from the poker table owing a gangster £500,000 was kind of the way I left that room an hour later. Body on automatic. Brain had checked out. Anyway, I made it to the library, picked a topic, cobbled together some notes, drove home, spent three hours hammering something together that cross-referenced the course’s source materials, printed it (near letter quality dot matrix… dzzzzzzt… dzzzzzt…. dzzzzt… for another half an hour more). Just sweating bullets, I drove back to the campus, found the Professor’s drop box, and with a sigh or resignation, I dropped off my essay… with maybe an hour to spare. I figured I’d get creamed, but at least I wouldn’t fail.

I got an A. A very guilt A. I must have just hit the right note or something with my taped-together thesis, but it did the trick. Not the way I wanted to earn an A, though, and I didn’t feel like I’d warranted it. I can’t say I never dropped the ball again, but I do know it sharpened me up quite a bit.

1. I have a similar story from high-school Chemistry. Let’s just call it grace under pressure and accept the grades we got!

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