“But I'm nobody, just a smith's daughter.”
“Not any more,” said Aria. “If you stay here and learn, you're going to be a wizard someday. There are a lot of smiths in Rado, but only a couple of wizards. You're joining a very small group of important people.” She took a deep breath.. “If I wasn't being raised to be Governor someday I'd be doing the same thing. But I can't.”
“But there's nothing more important than being the Governor! That's the most important job of all.”
“Maybe. But I'm in no hurry. Why don't you take a few minutes to unpack and freshen up while I check on my gardens? Then we can go back down to Xander's floor and see what he and Lester are up to.”
Chapter 18
Lester: a lesson in spinspace
“Imagination is more important than knowledge.”
– Albert Einstein
Xander watched Carolyn go off with Aria to fix herself a place to live. “You did well there,” he said. “I would have talked to the smith himself, not his daughter.”
“Too old,” said Lester. “He didn't grow up in a forge with an everflame. Fortunately for Carolyn, he took over for a smith who did have one, so she grew up exposed to it.”
“But from what you described, she would never even have touched the everflame.”
“True. She just operated his bellows. I guess she must be exceptionally sensitive to the Gifts.”
“Indeed.” Xander. “I confirm your own sensing, that she is capable. As I said, you did well there. Name your reward.”
“I'd like a lesson in spinspace, please.”
“But you're still working on pathspace.”
And I expect I will continue to do so. As you continue to exercise your pathspace, spinspace, and tonespace. But just as you are open to learning new spaces, so I am open to learning more than pathspace.”
Xander considered it. “All right. Have a seat. I'll be right back.” He went into his inner storeroom and emerged with a box of artifacts.
“The lessons from now on will have a recognizable form,” he said. “First, I'll show you what can be done. Then I will try to teach you how.”
The first thing he set up looked like a potter's idea of a pet volcano: a black tapered cone, fat end down, and a circular stand with a spike sticking up. Xander dropped the tapered cone over the spike and let it there. The outside of this artifact was black and striped with white. He thought the white was circles until he saw it from above and realized it was all one white spiral that wound from a point on the circumference of the bottom all the way to the top. A soon as Xander released it, the cone began to turn.
When the cone got up to its idling speed he saw the purpose behind the white spiral. You couldn't see the motion of the black cone, but when it was turning the white spiral would climb or descend the cone to show the rate of rotation. The cone, in other words, was a spinometer.
It is such an unlikely artifact that Lester has to ask “Where did you find that?”
“We didn't. I had an artisan make this for me. The only useful thing it does is provide a handy target for practicing your control of spinspace.”
“But I don't know anything about spinspace.”
“It's time to talk about it,” said Xander. You remember what I said about pathspace?”
“That every point in space has paths passing through it that control the motion of matter and energy? Yes. Why?”
“Because now you have to step into a larger view of reality. The pathspace you have learned is only one of many ways to think about space. Each way has its own advantages. From pathspace you have learned about invisibility and swizzles. Now it is time to learn a new way.”
“What do you call the larger view of space that has all of these useful aspects to it?”
:”I call it metaspace,” said Xander. The general term 'space' is already used to refer to simple, 3-dimensional coordinate space. Configuration space has also been used, to refer to the infinite number of ways space can be populated by objects.”
“I don't see the difference between coordinate space and Configuration space.”
“Let me give you an example,” said Xander. “Suppose you froze time and wrote down the coordinates of every human being on the planet at that moment in time. At that point you might say that the configuration space is the same as the coordinate space, other than the fact that you have chosen to highlight the coordinates of humans.”
“Sounds pretty much the same to me”, Lester agrees.
“But in reality,” Xander continued, “we have only defined a huge family of configuration spaces. For example, add the coordinate of religion. Immediately, there are an infinite number of variations possible in the configuration space. For example, we could have a planet full of Catholics, in which every one of the frozen humans is a member of that religion. Or we could have a planet full of Buddhists. For every major religion, you could imagine a configuration space in which every human belongs to that religion.”
“But that would be as meaningless as saying they all have red socks on,” said Lester. “It doesn't add much information to the picture.”
“Correct,” said Xander. “All of these one-religion configurations are trivial examples of a configuration including religion as a coordinate. They are just as trivial as saying everyone is wearing red socks or everyone has black hair.”
“So what's the point? What does it add?”
“I said these were trivial examples,” said Xander. “We could just as easily imagine non-trivial examples. If, for example, we changed the picture and imagined something more realistic, which differing geographical regions have different percentages of Catholic, Buddhist, etc. followers, then the additional coordinate begins to become more useful. If, for example, you see a boundary in which differing religions are popular on opposite sides of a border, then it is more likely that religious wars will occur between those countries.”
“You mean, like between Texas and its neighbors.”
