Through a serving hatch in the interior wall, I saw a small stainless-steel kitchen. A fat man with tattooed biceps and a too-tight T-shirt gave me a wave through the hatch and turned back to the pot on the hob.

‘Danny, the cook. Danny knows all the gossip.’

Quam stopped in front of two huge maps hung on the wall either side of the door. One was a topographic map of Utgard, mostly white, with Zodiac marked in the lower left-hand corner. The other showed the earth, not as you usually look at it with the equator in the middle, but as you’d see it from a spaceship hovering over the North Pole. The Arctic Ocean filled the centre, hemmed in almost continuously by the countries that bordered it. Nothing south of Shetland made it on to the map; even the southernmost tip of Greenland needed an extension.

‘The Antarctic is a continent surrounded by oceans. The Arctic is an ocean surrounded by continents,’ Quam said. Passable imitation of a fourth-form geography teacher.

I found Utgard, between Svalbard and Franz Josef Land and further north than either.

‘What’s that?’ I pointed to a grey shadow shaded on the map, a thousand-kilometre barb pointing down towards Finland. It covered Utgard like a bespoke rain cloud.

‘That’s the Grey Zone — the old disputed border between Norway and Russia. That’s why Utgard’s unique. In the seventies, when they agreed to disagree, both sides committed not to press their claims to the island until they’d finalised the border. When they did, a few years ago, they found the easiest compromise was to leave it as an international scientific wilderness, administered by us. Technically, we’re beyond all laws and governments here.’

‘Good place to commit a murder,’ I said facetiously.

‘Or to make a killing. The 2010 treaty also opened up the area to hydrocarbon exploration. There’s a company here now prospecting for oil and gas. They can’t touch the land, but anything under the seabed is fair game.’ He tapped the Utgard map, halfway up the west coast at a spot labelled Echo Bay. ‘You might see them around.’

I stared at the tiny blot on the map — and the vast space around it. Most of the world, and almost all its population, might as well not exist.

The tour finished back at the front door. Next to the gun rack, Quam showed me two plastic boxes nailed to the wall and labelled In and Out. The outbox bulged with paper; the in was almost empty. A vinyl-bound notebook sat on a shelf below.

‘This is where you check out. Whenever you leave the base, even if it’s just for a wee, you sign in and out in the field book. If you’re doing fieldwork, you fill in a risk-assessment form and put it in the outbox. When you come back, you transfer it back to the in-box. Understood?’

I nodded. ‘Is there anything else?’

‘You’ll receive a safety briefing.’ I had the sense of a recorded message being switched on. ‘Pay attention, learn the procedures and follow them. Up here, procedure will save your life.’

‘What about clothes?’

‘Greta will issue your ECW gear when she does the induction.’

‘The woman who brought me here?’

‘Our base mechanic, field guide, vehicle engineer …’ He looked as though he wanted to add something else to the description. In the end, he settled for, ‘She’ll find you.’

I lay on my bunk and tried to trick myself into going to sleep. Twenty-four hours of airports and aeroplanes had wrecked my body clock, even before I got to the land of the endless day. Light leached around the wardrobe. I reached behind it and felt a roller blind; I fumbled with it, but the mechanism was jammed. When I tugged, it collapsed off its bracket and rolled under the wardrobe with a puff of dust. I gave up.

My eyes drifted. In the half-light, I noticed some graffiti on the wall, white letters scarred into the wood panelling at knifepoint. I sat up and squinted.

You’ve got it in the neck. Stick it — stick it.

I rolled over on my side, back to the wall. The words chased round my head like a song I couldn’t shake. I tried to get my journal up to date, and found I could hardly remember a thing.

The door opened. Greta stood silhouetted in the corridor.

‘Come and learn how to kill polar bears.’

She issued me my gear from the ECW store — a cupboard overflowing with winter clothes. ECW, it turned out, stood for Extreme Cold Weather. Insulated trousers; a thick coat with a fur-lined hood; a balaclava and face mask; Black Diamond mittens; felt-lined boots; a helmet; a heavy all-in-one suit with zips up the legs.

‘Your snowmobile suit,’ she explained.

She grabbed two rifles from the rack on the way out, slung one over her shoulder and gave the other to me. The moment we went outside, I was glad of all the layers. I pulled the balaclava up over my nose as she led me to a row of parked snowmobiles. As we were walking, she pointed out the different buildings with cryptic explanations. The shop; the summer house; optics caboose; the bang store. Some looked as if they hadn’t been opened in years.

‘What’s that one?’ I pointed to a small wooden hut, well away from the other buildings. It stood outside the main perimeter, in the centre of its own circle of flags.

‘Magnetometer.’

‘How come it gets its own little patch?’

‘It’s sensitive. Don’t take any metal inside the circle.’

I scanned the perimeter. At the far end, where piles of rocks and rubble broke the snow, the poles had been crossed against each other to make five X’s standing up out of the ground.

‘The Gulch,’ said Greta. ‘Big hole, where the glacier comes down. Don’t fall in.’

‘Let me guess: the insurance doesn’t cover it.’

‘No, it does. But you won’t be there to get the money.’

We’d reached the snowmobiles. ‘Do you know how to drive?’ she asked.

I shook my head. She showed me a little plastic paddle on the right handlebar. ‘The accelerator.’ On the other handlebar, a curved metal lever stuck out like a bicycle brake. ‘The brake.’

‘Is that it?’

She thought for a moment. ‘If you tip over, don’t put your leg down. The snowmobile will crush it.’

She pulled the starter cord. If she had any more advice, the engine drowned it. I moved to get on, but she waved me away. Standing behind the snowmobile, she put her hands under the back and hoisted the rear end off the ground. She held it there a few moments, then put it down.

‘The tracks freeze to the ground when it’s parked,’ she shouted in my ear. ‘If you don’t get them loose, you burn out the engine.’

She got on; I climbed on behind her. I moved to put my arms around her, like riding pillion on a motorbike, but she shrugged me off.

‘You’ve got handles at the side.’

I hardly had time to grab them before she gunned the throttle. The snowmobile bounded forward with a pop — slowly, then quickly up to full speed once we’d left the perimeter. The wind chewed my face; belatedly, I realised I’d forgotten to put down the visor on my helmet. I let go with one hand to lower it, and nearly got pitched off my seat as the snowmobile hit a bump in the snow.

The rifle range was on a low ridge to the north of the base. There wasn’t much to define it, except for the inevitable flags staking out the corners. At one end, a paper target shaped like a penguin had been stuck on to an ice wall.

Greta showed me the gun. ‘This is a Ruger thirty-oh-six. You ever fire a rifle before?’

‘Yes.’

She looked sceptical. ‘Show me.’

I took off my mittens, chambered a round and sighted the gun on the grinning penguin. My hands were already beginning to shake in their thin gloves; I tried to imagine how much more they’d be trembling if there was a polar bear right in front of me. Not a lot of time to get off the shot.

I pulled the trigger. Twenty metres away, a white hole appeared between the penguin’s eyes.