Incandescence

8

Roi immersed herself in study, determined to reach the point where she could understand every detail of Zak’s ideas. Excited as she was by the simplicity and grandeur of his vision, until she could test the fine points for herself she knew that her instinctive sense that he was on the right track needed to be treated with caution. Anyone could thump their carapace and invent a story so big that it seemed to swallow the world. The one thing that made Zak’s account of weight and motion different was that anyone willing to make the effort could investigate the logic of his claims firsthand. On that, the whole thing would stand or fall.

Zak helped her to revise and extend her mathematical skills, starting with multiplication, then continuing all the way to something he called “template calculations”: manipulating abstract symbols as well as actual numbers, allowing her to perform a generic version of a sequence of computations without specifying all the quantities involved. After a while, it struck Roi that this was far more than a method for saving labor when she wished to repeat the same calculation many times on different sets of numbers. Just contemplating the template for the answer to a problem—without substituting any particular values for the symbols—could illuminate the relationship between all the quantities involved in a way that staring at endless lists of figures never would.

Zak was a patient teacher. Before she’d met him, Roi had thought of the unrecruited as pitiful creatures, lonely failures on the verge of death. Zak’s time at the Null Line had certainly damaged his health, but in his own way he had worked far harder than anyone she’d ever known. Roi had rarely been so confident that the respect she felt for someone was deserved, and not just a product of the haze of camaraderie.

Between their lessons, Roi managed to extract some of his story. Like every hatchling, Zak had found tutors to provide him with a rudimentary education, but when the time came to join a work team, he’d drifted from one recruitment to the next. He’d felt the buzz of cooperation every time, but it had never been strong enough to hold him for long.

One shift, while working as a courier, he’d stumbled upon a library out in the sardside. The cargo he was carrying had had nothing to do with the place, but an accidental detour had been enough to capture his interest, and on the return leg of his journey he’d gone back for a closer look.

The library was full of maps, work notes, diagrams of strange machines, fragments of calculations, and scrawls in languages nobody understood. The librarians painstakingly copied the sheets of skin to preserve their contents from loss or damage, and constructed catalogs and lists of cross-references, trying to piece together a larger picture from these bewilderingly disparate parts. Every now and then, they explained to Zak, someone would bring in a new find, a page or even a bundle of pages that had never been seen before.

Wandering through the collection, overwhelmed by the aroma of long-dead susk, Zak had suffered a giddying shift in perspective. People had been thinking and writing for an unimaginable time, and here, right in front of him, lay countless samples of their labors. A whirlwind tour of history, a million tantalizing snatches of overheard conversations, had been etched into these skins. Zak felt the presence of the thousands of generations that had come before him, and understood that it might be possible to join them in a vast endeavor, a project spanning the ages that he could as yet only glimpse.

He’d begged the librarians to recruit him on the spot, and once they’d recovered from their surprise they had agreed, but they were not the ones who had truly captured his loyalty.

“I was recruited by the dead,” Zak said. “Not in any rush to join them in their silence, but from the urgent need to understand what they might have thought and done that could survive them, that could speak across the ages, that could be continued even now.”

There was no coherent history of the Splinter, no account of one time following another, but everywhere Zak looked he found evidence of change. The language he understood, the language of his contemporaries, accumulated curious additions and alterations as he moved from page to page into the past. Other pages were written in scripts that, so far as his fellow librarians knew, no living person could decipher.

There were stories of the birth of the Splinter, of the old world being torn apart, but like the stories that spread through the work teams they did not agree on the details, and they all had the sound of having been retold over and over, accumulating embellishments and omissions, before being put into writing. Some even spoke of the calamity recurring many times, stretching back into the unimaginably distant past. How vast, how grand, the mythical First World must have been, if after thirty-six divisions even one of the crumbs that remained was inhabitable!

Hard as it was to believe these stories, let alone know which ones to trust, for anyone who’d so much as crossed the Calm the undeniable fact remained that the weight in the garmside tugged the opposite way to that in the sardside, and the further one went in both directions the stronger this discord became. If the Splinter had suddenly been doubled in size, it was not at all preposterous to imagine that the weight might have been enough to tear rock from rock.

The trouble was, this raised the question of how the old world could have held itself together for more than an instant. The most reasonable answer, it seemed to Zak, was that it must have been born under a different regime of weights, which had only later become so powerful.

