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How to Count in Binary

C.E. McKenna

        “Do you know how to count in binary?” says Dad. He’s sitting at the butcher-block countertop in my kitchen, sipping PG Tips. The discarded, soggy tea bag and canister of sugar crowd his laptop. I worry when he tilts the screen, he’ll knock something over and I’ll need to clean it up.

        I shake my head, smiling. “Zero zero zero zero zero zero one?” I say.

        “Binary—bi—base two. Two digits. Zero and one. So zero is zero, and one is one, but then two is one-zero, like ten—” Dad’s pontificating and I’m not listening. I’ve done a word as- sociation and instead of counting in binary, I’m thinking about the binary—yours and ours. You are zero. I’m one. Leslie is one. Xander is one. 011. There. I’ve counted to three in binary. But the zero at the front adds no meaning. It can just be dropped.

        Dad is pointing to his computer, to a 30-by-30 grid he has pulled up, its tiles filled in to look like a geometric turtle with a large diamond shell and four angled legs that jut into each corner of the square.

        The outline of the screen starts to blur. This is just like when he tried to help me with differential equations in high school. I’m swirling. Gone. In Mexico, feeling salt in the roots of my hair, thinking of the baby sea turtles we set free on the beach in Sayulita, their limbs making tiny, whispering indentations in the sand as they crawled towards the ocean.

        Leslie came on that trip, her last vacation before getting pregnant with Rowan. I wish she was here, in the kitchen, her reaction predictable. She would shake her head and make exaggerated cartoon eyes, scanning for the exits. “Why on earth would I need to know this?”

        If Xander was here, he would lean forward in his chair and say, “Yeah, uhh.” Then he would let out one of those belly laughs that booms, shuddering through his shoulders.

        How would you respond?

        You, the one we never knew. Would you have acted like this was the easiest question in the world, like reciting the alphabet? Would you have felt dumb and embarrassed? Or worse—would you have run away long ago because the pop quizzes felt condescending, made you anxious and insecure?

        “Isn’t that cool?” Dad’s eyes are bright. He’s smiling wide, hand tangled in his coarse beard, his mug of tea losing steam, full, forgotten.

        My phone buzzes. It’s Annie. We’ve been best friends since third grade. I face the screen down. Sure, I wasn’t paying attention to the math lecture but I’m not going to be an asshole about it.

        Our dad is fascinated by space-filling curves, lines that traverse across grids, never cross- ing, never touching. That’s what he’s trying to show me on his laptop. When the grid is copied, flipped, and joined onto the end of the previous map, it can continue—infinitely if you want—through space.

        He has studied these for 40 years. Since before you were there and gone.

        I’m not motivated by math. I can appreciate its security, though, its fractal beauty, the depths of exploration it inspires.

        It’s just that I feel more passion for people.

        So I say, “That is cool,” because I know it will make Dad happy.

        But I don’t understand. Not in the way he hopes. I take his theorems and morph them into metaphors. I fix my eyes on the screen, decide to focus, concentrate on the idea that this line can never go backwards, never share the same pixels. It repeats a pattern over and over again, contorts itself into the boundaries it’s given.

        Dad holds up his hands, making right angles of his thumbs and forefingers, positioning them diagonally from each other to make a square. “If an arbitrarily small change happens here—” He wiggles a digit. “That causes an arbitrarily small change over here—” Another. “Then it’s a continuous curve.”

        Like a timeline, I suppose. Or a life.


        You were aborted sometime in the mid-‘80s. I don’t know the exact date. It’s not marked in Mom’s calendar like our birthdays, their wedding anniversary, the weeks the house must be baby-proofed because Leslie’s bringing Rowan to stay.

        You’re spoken about rarely because you weren’t a person. You were just feelings—fear, anxiety, the heart-hammering unknown. You were an easy decision.

        The first time you came up was in the car on the way to Costco. This was when Leslie and I thought we were grownups and Xander still got Pokemon VHS tapes if he made it a week without biting. We liked to help grocery shop, circling back to the samples of frozen cream puffs.

        Mom must have thought it was best to explain a woman’s choice when she had her daughters together, captive in the Volvo.

        “When you’re older, you might have to get one. And you shouldn’t be ashamed. It’s okay if you’re not ready.” That was Mom’s lesson for her girls. She shifted into fourth, overtaking a car camped in the left lane. “There was a time when I wasn’t ready, either.” Her thumb fondled the indent on the nape of my neck, massaging, mesmerizing. “You’ll know.”

        Dad never said anything. The thought of you didn’t seem to cross his mind, typing at his kitchen table, writing essays on the elegant dimensions of Hilbert Curves.

        Xander’s a separate mystery. I’m not sure he knows you existed at all.

