You can sense its happening. A thickening of the air, a prickling of the skin, and the distant thunk of the generator all come a moment before the lights buzz on and the ancient aircon groans into service. It can only have been off for ten minutes, but already the air is sticky and condensation has begun to form on all the glass surfaces of this small, misshapen room. She is sprawled in the corner examining her feet. All legs and sweat and softly crumpled clothes.

I stand. Walk to the aircon unit. Hold my hand up to the vent. The soles of my feet leave perfect outlines on the tiles. Feeling the stream of air is like waving my hand in a bowl of tepid water. I cannot work out whether I am hot or cold. Can’t tell whether the stream of air now emanating from the vent is hotter or colder that its surrounds. Can’t decide whether I want to be here. This displacement, this loss of the sense of now, I don’t think it is exclusive to the tropics. But it is exacerbated by them.

The aircon beeps again, and does its function. My brain swims languid strokes and seems quite content with this momentary discombobulation. “We’ll get there. We will get there in the end. But you will need to be content with the journey,” it whispers to me. This is the moment where you hear a snippet of a song, that until then had existed only as a fully realised part of another song. And this displacement is unsettling to you, and it upsets the natural order of things.

The humidity clings and grabs. My hand is now noticeably cold.

“The lights are still off, in the main building, look,” I say. “But ours are on. And the aircon. How does that even work? Seems a little unfair.”
“Unfair is that it is your nominated duty to go down there and get me a snack.”
“If they don’t have lights, what makes you think that they have the facilities for snack.”
“Snack is versatile.”
“Not fair. What do I get out of this transaction?”
“Me. And I will tell you a bedtime story. This is what I will do. And it will be about a hotel, hollowed into a cliff, that stretches forever and ever. But, if I am to tell you this,” she says in a mock-whisper, “you have to promise.”
“You must promise to never ask me about the keys to the room, my toenails, or the reason I’m sitting in the corner. Also you must get me a beer.”
“The power has been off, and...”
“Jesus. They’ll be fine. Look, just listen. There is a room and, of course, it looks nothing like this,” she says as she taps the side table she is leaning against, held together in some inexplicable conclave between duct-tape and gravity.
“No, it is white stucco. There are thick round beams of unruly wood, smoothed by the wind, that run across the ceiling in lines. Just below them, but above the door, there is a mosaic of tiny tiles, azure and lapis, and they sparkle in the setting sun. And next to this room there is another.”
“The same?”
“Yes, there is sand on the floor and an immaculately made bed with the finest sheets.”
“How’s the thread-count?”
“Uncountable. Immeasurable.”
Someone walks past the room, along the winding path down to the beach, and I watch the monster shadows dance across the roof. She stops for a second, until the shadow has passed, then continues. “And next to this room, there is another. And again. And again. Until infinity.”
“An infinite hotel.”
“The infinite hotel. There is only one. And every room is full. Every single one,” she says as she unfolds against the door. Staying low, against the cool of the tiles. An advertisement for fire action. Stop, drop, roll and keep low. Go? Go!
“And the rooms are full?”
“Yes, all of them. And this girl rocks up at the front desk. Says she wants a room. Says you need to make space for her.”
“But all the rooms are full?”
“Yes, all of them.”
“That doesn’t sound particularly logical,” I say.
“The point is its illogicality,” she says. “This story represents the difficulty people have wrapping their heads around infinity. The concept of infinity.”
“I’m not sure that’s what it represents. Trying to understand the fullness of infinity, actual infinity, seems a fundamentally stupid exercise for the human brain.”
“Sure, whatever, but that’s the point. It’s a paradox. They all seem ridiculous at first.”
“I’m not saying I don’t understand it, I’m saying it’s stupid.”
“Yes, well…” and she points her leg out, toes flexed, making a sight line over her shins. “I’ve fucked this one up. Torn it,” and she begins to fiddle with the clippers and the nail. The paint is chipped, I can see that from here, chipped and the edge is ragged. This is a far cry from the pearlescent knife-edge achieved with the help of a woman in dungarees in a crowded mall in the big city. The Mani/Pedi capital of the universe. Or so they say.
“So explain it then,” I ask. I check the beers in the the tiny bar fridge crammed into the corner. Cool enough, but not for long.
“Bloke called Hilbert thought of it,” and she punctuates this with short, precise motions with the nail clipper. There is an audible click as the nail falls onto the checkerboard tiles. Grimaces. Looks out the window. The last vestiges of the setting sun, and the creeping beads of condensation on the inside of the window make it hard to see beyond vague shapes. Still no lights down there. “Okay, so here’s how it works,” she says, “here, hand it over,” gesturing to the bottle in my hand. I pass the beer, reach for another for myself.

She rolls onto her stomach and fingerpaints a line of clear into the condensation of the window. “So, your girl, she’s n,” and even from the other side of the room I can see the italics in the tiny notation formed in droplets. “And me, in the next room, the first room, I’m +1.”

“Well +1, the lights just came on down there. I will now facilitate ‘snack’ and whence I return I expect to be told how I too can enjoy mosaics and fine sheets without asking about keys.”
“Or toenails?”
“Or toenails.”
“Or the countably infinite.”