During shift after shift in the library, he came across fragments of speculation on these matters, but there was nothing whole, and nothing convincing. The thinkers of the past had left many hints and guesses, but if they had ever fully understood the truth about these mysteries, it had not survived. In the end, Zak decided that he couldn’t spend his life merely sifting through these skins, searching for one more inconclusive sign that his reasoning was not completely misguided. If weight had dictated the history of the Splinter, and however many worlds that had come before it, then weight was what he needed to understand.

Armed with the Map of Weights, some plans for ancient instruments, and copies of the few surviving notes on his predecessors’ methods and philosophies, he’d walked out of the library and headed for the Null Line, ready to begin uncovering the secrets of weight and motion, and to search for something simple that had torn the world apart.

Roi still didn’t understand the wind.

On one level, Zak’s idea of natural motion seemed to explain it perfectly. If things moved in circles around the distant point in the Incandescence that she and Zak had come to call the Hub, and if the smaller the circle the faster they moved, then everything about the wind made sense. On the garmside—closer to the Hub—the wind was moving faster than the Splinter, and so it overtook the rock, blowing in from the sharq ever faster the further garm you went. On the sardside—further from the Hub—the wind was orbiting more slowly so the Splinter overtook it, ploughing through it, making it seem to blow in from the rarb when in truth it was merely failing to flee with sufficient haste in the opposite direction. And between them, in the Calm, wind and rock moved together at exactly the same pace, leaving not so much as a breeze to be felt.

The trouble was, while Zak’s theory gave a simple, persuasive account of the phenomenon, Roi couldn’t reconcile it with the mundane reality of weights. If weight was determined by natural motion, why didn’t the wind follow the weights? If she stood anywhere in the garmside, and a crack opened up in the rock beneath her, surely she would fall away from the Splinter, garmwards. Notwithstanding the wind’s speed in the cross-direction, which might make such motion harder to spot, and the way the rock and the tunnels worked to divert and complicate its flow, Roi’s time among the crops left her thoroughly convinced that the wind wasn’t falling at all.

Shift after shift she struggled with this problem, hoping she might solve it by her own efforts. Finally, she had to admit that the resolution was beyond her. The next time she met Zak, she asked him to defer their scheduled lesson in template mathematics, and she begged him to make sense of the wind before she lost her mind.

Zak was both amused and chastened. “This is my fault, Roi; I should have explained this much sooner. The weights on the map are fine—give or take the question of three versus two and a quarter—but they’re not the whole story.”

“There’s something missing?”

“Yes. There is a kind of weight that the map doesn’t show at all.”

Roi was baffled. “How can that be? Weight is weight. I’ve felt it, I’ve measured it. It’s not something you can hide.”

“No, but the map only shows weights for objects that are fixed firmly to one place in the Splinter.”

“I’ve moved from place to place in the Splinter,” Roi protested, “and the map described correctly how my weight changed.”

“That’s not what I’m talking about,” Zak said patiently. “You moved at a walking pace to a new location, you didn’t race the wind. The wind feels something extra, everywhere, compared to the fixed weights on the map, simply because it’s in motion, not because those fixed weights change from place to place.”

If this was true it had the potential to resolve the paradox, but the idea still struck Roi as very strange. “Why should it feel something extra just because it’s moving?”

“Because the Splinter is spinning,” Zak said. “Now, I know the map already takes account of that, in part. An object fixed to the Splinter is really turning in a circle—a small one, much smaller than its orbit—which frustrates its natural motion and contributes to its weight. There’s one further twist, though. Imagine a stone that’s moving in a straight line, as seen from outside the Splinter. Because the Splinter is constantly turning, as the stone moves, we’re moving too. If we try to trace the path of the stone against our surroundings—against the rocks and tunnels we think of as fixed, but which in truth are turning—the line we see it following won’t be a straight line, because of the way our motion adds to the stone’s. Its path will seem bent, as if there were a weight constantly pushing it sideways. And the faster the stone moves, the greater the apparent weight bending its path.”

“The faster it moves in reality, or the faster we think it’s moving?”

“The faster we think it’s moving.”

Roi struggled to visualize it. If a stone moved in a straight line away from the axis of spin, then the rotation of the Splinter would make it seem to follow a spiral path, forever turning. And if the stone was sitting completely still? Then the motion of the Splinter meant that it would appear to be moving in a circle, again with its path constantly veering sideways.

