Schild’s Ladder

He said, "I’m going up on the roof."

Mariama blinked at him in the lamplight, apparently at a loss for words.

Tchicaya put on his shoes and walked outside, taking the lamp with him.

He circled the building twice, before settling on a sturdylooking drainpipe. The lamp was attached to a chain; he hung it around his neck, like a pendant worn backward, and gripped the drainpipe between his forearms and knees. There were no handholds, and the frosted surface was slippery. The first time he found himself sliding back down, he panicked and almost let go, but the friction from the polymer surface was never enough to really hurt him. After ending up back on the ground twice, he found that if he tightened his grip the instant he began to slip, he could bring himself to a halt in a fraction of a second, and retain most of his hard-won altitude.

He reached the roof with his limbs numb and his chest soaked in icy perspiration. He crouched on the sloped tiles, flapping his arms vigorously to try to restore the circulation, until he realized that this was driving him slowly backward toward the sevenmeter drop behind him. If he did real damage to his birth flesh, there’d be no prospect of concealing it from his parents. And to take on a new body at the age of twelve would make him a laughingstock for centuries.

He rose up on his haunches and waddled across the roof, as wary of gravity now as if he’d been back in Slowdown. He had no idea whether he was heading in the right direction; the dark shapes looming ahead of him might have been anything. He stopped to work the lamp around from his back to a more useful position, and noticed a long gash along the inside of his right leg, wet with blood. Something had cut him as he’d slipped along the drainpipe, but the wound wasn’t painful, so it couldn’t be too deep.

Up close, the radiator fins were massive, each as wide as his outstretched arms. He ambled around the structure, shining the lamp into the angled gaps between the fins, hunting for the source of the leak.

Mariama called out to him, "What have you found?" She was outside, on the ground somewhere.

"Nothing, yet."

"Do you want me to come up?"

"Suit yourself." He felt a twinge of guilt at the way that would sound, but it was hardly an expression of lofty disdain by the standards she’d set. This was the first thing he’d done since he’d joined her that wasn’t part of some complicated strategy to please her, or confound her. He had to be indifferent to her, just this once, or he’d go mad.

When the lamplight finally returned the rainbow sheen he’d glimpsed from inside the building, it was unmistakable. An irregular, glistening patch of some filmy substance covered half the fin. Tchicaya approached, and touched it with a fingertip. The substance was slightly sticky, and the film clung to his finger for a fraction of a millimeter as he pulled away. When it parted from his skin he could feel it snap back elastically, rather than tearing like something viscous and treacly. He held his finger up for inspection; the skin was unstained, and when he rubbed it against his thumb there was no moisture or slickness at all. This wasn’t any kind of oil he’d seen before, and it definitely wasn’t ice.

He held the lamp closer to the surface, hunting for some sign of a damaged coolant channel. This had to be the residue left behind by a leak, though why the coolant would contain some sticky impurity was beyond him. Antifreeze? He was shivering with cold, but he was in a stubborn frame of mind.

A small hole appeared in the film at the center of the circle of lamplight, and grew before his eyes. He held the lamp as still as he could; once the boundary of the film had retreated into the penumbra cast by the lamp’s housing, the hole stopped growing.

Tchicaya moved the lamp to another spot. The same thing happened: the lamplight seemed to melt the film away. But the beam carried no heat whatsoever. Was it driving some kind of photochemical reaction?

He turned back to the original rent in the film. It had shrunk to half the size it had grown to when he moved the lamp away. He made a hole in the film in a third location, then took the lamp back to inspect the second hole. It was closing up, too.

Tchicaya stepped out from the gap between the fins and sat huddled on the roof tiles, his teeth chattering. Maybe the light broke up whatever molecules the film was made from, while the chemical process that had formed it in the first place rebuilt it when he took the light away. Some mixtures of simple chemicals could behave in a complicated fashion. He had no right to start summoning up phrases from his biology lessons, like negative phototropism.

His arms were shaking. Mariama had been silent since their last exchange; she had probably gone back to bed.

He rose to his feet, and scrupulously searched the other parts of the radiator, but it was only one side of one fin that bore any visible trace of the film.