“Yes. The more you understand the configurations possible in metaspace, the more you can predict and control the behavior of matter and energy in space. For example, using only the part I call pathspace, you can make swizzles or go invisible.”
“And the more aspects of space I understand, the more I will have in my bag of tricks as a wizard.”
“Yes. But since there are so many possibilities, I find it is usually more effective if the student trains on only one aspect at a time. You have been training your ability in pathspace. Now it is time to begin adding spinspace to your toolbox.”
“Are there lethal applications?”
“Yes,” said Xander. “But let's not be in too much of a hurry to get to them, shall we? It's good to be able to defend yourself, but I would prefer that killing not be the first thing that comes to mind.”
“All right. I can see that. What's the first thing I need to do?”
“The first thing you need to do is to work on adding the coordinate of spin to your configuration space. Right now this spinometer has x,y, and z coordinates for you. But it isn't spinning yet. You have to engage that part of your metaspace and learn how to manipulate it.”
“So teach me. How do I go about doing that?”
Instead of answering, Xander took a square wooden board out of his box. Its surface was marked with the familiar alternating checkers of black and white square. In the center of each square was a tiny dimple. Then he pulled a handful of tiny tops out of the box. He set the bottom points of them into some of the dimples and spun them with his fingers to set them rotating.
Lester expected them to run down and fall as all tops did, but they didn't. In fact, some of them seemed to spin a little faster. He decided that Xander was stoking their spinspace.
“Imagine that all space is filled with tops,” said Xander. “Not just the dimples on this board, but all the points in between, and all of the points above and below them.”
Lester tried, but that was an awful lot of spinning to imagine.
>
“Now for the hard part,” said Xander, as if what he had just described was too easy. “Now shrink all of those tops down to nothing more than points. In other words, imagine you are dealing with a space that has an x,y,x, and spin associated with every point in it.”
“That's pretty hard,” said Lester.
“I know it is,” said Xander. “At first. But the more you practice it, the easier it will get, as imagining pathspace was.”
“This space I am imagining,” said Lester, “sounds like the idea of pathspace with spin replacing the coordinate of path direction.”
“Exactly,” said Xander. “I have not asked you to imagine space plus path plus spin yet. We have just swapped out path direction and replaced it with spin direction. It is a little more complicated.”
“Why so,” said Lester, still imagining a space filled to the brim with spinning points.
“Well, you might suppose that it's of the same order of complexity, with the arrow of spin,” he gestured at the tops, “represented here by the direction their heads are pointing in. But in fact, it is a little more complex, because while in pathspace you might imagine slowing down and heading back the other way, in spinspace the spins can actually flip while staying in the same place.”
He picked up one of the tops, halting it, and then turned it over and set the point of its “hat” into the dimple of the board. A little leg now stuck up from the upward-pointing “bottom” of the top.
He gave the inverted top a twist to start it spinning. After a few seconds something remarkable happened. The top blurred out horizontally and then recovered with its hat pointing back up again. “Whereas in pathspace, a particle's momentum will keep it moving forward until it hits something, in spinspace the direction of spin can be reversed without hitting anything.”
Lester looked at the now right side up top. “But it didn't,” he noticed. “The top is not upside down any more but it is still spinning in the same direction.”
“Yes and no.” Xander held out his hands and curled his fingers letting his thumbs both point toward the ceiling. “Both of my hands now illustrate spins pointing 'up'. But the curling of my fingers goes in opposite directions. They used to be called 'clockwise' and 'counter-clockwise' because the way my left hand fingers curl is the same direction the hands move on an old-fashioned clock.”
Now he rotated his right hand so that his right thumb pointed down toward the floor. “For convenience, we could just as well call these spin directions plus and minus, and stop referring to clocks.
“With particles, spin tends to be quantized, but we'll talk more about that later. For now you can imagine spin as a quantity that can be larger or smaller, and positive and negative. The convenience of using + and – to describe it is now you only need one hand.”
“All right,” said Lester. “So we can imagine spinspace as the same as coordinate space, with the addition of a value of spin for every point in space that can be positive or negative.”
“Almost,” said Xander. “But there is a bit more to it. On this board the only stable configurations are spin up or spin down. In real space, however, there is no board to constrain motion, so in real space the spins can all be positive or negative or zero, and their spin axes can point in any direction in 3-space.”
He passed a hand over the tops and they all slowed to a stop and fell over on their squares. “Now let's get back to the spinometer. The first thing you have to learn is crude manipulation of spinspace. “
Lester tried to imagine reaching out and grabbing the cone to set it spinning. This had no effect other than making it rock slightly on its support.
“You will need to remember how you solved the swizzle,” said Xander. “I imagine your first efforts were like imagining pushing the air down the middle of a tube.”
“Yes,” said Lester. “Didn't work.”
“But I imagine what did work was imagining the total pattern of the pathspace around the tube – part of which was the motion outside the tube.”