“I think I understand,” she said. “But the wind doesn’t wrap itself into a spiral. On the garmside, it blows straight from sharq to rarb.”

Zak said nothing.

Roi struck her carapace. “Of course, that’s the whole point! I’ve been wondering why the weights from the map don’t push the wind garmwards, in some kind of curve plunging back out into the Incandescence. But the extra weight from its motion must push it in the other direction, balancing the ordinary weight exactly.”

“That’s right,” Zak said. “The further garm you go, the stronger the garmwards weight, but because the wind is also blowing more strongly, the weight from its motion keeps perfect step, and the two of them always cancel.”

Roi was pleased that she’d finally grasped what she’d been missing, but there was still something frustrating about the whole matter. The Splinter was turning, Zak claimed, and this claim turned out to be absolutely vital in order to make sense of the rest of his vision. Without the strange distortions in weight and motion brought about by the spin, it would have been impossible to reconcile a simple concept such as circular orbits for the wind with the ordinary realities of the Splinter.

However, everything about the Splinter’s rotation seemed to involve a kind of conspiracy of self-effacement. It contributed to the garm-sard weights on the map, but who was to say exactly how much it added? It balanced a hypothetical rarb-sharq weight exactly, but that perfect balance left nothing behind to be felt or measured. And now it conspired with the garm-sard weights again. in order not to bend the wind.

Roi understood that at least some of this was a logical necessity, not a matter of coincidence. The two points of view, one tied to the rock of the Splinter, the other taking a grand cosmic perspective, were describing exactly the same reality, so of course they had to agree with each other, once you knew how to translate between them. Nonetheless, she couldn’t accept that the fact of the Splinter’s rotation could be both crucial and completely invisible, impalpable, and immeasurable.

She said, “When I throw a stone in the Null Chamber, why can’t I see its path being bent?”

“It’s a subtle effect,” Zak said. “I’ve made some crude measurements of it, but it’s hard to detect just by looking.”

“You’ve measured the Splinter’s rotation!” Roi was astonished. “Why didn’t you tell me that before?”

“I wouldn’t say I’d measured the rotation. My measurements show that the rotation exists, but I haven’t come close to quantifying the rate of spin.”

“But you’ve seen the effect itself?”

“Absolutely,” Zak said.

“Can you show me?”

They went to the Null Chamber, and Zak fished out a device he called a spring-shot from one of the storage clefts. It was a tube fitted with a spring-loaded plunger that could be cocked to varying degrees of compression and then released, propelling a stone from the tube. The projectile emerged in a reasonably predictable direction, with a choice of velocities.

He attached the spring-shot to the wire that marked the Null Line. Then he prepared a “target board”, a flat sheet of cuticle that he coated first with resin, then with a kind of powder. If you pushed a stone against the surface of the target, however gently, the powder sank into the resin, changing the way the two of them scattered the light, leaving a visible record of the point of contact.

He fixed the target board to the Null Line with a bracket, six spans or so rarb of the spring-shot.

“We’re sending this stone straight down the Null Line, so according to the map it should feel no weight at all,” Zak said. “First I’ll make it move as fast as possible, and we’ll see what happens.”

He squeezed the plunger as tightly as it would go, then released it. The stone flew out rapidly, more or less following the wire that marked the Null Line, and struck the target. When they went to examine the board, it was, unsurprisingly, marked at the edge, just beside the wire.

“Now we reduce the speed.”

Roi said, “Now I’m confused. I thought this weight was supposed to increase with speed.”

“It does. But greater speed also gives it less time to act before the stone hits the target. By making the stone move more slowly, the weight that bends its path becomes weaker, but the extra time the stone spends in flight more than compensates for that.”

Zak was right. With the spring half-compressed, the stone emerged less rapidly, but the mark it made was shifted to the sard side of the Null Line by about twice the width of the stone itself. In a third experiment, with the compression reduced further, the sardwards shift was even more pronounced.

Roi could picture what was happening very clearly, now. While the stone was in flight, the Splinter was turning, carrying the wire and the target board a small way garmwards, leaving the un-rotated path of the stone to strike the target askew.

She said, “Why can’t we use this to measure the speed of the rotation?”

“It’s a crude experiment,” Zak insisted. “If I release the stone several times in succession with the spring compressed by exactly the same amount, the point where it strikes the target still varies. And how can I know how fast the stone is moving? It’s traveling too quickly for me to time its motion accurately.”

