Incandescence

„Nothing. Ignore the particular value, it's just a measure of such things as how fast you count, and how we assign numbers to weights. The important thing is, we always get the same value, however fast or slow the stone is moving. There's a rule here, there's a pattern.“

„Not a very simple one,“ Roi protested.

„Be patient.“

Zak modified the experiment, shifting the spring and the stone further along the tube, doubling the stone's distance from the pivot. Six more times they spun the tube. When Zak calculated the same quantity again, it was no longer fixed around two hundred and seventy, but had doubled to five hundred and forty.

He repeated the experiment again, then again, each time with the spring shifted further.

„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.“