        The thing Annie texted about—she couldn’t sleep. She spent last night staring at the black ceiling, angry at the shadows, tangling covers around her foot, hot, then cold, then sweating.

        She would give anything for you—a blastocyst. Healthy. Implanted.

        Instead, she takes shots every day, right in the stomach, with a long needle. It has been a year of that.

        When Annie calls me because she’s awake at night, when she needs someone to hold her hand at baby showers, when the phone rings and I know just by the time of day that I need to pick up with, “You okay?” That’s when I think of you.

        People always talk about what might have happened to an embryo after an abortion. They rally armies of what ifs: What if that future child found a way to cure cancer? What if he had be- come president? What if they could have ushered in world peace?

        It’s a facile diversion.

        But I have a subjunctive what if of my own: What if you hadn’t been aborted?

        The problem is, had that happened, I wouldn’t exist. That, I’m sure of.

        I’m sure because of probability more than anything else. If you had been born, the timing wouldn’t have worked out for me. Even if they wanted a second kid right after the first, it’s not likely that the egg I came from would have been fertilized. Or Mom might have died in childbirth with you. She almost died with me. If you weren’t aborted, the chain of dominoes would have fallen in a different direction.

        And I like my life. I’m thankful for it. So thankful, in fact, there are days when you seep into every moment.

        I thank you when I’m riding my motorcycle on the Peak to Peak Highway, yellow aspen leaves crinkling and shivering in the low-angled sun. I thank you at the Sundown Saloon when I’m on the eight ball and catch my opponent’s eye, hear him whisper, “All spank, no tickle, huh?” I thank you in the wet, delicious moments after an orgasm, forehead buried in an Old Spice armpit, huffing comforting flurries.

        I thank you when our sister calls.

        Leslie just miscarried. She was early on, only a few weeks—earlier, even, than mom was when she went into the clinic.

        So far, Leslie hasn’t cried. Not to me, at least. The same week the doctor confirmed it, she took Rowan bowling and he pitched the child’s ball straight into the gutter three times in a row.

The final time, he tripped on his heavy rental shoes, got up, ran in place on the slick lane, fell again, laughed laughed laughed.

        I told Leslie, “Maybe your body knew something about that embryo. Maybe it wouldn’t have survived for some reason.”

“Yeah,” she said. “We’ll try again.”

        The problem with thanking you is that I’m not sure you ever existed. You never had consciousness, never a breath or a whisper. And I don’t know if a soul is any different from chemicals, electricity, exciting patterns—curves—in our brains.

        Mom, Dad, our grandparents—both sides—atheists, all. Sure, we had Easter baskets and Santa Claus, the trappings of Anglican tradition. But no God, no entity in the sky deciding our fate, setting an obstacle course perfectly crafted for individual growth.

        If humans are organized, if there’s a library shelf somewhere inside me reserved for pious texts, I like to imagine mine has just two books there, instead.

        One is a leather-bound copy of the Complete Works of William Shakespeare.

        And the other is Frank Ramsey’s Truth and Probability.

        The first taught me that the human condition is a delectable adventure.

        The second, that I’m damn lucky to be sipping tea in a warm house with a father who wants to share his thoughts with me.

        Dad has a trimmed gray beard and smiling eyes, magnified by thick lenses in a ‘70s aviator frame he’s never swapped for something more modern. Those glasses are what kept him from Vietnam.

        I know men—lots of men—who didn’t have the luck of physical malady. One fled to England. Another, to Canada. And some were sent—no choice—to a platoon in the jungle. I know a man who became so death-shocked, so deranged, he cocooned his bunk with parachutes and sat inside with an arsenal, refusing to move.

        I should be thankful for our dad’s bad vision. Probably more so than your disappearance. And yet, when I consider it, no matter the distant movie I construct about humid putrescence and fearful madness, a less-blind version of Dad bleeding face-down in a paddy field, I am still much more swayed by the idea of your sacrifice. Why is that?

        In 2019, Leslie and I met at a fried chicken place in town. We ordered diet cokes and deviled eggs and a whole bird, Nashville hot. Leslie said she had something to tell me, then slid an envelope across the table.

        I knew what it was before I opened it. The moment I saw Rowan in medical black-and- white, I loved him. I wanted him there with me, to swing at the park and demand to go higher. I wanted him to point out brown plops on the bike path and yell, “Oh, no, Cookie! That’s poop!” so I knew to steer the pram in a different direction. I wanted to watch him blow bubbles in the bath, giggle when a dog licked his ear, and pretend to ride rollercoasters at the dinner table.

        “I knew you’d be excited,” said Leslie, grinning, crying. “I knew it. Mom’s gonna be concerned but I knew you’d be so happy.”

That’s when I started crying, too.