“Let it move more slowly, then. You’ll get a larger effect as well.”

“There’s a catch,” Zak said ruefully. “The more the stone gets pushed away from the Null Line, the more it comes under the sway of the ordinary garm-sard weight as well. What we’re measuring will no longer be one simple thing. When you combine that with the uncertainties in the aim and the velocity, I don’t think there’s much hope of getting a meaningful number out of the results.”

Roi could see how daunting the complications were, but she wasn’t ready to give up. “Can I try it? Slowly? Just to see what happens?”

“Of course.”

She squeezed the plunger down to the first notch, the smallest compression possible, then released it. The stone emerged at an absurdly leisurely pace, and even as she watched, it veered visibly sardwards. By the time it had traveled less than half a span toward the target its path had turned sideways, and not long after that it had swung around so far that it was level with the spring-shot again, albeit some distance sard of it. While continuing to move sardwards, its velocity along the Null Line had been completely reversed.

Roi said, “This is not what I’d expected.”

“It’s just following the rules,” Zak said.

Roi moved aside to let the stone pass her. Eventually, its sardwards drift seemed to level out, and it was simply moving backward, parallel to the Null Line, much faster than it had been moving when it had left the tube. Its direction continued to change, though; the relentless sideways tug of the weight of motion was stronger for this stone than it was for the wind, and it began to veer back toward the Null Line.

As the stone approached the Null Line, the sharqwards part of its motion slowed, leveled out, and reversed, so it was now heading back toward the spring-shot. This didn’t last long, though. When it reached the Null Line itself, almost grazing it, the stone executed a small loop that took it first sardwards, and then—in a replay of its original manoeuvre upon being launched—swung it around sharqwards once more. It was far behind the spring-shot, let alone the target, and showed no sign that it would ever come close to either again. Rather, it seemed to be cycling back and forth between the Null Line and a certain distance sardwards, while it drifted—mostly, though not constantly—ever more sharqwards.

Roi approached Zak. “What’s the simple explanation? I suppose I can accept that the sardwards weight combined with the weight of motion did all of that, but there must be an easier way to understand it.”

Zak said, “Think about the orbit of that stone. The stone was always on the sardside of the Null Line, so its whole orbit was larger than the orbit of the center of the Splinter. Larger orbits have longer periods, so the stone took longer than we did to go around the Hub. That’s why it drifted backward. It wasn’t as fast as us.”

“But it started out faster,” Roi protested.

“That’s true. At the same distance from the Hub, where its orbit touched ours, it was faster than us. That’s why we weren’t constantly outpacing it, and it didn’t move backward all the time. But over a complete orbit, we were faster.”

This made sense, but Roi still wasn’t satisfied. “Why didn’t the stones you launched go backward? Was that because they were moving faster than mine?”

“Definitely not!” Zak was emphatic. “The only difference was, they hit the target before they could swing around and go into reverse. If we had taken the target away—and the walls of the chamber too, if necessary—then those stones would have followed exactly the same kind of path as your one. The fact that they were moving faster made their paths larger, and we only saw a small part of each path, but other than that everything about them was the same.”

“I see.” The whole point of Zak’s version had been to concentrate on the very start of the motion, before the garm-sard weight could complicate things. “Can I try something else?”

“Anything,” Zak said.

She detached the spring-shot, then reattached it pointing in the opposite direction: sharq along the Null Line. Now the stone would be moving backward from the start, making it slower than the Splinter at the point where their orbits touched.

Its path followed exactly the same pattern as before, except that rarb became sharq, and sard became garm. After leaving the spring-shot the stone veered garmwards; halted its leisurely sharqwards progress and went rapidly into reverse; reached a maximum distance garmwards from the Null Line and started back toward it; then, close to the Null Line, performed a small loop that took it back into the same cycle, albeit many spans rarb of where it had begun.

Roi said, “Its orbit was smaller than ours, so it was racing ahead of us?”

“Yes.”

“And the way it moved away from the Null Line and then back again, that’s because the orbit wasn’t a perfect circle?”

“Right,” Zak said. “We remain a constant distance from the Hub, but there are orbits like this that draw closer to the Hub and then move away again.”

Roi contemplated this. “What if we could put a stone into an orbit that wasn’t a perfect circle, but was still the same size as ours, overall? With the same period?”

