Mathematically Sound

by Marinda Kotze

I wake up.

It’s pitch-dark.

Static white noise buzzes in my ears.

I stretch my hand out from under my duvet to grab my phone from the bedside table. Instead, my knuckles punch straight into something hard right next to me.

Then I remember that I’m not in my bedroom.

I’m in a sleeping pod in a capsule hotel in Tokyo.

The last few days slowly drift into focus…

…I’m here to present my paper on using fractal concepts in image analysis at the International Conference on Applied Mathematics. I boarded a plane in New York at 11:00 PM on January 12^th and landed in Tokyo on the 14^th.

I remember walking out of Narita International Airport, convinced that it was dusk, but my phone insisted that it was 9:15 AM.

I guess that’s what happens when you travel nineteen hours across fourteen time zones: You lose your grip on time and space.

I paw at the capsule’s smooth surface and catch hold of a button. As I press it repeatedly, a soft yellow glow starts to bloom from the LED light panels in the curves of the ceiling. The smooth beige sleeping pod extends like a tube around me. A soundproof door resembling a spaceship’s door is at my feet. The smell of lavender, sandalwood and talcum powder hangs in the air.

I vaguely remember checking in at the hotel’s front desk, taking the elevator to the fifth floor, pushing my suitcase and laptop bag into a narrow locker, exchanging my worn-down sneakers for a pair of soft slippers, and following the cabin number signs through the dimly lit labyrinth of stainless-steel capsule bunk beds to my sleeping pod, number 56974. I crawled in and fell asleep immediately.

I find my phone nestled under my pillow – 10:45 PM.

Did I sleep twelve hours? I can’t remember sleeping this much since I started my PhD.

My stomach growls. The hotel has a kitchen with complimentary drinks, soup, rice and eggs. The clerk at reception said something about taking the stairs up to floor six, so maybe that’s where the kitchen is?

I get on my hands and knees and crawl towards the capsule lid. I disengage the latch, and with a gentle pull, it pops open and rises to the cabin’s ceiling.

I tumble out of the capsule hands-first onto a soft wool carpet and quickly clamber to my feet to avoid looking like a fool.

But the hallway is empty.

The smooth flow of white noise is the only sound I hear.

The corridor stretches endlessly in both directions – an infinite series of glowing yellowish-beige sleeping pods framed by rounded square entrances. A strip of green LED lights in the middle of the ceiling luminates the corridor. It reminds me of an endless asymptotic curve that stretches into infinity.

Weren’t there lots of people in the hotel foyer when I checked in? I could’ve sworn that two men in business suits and a group of backpackers were behind me in the front desk queue.

But the more I think about it, the less certain I become.

I wander down the corridor. It’s just more of the same – glowing yellow-beige sleeping pods arranged in endless rows of stainless-steel bunk capsules.

Wait, is that…

…someone sleeping in a capsule?

I lean in closer.

Nope.

It must’ve been a trick of the light. I thought I saw the curved outline of a person under a duvet.

Are all the pods really empty?

A sonic mist of white noise continues to hum around me.

After dinner, I could get my laptop from my locker and rehearse my presentation one last time. Where’s my locker again? It was on this floor, right?

Once I’m done with this conference, I should be ready to submit my thesis. I can’t wait to say farewell to the limbo hold this PhD has put on my life. I’ll finally be able to hang out with my friends again.

Ah! There’s a cross corridor a few steps ahead of me. I only barely noticed it because there was a slight break in the endless pattern of capsules.

I step into it.

A burst of cold air rushes through the hallway.

I pull my cardigan tighter across my chest.

The cross corridor leads to a walkway that wraps around a gigantic circular atrium.

Inside the atrium is a network of interconnecting flights of black lattice stairs.

I walk up to the atrium’s metal railing and look up. Didn’t this building have nine floors? It certainly didn’t look so expansive from the outside.

Each floor is identical and forms a perfect circular disc around the atrium.

I try to count the number of floors, but it’s pointless. There must be tens, no more like hundreds of floors extending above and below me.

Whether I look up or down into the atrium, everything looks identical.

The longer I look up or down, the more the staircases and floors seem to merge into a never-ending Mandelbrot Fractal that curls in upon itself into infinity.

My vision begins to blur, so I take a step back. 

A Perspex floor diagram against the wall catches my eye.

Finally, a map! I hurry towards it.

The text is entirely in Japanese. Damn.

The diagram itself is also nonsensical. The hallway shapes don’t correlate with anything I’ve seen in the hotel thus far. The only comprehensible thing on the board is an icon of a blank face holding a finger in front of its lips.

At least I’ve found the stairs.

I walk around the atrium to the staircase landing…

…but, what the hell?

The staircase doesn’t actually connect to the floor. The staircase landing stops a few feet away from the floor.

I look up and stare through an infinite series of identical gaps between the floors and staircases above me.

Could I jump across the gap?

No, that would be crazy. It’s too high.

I’ll just stay on this floor. Hopefully I can find the eleva…

…What was that?

I saw a fleeting glimpse of…someone…a man? Yes, a man. A man wearing a cardigan. Like mine? He was gazing down the atrium from one of the floors above me.

“Hello…

ello…

ello…

ello…

lo…”

My voice echoes through the atrium.

The white noise crescendos into a piercing “Shhh!”.

I cover my ears with my hands and study the floors above me.

There’s no one up there.  

I must’ve imagined it.

Three other corridors connect to the atrium’s walkway on my floor. I enter the closest one and step into a dimly lit hallway…

…lined by glowing yellow-beige sleeping pods.

This hallway looks precisely like the others.

Perhaps if I just walk a little bit further…?

I walk-run for a while, but it’s no use.

It’s just more of the same.

“Pfft!”

That sounded like the sound my capsule door made when I opened it!

There must be someone else here.

Surely, there has to be.

I peer down both sides of the hallway and wait…

Nothing.

Just perfectly uniform capsules symmetrically lining the passageway in both directions.

The white noise has taken on a different tone. It almost sounds… restless? The “shhh!” has subsided. Now, it sounds more like TV static. Like I’m just a slight turn of the dial away from a channel.

I turn around and walk back to the walkway that wraps around the atrium.

Why does it look like I’m higher than I was before?

The top of the atrium seems closer, and the bottom looks further away.

I need to take a photo of this – it’s just so surreal.

I pull out my phone.

The time catches my eye – 10:45 PM.

That can’t be right.

I’ve been wandering the hallways for what feels like at least thirty minutes. Or did I misread the time when I woke up?

I look down into the atrium again.

The circular disc floors and lattice flights of stairs appear to have converged at the bottom – forming a vortex that twists and spins the longer I gaze at it.

I can’t help staring. It’s hypnotic. It’s… beautiful.

This jet lag is hitting me hard. Maybe I should get back to my capsule and lie down for a bit.

The passageway entrances have also started to spin. Not fast, just… gently moving in a clockwise direction.

Six entrances intersect with the atrium walkway. Weren’t there four before?

Holding onto the railing for support, I make my way to the nearest entrance.

An unbroken series of yellowish-beige sleeping pods stretches out ahead of me.

I search the cabin numbers for mine.

This is odd – the capsules are numbered out of order: 49387 is on top of 57633 and next to 74391 and 30318.

My cabin number is 56795, right?

Yes.

Perhaps the cabin numbers follow a calculable sequence?

If only the white noise would stop. Then I could concentrate. Figure this out.

But it doesn’t stop…

…It never stopped.

© Marinda Kotze, 2025

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