Incandescence

She said, «I understand that we couldn't tell the difference from a straight line. But even if it's true, how would we ever know? Why should we believe it?»

Zak said, «Because of this.»

He produced a second loop of wire and held it together with the first, in such a way that the two circles shared a common center. They did not coincide completely, though; a small angle separated them, so they only actually touched at two points. «Imagine two stones, moving along two circles like these. They come together, they pass each other, they move apart, then they come together again. Over and over.»

Roi pictured it, following two points around the two loops. It was half true: the separation of the two points followed the same pattern as the separation of the two stones. «But these stones aren't going around in circles,» she said. «Not even big ones that might be mistaken for straight lines.»

«How do you know that?» Zak countered.

«Because they're right in front of me! They're not moving away from me!»

«And how do you know you're not moving, yourself?»

This was becoming surreal. Roi replied patiently, «Because then I'd slam into the wall of the chamber.»

«And how do you know that wall isn't moving? How do you know the whole Splinter isn't moving?»

Roi tensed her limbs ready to reply, then found she had nothing to say.

Zak said, «I believe the Splinter is moving in a very large circle, around a point far away in the Incandescence. When we let two stones, displaced from each other along the shomal-junub axis, move without interference, they come together, then move apart, just as if they were following two such circles inclined at a small angle to each other. And I believe that the time it takes for the stones to complete their cycle tells us how long it takes for the Splinter to make one orbit around that distant point.»

Roi looked back at the stones. The first one, the «moving» one, had almost returned to the midpoint of the tube. If Zak was right, though, then they were both moving in exactly the same way. There really was no difference between them.

She said, «Then what's the Null Line? Why is it special?»

«The Null Line is a piece of the circle that the center of the Splinter traces out as it moves,» Zak replied.

«But why are things weightless only there,» Roi protested, «and not along other circles?»

Zak gestured at the two stones. «Both of these are equally weightless, because both are free to move along their natural paths. The only real difference between them is that the one at the Null Line has the whole Splinter keeping step with it, so we think of that one as 'fixed' and the other as 'falling'.

„When you're shomal of the Null Line, your unhindered path would be just like the path of the 'falling' stone, but the floors of the tunnels and chambers won't permit you to follow that path, and their refusal is what you feel as weight. The further shomal you are, the greater the difference between your preferred and actual motion, the harder the rock has to push up on you to keep you shomal, and so the greater your weight.“

Roi turned these propositions over in her mind, torn between skepticism and amazement. She was not yet convinced that Zak was right, but she was beginning to see how his grand vision of weight and motion might fit together.

„What about garm and sard?“ she said. She struggled to picture Zak's extraordinary cosmology: shomal and junub pointed out of the plane of the circle that the Splinter followed, and the directions along the Null Line, rarb and sharq, pointed along that circular path. „Is the center on the garmside or the sardside?“ she asked.

„The garmside.“

So garm and sard pointed toward, and away from, the center of the circle. „If I'm garm of the Null Line,“ Roi mused, „but not shomal or junub, the Splinter will still carry me in a circle around the same point. And the same is true if I'm sard. So why can't those circles count as natural motion, just like moving along the Null Line?“

„This is where things become trickier,“ Zak admitted. „I claim that following a circle around one special point comprises natural motion, but I believe that's only true if you're traveling at the right speed. That speed depends on how large the circle is.

„The center of the Splinter must be following its natural path — otherwise objects at the Null Line would not be weightless. On the garmside, though, the circle will be slightly smaller, and on the sardside, slightly larger. The natural motion that corresponds to these circles must involve slightly different orbital periods, but the Splinter is a solid object, it has to move as a whole. Because every part of it must complete an orbit in the same time, there's a mismatch between the speed at which things are moving and the speed of a naturally circular orbit. Wherever there's a mismatch like that, the natural path can't be circular any more.