Zak didn’t reply immediately, but his posture made it clear that he was intrigued by her suggestion. “That could be very useful,” he said eventually. “We ought to see it execute a fixed, cyclic motion instead of running away across the chamber.”

Roi detached the spring-shot from the Null Line again, and attached it pointing sardwards: perpendicular to the Null Line, “halfway between” the two directions she’d already tried. She was acting purely on instinct, and even as she tightened the clips she wondered if launching the stone away from the Hub meant she’d be putting it into an orbit that would keep it perpetually on one side of the Null Line. But then, shooting the stone along the Null Line itself, which seemed more symmetrical in that respect, certainly didn’t work, so what she was trying made as much sense as anything.

She squeezed the plunger one notch, then released it.

The stone veered sideways as it emerged, but not as sharply as it had in the previous two experiments. As it moved, it picked up pace, but nowhere near as rapidly as before. Roi was surprised; she’d half expected the sardwards weight to take over and drag the stone into a frenzied spiral as the weight of motion twisted its ever-quickening flight. Instead, the stone continued to turn in a smooth, shallow arc, still progressing sardwards while swinging around ever more to the sharq.

Eventually, its sardwards motion leveled off, about two spans from the Null Line. It was moving perhaps three times faster now than it had when she’d launched it. It continued to swing around gently, coming back toward the Null Line, while its sharqwards speed lessened.

As it approached the Null Line, Roi tensed. It was no longer traveling sharqwards, but it would probably perform the same annoying little loop as the others, and then it would be lost to them, drifting away across the chamber.

It didn’t. It crossed straight over the Null Line, at about the same speed as it had left the spring-shot, and veered to the rarb. The symmetry was unmistakable: it was performing exactly the same kind of motion as it had when she’d fired it, only with garm in place of sard and rarb in place of sharq. If that symmetry held true, there was only one place where it could cross the Null Line again.

When the stone finally approached the spring-shot, Roi thought it might collide with it, but her aim hadn’t been that perfect. It was close, though. The stone passed less than half its width from the tube before continuing on around the same closed loop as before.

“I can’t believe I missed this,” Zak said. “A new periodic motion! Congratulations!”

Roi said, “What are we seeing, exactly? Is this showing us the Splinter rotating?”

“What we’re seeing is a stone in orbit, moving back and forth between its nearest and furthest points from the Hub,” Zak replied. “If we try to explain that from a Splinter’s eye-view, the motion will depend on the strength of the garm-sard weight, as well as the speed of the Splinter’s rotation. Once I would have said that those two things should combine in a very simple way, but now I’m not so sure. The two and a quarter has taught me to be more cautious.”

Roi launched another stone directly sardwards, this one faster than the first. The loop it followed was larger, but the shape was the same—about three times as long as it was wide—and the faster stone completed each circuit in the same time as its slower companion. These stones were spending half their time sard of the Null Line, moving more slowly than the Splinter, and the other half garm of the Null Line, moving faster, so over time they were keeping pace both with the Splinter and with each other. Surely that meant that each cycle they completed marked the time for all three to complete an orbit around the Hub? And surely the Splinter’s rotation around its axis shared the same period, too, as a matter of simple geometry?

Zak said, “I know what we should do.” He found an empty tube, attached it to the Null Line aligned shomal-junub, then placed a stone in its mouth and let it begin its slow fall. Now they could compare the two kinds of motion directly, without having to worry about the accuracy of their counts to time the periods.

It soon became obvious that the periods were not the same: the looping stones were taking far longer to complete each cycle than the stone falling shomal and then junub. For a while, Roi wondered if the slower cycle might be exactly twice as long as the faster one—and if some simple aspect of the geometry that she’d neglected could make sense of this—but that hope proved misplaced. The shomal-junub stone completed seventeen cycles while the looping stones completed nine. There was nothing simple about that.

Zak seemed forlorn at first, but then he proclaimed, “There’s something encouraging about the way these numbers demolish half of my assumptions, yet the whole notion of orbits seems to survive. Watching these stones, can you honestly tell me that you don’t believe they’re going around the Hub?”

Roi said, “The idea still makes sense, but we’re missing something.”

Zak regarded the shomal-junub stone. “If orbits still make sense at all, then this stone tells us how much time passes for something orbiting at a small angle to the Splinter’s orbit to come back to the same height above us each time. The stone doesn’t go wandering off along the Null Line, so the periods of the two orbits must be the same. But what if the place where the orbits are farthest apart isn’t fixed? What if that point moves around? Then this need not be telling us how long an orbit actually takes.”

