“Now we divide by the distance. Weight multiplied by time, by time again, divided by distance.” All the numbers this new calculation produced were more or less the same, regardless of the distance from the pivot. By combining all the variables in this way, a constant value again emerged.
Roi had no idea why. She said, “Spinning the tube around gives the stone weight, I can understand that much. But these numbers.”
Zak replied, “Why does the stone acquire weight?”
She stared at the apparatus, and struggled to articulate the reason why this phenomenon hadn’t greatly surprised her. “A stone without weight moves in a straight line. This stone moved in a circle, so it couldn’t still be a stone without weight.”
“All right, that’s logical. But what made it move in a circle, when I struck it? As opposed to the one that flew straight across the chamber?”
“This one’s tied to a spring. The spring holds it back.”
“Exactly,” Zak said. “The spring forces it to follow a circle, frustrating its preference to move in a straight line. And the effort, the toll this takes on the spring, shows in the spring’s extension. Just as the effort it takes for the spring to keep the stone from falling, when they’re far from the Null Line, shows in the same way.”
Roi couldn’t see how this comparison explained anything. “The stone following a straight line is simple, for sure. So the spring has to fight to complicate the motion, to make it a circle instead. But what’s simple about all the different ways that stones fall, all around the Splinter? Keeping them still, keeping them from falling, seems much simpler to me.”
Zak chirped approval. “A fair comment. All I can do is ask for a little more patience.” He held up the skin. “This is where the numbers start to help us. You say the spring has to fight to complicate the motion of the stone, to bend it away from the straight line it would prefer to follow. How can we make that hypothesis precise, though?” He sketched the spring and the stone, then drew in a circle—the path that the stone actually followed—and a straight line, the path it would have followed had it not been tied down.
“How far would the stone travel in a count of one, if the spring wasn’t there?” Zak marked off a small section of the straight path. “And how far does it actually travel?” He marked a similar section of the circular path. “What is the difference?” He joined the two marks with a third line, an indication of how far the stone had deviated. “The length and direction of this line is a measure of the effort the spring needs to make, to pull the stone away from its natural motion into the path it actually follows. I call this a weight line, because that’s what it measures. I believe weight is nothing more than the difference between preferred and actual motion.”
“So where does the pattern in the numbers come from?” Roi demanded.
Zak said, “Think about the way the weight line changes as we change the two things we can alter in the experiment. If we make the distance from the stone to the pivot greater, everything I’ve drawn simply grows in proportion to that distance, including the weight line itself. But if we increase the time it takes for the stone to make one complete rotation, then the distance the stone would travel, or does travel, in a count of one gets smaller. However, not only do those two paths get shorter, the angle between them shrinks as well. So all in all, the separation of their endpoints—the weight line—shrinks in proportion to the rotational period multiplied by itself.
“The pattern in the numbers bears all of this out. The value I calculated reverses these two influences on the weight, canceling their effect, yielding a constant result.”
Roi found it difficult to follow the details of Zak’s calculations, but if she stepped back and looked at the overall picture, it was a startling idea. Weight is the difference between preferred and actual motion. What her body felt as it pressed against the floor of a tunnel was a kind of struggle against falling, a struggle she could only perform with the aid of the rock beneath her. What she felt now, the absence of that struggle, only seemed dangerous because in a more normal place any such lapse would be punished with serious injury if it lasted more than a heartbeat or two.
“All right,” she said. “The principle you’re asserting is simple enough, and I think I understand what’s happening with the spinning tube. How can this explain the pattern of weights across the whole Splinter?”
Zak said, “For that, we need another experiment.”
He led her across the web, to a tube anchored firmly to several wires. “The axis of this cylinder runs from shomal to junub; the midpoint is precisely on the Null Line.” He took two stones from his carapace, then placed one gently in the mouth of the tube, and the other beside the tube’s midpoint. Both floated where he left them, showing no immediate evidence of motion.
“What do you think will happen?” he asked Roi.
She thought carefully. “The stone that’s a little bit shomal will have a little bit of weight, slowly pulling it toward the Null Line. So given time, it will fall down to the Null Line.”
“So let’s wait and see.”
To help pass the time, Zak asked Roi to recount the details of her journey, and they chatted about the different work teams she’d seen, the changes in vegetation from place to place, the rumors of food shortages. As they talked, the first stone did indeed gradually descend into the tube, while the second one remained where Zak had placed it.
As the moving stone approached the fixed one at the midpoint of the tube, Roi said, “I was right, wasn’t I?”
“Keep watching,” Zak insisted.
The stone didn’t stop at the center. It kept traveling slowly down the tube, away from the Null Line.
“But there is no weight at the Null Line!” Roi said. “If you’re exactly at the Null Line, you should go nowhere. You don’t start falling junub!” She gestured at the other stone, which continued to float where Zak had left it.
“Move away from the Null Line, and throw a stone across it,” Zak suggested. He pointed to the slender wire that marked the invisible line, then handed her a projectile.
Roi complied, bracing herself on a cross-wire. The stone didn’t quite touch the wire, but it came close before sailing smoothly past it.
“It kept going,” she mused. That didn’t surprise her; she hadn’t really expected the Null Line to magically rob the missile of its velocity. So why had she been surprised that the stone that had fallen under its own weight, rather than being tossed, had also kept moving?
She went back to watching the stone in the tube. Eventually, it reached the mouth opposite the one where Zak had placed it. She waited for it to emerge from the tube, but again her guess proved ill-founded. Moving just as slowly as it had at the start, it now reversed its motion and began to fall back into the tube.
“A little junub,” she said, “means a little weight back toward the Null Line again. And somehow, it all balances out. When the stone first crosses the Null Line, the weight begins to act in reverse, but not enough to halt it completely, only to begin to slow it down. Only when it reaches as far junub as it began shomal does it halt completely. And then it starts the very same motion again, in reverse.”
“Right,” said Zak. “But where does this beautiful pattern come from? The weight, the motion, two stones coming together and moving apart?”
“I have no idea,” Roi confessed.
“What comes back to itself, over and over? What repeats itself, endlessly?”
Roi was blank for a moment. “A circle?”
“Yes.”
“I don’t see any circle.”