Pathspace: The Space of Paths

by Matthew Kennedy

  But he was already unbuttoning his coat. As always, he had his white robe on underneath, with its gold Star if David on the breast with the number '36'. Quickly, his fingers drew the hood out and over his head. “If a task presents itself, then I must step up, nu?” And just like that, he yanked open the door of the coach.

  Winter air blasted into the interior, blowing the pages of Nathan's book. “What is is Father doesn't have to do?” he said, laying the book down for a minute.

  His mother didn't answer. Nathan frowned. Without planning it, he found himself wrenching the door open again.

  Again the icy wind invaded the coach.

  “Nathan! Don't go far!”

  He didn't. He stepped out and stood by the coach, watching as his father strode forward into a crowd of people who parted before him like the Red Sea did for Moses. He heard a word whispered: Tzaddik.

  The people fell silent, so Isaac addressed them. “What is the problem here, citizens?”

  A man stepped forward, holding his hat in his hands. He cleared his throat. “Sorry to hold you up, sir. It's the spring. It's on my neighbor's land, and he won't let my livestock cross over to use it. The boundary between our farms is this road, so I'm afraid sometimes it holds up traffic.”

  “Don't listen to him!” Another man lurched forward. Why should I have to chase his animals off and mend my fences every time he wants to use our water? Look for yourself,” he said, gesturing to the snow all around them. There's plenty of water everywhere. He doesn't need to come on my land for water.”

  Isaac shook his head. “It is not for me to say who is right and who is wrong. But blocking the road, that is wrong.”

  He turned to the man holding his hat. “How far is it to your house? My wife and son are waiting for me.”

  “Not far, Righteous One. Just over the hill to the left. See, there is the road up ahead.”

  Isaac looked ahead and nodded. “Very well. This is what will happen. You and your family and your animals will lead the way back to your house, and we will follow. When we get back to your house I will see what can be done.”

  He then looked to the second man who had spoken. “Your land will not be trespassed. Please take your family home and clear the road. I'm probably not the only one who wants to get home before it snows again.”

  Both men bowed and backed away, and Isaac returned to the coach. “Why didn't you stay in the coach?” he asked Nathan.

  Nathan hurried back inside the vehicle. “I wanted to see what was going on. What does it mean, Tzaddik? I heard someone say that.”

  “We'll talk about it later,” said Isaac, climbing in beside him. He rapped on the roof, and the driver picked up his reins.

  The coach lurched ahead. Isaac looked at his wife. “What could I do? It's my job.”

  Rebekah laid a hand on his arm, melting a few snowflakes that hand landed on his sleeve. “You don't have to solve every squabble, you know.”

  “No,” he agreed. “Only the ones I know about.”

  The coach jolted as the driver pulled off the road onto the farm path. Rebekah shook her head, but Nathan could see she was smiling.

  Soon enough, the driver pulled up in the driveway of an old farmhouse. The man with the hat was standing there among a flock of sheep, gesturing to his right. “You see? The pond is frozen over. My neighbor has a pond with a spring, and it keeps the ice melted over where the water comes up. But I don't have a spring.”

  Isaac got out of the coach again. “I see,” he said. He turned to the farmer with the hat. “Do you have faith, sir?”

  The man swallowed. “As much as any man.”

  “That will have to do. If God allows you water, will you agree never to lead your livestock to trespass on your neighbor's farm again?”

  The farmer nodded, never taking his eyes off Isaac.

  “Very well,” said Isaac. “Lead your animals down to the edge of the pond.”

  Looking baffled but hopeful, the man picked up a shepherd's crook and began to lead the sheep down toward where the frozen pond lay nestled in the cupped hands of the earth.

  Nathan looked at his father in that white robe. “But it's still frozen.”

  “Watch.”

  The man and his sheep were almost to the edge of the pond. Suddenly, as if on cue, a semicircle of ice at the edge simply melted away.

  He heard the farmer's joyful cry as the sheep began to cluster around the melted part, drinking the water.

  Nathan looked at his father again. “What happened?”

  Isaac shrugged and smiled. “A miracle,” he said, and climbed back into the coach. “Let's continue on,” he told the driver. “If we linger we'll be here half the night.”

  Nathan climbed back in too. He looked at his father again, as if seeing him for the first time. It occurred to him suddenly that he had never asked his father's occupation.

  End of preview

  Appendix I: Pathspace

  It is easy to imagine that the concept of pathspace as presented in this novel is simply an invention for narrative convenience.

  However, I feel it is my duty to point out that some aspects of it are definitely not fictitious.

