It was, fortunately, far too late to phone Melissa, and too early to phone Darlene, who would be at work. All he had the strength for was the remote. Before it came on, the TV set gave out a homely, muffled crackling sound of warming electronics, as kindly and familiar as a mother's kiss. But not his mother's. He was tired and drunk and all he could do was surf. Here were the usual, unsurprising things – game and chat shows, tennis, cartoons, a congressional committee, moronic ads. Two women to whom he would at that moment have entrusted his life spoke to each other about their husbands' Alzheimer's. A young couple exchanged a meaningful look that provoked a gust of cackling from a studio audience. Someone said, as though in protest, that President Obama was still a saint, still loved. These days Beard described himself as a 'lifelong Democrat'. He often spoke at climate-change events of the fateful moment in 2000, when the earth's fate hung in the balance, and Bush snatched victory from Gore to preside over the tragedy of eight wasted years. But Beard had long ago lost interest in the plenitude and strangeness of America as represented by its television. They had hundreds of channels in Romania now, and everywhere else on the planet. Besides which, if it was on TV, it was no longer strange. But he was too tired to lift his thumb from the channel-up button, and for forty minutes he sat in a stupor with an empty glass and empty wrapper on his lap, then he made himself comfortable on the cushions behind him and fell asleep.

Ninety minutes later he was disturbed by the ring of his palmtop, and came properly awake with it already pressed to his ear as he listened to the voice of the girl whose existence he had done all he decently could to suppress. But here she was, Catriona Beard, as irrepressible as a banned book.

'Daddy,' she said solemnly. 'What are you doing?'

It was six o'clock on Sunday morning in England. She would have been woken by the early light and gone straight from her bed to the sitting-room telephone and pressed the first button on the left.

'Darling, I'm working,' he said with equal solemnity. He could easily have told her he was sleeping, but he seemed to need a lie to accommodate the guilt he immediately felt at the sound of her. Many conversations with his three-year-old daughter reminded him of dealings over the years with various women in the course of which he had explained himself implausibly, or backtracked or found excuses, and had been seen through.

'You're in bed because your voice is croaky.'

'I'm reading in bed. And what are you doing? What can you see?'

He heard her sharp intake of breath and the sucking sound of clean tongue on milk teeth as she considered which part of her newly acquired net of language to cast about her. She would be by or on the sofa which faced the large bright window and a cherry tree in leaf, she would see the bowl of heavy stones which always interested her, the Moore maquette, the neutral colours of the sunlit walls, the long straight lines of oak boards.

Finally she said, 'Why don't you come in my house?'

'Dearest, I'm thousands of miles away.'

'If you can go you can come.'

The logic of this made him pause, and he was beginning to tell her that he would see her soon when she cut across him with a cheerful thought. 'I'm going in Mummy's bed now. Bye.' The line went dead.

Beard rolled onto his back and closed his eyes and tried to imagine the world from his daughter's point of view. Of time, time zones and physical distance she had as yet no proper conception, and she lived with a machine whose wondrous properties she took for granted. At the press of a button she could speak to her disembodied father, as though at a s̩ance to a spirit of the dead, a ghost on the other side. Sometimes she could summon him in person, mostly she failed. When he did show up, he always brought a gift, clumsily chosen in an airport, often inappropriate Рa pack of twelve rainbow T-shirts that were too small, a soft toy she thought too babyish but was too kind to say, an electronic game she did not understand, a box of chocolate liqueurs he was obliged to eat himself in one go. Melissa tried to talk him out of bringing presents Р'It's you she wants' Рbut Beard's lifelong habit of mollifying girls with surprises buried in wrapping paper was impossible to break. Without a present, he arrived naked, exposed to raw, unpredictable demands, unable to make amends for his absence, required to exert himself in an uncomfortable personal dimension, obliged to engage.

Even at the age of three, Catriona was the kind of person who felt on opening a gift a responsibility towards the feelings of the giver. How could a consciousness so new be so finely attuned? She did not want her father disappointed in her pleasure. The T-shirts, so she reassured him, were not wasted, for one day they would be useful to her baby brother, a tender being whose arrival she anticipated with eerie confidence. She was an intimate, sociable girl of near-unbearable sensitivity. She might hear in a chance remark an inflection, a raised tone, that she took to be a criticism or a reprimand and she would be horrified, and tearful, and then, quite often, she would be sobbing, and not easily reassured. Sometimes, it seemed, she experienced another mind as a tangible force field, whose waves were overwhelming, like Atlantic breakers. This awareness of others was an affliction and a gift. She was bright and confiding, funny and astute, but her emotional delicacy made her vulnerable, and made her father uneasy. Once, some harmless remark of his, some mild expression of impatience, had caused her great unhappiness and brought her mother hurrying into the room to gather the child in her arms. He did not enjoy being made to seem a cad, nor did it suit him, it was constraining, to be sensitive all day long.

Would he have been better off with a bullet-headed, shin-kicking son? Probably not. What bound him to her – at least, as far as he could be bound to anyone – was her insistence, her unconditional, uncritical love. For Catriona, it was simple. He was her father and she claimed him for herself. She understood that his job was to save the world, and since the world was her mother, Primrose Hill, the dance shop and her playgroup, she was fiercely proud. What use Melissa saying that the father did not need to be involved? Catriona would not permit him to defect. She did not care or even notice that he was fat and short and was not very nice and was growing a triple chin, she loved him, and she owned him. She knew her rights. That was another reason why he felt guilt, and brought her presents to distract her from throwing herself at his stomach as he came through the door, and climbing onto his lap and whispering a little girl's secrets in his ear the moment he had sat down after a tiring journey. Like his own father, Beard did not find it easy to be physically affectionate with a child. Like her mother, Catriona was prepared to love unequally, and did not notice his reticence.

In all, he was an irresolute parent and lover, neither committing to nor decently abandoning his family. He clung from habit to a youthful notion of independence that was unusual in a man of almost sixty-two. On arriving back in London he often stayed in the Dorset Square flat, at least for the first two or three nights, until its grime and multiple defects drove him out. Yellowish-grey mushrooms were flourishing along a line where the wall met the ceiling in the kitchen. A gutter outside, which in theory belonged to a neighbour, had cracked and rainwater was penetrating the brickwork. But Beard did not want to confront the belligerent, partially deaf man upstairs, and he did not want to initiate the hacking and plastering, noise and intrusion of a thorough repair. In the hallway the light always failed, however often he changed the bulb. As soon as he turned the switch it popped. In his bathroom upstairs the cold water had long ago run dry. To shave, he ran the hot slowly, and became adept at finishing before the water scalded him. To take a bath it was necessary to fill the tub and let the water cool for an hour or so. These and other small problems required deep attention, and so he preferred to improvise. A large vase collected raindrops in the spare bedroom, an iron foot scraper held the fridge door closed, a frayed and curling length of grubby string substituted for a chain on the ancient lavatory cistern.