Schild’s Ladder

However many mutations were part of the throng, they couldn’t include an exhaustive catalog of all the possibilities. The toolkit was X-raying each gate and designing the perfect key as they approached; that strategy had to win out some of the time.

If not always by a wide margin. Tchicaya was just beginning to picture the Sarumpaet streaking ahead triumphantly, when the second barrier fell to the Planck worms.

He addressed the toolkit. “Is there anything we can throw in their way? Anything we can scribe that would act as an obstacle?”

“I could trigger the formation of a novel layer population. But that would take time, and it would only stretch across a single vendek cell.” However long the artificial barrier held, the Planck worms would still percolate down along other routes.

They glided through a dozen more cells, maintaining a tenuous lead. Even when they appeared to be widening the gap, there was no guarantee that they wouldn’t plunge into a cell to find that the Planck worms had reached the same point more quickly by a different route.

The honeycomb stretched on relentlessly; the Sarumpaet gained and lost ground. After eight hours of nominal ship time, they’d crossed a thousand cells. In near-side terms, they were a millimeter beneath the point where the border had last rested, and the chase had gone on for mere picoseconds. The Planck worms had spent more than two hours diversifying before they’d learned to penetrate these catacombs, but having found the basic trick they appeared to be unstoppable. So much for the strategy of burning away one vendek population and the predators trapped within it; that would have been like trying to cure a victim of bubonic plague by sterilizing a single pustule.

Tchicaya said, “If this goes on for a hundred kilometers, I’m going to lose my mind.”

“We could go into Slowdown,” Mariama suggested. “We wouldn’t risk missing anything; the ship could bring us up to speed in an instant.”

“I know. I’d rather not, though. It just feels wrong.”

“Like sleeping on watch?”

“Yeah.”

Three days later, Tchicaya gave in. The honeycomb could prove to be a centimeter thick, or a light-year; the probes could barely see half a micron ahead. They had no decisions to make; until something changed, all they were doing was waiting.

“Just don’t go dropping out on your own,” he warned Mariama.

“To do what?” She gestured at the spartan scape. “This makes Turaev in winter look exciting.”

Tchicaya gave the command, and the honeycomb blurred around them, the palette of false colors assigned to the vendeks?—?already recycled a dozen times to take on new meanings?—?merging into a uniform amber glow. It was like riding a glass bullet through treacle. Above them, the Planck worms retreated, crept forward, slipped back again. The Sarumpaet inched ahead, but in fast motion the race looked even closer than before, their advantage even more tenuous.

As the Slowdown deepened, their progress grew smoother. After a full nanosecond of near-side time, they appeared to be leaving the Planck worms behind. After a microsecond, the worms slipped back out of range of the probes, and there was nothing to be seem but the Sarumpaet itself, and the honeyed esophagus down which it was gliding.

At sixty microseconds, the toolkit signaled an alarm and the ship dragged them back to full speed.

The Sarumpaet had stopped moving, in the middle of a cell of pale blue vendeks. “The probes can’t go any deeper,” the toolkit explained. “We’ve reached a new kind of boundary: whatever’s behind it is qualitatively different from all the vendek mixes we’ve encountered so far.”

Tchicaya glanced down into the darkness, as if his eyes could reveal something that the probes, responsible for the entire scene, had missed.

Mariama frowned. “Different how?”

“I have no idea. The probes don’t even scatter back from the boundary. I’ve tried redesigning them, but nothing works. Anything I send down simply vanishes.” For all its knowledge and speed, the toolkit had never been intended to act as much more than a repository of facts. It couldn’t begin to cope with novelty in the manner of the people who’d contributed to it.

They sat and discussed the possibilities. Tchicaya had learned quite a bit from his faction’s experts, and Mariama even more, but they needed a bigger group; on the Rindler, everyone’s ideas had sparked off someone else’s.

For weeks, they argued and experimented. They took turns sleeping for an hour each; even without any fixed, bodily need to recuperate, their minds were still structured to function best that way. The toolkit diligently analyzed vast lists of possibilities, sorting through the quantum states that might be swallowing all their probes without a trace, hunting for a new design that would avoid that fate and return with solid information.

Nothing worked. The darkness beneath them remained inscrutable.

They had no way of knowing how long it would be until the Planck worms came flooding down after them. On bad days, Tchicaya consoled himself with the thought that when they died, the Planck worms might be buried with them. On worse days, he faced the possibility that brute mutation would find a way through, where all their passion and borrowed ingenuity had failed.

On the thirty-seventh day, Tchicaya woke and looked around the scape. They’d tried all manner of distractions for the sake of inspiration, but no stroll through a forest, no mountain hike, no swim across a sunlit lake had led them to the answer. So they’d stopped ransacking their memories for places to camp, and returned to the unpalatable truth. They were stranded in an ugly, barren cave in the pockmarked rind of an alien universe, waiting to be corroded into noise by a billion species of ravenous sludge.

Mariama smiled encouragingly. “Any revelatory dreams?”

“I’m afraid not.” He’d dreamed he was a half-trained Sapper from the legend, suddenly confronted by a new kind of bomb, falling beside it toward a landscape of shadows that might have been anything from a desert to a vast metropolis.

“My turn, then. Come on, get up.”

“I will. Soon.” She could just as easily conjure up a bed of her own, but taking turns with one imposed a kind of discipline.

Tchicaya closed his eyes again. Sleep had lost all power to assuage his weariness, but it was still an escape while it lasted. He’d understood from the start that their struggle was quixotic, but he’d never imagined such a dispiriting end. They’d spend their last days writing equations on paper planes, and tossing them into an abyss.

As he drifted back toward sleep, he pictured himself gathering up a mountain of crumpled paper and heaving it out of the Sarumpaet into the darkness below. If by chance some scrap went wafting through into another world, he’d never even know that he’d succeeded.

He opened his eyes. “We launch all our paper planes at once. Then we throw a message back, and use it to clear away all the garbage.”

Mariama sighed. “What are you ranting about?”

Tchicaya beamed at her. “We have a list of the kind of states the region below us might be in, and we have strategies for dealing with them all. But we still haven’t found a probe that will cross through and return?—?giving us a definite answer, letting us know which strategy to use. Fine. We put the Sarumpaet into a superposition of states, in which it tries them all simultaneously.”

Mariama was speechless. It took Tchicaya several seconds to interpret this response; he had rarely surprised her, and he had certainly never shocked her before.

She said, “Who cares about quantum divergence, if one world out of every quadrillion is the best of all possible worlds? That sounds like some desperate fatalist nonsense from the last days before the Qusp.”

Tchicaya shook his head, laughing. “I know! But it’s not! Answer me this: a quantum computer does a search for the solution to an equation, testing a few trillion candidates simultaneously. In how many worlds does it fail?”

Mariama scowled. “None, if there’s a solution at all. But that’s different. The divergence is all internal and contained; it doesn’t split the environment into branches halfway through the calculation.” A flicker of uncertainty