        “You’ll teach this baby to be a kid,” said Leslie.

        “I’m going to love the shit out of it,” I said, pushing the deviled eggs towards her. “Eat more. You need fuel.”

        So that’s the conundrum. Why is it that you were just—poof!—nothing, but Rowan?

He was implanted in my heart sure as he was in her womb. Before he was ever born, he was with me.

        Before he was ever born, he existed and I loved him.

It’s unfair how some couples can get pregnant after trying once while others are forced to spend tens of thousands of dollars to realize their dream. Do you think that’s the blastocyst’s fault, not implanting properly? Then there are the mothers who become pregnant when they’re desperate not to be—like Grandma. She threw herself down the stairs. It was a better option than going to the city, paying someone to hurt her. Was it the zygote’s fault for cleaving to a mother so overwhelmed by four children that she would rather risk a traumatic brain injury than add a fifth?

        Annie’s round didn’t work. She couldn’t bear to talk on the phone, rehash everything. So she texted. They only have two blastocysts left and neither has a high probability of surviving implantation. An odd word, surviving—it feels like, to survive, you ought to have life first, fight for it. That’s what Annie did. She was born four months too soon. Spent her early life in the NICU, in a hospital incubator. I’m so glad she fought. Glad she still fights.

        Can a zygote survive? Can a blastocyst? Or are they just things—biological building blocks that either fail or succeed in a person’s uterus? No different than one of the possible space-filling curves that flick by on Dad’s screen. An option.

        No matter which words I use to describe the science and the humanity, it sucks.

        I rode my cafe racer to Annie’s house last weekend and we walked to the arts and crafts fair. There’s one every winter. I bought a small, upcycled dog sweater for Leslie’s Pomeranian and then another, larger, blue cashmere sweater for my dog, Otter.

        If I had never been born, where would Otter be now? Maybe still in Texas, or with that frat boy who came up to me at Santiago’s to tell me he’d applied for the black-and-white puppy in my lap. I’m glad Otter didn’t go to him. He seemed like the type who would never train him but insist he’s an off-leash dog.

        Instead, this strange mutt is curled at my feet, keeping my toes warm.

        Who would walk through the old cemetery with Annie, if you had been born? The one on 9th Street, all filled up by the 1930s. Looking at the stones—once people, their consciousness in the black, etchings in rock, gone but for the stories they told—I’m not afraid that one day, I’ll be scattered nothing.

        Is it strange to believe in science and also fate? Or maybe fate is just history, up to this moment. Nothing more than a timeline of interconnected choices.

        Everything seems inevitable, once you get to the present.

        Last night, Rowan FaceTimed me with his underpants around his neck. He was eating purple pancakes for dinner and singing a counting song in Spanish. “Uno, dos, tres, cuatro, cin- co, six!” He dropped his head back and laughed like he was about to pee his pants. It’s good he didn’t, though, ‘cause as I said—his underwear was being used as a scarf.

        Rowan was once a zygote, too. Then a blastocyst, then an embryo, then a fetus, and finally, on a late September night, under a full moon that hung low above the Sandias, a fat, squinty baby who stared into my eyes, perhaps wondering why I looked so much like his mother.

        If you hadn’t been aborted, would you have driven the seven hours from Boulder to Albuquerque to be there for Leslie? Would you have cried in sympathy outside her hospital room when you heard her screams? Would you go again, a few months later, when her husband left the state for work?

        A scarier thought—if you hadn’t been aborted and I didn’t exist, then she might not either.

        No Leslie, no Rowan.

        The thought catches in my throat and vibrates in my sinuses, the bottoms of my eyes.

        There was nothing you gave up, back then. Just black and black. You never got to know what could have been.


        Dad chugs his lukewarm tea and slaps the kitchen counter with his hands.

        I want him to ask me again, “Do you know how to count in binary?” But we’re past that. He tucks his laptop back into a black carrying case, sets his empty mug in the sink, takes candy from the glass container I stock with whatever is in season from Trader Joe’s.

        The things I want to say: I count in binary when I dip Nashville hot chicken in mayo and lick salt fat from my lips. I count in binary when the phone rings and a full, chortling toddler bounces onscreen to tell me ghosts are sharks.

        Dad, I count in binary when my heart hurts from thinking you’ll die one day.

        But is it binary at all? This whole time, maybe I misunderstood. Maybe we’re not counting in binary and are, instead, in a space-filling curve, twisting through patterns of thoughts that keep me hopeful. I want to tell dad to take his laptop back out, set it on the counter. I’ll put the kettle on.

        I promise to pay attention this time.

        It’s too late. His 4Runner fires up. I wave goodbye from the window, put the stained mug in the dishwasher, and get out the phone to call my sister, my baby.

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