“Look at that,” he whispered. “He wants you to put him in a death camp for his sexuality. You want to choke him because he’s a prat.” He wiped his mouth and stood up. “Maybe the two of you can get together.” Later, in their hotel room, they looked down at what they had done to the boy. “See that?” Sprake said. “If that doesn’t tell you something, nothing will.” When Kearney only stared at him, he quoted with the intense disgust of the master to the apprentice:

“ ‘It was a mystery to them that they were in the Father all along without knowing it.’ ”

“Excuse me?” the boy said. “Please?”

In the end these promises of understanding amounted to little. While their association never quite came to seem like anything as positive as a mistake, Sprake revealed himself over the years to be an undependable accomplice, his motives as hidden—even from himself—as the metaphysics by which he claimed to understand what was happening. That afternoon on the Euston train he had been looking for a cause to attach himself to, the folie à deux which would advance his own emotional ambitions. For all his talk, he knew nothing.

It was late. Candlelight flickered on the walls of Anna Kearney’s apartment, where she turned in her sleep, throwing out her arms and murmuring to herself. Sparse traffic came out of Hammersmith on the A316, crossed the bridge and hummed away west and south. Kearney threw the dice. They rattled and scattered. For twenty years they had been his secret conundrum, part of the centralising puzzle of his life. He picked them up, weighed them for a moment in the palm of his hand, threw them again, just to watch them tumble and bounce across the carpet like insects in a heatwave.

This is how they looked:

Despite their colour they were neither ivory nor bone. But each face had an even craquelure of faint fine lines, and in the past this had led Kearney to think they might be made of porcelain. They might have been porcelain. They might have been ancient. In the end they seemed neither. Their weight, their solidity in the hand, had reminded him from time to time of poker dice, and of the counters used in the Chinese game of mah-jong. Each face featured a deeply incised symbol. These symbols were coloured. (Some of the colours, particularly the blues and reds, always seemed too bright given the ambient illumination. Others seemed too dim.) They were unreadable. He thought they came from a pictographic alphabet. He thought they were the symbols of a numerical system. He thought that from time to time they had changed between one cast and another, as if the results of a throw affected the system itself. In the end, he did not know what to think. Instead he had given them names: the Voortman Move; the High Dragon; the Stag’s Great Horns. What part of his unconscious these names emerged from, he had no clue. All of them made him feel uneasy, but the words “the Stag’s Great Horns” made his skin crawl. There was a thing that looked like a food processor. There was another thing that looked like a ship, an old ship. You looked at it one way and it was an old ship. You looked at it another way and it was nothing at all. Looking was no solution: how could you know which way was up? Over the years Kearney had seen pi in the symbols. He had seen Planck’s constants. He had seen a model of the Fibonacci sequence. He had seen what he thought was a code for the arrangement of hydrogen bonds in the primitive protein molecules of the autocatalytic set.