“Yes,” said Lester. I finally got the pattern I wanted when I saw one of the guards at the prison blow a smoke ring.”
“Very good,” said Xander. We must remember to use that image with the students. For the spinometer, what I have found works better than imagining it twisting is to imagine all the spin you want distributed in the space around the cone, and then gathering all of that spin into the cone, like you are focusing it.”
“I don't understand,” said Lester.
Xander reached into the box again and came out holding a circular piece of glass in a metal rim with a handle. “By now,” he said, “you may have learned how to manipulate light paths to do more than make yourself invisible.”
“Well, yes. I learned how to use it to see though walls and to make distant objects look closer.”
“Excellent. The Ancients could do that without pathspace by using specially shaped pieces of matter to bend the pathspace for light. This is a convex lens. You can see how it can be used to magnify objects, to make them look closer.” He held it over the top of the cone and moved it toward the cone and away from it.
“But it can also be used to concentrate light to a focus.” he picked up the board and the tops fell off it onto the table. Holding up the board, he caught the light coming in the window on it. “Now watch,” he said, and held up the lens in the path of the light.
The sunbeam coming through the window, barely visible from small motes of dust in the air it was slicing through, went through the lens and the beam narrowed. The spot of light on the board became smaller but brighter. For a moment, he moved the lens so that the light on the board came to a single point. When he did this a tiny plume of smoke curled up from the point, then he moved the lens out of the beam.
“As you can see, the lens can take the energy in the light and focus it into a small region to burn things. On any decently sunny day you could use a lens like this to start a campfire.” The burned spot on the black square stopped smoking. “You will also have notices that when you focus the light this way, the bright spot is surrounded by a shadow where the light is less.
“The first thing I want you to work on,” he said, “is imagining the spin distribution in the space around the cone and then focus it on the cone, so there is less spin in the space around it and more spin in the cone.”
Lester tried again. From what Xander had said he decided it would be simpler if all of the spin was in the same direction. He imagined a cluster of spins around the cone, all pointing up, all with left-handed spin.
That part was hard enough. Now holding that picture in his mind, he tried to imagine redistributing the spin, seeing flowing radially inward, so that the space near and containing the cone got more than its share of spin while points further away lost some of theirs.
After concentrating on this for a minute the cone began to slowly turn on the left-handed spin direction.
“It worked!” he said. But in the instant that he let his concentration slip to formulate the thought, the cone stopped accelerating and settled down to a constant slow spin rate.
“Yes,” said Xander. “Well done. You have succeeded in your first spinspace manipulation. You have also discovered that concentration is key. In the beginning your work with spinspace, like your work with pathspace, will require all of your concentration to succeed. Later on, as you grow more adept at it, you will find it easer to do and it will take less of your attention.”
At this point Carolyn came back from her settling in. “What are you guys up to?”
“I was just rewarding Lester for finding you with an advanced lesson,” said Xander. “To repay me, he is now going to give you your first lesson in pathspace.”
“I am?”
“Yes, you are. Consider yourself promoted from student to assistant professor.”
Chapter 19
Nathan: falling
עבור אדם צדיק יפלו שבע פעמים
“a righteous man may fall seven time
s”
– Proverbs 24:16
The door to the study opened and the men in white robes came out and out their coats back on. Isaac was the last to emerge, and he had a look on his face that Nathan had never seen before.
Rebekah closed the font door. What is it, Isaac?”
Isaac looked like a man who is lost. “I have been asked to go to Denver,” he said, in tones that didn't believe it.
“What? But your life is here, with your family. How can they not know that?”
Isaac slumped onto a couch. “They know. But I have been asked to go anyway.”
Rebekah sat down next to him. “Husband, you have responsibilities.”
He just looked at her. “Yes,” he said. “Yes, I do have responsibilities. To help the poor, to defend the weak, to settle arguments...and to serve my nation when called.”
“Tell them to send someone else, then.”
Isaac gazed at his wife and reached out to stroke her hair. “It is part of my job,” he said. “I have not been called for many years, because they knew I had a family. But I cannot shirk my duty now, when I am needed. Yonatan has served his time, and my own turn has come.”
“But why Denver?”
“Things are stirring there. Things that the brethren are concerned about.”
“Well then, we're coming with you!”
Isaac kissed her. “I would like that,” he said. “But you know that's not how it works. I've taken an oath to fulfill my duties, and this is one of them.”
Rebekah was having none of it. “Your duties to us – “
“I know,” he sighed. “This is one of those times when I cannot do both. If I go, I will be failing you, and if I do not I will be failing our country. There is no win here. Either way I will be falling down.”
She laid one of her hands on his. “A righteous man may fall seven times, but he gets up again,” she quoted.”Husband, if you are serving God, you are not failing us.”
Spinspace: The Space of Spins (The Metaspace Chronicles Book 2) Page 6