  Ever since Einstein released his General Theory of Relativity, we have been able to visualize gravity not as a mysterious force that somehow “pulls” us toward massive objects, but, instead, as simply a pattern in space that dictates the sort of paths objects will take when moving through that region of space.

  Unfortunately, the geometry that Einstein used to map gravity onto space has more than three dimensions, which makes it rather difficult to visualize. To make it easier, people who lecture on this subject usually subtract one dimension and say something like this. “Imagine a bowling ball lying in the middle of a waterbed. The weight of the ball distorts the flat surface of the waterbed. If you roll a tennis ball on the waterbed it will travel in a curved line (usually ending on the bowling ball unless you roll the tennis ball really fast) because of the presence of the bowling ball. This is similar to the way that the Sun's 'weight' distorts space around it and makes the Earth travel in a path that keeps curving around the Sun.”

  There are couple of problems with this explanation.

  In the case of the bowling ball, it is weight (the force of gravity on the ball) that makes it press down on the waterbed. Weight is what you experience when you try to keep something from going where it wants to go in a gravity field. If you were falling off a building with the bowling ball next to you it would not appear to weigh anything.

  But the Sun has no weight! Nothing is keeping it from orbiting the center of the galaxy. It is like a skydiver in free fall.

  The Sun's effect on space is due to its mass, not its “weight.”

  Another problem with the bowling ball + waterbed analogy is that it fails in the 3rd dimension. If you toss the tennis ball above the bed, it feels a need to curve down toward the floor, but it is not the surface of the waterbed that is causing this.

  A better way to imagine the Sun's gravity field might be to imagine a hole in space into which space is falling from all directions in an inward radial waterfall If you throw a tennis ball past such a hole the radial inward movement of the space it is traveling through will cause the ball's path to curve toward the hole. If it is moving too slowly, it will be pulled into the hole. If it is moving faster enough it will be caught in an orbit around the hole. If it is moving even faster, it will fly past the hole and curve only slightly toward it as it passes.

  This is how objects behave near the sun It is almost as if the space itself were getting pulled into the sun, and dragging anything embedded in the space along with it

  The idea of space “moving” is pretty incomprehensible, so physicists speak instead of the “curvature” of spacetime. The equations describe it well enough, even if it is hard to visualize.

  Fine. But my point is this: it is just as easy to say that there is a distortion in the pathspace around the sun. Every object that travels
is traveling on a path – we call them trajectories. If the space the path passes through is distorted, the path will be curved by an amount that is less noticeable at higher speeds because the distortion has less time to affect the momentum of the object.

  Simply put, Einsteinian “space curvature” is a simple kind of pathspace, a kind caused not by human telekinesis but by the presence of matter. When it is oriented radially in a gravity “field”, an elevator shaft is definitely a kind of swizzle! While fast-moving objects like hot air molecules or motorcycles can hop across the elevator shaft opening and ignore it, slower-moving objects like cold air – or a walking person – will definitely be sucked into the shaft if they get to close and accelerate toward the other end.

  Now if we remove the gravity field – say by moving the elevator shaft far from any sun or planet out in flat” space – then we have “turned the swizzle off” – now if we step into the open end we will just float there instead of falling in.

  Now turn the analogy around. A swizzle is simply a portable spacetime distortion, like a piece of a gravitational field that you can carry around and point in any direction you want. If it is strong enough, you can make water flow uphill or even fire tennis balls straight up.

  The only difference between the elevator shaft and the pipe swizzle is that in my novel, the distortion is imposed by a sentient mind rather than a big hunk of matter. Just as the gravity field of the Earth's pathspace is anchored by the actual matter of the Earth (so that it follows the Earth around and keeps affecting us and the moon), so the pathspace of a swizzle is anchored by the matter of the pipe it is defined upon – so that it follows the pipe around if you are walking around while holding it.

  If you activate a swizzle and drop it into a fluid – such as seawater or the thin gas of interstellar space – it will accelerate until the drag equals its thrust.

  The only real difference between a pathspace weave and a piece of Earth's gravity well is that the mass particles of the Earth do not have to “concentrate” to create their pathspace distortion. It is part of them. If a photon decays into an electron and a positron, each of the particles is born with mass and a charge and a gravitational field – their pathspace distortions appear when they do.

  Einstein's space-curvature tensor is simply a compact and elegant way of specifying the local pathspace – the space of paths.

  --- MRK

  Other books by Matthew R. Kennedy

  The Gamers and Gods trilogy

  Gamers and Gods: AES

  Gamers and Gods II: MACHAON

  Gamers and gods III: ALEXANOR