First they laid dry wood over the ventilation-ditches, then a layer of oak logs – they burned well – then women who'd been killed, then more wood, then men who'd been killed, then more wood, then the bits of human bodies that were left over, then a can of petrol, and then, right in the middle, an incendiary bomb. Then the Scharfuhrer gave the order; the guards were already smiling as the brenners shouted out: 'It's alight!' Finally, the ash was shovelled back into the grave. And it was quiet again. It had been quiet before and it was quiet again.

Then they had been taken further into the forest. This time there was no mound in the middle of the green clearing and the Scharfuhrer ordered them to dig a pit four metres long by three metres wide. They had understood at once: they had completed their task… 89 villages, 18 shtetl, 4 settlements, 2 district towns, 3 State farms – 2 arable and one dairy. Altogether that was 116 localities, 116 mounds they had dug… Rozenberg the accountant was still counting as he helped dig the pit for himself and the other brenners: 783 last week, and 4,826 during the thirty days before – that made 5,609 bodies they had cremated. He counted and counted and time slipped imperceptibly by; he was working out the average number of items – no, human bodies -in each grave: 5,809 divided by 116, the number of graves – that made 48.35 bodies in each communal grave, 48 in round numbers. If 20 brenners had been working for 37 days, then each brenner.. . 'Fall in!' shouted the chief guard. 'In die Grube marsch!' bellowed the Scharfuhrer.

But he didn't want to be buried. He started to run, he fell down, he started running again. He ran slowly – he didn't know how to – but they didn't get him. Now he was lying down on the grass, surrounded by the silence of the forest. He wasn't thinking about the sky above, nor was he thinking about Golda who had been killed in her sixth month of pregnancy; he was counting, trying-to finish the calculations he had been doing in the pit: 20 brenners, 37 days… So, first, the total of brenner days; second, how much wood per man; third, how many hours each item took to burn, how many…

A week later he'd been caught by the police and taken to the ghetto.

And here he was in the cattle-wagon, still muttering away, counting, dividing, multiplying. The accounts for the year! He would have to hand them in to Bukhman, the chief accountant at the State Bank. And then suddenly, while he was dreaming, his tears had come gushing out, burning him, breaking through the crust that had formed over his brain and his heart.

'Golda! Golda!' he cried out.

The window of her room looked out onto the barbed-wire fence that surrounded the ghetto. Musya Borisovna the librarian woke up during the night, lifted the hem of the curtain and saw two soldiers dragging a machine-gun. There were blue patches on its polished body and the spectacles of the officer walking in front were glittering in the moonlight. She heard the quiet hum of motors. Cars and lorries with dimmed headlights were approaching the ghetto. The heavy, silvery dust swirled around their wheels; they were like gods floating through the clouds.

Musya Borisovna watched as sub-units of the SS and SD, detachments of Ukrainian police, auxiliary units and a column of cars belonging to the Gestapo drew up at the gates of the sleeping ghetto. In these few minutes of moonlight she took the measure of the history of our age.

The moonlight, the slow majestic movement of the armoured units, the powerful black trucks, the timid ticking of the pendulum clock on the wall, the stockings, bra and blouse that seemed to have frozen on the chair – everything most incongruous had fused together.

Natasha, the daughter of Karasik, an old doctor who had been arrested and executed in 1937, tried now and then to sing in the cattle-wagon. No one seemed to mind even when she began singing during the night.

She was very shy. She always looked down at the ground when she spoke and her voice was barely audible. She had never visited anyone except her close relatives and she was astonished at the boldness of girls who danced at parties.

She had not been included in the small number of craftsmen and doctors whose lives were considered useful enough to be preserved… A policeman had pushed her towards a dusty mound in the marketplace where three drunken men were standing. She had known one of these men before the war: he had been in charge of some railway depot; now he was the Chief of Police. Before she had even understood that these three men were the arbiters of life and death, the policeman had given her another shove; she had joined the buzzing crowd of men, women and children who had been pronounced useless.

Then they had walked towards the airfield in the stifling heat of their last August day. As they walked past the dusty apple trees by the roadside, they had prayed, torn their clothes and uttered their last piercing cries. Natasha herself had remained quite silent.

She would never have thought that blood could be so strikingly red. When there was a momentary silence amid the shooting, screaming and groaning, she heard the murmur of flowing blood; it was like a stream, flowing over white bodies instead of white stones.

The quiet crackle of machine-gun fire and the gentle, exhausted face of the executioner – he had waited patiently as she walked timidly to the edge of the pit – had hardly seemed frightening at all… Later, during the night, she had wrung out her wet shirt and walked back to the town. The dead don't rise from the grave – so she must have been alive.

When she made her way back to the ghetto, through the small alleys and yards, she had found people dancing and singing on the main square. A band was playing a sad, dreamy waltz that had always been one of her favourites. Couples were whirling round in the wan light of the moon and the streetlamps; the shuffling of soldiers' boots and girls' shoes merged with the music. At that moment this young, drooping girl had felt joyful and self-assured. Quietly, under her breath, she began singing in anticipation of some future happiness. From time to time, when no one was watching, she had even tried to waltz.

David could only very dimly remember what had happened since the beginning of the war. There was one night, though, when a little of what he had just lived through came back to him.

It was dark and his grandmother was taking him to the Bukhmans. The sky was full of stars and the horizon was quite light, almost lemon-green. Burdock leaves brushed against his cheeks like cold, moist hands.

Everyone was sitting in a hiding-place in the attic, behind a false wall. In the sun the black sheets of corrugated-iron roofing gave off a fierce heat. Sometimes the smell of burning penetrated their hiding-place. The ghetto was on fire. During the day they had to lie absolutely still. The Bukhman's daughter, Svetlanochka, kept up a monotonous crying. Bukhman himself had a weak heart and in the daytime he looked as though he were dead. During the night he ate some food and quarrelled with his wife.

Suddenly they heard dogs barking. And words in a foreign language: 'Asta! Asta! Wo sind die Juden?' There was a growing rumble over their heads: the Germans had climbed out of the dormer-window onto the roof.

Then the thundering in the black tin sky died down. Through the walls they heard quiet, sly blows – someone was testing for echoes.

The hiding-place became silent. It was a terrible silence, a silence of tensed shoulders and necks, of bared teeth, of eyes bulging out of their sockets.

Then little Svetlana began her wordless lament. Her cries broke off very abruptly. David looked round and met the frenzied eyes of her mother, Rebekka Bukhman.