He moved to the looping stones. “And when you deform an orbit so it’s no longer circular, what if the point of closest approach to the Hub isn’t fixed either? That point, too, might wander around.”

Roi struggled to picture what he was describing. “So these other orbits wouldn’t close up? The Splinter would follow a perfect circle, but these stones would be weaving up and down, or back and forth around that circle, never quite repeating their paths?”

“Yes.”

Roi was dismayed. “If the things we thought were landmarks can’t be trusted to stay still, how can we ever decide how long it takes for the Splinter to complete an orbit?”

Zak said, “Good question.”

Neither of them had the answer to it, so they set about calculating what Roi’s looping stones actually did tell them. They worked side by side until the end of the shift, slept, then worked through two more shifts.

Finally, they had templates describing the relationship between three things: the strength of the garm-sard weight, the period of the Splinter’s rotation, and the period of the looping stones. These calculations made no assumptions at all about the existence of “orbits around the Hub”; they just followed the effects of the weights directly—though they did rely on a correct understanding of how spin contributed to weight.

When Zak inserted the numbers, the template told them that the Splinter was rotating with a period about one and a quarter times the shomal-junub cycle.

If you believed in orbits, this meant that for a stone in a tilted orbit to return to its highest elevation was the fastest thing. For the Splinter to rotate around its axis took a little longer. And for a stone in an eccentric orbit to return to its greatest distance from the Hub took longer still.

Three phenomena, three different times.

“Where has all the simplicity gone?” Zak lamented.

Curiously, if he fed his original assumptions into the templates—if the shomal-junub weight was equal to the hidden rarb-sharq weight that was balanced by the spin, and if the garm-sard weight was, in total, three times as much—then all three periods would have been identical. The number three really would have made things very simple.

Roi took a break from the Null Chamber, and traveled a short way into the garmside to give herself some weight again, lest she lose too much strength. Even as she headed out of the Calm into the sights and sounds of ordinary life, she couldn’t stop thinking about motion and orbits. At the end of each shift, when her mind had once filled with the images of weeds, now she saw stones, bouncing and looping and swerving in front of her. When she woke, her first thought was always of finding a new way to check Zak’s conclusions. Their calculations deriving the Splinter’s spin from the looping stones could be flawed. Or the weight measurements they had fed into the templates could be wrong.

Zak’s simple experiment, when he’d launched a stone along the Null Line, had been compelling: it had made it obvious that the Splinter was turning while the stone was in flight. There had to be a way to measure the Splinter’s rotation directly using that effect, without allowing the complications of the garm-sard weight to intrude. If you could keep the stone moving somehow—without ever letting it go too far from the Null Line—its path would act as a reference against which the turning of the Splinter could be judged.

How could you rein it in, though, without stopping it completely?

When Roi found the answer, she turned around and headed straight back to the Null Chamber. Zak wasn’t there when she arrived, but she felt no hesitation about helping herself to his stores of material. They were a work team, now. These things were their common tools, not a lone eccentric’s hoard.

Zak arrived just as she was putting the finishing touches to her apparatus, trial and error having led to some changes in the original design. Two equally heavy stones were glued firmly to the ends of a small bar. The bar was free to pivot around its center, where it was threaded by a stiff metal wire, which was bent around into a flat rectangular supporting frame large enough for the bar to turn continuously without obstruction. Another pivot, opposite the bar, attached the frame to the wire of the Null Line; this pivot left the frame free to rotate around the shomal-junub axis.

After they’d exchanged greetings, Zak watched in silence as Roi greased the pivots, marked the initial alignment of the frame on a card fixed to the wire above it, then gave the bar a flick to set it spinning.

An earlier version—with the bar spinning around one of its ends, and a single stone at the other—had been unbalanced, shuddering mercilessly, causing the frame to slip back and forth. This design seemed to have fixed that problem. All Roi could do now was wait.

Slowly but unmistakably, the plane of the spinning bar turned. Or, stayed fixed while everything in the chamber, everything in the Splinter, wheeled around it.

Zak said simply, “Who can doubt it now?”

There was no need to measure the speed of the stones. There were no elaborate calculations to perform. One rotation of the frame corresponded to one rotation of the Splinter, if they understood anything at all.

