She bid him farewell, and launched herself across the chamber to the point on the web where her own equipment was set up. Every shift, she counted a few cycles of the three periodic motions to see if anything had changed in their relationship. Once Ruz’s clock was declared trustworthy as a standard in its own right she’d start using it to measure the absolute durations of the cycles, but until then she was content to record the ratios between them.
She set everything in motion and then watched patiently, counting the passage of the cycles using a trick she’d picked up from Gul, a recruit who’d worked in a storage depot: sliding a series of stones threaded on wires, rather than trusting everything to memory or wasting precious skin by making a scratch for each event. Though all three motions slowly diminished over time—however thin the air the stones were moving through, however well-greased the pivots on the Rotator’s spinning bar—the periods she was measuring were unaffected, and as long as each cycle could be clearly tracked this gradual decay caused no problem.
As Roi watched the stones, in her mind’s eye she pictured the way their paths might have looked to some impossible cosmic observer, floating in the Incandescence high above the Splinter’s orbit. The problem of how these paths wrapped around the Hub entranced and infuriated her. If the Map of Weights could be believed, then long ago—and, presumably, further from the Hub—anything falling freely would have traveled endlessly along the same closed curve. Whether it was simply going around in a circle, or whether it was also detouring up and down or in and out made no difference, because the periods for all three motions were the same. Now, it was as if something had taken that simple pattern and squeezed and twisted it, forcing the different cycles to break ranks, and yet miraculously preserving Zak’s balance of weights.
She finished her count. In eighty-five cycles of the shomal-junub stones, the plane of the rotating bar turned sixty-eight times, and the looping stone completed forty-five loops. These numbers hadn’t changed since she’d begun measuring them.
Roi recorded the results with the usual mixed feelings. Any change would be the cause of great excitement, the start of a new opportunity to prise apart the mysteries of weight and motion. The numbers had spoken eloquently when she and Zak had first identified the three cycles, but their silence since then had been disappointing.
At the same time, she knew that any change would mean far more than an intellectual impetus for the team. If the weights increased, the strength of the rock beneath her would be tested, and everyone in the Splinter would be at risk. However great her hunger for revelation, she could not deny a powerful sense of relief that the numbers continued to seem immutable, and that she might yet live out a quiet life merely contemplating their mysteries without ever feeling their sting.
The overview meeting was held in a chamber a few dozen spans from the Null Line. This place was large enough for the whole team to fit, clinging to the walls, but not so large that people could split up into individual project groups with the members audible only to each other.
Tan spoke about his group’s continued efforts to explain natural motion geometrically. “First, we need to extend the idea of direction to include speed. We can understand the direction ‘three spans garm for every one span rarb’, so why not also include the idea of speed, and talk about ‘three spans garm for every heartbeat that passes’? But then, if we talk about the garm direction, the rarb, and the shomal, there is a fourth simple direction we must add to the list: time. In fact, every path that’s traveled includes some component in that direction; we can’t travel garmwards a single span without some time also passing.
“Once we can describe both speed and direction in the same framework, it makes sense to understand natural motion and spin as two aspects of the same thing. When an object is weightless, that means its velocity is simply following the geometry it encounters: there is no rock, no claw, pushing against it, so the only thing that can influence it is the way empty space itself is shaped. Similarly, when an object isn’t spinning, the directions it carries with it must be following that same general rule. We know that the directions tied to the rock of the Splinter aren’t following that rule, because of the swerve weight”—the sideways weight of motion connected to the Splinter’s spin—“that we see if we treat those directions as fixed. But I believe the directions tied to the frame of the Rotator obey the same laws as natural motion, and that is why we can declare that it’s the Splinter that is spinning, not the frame, however compelling the opposite scenario must seem to a casual observer.”
In Tan’s view, at every point in space and every moment in time it ought to be possible to summarise the effects of the local geometry with a simple mathematical rule for the way directions and velocities were “naturally carried” along any given path. Zak had proposed that circular orbits around the Hub, with a certain period that depended on their size, comprised one form of natural motion. Tan wanted to find a single rule that could account for that, and also the behavior of the Rotator: a single template into which he could insert a direction or a velocity in order to calculate how much (if at all) it was changing, compared to the dictates of geometry. Feed in the Splinter’s velocity, and the answer would be: this is natural motion, there is no change. Feed in the direction garm and the answer would be: this direction is constantly turning, at a certain rate, around the shomal-junub axis. Feed in any direction tied to the Rotator’s frame, and the answer would be: there is no change.
If Tan’s ideas were dizzyingly abstract, the next speaker proved to be an antidote. Bard had been a miner, searching out and extracting metal, and he had a bluntly practical approach to his new team’s work that side-stepped speculation in favor of tangible results.
“We have no way of knowing exactly why the weights changed in the past,” Bard declared. “The Splinter seems to have shifted closer to the Hub, but it isn’t clear what made that happen. Was it a gradual effect, spread over many generations, or was there a sudden, violent change in the wind that forced us off our earlier path and into our present orbit?
“The wind on the garmside pushes us faster along our orbit, which tends to move us away from the Hub, while the wind on the sardside acts to slow us down and bring us closer to the Hub. If everything about the Splinter was perfectly symmetrical, the two influences would balance exactly. I doubt that the symmetry is perfect, but even if it’s not, we’ve been unable to measure the consequences in the short time that this team has existed.”
“However,” he continued, “whether these dangerous shifts come slowly or quickly, it seems likely to me that the Splinter would be safer if we could move it further from the Hub. If we could reduce the weights, taking them back to the values they had before the last division, there would be a far greater margin for surviving any subsequent change.”
Zak interjected, “I agree with everything you’ve said, but how do you propose to move us?”
“We cut a tunnel,” Bard replied, “through the sardside. Maybe two or three tunnels. If the Splinter now feels roughly the same force from the wind on the garmside as it does on the sardside, we can shift the balance by letting some of the sardside wind pass right through, delivering no force.”