I waved Callie over to the table when I saw her enter the campus cafeteria. She was dressed to withstand the brutal summer heat, in cutoff jean shorts, a tank top, and flip-flops. She looked different — prettier, perhaps. Definitely not the little girl with whom I’d once climbed trees and played chess.

“Hi there,” I said as she dropped her backpack and sat down at the table. She had changed her hair a bit. A neon blue streak now ran from her bangs down over one ear. I briefly wondered if I should mention it, but that’s not the kind of trivial topic we normally talk about.

“Hey, Russell,” she said. “I was happy to get your text. It’s been a while.”

“Yeah, you know. Classes, midterms, all that stuff.”

“Oh, I get it alright. I thought the summer semester was supposed to be more laid back and relaxed,” she said.

“For undergrads, maybe. Not us grad students.”

Callie and I had been buddies since childhood and had ended up attending the same university. We were both geeks but in two completely different flavors. She majored in philosophy and I studied mathematics. She was outgoing, talked too much, and loved being around people. I was… none of those things.

“How have you been?” I asked.

“I’m feeling pretty good,” she said. “I got a surprise package delivered yesterday. Something I ordered months ago, but it took forever to get here. I’d forgotten I’d even ordered it.”

She jumped up to go grab a salad for lunch, then continued without hesitation.

“I mean, it wasn’t anything special, just a little gadget I’d seen online. But it was a pleasant surprise to get it finally. You know?” She didn’t wait for my reply, which is pretty typical. One of the things I love about my friend is I never need to carry the conversation when she’s around. So I grabbed the pencil from behind my ear and started doodling on a paper napkin while she talked.

“It wasn’t the thing that happened that made me happy, I guess. It was my reaction to it. I mean life is a long string of stuff that happens to you, right? What’s interesting is how we react to it.”

On the napkin, I scribbled:

R = F(t)

I said, “Yeah, life is like a forcing function. Good things and bad things happen to us all the time and we each have our own reactions to them.”

“Of course, some of us react more sensitively than others,” she joked, kicking me playfully under the table.

I made a small addition on the napkin.

ωR = F(t)

“Anyway,” she continued, “I don’t think it was the delivery itself that made me happy. It’s just these damn summer doldrums. Everything’s been rolling along the same way for weeks with no big ups or downs. I think I was just bored. Any little change would have made me happy or sad.”

“So you think it was the change more than the actual event that made you happy.”

I added another term with the pencil.

R′ + ωR = F(t)

“Are you still as happy about it today as you were yesterday?” I asked.

“Nah,” she replied, “it’s started to wear off already, I guess.”

“So there’s a damping factor…”

βR′ + ωR = F(t)

“Sure, if you want to call it that. But then this morning, you texted me! And that made me happy again. I think my luck is changing, don’t you?”

“Hmm,” I pondered. “Maybe you get happier if it looks like good things are happening more rapidly than before, like if your good luck seems to accelerate.”

“Or sometimes the opposite,” she replied. I remembered last year when Callie’s grandfather had passed away from Covid complications and then she’d been too sick to attend his funeral.

The equation on the napkin now had four terms:

αR″ + βR′ + ωR = F(t)

“So now I’m feeling happier just looking forward to the next good thing that might happen. Anticipating it.” She clapped her hands together like a little girl about to get an ice cream cone. It was kinda cute, so I chuckled.

“But luck is a fickle thing, isn’t it?” she asked. “Whenever I have a string of good luck, I start to dread what might come next.”

“Jerk!” I blurted.

“What the hell?” she exclaimed.

“No, not… that’s not what I meant. ‘Jerk’ is what we mathematicians call the third derivative. It’s the rate at which change… changes. Get it? Anticipation or dread.”

And now I had the completed equation written on the napkin:

R‴ + αR″ + βR′ + ωR = F(t)

“What are you writing on that thing?” she asked. “You’ve been tinkering with it since we sat down.”

I slid the napkin over to her and she looked at it briefly, unable to decipher the scribblings.

“I’ve always loved this about you, Russell. You’re calm on the surface but so deep on the inside. What is this?” she asked, nodding at the hieroglyphs on the napkin.

“Oh, it’s just a differential equation I’ve been working on.”

“Can you solve it?”

“Maybe. I’m afraid the problem is nonlinear, though. So there’ll be some chaos involved.”

“That’s not always a bad thing, is it?”

“No, it isn’t.”

I looked at her, and our eyes locked together. When she smiled, it triggered a reaction I’d never felt before. At that moment, Callie was the most beautiful thing I’d ever seen.

“On the bright side,” I murmured, “there will be a strange attractor in there someplace.” I reached across the table and covered her hand in mine, and it felt as if we had balanced an important equation. Joy flowed out of our bodies, through our hands, and across the gap between our eyes.

“I like your hair,” I said without breaking the connection.

“Thanks. I wanted to try something different today. For you.”

“It makes me happy,” I said.