The Nuptial Dance in Xs and Ys

By Michael De Rosa

Melete and I were in the same college math class. I would see her three times a week at 9 AM. Coming in early but not crowding around the prof’s desk as the other early birds, I would always sit in the same place. Melete, with her auburn hair and a dancer’s grace, as fascinating as her name, would come in a couple of minutes before class began and never sit in the same place twice. And while I cultivated a conspicuously inconspicuous look, she never wore the same outfit. Each outfit had an accent piece: a wide belt as scarlet as that of any tanager, scarves as blue as that of any robin’s egg, yellows, and oranges to make orioles jealous. Students stopped missing class or coming in late to watch her come in. Melete was not just beautiful she was bedazzling and brilliant.

The class was diffyq — differential equations. Differential equations are studied after you finish calculus, or calculus is finished with you. Briefly, differential equations deal with properties that change, for example, with time. 

You probably think that math, while challenging, was cut and dry. You put in the value of ‘x’, and out comes the value of ‘y’. Not differential equations, many can’t be solved. That’s right; they have no exact solution. The course was devoted to finding how to approximate — get as close as possible — to the correct answer, almost as with life itself. 

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I was ambling along one of the leafy paths on campus. I stopped in my tracks when I saw her moving towards me, wearing a hyacinth-colored scarf that I had never seen before. Melete looked so lovely walking on the strewn white petals of the magnolias that towered above her, backlit so that her hair glowed red in the sunlight filtering through the trees.

If I had been a male golden-headed manakin, I would have started my courtship dance to gain her attention. Instead, as Melete came close enough for me to see her face, I gave her my second best smile. Automatically she returned it. We formally introduced ourselves. Melete saying, “call me Mel.”  “Your scarf reminds me of Hyacinth Macaws.” She laughed from her diaphragm and said, “I have always wanted to go to Brazil’s Pantanal to see them.”

We were both birders. 

That was how our friendship started. She told me her favorite bird was a painted bunting — a bird both of us had seen — and for me it was a Gouldian finch from Western Australia. Dreamed about, but not yet seen. We compared notes on the birds we had seen on campus. “I saw a rare prothonotary warbler at a pond on campus,” I told her. A new bird for her, we made plans to go to the pond early the next morning before class. I told Mel, “I’m walking to take my mind off the homework assignment due tomorrow.” “I’ll be happy to help you,” Mel volunteered. 

Early next morning, we set off to the pond. The pathway, still dark under the tree canopy, we walked through a soundscape: the staccato drumming of a red-headed woodpecker, warbler songs, and in a small island of light, a wood thrush and its flute-like song. 

Sitting on one of the benches at the pond, we took our binoculars out of our book bags and waited and waited some more. We heard the warbler before we saw it.

sweet-sweet-sweet-sweet-sweet

Finally, a dark shape flitting from branch to branch; freezing, holding our breaths, we watched it come out of the shadows, drop down to the water’s edge, seemingly kissing its perfect brilliant-golden reflection as it drank. We followed it with our glasses as it flew into the bushes to forage for insects, and then with a loud seep, was gone. We followed, hurrying back to get to math class on time.

Mel became my diffyq tutor. Compared to her, the rest of us in the class were mathematical muggles. She carried a book bag, but she never took anything out or took notes. The professor took note by the second lesson and called Mel to the front of the class, asking her to do the problem he had put up on the blackboard. She looked at the equation and then wrote the answer almost as fast as it took her to read the equation. To say our prof was nonplussed would be an understatement. His next question, “Please show us your work.” She proceeded to do it faster than any of us would have been able to write the solution’s first line. 

At our first tutoring session, I asked, “How do you do it?”

“As soon as I see the equation, I see the solution.”

Mathematics was a language to her, one that she tried to teach me. To her, every term, exponent, and algebraic sign held meaning. Just as a chess master can look at a position and declare checkmate in three, Mel could look at an equation and instantly know the outcome. I did learn to see patterns. But there was no elegance to my work. It still took time to grind out the answer.

On one of our bird walks, my hand touched hers; I took it in mine, she did not pull it back. We walked holding hands until we parted ways. She kissed me on my cheek, her lips moist, and told me: “If you solve it, you can have me.”

Dazed, I walked back to my dorm with no awareness of my surroundings. Trying to figure it all out. Had Mel said what I thought she had said? And what was “it” — riddle, problem, conundrum? Mel being Mel, “it” had to involve math or birds, or even both. 

Intuitively, I felt mathematics held the key. And since we were in diffyq, it must involve change. Two things stood out: the changes in the colors she used and her movement in class. As a birder, I imagined maybe she was a different bird every time she came to class. Each color of the rainbow has a characteristic energy, frequency, and wavelength. But I could find no periodic changes in any of these properties.

Movement? Was it Mel’s velocity (distance vs. time) or acceleration (velocity vs. time) as she moved? Either of these would only tell me if she was moving faster or slower. There had to be a pattern — a mathematical pattern.

Then I had my Eureka moment: plot Mel’s movements. I imagined the classroom as a Cartesian grid of nine-rows with five-seats per row. When I plotted my position, I always sat in 5C, in the exact middle of the room. If I found the correct mathematical function, I could extrapolate Mel’s movement back to the first class and forward to predict where she would sit next class. After a week of classes, I had my answer.

I came in a bit earlier than usual, waiting, my pulse quickening as she got closer and closer to sit where I had calculated. Next class, I took a piece of paper, wrote a single word on it, folded it exactly into quarters, and put it on the seat of the chair I expected her to sit on. Mel walked in, headed for the chair, saw my note, unfolded it and read:

Fibonacci!

She gave me her number one smile that melted my heart, made me weak in the knees, and completely discombobulated me. Later, when I looked at my class notes, I found that just as in junior high, I had doodled a heart with both our initials pierced by an arrow. 

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We walked hand-in-hand towards what was to become our pond. A friend had told me he had heard but not seen an elusive least bittern at the pond. The bittern was a new bird for us both. We stopped and sat on a bench, warmed by the sun. I pulled out a copy of her Fibonacci spiral and, with my finger, traced her path through the classroom until it ended at 5C — both of us occupying the same square. Mel smiled.

I asked her: “why me?”

“When I first entered the class, I saw you were sitting in the exact center of the class trying to hide in plain sight.” “I was intrigued.” “Why were you hiding?” Looking slyly at me, “What algorithm were you using to get laid?” At this, I started to blush; Mel began to giggle and then laugh. The more she laughed, the redder my face. She put her warm hand on my face and said it reminded her of a rose-breasted grosbeak.

We got up and continued walking in companionable silence until the shadows of the path gave way to the sunlight of the pond. Sitting on the grass, shaded by a weeping willow, near a stream spilling into the pond, yellow marsh marigolds and red cardinal flowers along its banks. Here there was a marshy section filled with cattails and reeds — perfect habitat for bitterns. 

We tried to keep quiet, but the silence was broken by raucous male red-winged blackbirds in the cattails, chasing each other, vying for territory trying to entice females. Spring peepers trilled and whistled, joined by the basso profundo of bullfrogs. 

Several times we heard the low coo-coo-coo of the bittern but did not see it. Patience rewarded. She touched my arm and pointed with her face. I followed her gaze and saw motion close to the water, the least bittern straddling some reeds. We watched as it got closer to the water, stretched its neck, and caught a fish with a fast jab. And then it became one with the reeds, disappearing from view, but we could still hear its coo-coo-coo softer and softer as it moved deeper into the reeds.

Turning to each other, we high-fived, hugged, and I felt the touch of her lips on mine for the first time — the nuptial dance began.