The Origami Paradox

by Alistair Robinson

When I opened my eyes, Anna was sitting up in bed next to me. By the light of her bedside lamp, she was folding a crumpled square piece of paper into the shape of a bird, then carefully unfolding it again, repeatedly. I lay still and silently watched her perform the strange folding ritual, her hands dancing across the paper like a spider spinning a web.

“What’s that?” I asked, just as she was about to dismantle her creation yet again.

Her hands paused their dance and presented me with the paper bird. “It’s an origami crane,” she answered.

I nodded. “Oh, right. And, um, why did you decide to start folding origami cranes all of a sudden?”

Her eyes stayed fixed on the paper bird that now stood in the palm of my hand. Something about her expression felt strangely distant. A prickly wave of anxiety suddenly came over me.

“Are you feeling alright?” I asked cautiously, placing the paper bird to one side and propping myself up in bed.

“Yeah,” she shook her head, “I mean, I’m fine, it’s just... it’s hard to explain.”

“It’s alright, I believe you,” I reassured her. “Do you want to try talking about it anyway?”

She considered the question, then picked up the paper bird from the bed and slowly unfolded it.

“Imagine that this is the universe,” she explained, holding the wrinkled paper square flat in her hand. I nodded, though my confusion must have shown because she gave me a quiet laugh as I did.

“It’ll make sense, I promise,” she added. “So this flat piece of paper is the universe, right at its beginning, and over time, the state of the universe changes, you see?” She demonstrated this by folding the paper diagonally in half over a well-creased line, reshaping it into a triangle. Then, she folded the triangle in half again, following along another existing fold. Her hands were slower and more methodical as they worked this time, like they were teaching their dance to a new partner.

Handing the paper triangle back to me, she asked, “Do you think it's possible to undo the first fold that I made without undoing the second one?”

“I guess not,” I answered, turning the shape over in my hands.

“Yeah, exactly. There’s a necessary order to things. You can’t undo folds in the wrong order, and in the same way, you can’t make folds in the wrong order either.”

“Sure, makes sense so far.” She was at her most beautiful when she allowed her thoughts to just flow freely like that, I thought to myself, as I handed the paper back to her.

“So the universe can change, one fold at a time,” she continued, as her hands weaved more folds into the paper. “But look: it doesn’t really matter whether the changes are made or unmade, folded or unfolded, forwards or backwards, as long as the overall order of events in the universe remains correct.”

To demonstrate this, she undid a series of folds in quick succession, then recreated them again in the opposite order to how they’d been unfolded. The end result was identical.

“Wait, hang on, though,” I asked. “You’re saying that things in the universe can happen in either direction; but what about the second law of thermodynamics?”

“Oh,” she laughed, “so you have been paying attention to my physics lessons.”

“You know I always do, I’m just very good at pretending not to sometimes,” I joked. “But anyway, the second law: I thought the whole point of it was that some things can only happen in one direction. Don’t things always move to a point with less entropy?”

“Yeah, that’s a good point. But there’s a catch: something called the reversibility paradox. The idea is that there’s nothing to actually stop the universe from breaking the second law, on a micro or macro scale—it’s just really unlikely. Put it this way: for every scenario that satisfies the second law, there’s an equal and opposite scenario that doesn’t; both are theoretically and physically possible, even if one looks significantly less likely from our perspective.”

“OK, right,” I said, trying to wrap my head around everything Anna had said so far. She put the finished paper bird back into my hand. It looked so elegant and simple compared to the complicated physics that she was trying to explain to me.

“The other day,” she went on, “I was folding one of these cranes and... the realisation just hit me. At the end of the universe, when it’s reached its final state and there are no folds left to make, what will happen?”

I looked down morosely at the paper bird that suddenly represented our oblivion. “I don’t know... maybe it’ll just stay like that forever?”

“Maybe it will, for a while—but if there are no more folds that can be made anymore, what if the universe starts to unfold instead?”

“You mean, undo itself?”

“Exactly,” she muttered, picking the bird out of my hand and slowly deconstructing it back to its original shape. “Think about it. The reversibility paradox means there’s nothing to stop everything moving in the opposite direction relative to time; and because the changes, the folds of the universe have already been made, there might only be one way that they can unfold themselves. Everything might eventually just revert back to the way it started. Everything we’ve done, everything that we will do to try to make the universe a better place: it all becomes meaningless. Eventually, there’ll be nothing left of it at all, not even a trace. Back to square one.”

