Fractal Memories

            Summer school, sixth grade. Or these four kids’ ticket to seventh grade—sort of my call, the principal said. I wanted clarity: “sort of?”, and the principal just shrugged. He showed me the room we’d have at our disposal, bade a bonne chance, and vanished.

            After listening to the kids’ goals for this imposed opportunity—mainly to see the end of July—I pointed them to the common need for our first couple lessons: fractions. They groaned like buffalos.

            “So, as I remember when I was your age,” I proffered, “fractions come down to pizzas and the people who eat ’em.”

            “You tryin’ to be funny?” asked Emil, bespectacled.

            “Yeah, how un-original,” Bryn informed.

            “Okay—so solve this, then: I got seven people who order five pizzas—how many pieces does each person get?”

            Silent calculation, mostly on my part. “As much as each person wants,” decided Jenny, and when asked to defend, she reasoned, “it’s just pizza; a piece or two does the job.” Sigh.

            I put a couple fractions on the white board—5/7 and 7/5 —and asked which one would be more helpful. As silence shrouded the room, my mind paced a conflicted stage. “Why didn’t I use even numbers?”, on a practical level, and “What would Mr Kholer think right now?”, a loathed-to-loved teacher of my far-away maths. He would chalk more of an equation on the black board, then step back in wonderment: “let us peruse the problem”, as if it materialized not by his own slap-happy hand. Maybe Mr Kohler would chortle at my remedial display, suggesting there wasn’t in fact a problem here: 5/7 and 7/5 are nothing without further variables; maybe that’s what Emil et al were to suss out for themselves, recalling elementary tools like > or <…

            “What kind of pizza?” queried Brent, apparently attached to Jenny’s idea.

            “Why should that matter?”

            “Because,” Emil elbowed in, “if it’s pepperoni, then the pieces have to give everyone that much the same.”

            “What if it’s just cheese,” Bryn ventured. “What’s the fucking difference?”

            “Hey, hey!” I needed to admonish, “no swearing at summer school. This is supposed to be just like sixth grade.”
            “I failed sixth grade. Obviously.”

            “But she’s right,” Jenny opined. “Pizzas are more than toppings.”

            The room disappeared a bit as my penchant for nostalgia journeyed back to college discussions on the dichotomy of ‘essence and accident’, the conundrum by which we call a thing a thing and yet associate that thing with more or less the attributes that deems the thing a thing. Emil, noting my departure, evidently wanted to bring ‘things’ back, taking the liberty to sketch on the board a circle with a outer ring of eight smaller circles and one in the center. “And Tombstone has even more pepperonis—” 

            “We’ll get to each pepperoni in due time,” I adjudicated, “risking the notion that, say, quattro-formaggi is another can of worms…” Bryn stared death at my dead-pan. “In the meantime, Jenny, why not get us back on track: seven people want to divide five pizzas equally. What should we do?”

            “I think it would be easier,” she said, “if five people want to divide seven pizzas. It’s like you could choose more toppings.”

            Damn straight. I wished the late Mitch Snyder could tag me out at this point. As an advocate for the homeless, he spoke at a grad school symposium and forthrightly challenged us to disenroll and start doing something good for the world, a world which could justly feed itself if more goddamned people had only the heart and will.

            Instead of Mitch, I resigned myself to realpolitik. “Divide five by seven and you’ll get less than one. Fractions, then, are always about dealing with the less-than-one.” I markered above Emil’s poor man’s tombstone: 5/7 <  7/7, which = 1. But the general attention had eloped to the ether: theirs to the fact that mobile phones and WolframAlpha would supply math solutions; mine to the memory of Ms Hallahan, who had a sexy way of teaching reciprocals, flipping fractions like a ballerina.

            “What do you mean?” Bryn invaded. She was totally correct to destroy that recollection, then and there. “Fractions don’t stop at the one.”

            “That’s thoughtful,” I tried to affirm, winging it shamelessly. “If we, for instance, say that five people want equal access to seven pizzas—”

            “You started with the opposite,” snarked Emil, “it was seven people for five pizzas.”

            “So it was. I now know that you—the collective you—are paying attention.” Not entirely true: Brent had fallen asleep, tuckered out after his inchoate participation. The bigger problem was hardly shared: where to go next. Emil’s pizza had nine pugnacious discs to get in the way of carving it clean. Bryn was drumming her fingers and Jenny was looking out the window, thinking perhaps of her own Mitch Snyder. I channeled again Mr Kholer and his procedures for how to peruse. My mind blanked on them, however, preferring instead the procedures of Ms Hallahan. I was doomed never to leave summer school.

            Out of the blue, Jenny divined: “seven divided by five is seven-fifths. That’s more than one.”

            “But one what?” Emil foraged. “Are we talking people or pizzas?”

            “You are on the right track.”

            “What, for asking ‘what’?” Bryn bristled.

            “For questioning the numerator and the denominator. The top number—the thing you start with—divided by the bottom—the parts you end with. Wait—just checking—yes, that’s right.”

            “You’re not really a math teacher, are you,” Bryn deduced.

            I looked out the window. From some brain cavern the term ‘autodidact’ tried to inform my premise and purpose (to get them to be), but my vocal chords wisely demurred. We’d be starting this afternoon The House on Mango Street, and I knew the narrator Esperanza would be better at defining difficult things. For now, I let these fractals know, “we learn from memory.” Then, “will somebody please wake up Brent?”

Daniel Martin Vold Lamken (2018)