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.