She held up the unfolded square of paper in front of her and stared at it, the pointless destiny of the universe that she occupied, with tearful eyes. I quietly put my hand on her arm, comforting her, or at the very least reminding her that I was still there, trapped in the same universe as she was.

“And what do you think happens after that?” I asked after a short pause. She shrugged.

“Maybe it starts all over again, from the beginning. Maybe the folds are reproduced identically, following the same hidden creases of the universe that they always do, that they always have done; then, once they’re all undone again, the cycle repeats...” she sighed, tracing the creases of the paper with her fingertips as though she was reading them like braille. “Everything that can happen has already happened.”

I imagined the storm that was playing out inside her head: the paper, folding and unfolding itself; the universe, creating and destroying itself; reality, expanding and contracting; it was breathing, like a living organism—an endless, magnificent, absurd organism that nurtured us as much as it trapped us.

I gently took the paper from her hands and tried to fold it as I’d seen her do so many times now; but contrary to her idea that the universe always developed along the same lines, no matter how delicately I attempted to follow its existing creases, the paper always turned out slightly misshapen, slightly different than how it had been before. A few folds before it would have looked finished, I handed it back to her in its new, semi-complete form.

“What’s this meant to be?” she asked, confused. The new shape that I’d folded was oddly bizarre and asymmetrical. From one perspective, it looked like two diamonds that had crashed into each other at high speed; from another, the jaws of an apex predator closing around its prey; from another, a professional gymnast vaulting through the air as a crowd gasped in awe; from another, the sail of a majestic speedboat bounding over the ocean. She turned it over in her fingers, playing with each unique angle of the strange object.

“That,” I declared with comically exaggerated triumph, “is today. Halfway between the creation of the universe and its destruction.” She laughed.

“It’s not perfect,” I admitted with a slight shrug. “It looks a bit of a mess, and some bits might be going through time in the wrong direction, but that’s all part of what makes it beautiful, don’t you think?”

“Yeah, you’re right... it’s much more beautiful than the crane.”

She was smiling too now. I gently put my hands around hers. Together, they enclosed the paper object.

“I know you’re scared,” I whispered, serious now, as we stared into each other. “I know you’re scared that nothing we do matters. That everything’s meaningless. I know, because I’m scared of it too. And I don’t know what will happen to us when we’re gone, when everything’s gone. But if what you’re saying is true; if time really repeats itself, if it could bring us back together again billions or trillions of years from now, if there’s the tiniest chance that I could spend today again, with you: then I don’t care if it’s all meaningless—it would still make me the happiest person in the universe.”

She closed her eyes, leaned forward and rested her forehead against mine. “Me too,” she added, leaving the paper object to one side. We kissed and held each other tightly for a few wonderful moments.

I picked up the paper and carefully unfolded it until the creases were gone from its surface. I returned it, pristine, to the stack of note paper on her bedside table. We got changed and brushed our teeth. Then we sat on our sofa watching a comedy film, laughing at the punchlines and waiting expectantly during their setups, as we slowly filled bowls of ice cream in our laps, savouring every burst of sweetness. Once our bowls were full, we decanted them into the ice cream tub on our coffee table. We left it to freeze in the comfortable warmth of our living room before putting it away.

We always cooked together on Saturdays, rain or shine. We took our dirty bowls from the dishwasher and laid them out on our tiny kitchen table. We refilled them, slowly, bite by delicious bite. The wine flowed freely from our lips into our glasses, then eventually back into a bottle that Anna carefully sealed with a corkscrew once full. We returned our dinner to the pots on the stove, then slowly removed each ingredient in turn, repackaging them into their respective containers from the bin. We loaded them up into bags and carried them back to the supermarket, exchanging them for cash at the till and restoring them to their rightful place on the store shelves.

We took a detour through the park on the walk home. It was a cold afternoon, but the winter sun was shining bright and casting long dramatic shadows with the trees. Around us, Anna had once told me, the universe was imperceptibly contracting. The space between every atom was getting closer and closer, until one day, everything would be crushed together into a single point. No one really knew what would happen after that. When I first learned about this, I remember feeling terrified by the idea; but today, for whatever reason, the thought of our particles being brought together again in the final moments of the universe felt more romantic than anything else.

We both knew that one day, very soon, we’d wake up and be total strangers to each other. I wouldn’t even recognise Anna if we passed in the street. The fear of losing the person that we’d loved for our entire lives weighed heavily on both of us; but until that day came, I thought to myself as we watched the clouds drifting slowly across the sky, regardless of whether or not we’d find each other again after the inevitable collapse of reality, I knew that we still had each other right now. We still had today.