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One thousand seven hundred and fifty. I have just crossed the first tributary. Which seems right. One thousand seven hundred and fifty paces works out at one kilometre. According to the map this watercourse comes to an end a little less than one kilometre from Lake Lievnasjaurre. Well I never! It all seems to work out remarkably well! I didn’t know I had it in me. I might even get quite good at this kind of thing — finding my way across Norway without so much as a compass. To celebrate my success, I sit down for a rest and take out a cigarette. I have eight left. It’s turned misty again and the sun is as pale as the moon. I light my cigarette with one of my last five matches. Not to worry, Arne has plenty. Another nine kilometres — oh all right then, ten. Four to the Rivo-elv, and five or six to the ravine. The map is very vague. You can’t tell exactly where the ravine begins. Not that I know exactly where Arne is either. Ten kilo metres, that’s an hour and three quarters on a footpath in Holland. How much is it here? Five hours? Four maybe, because I don’t have to cross mountains. Arne won’t be surprised. He’s been expecting me to turn up for days. He won’t hold it against me, and he’s not the type to bear grudges. Nor will he belittle me. I feel small enough as it is.

To think that Nansen was roughly my age when he crossed Greenland on foot from east to west, three thousand kilometres over ice at fifteen degrees below zero. Entirely alone. No sahib-venerating Sherpas for him!

I wonder what sort of life I should have had to render me capable of such feats of achievement. To begin with, my father should not have got killed when I was seven years old. But if that hadn’t happened I might not have studied geology, I might not have gone to university at all. I might have become a flautist. A great flautist? Not necessarily. Regret? No. I am long past regretting. Playing the flute would not have vindicated my father’s death, it would not have given me a chance to go right where he went wrong.

I stand up. Better get cracking. At least I can still walk, I’m still on my feet. Even if I do get lost, make a complete fool of myself, bungle everything, I’ll still be hanging on and that’s the only thing that matters.

That is all that matters. Until now there hasn’t been a challenge I have not risen to. Everything is going to be fine, success is round the corner. I will discover a meteor crater in due course, and may even return with some meteoric stones. I can see myself showing them to Sibbelee. ‘Ah well,’ he says with his most condescending smile. ‘Of course men like Nummedal made a valuable contribution to science in their day. But when they grow old they become resistant to new ideas. It seems to me that the best time for Nummedal to have resigned would have been forty years ago, when he was at the height of his fame.’ We laugh heartily. I place the precious meteorites on his desk one by one. Next I’m facing five professors in academic robes across a green baize table. I’m wearing my tailcoat and my head is bowed, not out of deference but to decipher the PhD certificate lying on the table, upside down from where I am standing. A huge, handsomely calligraphed document bearing a red seal the size of a fried egg. Cum laude.

The score on the scrap of paper in my left hand is three rows of five tally marks and a final row of four. Ninety-five marks! Nine thousand five hundred paces. Multiply by two and divide by three and a half and I’ll have the distance in metres: roughly five thousand. I was right! I can stop counting now. I’ve crossed three tributaries already, and the one I’m reaching now, the fourth, flows down into a deep valley. This must be the Rivo-elv. There’s no need, really, to keep to the water in this case. I couldn’t possibly get lost now, so I might as well take a short cut up the side.

Having climbed sixty metres, I’m on a crest from which I can see both the Lievnasjokka and the Rivo-elv. Foaming currents interspersed with shallow rapids.

I try to imagine what the valley of the Rivo-elv will look like further along, where it narrows into the ravine where I’ll find Arne. But how am I to find him? I must now take a crucial decision: keep to the river or walk along the top of the left flank of the valley. Which is best? Taking the high route means I may not see Arne if he’s down in the valley or on the opposite side of the river. And vice versa: keeping to the river means I have a good view of the slopes, but then he may have pitched his tent in a spot you can’t see from the bottom of the valley. But he wouldn’t do a stupid thing like that. He’ll be doing everything he possibly can to make it easy for me to find him. Of course he will. And as it’s so much easier for me to walk along the river, and as Arne will realise this, that’s what I decide to do.

The valley grows deeper and narrower, the sides get steeper, too steep for plants to spread their roots. Some of the rock strata protrude like book shelves. They are lined with snow, which won’t melt all summer. Snow. Speckled with black. But also red snow. I gather a handful and study it through my magnifying glass, but it melts before I get the chance to see the microbes that stain it red. They probably wouldn’t be visible anyway. Shouldn’t be wasting my time. If I keep up a steady pace I may come upon Arne within the next hour or two. Two hours — an irrelevant measure of time if you don’t have a watch. Before nightfall — equally irrelevant in a place where it never gets dark. As soon as possible, then.

What will I say when we meet? ‘Doctor Livingstone, I presume,’ of course.

Doctor Livingstone, I presume! Laughing comes easily on an empty stomach. And it isn’t even funny, because it was Qvigstad who made the joke in the first place, and I haven’t found him either.

I reach into my trouser pocket for the tube of honey and squeeze it into my mouth as I walk. The last vestiges of doubt evaporate: this is certainly the right valley, although I can’t say I recognise anything in particular from last time. Yes, the bed of the valley is lush and marshy as I remember it, and then suddenly my eyes light on the glacier on the left bank! The same glacier! The rush of water becomes louder, compounded now by the streams running down from the thawing glacier. It won’t be long before I see Arne, surely. Doctor Livingstone, I presume.

‘My compass indicated a different direction from yours. I’m sorry. You were right.’

‘Where is it?’

‘Lost.’

‘That beautiful compass? Pity.’

‘Good riddance, I’d say.’

‘You must have misread it.’

‘Don’t worry. I have only your compass to go by now. Mine was given to me by my God-fearing sister. A typical present from her! I wonder where she got all those funny ideas from. My father was not a believer, my mother isn’t one, and I’m not either. But she has taken it upon herself to point us in the right direction!’

‘Where to?’

‘Don’t ask me! To the North Pole, like a compass, who knows? A bit cold, but then she makes up for it by being crazy about Negro spirituals.’

‘Ha, ha, ha.’

Treading with care, I walk on, keeping as close as I can to the side of the valley so as to avoid the marsh. Three enormously fat Negresses, each weighing at least 200 kilos, clap their hands, sway from side to side, stamp their high-heeled shoes and scream hallelujah. I’m seized with pity for the Negroes, who even at the best of times are likely to be pictured in stupid, ridiculous or vulgar poses: yelling and screaming, leaping about, rolling their eyes, setting the place on fire, sweating profusely as they play their trumpets, clobbering each other in boxing rings, demanding equal rights under the guidance of a reverend minister of the very religion that oppresses them. On television or in the news papers you never see a black scientist in a laboratory, or a black astronaut, or a Negro reading from his poetry — and yet they exist.