They set up a shomal-junub stone a short distance away, to compare the motions. After a while, no doubt remained that the period of this new phenomenon agreed with their earlier calculations, based on the more complex motion of the looping stones. The plane of the spinning bar took one and a quarter times longer to complete one turn than it took for the shomal-junub stone to complete one cycle.

Roi didn’t know what to feel. She was relieved to see two lines of evidence converging on the same answer for a change, but she’d actually been hoping that this experiment might yield a different result, one that removed some of the complexity that had begun to infest the theory of orbits.

“Where did all the simplicity go?” she joked, echoing Zak’s refrain.

“I think I know where some of it went,” he replied. “I didn’t dare mention this before, because I wasn’t confident in our results. But now that you’ve confirmed the period of the spin, it doesn’t seem so foolish any more.”

Roi said, “Go on.”

Zak had been forced to give up his beloved three, and the simple assumption that the shomal-junub weight would be equal to the hidden rarb-sharq weight, which the spin canceled out exactly. Since the shomal-junub cycle was faster than the spin, the shomal-junub weight was stronger than both the spin weight and its equal, the rarb-sharq weight.

Call the shomal-junub weight one. The rarb-sharq and spin weights could be quantified now: they were sixteen parts in twenty-five (the square of the ratio of the shomal-junub period to the spin period). The total garm-sard weight was two and a quarter, according to the weight measurements taken throughout the Splinter, and supported by the fact that the looping stone calculations, based in part on that figure, gave the same rate of spin as Roi’s new device.

If you stripped away the complications of spin, the hidden rarb-sharq weight was revealed—sixteen parts in twenty-five—and the garm-sard weight was reduced, down to one and sixty-one parts in a hundred, which was just three parts in a hundred short of one and sixteen parts in twenty-five.

The sum of the two weights that pushed things toward the center of the Splinter was, within the limits of the accuracy of their measurements, equal to the weight that pulled things away from it. The forces that squeezed and the forces that stretched were in balance after all. The number three was nowhere in sight, but of all its beautiful corollaries, the one symmetry that Zak had most admired had somehow outlived it.

Zak said, “We don’t know when the Map of Weights was drawn, or what its purpose was. It might be nothing but a guess, or a crude approximation, or a record of someone’s wishful thinking. But suppose it’s none of those things. Suppose it’s an accurate record of the truth, of the weights as they once were.

“This map can’t tell us if the weights have grown stronger since it was drawn, because we don’t know what scale was used to depict them. It does tell us two things, though: first, that the ratio between the weights has changed, and second, that a hidden relationship between them has stayed the same.”

As Roi contemplated this she realized how unsettling it was. It was easy to invent stories about the world being torn apart: one time, many times, take your pick, the event happening for no particular reason and making no particular sense. Everything she’d seen or heard on the subject was either six generations removed from a reliable witness, or had many other explanations. But above and beyond the flimsiness of the evidence was the apparently arbitrary nature of the claims. When a disaster could be invoked without cause or constraint—at some fabulist’s whim, as it were—it was easy to doubt its authenticity.

Who would have fabricated a map, though, which secretly implied the very same symmetry as all the painstaking measurements that she and Zak had just made? This hidden thread of order didn’t yet tell them why or when the weights might have changed, but the hint that they couldn’t just shift any way they liked suddenly made the possibility of change seem far more real to Roi than it had ever been before.

“What now?” she said.

“We have a candidate for a guiding principle,” Zak said, “but it still needs to be checked, to be verified somehow. And we still don’t know how it manifests itself in the rules of natural motion; we know the weights close to the Splinter, but we don’t know the precise rules governing orbits in general.

“We also need to discover, or deduce, the rules that govern the history of the Splinter, past and future. We need to know if the weights really could have changed, and when and by how much they will change again.”

Roi could have recited the same demands herself, but hearing them spelt out this way made her feel as if she’d been loaded down with an impossible burden.

“It’s too much,” she said. “Too much for your lifetime, and mine.”

“Of course it is,” Zak replied. “One solution to that would be to write down what we’ve learned, put copies in all the libraries, and hope that in the future someone curious, intelligent, and fiercely independent will come along, understand what we’ve written, and take up the task where we left off.”

Roi said, “That might not happen for a hundred generations.”

“Then we’re left with no other choice,” Zak said. “We need to recruit more people to help us, here and now. Then we can both see the job completed, and we can both die happy.”