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Isla called her colleague Mike about this. She was worried, she said. She sat in the kitchen of her house in Cambridge and showed him the last letter from Banacharski. What could he mean? Mike shook his head. ‘Buggered if I know,’ he said. ‘Your boyfriend is, let’s not forget, mad as a badger.’

‘A metre,’ she said. ‘It’s a measurement. He’s preoccupied by measurements. And he’s trying to build a machine. He says he’s finished it.’

‘Clear as flaming mud, love. I’d leave it. Write back and tell him it’s something to do with Napoleon. He probably thinks he’s something to do with Napoleon.’ Mike seemed moderately pleased with the witticism. He fetched himself another of Isla’s biscuits and moved on to some faculty gossip.

‘What is a metre?’ he said as he left. ‘A hundred centimetres, eh?’

Isla did not show Mike the letters she had got privately. And she did not tell him about Ana’s ring. She was still turning it over in her mind two days later. She was leaving for her 10 a.m. seminar, running late and with her hair still slightly wet against her neck, when she picked up the post from the tiled hallway. There were two letters, forwarded from Nice. Both were bulging, as if there was more paper in them than their envelopes were strictly designed to bear.

She tucked them under the arm of her duffel coat as she stepped out into the street. She slipped open the first one with a thumbnail, her bag on her lap, as she settled on the top deck of the bus on the way in to the faculty. She felt her cheeks grow cold as she read.

The yellow legal paper was in some places torn with the force of the handwriting. Block capitals alternated with lower case, no one letter joined up with another, and words of German and French mashed into English sentences. The ruled lines on the paper were only ever a loose guide when Banacharski was excitable – but here the lines of his script were flapping off them like an untethered mainsheet in a gale.

It was a wad of incoherent fury, calling her a ‘thief’, a ‘liar’ and a ‘Judas’. It accused her of working with ‘the enemy, the murderers, the Moloch’. The second letter was shorter, and barely in prose at all. On the first page, her name was written in block capitals, dead centre, and a series of numbers scribbled underneath – separated by dashes and subject to a whole succession of transformations that brought them out to new numbers. She leafed through. He was using the letters of her name – it would be Kabbalah, she guessed; he had spoken to her about using Kabbalistic practice for, he said, exploring ‘the relationship between speech and number’.

On the following pages the letters of her name had been anagrammed, and further manipulated into numbers; or, the letters of her name were written out as a matrix, and multiplied by another matrix constructed from the same letters. Her eyes started to swim. He couldn’t have slept. Nobody could physically have achieved the rate and ferocity of work in these letters – would not physically have been able to write them down – in the time between them.

They were both dated the same day, though they bore different postmarks and had clearly been held up a few days between Paris and London. Isla, scouring her memory, couldn’t swear to it that they hadn’t been written on the same day as the original letter posing the riddle. The final page of this second letter ended: ‘Nothing comes of nothing. Nobody’s here. We are divided by nothing. Forgive me.’ His signature at the bottom was also bristling with numbers, all of them cancelled to zero.

She missed her stop. She was twenty-five minutes late for her seminar by the time she got there and she noticed her hands trembling as she wrote on the whiteboard. She felt very afraid. She cancelled drinks with Mike and Jude. She spent the afternoon talking to the faculty and the college about a temporary, emergency leave of absence. The first flight she could get to Toulouse was the following lunchtime. It would cost her. She didn’t think about that.

The following morning, a third letter arrived. On the envelope it said: ‘To the Supposed Isla Holderness.’ She read it on the way to the airport.

‘You are not who you say you are. I am not who I was. Nobody is here,’ it began. Almost every other sentence contained a sarcastic intimacy – ‘my dearest “Isla” ’; ‘my trusted “Miss Holderness” ’ – as if parodying the man who had written her those private letters about his life over the past couple of months. The brusque kindness she remembered from the shack was gone. She found it unbearable.

It ended with a signature: not ‘Nicolas’ or even ‘NB’ this time, but ‘Fred Nieman’.

And so, fast-forward to Isla, walking round the final curve of the approach to Banacharski’s shack, feeling that she knows what she is going to find.

The fire had long gone out, doused in cold rain. But the smell of burning came through, wet burned wood. Droplets stood on melted plastic. The shack was gone – a black stain on the ground, a couple of jutting teeth of carbonised wood. Across the wet grass to either side were wisps and fragments of cinderated paper, the odd rag of sodden yellow in the fingers of the green.

The Calor canister under the wall of the shack had obviously gone. Half of it was there, its skin twisted and blackened. Its shrapnel had half dug turves out of the ground, and the grass was radially scorched on that side. The wooden floor of the shack was gone from the centre, where the fire seemed to have started. There were threads of rug towards the outside – where the stump of a piling emerged from poured concrete foundations. A stick of table leg was there.

The wind had blown the fire away up the hill, drying and burning the grass in patches up behind the shack. The beanstalks, the ones nearest the hut, were scorched but those towards Isla were intact, if more overgrown than when she had been here. The leaves were blowsy, the season long gone. Isla walked closer.

Too late, she thought. She had run out of time. He was gone.

She twisted a pod off one of the beanstalks, and thumbed it open. Inside, a broad bean – the only one full-size – sat in its velvety white cushion like a ring in a jeweller’s box.

She walked round the shack, looking for him. She thought of calling for him, but it felt wrong, somehow, to raise her voice. He was gone. She knew that. Not dead – she didn’t know why she was so sure of that, but she somehow felt confident of it – but gone. Beyond her help. Nobody could help him.

Her good Gore-Tex boots kept the wet out. She remembered him drawing his diagram: ‘And here is the map of Nicolas Banacharski in the world. And here is the map of Miss Isla Holderness in the world.’ She understood now why this was strangely comforting.

In among the bean shoots the chickens picked, pecking morosely at the wet grass, shivering their wings. Had he left them? Their henhouse was intact. She peeked into it. There was straw in there, and the hopper was dry, and full of grain.

Isla walked back down into town, and caused the police to be called. They came up, took a statement – Isla struggling a little with her French – filed a missing persons report, and late that evening told her she was free to go home. She spent the night in an auberge, and set off the following morning, early, resolute, sad: telling herself she had done everything she could and not believing it for a second.

When she arrived back in Cambridge, she came home to find that she had been burgled. Her laptop had gone, as well as her video recorder, the contents of her underwear drawer and medicine cabinet, and the nearly full bottle of vodka she had kept on the dresser. A pane of the front bay window had been smashed. A creditable but, finally, unsuccessful attempt had been made to remove the television.

Also, her jewellery box was gone – and with it, which somehow at that moment felt more important to her than even her own christening presents, Ana’s ring. Isla had sat down on her living-room floor and, before she called the police, cried for a long time.