by Lyndon Hardy
“Look at the pattern closely, see how all thirty-seven form a beautiful pattern that is invariant if it is rotated through the small angle drawn over there.” The warrior’s face widened in a satisfied grin. “As the first protocol states—the greater the symmetry the greater the power. In perfect synchronization, those of us occupying the first node of the set began the journey to the second; those at the second unto the third. The reflectives who occupied part of the pattern were totally unprepared and the pressure to preserve symmetry was too much to resist. They were dragged from their fortifications into other nodes where yet more of us waited. We have won possession of more than a dozen.”
Kestrel looked at the map where two of the warriors were busy erasing some sort of symbol by some of the nodes and replacing it with another. He glanced at Astron in confusion, but then relaxed when he saw that the demon had not wrinkled his nose.
“This map then is a reproduction of all that we see.” Astron waved his arm outward toward the desert. “These oases are the nodes and the lattice lines the paths between them.”
“It is a record of all the realm,” added one of the warriors.
“And the symbol you are erasing—the nodes that are marked with it are under the control of the ones you call the reflectives.” Astron stopped and studied the parchment for a moment. “You hold your territory most unlike the fashion of the realm of men,” he said. “Look at how interspersed you are. How can you possibly say who has the greater advantage?”
“It is not a matter of adjacency, but of symmetry. Look at the beauty of the nodes that we possess. Of very high order are the subgroups that describe our lands.”
“And that symmetry gives us power, power to strike at a dozen vertices as one, power to use the innate forces of the realm to aid us rather than fight against it in furthering of our aims.”
“But why fight at all?” Astron asked. “What motivates you against these you call the reflectives?”
“Their symmetries are most foul,” the first of the warriors spat. “They are invariant under reflection whereas ours remain the same when subjected to rotations instead. And as the fifth protocol states—victory is total, only one of two will be left. It is the duty of every rotator to resist reflectives wherever we can, to strive to eliminate them until none are left to poison the beauty of the true symmetries that we will build when they are gone.”
“I don’t understand any of this,” Kestrel said. “It must be some sort of threadbare dream—scattered oases in a vast desert linked by geometrical designs, warriors engaged in mathematically obtuse campaigns. What of women and the crops that supplement these few fruits? Who weaves the clothes you wear on your backs and from where do the woolens come?”
“Most of your words make no sense whatsoever,” the first warrior said. “Our lives are to fight the reflectives until either we receive mortal wounds or have totally won. The fruit of the trees provide us subsistence; our armor protects us from blows. Of these other things we have no need.”
“But replacements,” Kestrel persisted. “What happens when some of your number are indeed struck down?”
“Replacement?” the warrior echoed. “I do not comprehend. We fight the reflectives until one of us is victor. If some of my comrades fall, we recompute the symmetries for the numbers remaining, so that we have freedom of movement about the subnodes, as you see we have done here. There are no replacements. There never have been since the beginning of time.”
Kestrel looked quickly about the oasis and noted that the warriors were deployed in what appeared to be a random fashion only at first glance. Closer examination revealed that the subgroups by each tree were different in many distinct ways from all the rest. Each had a different number, and the heights and weights were well distributed as well. The camp tasks they had undertaken were all unique and the identical weapons were stacked only where other differences outnumbered the similarities.
Kestrel glanced at Phoebe’s almost vacant stare and Nimbia’s listless shell hunched next to her. He looked back out onto the featureless desert. All that he could see was no more than the creation of one of the fey, he realized. It all had come into existence only by the force of thought—just like a scribe transcribing flights of fancy for the sagas, leaving out all nonessential detail. One could not really expect any more.
And they were marooned! The words boomed through his mind. Marooned in a universe in which all life apparently had to offer were the few simple rules of a game.
CHAPTER EIGHTEEN
Artifacts of the Chronoids
KESTREL looked across the new oasis at Phoebe and forced his face into a smile. He had lost track of the number of nodes to which they had been transported, but it would do her spirits no good to show how low his own had sunk. Far better it would be as well if they could share the same subnode, but the rotators, with their rigorously balanced deployments, insisted that they be kept apart.
Nimbia on occasion seemed a little more alert, but most of the time she still dozed in her stupor at the base of the tree to the right of Phoebe’s. Although Astron was at Kestrel’s side, the demon again was occupied with learning about some obscure detail of the realm. Kestrel was alone with his thoughts.
More than he feared, the life of a rotator was one of almost complete ritual. In a rigid sequence they would plan, eat, sleep, and then, simultaneously with everyone else in the realm, rush over the sands to a new node that looked almost exactly the same as the one they had left behind. Then, if the new node were unoccupied and there were no battle, the cycle would begin again. Plan, eat, sleep, move—they were merely playing pieces on a complex board, jockeying for position without ceasing.
Kestrel looked at the six fruit-bearing trees that ringed the small pond of water and then out over the featureless desert, trying to channel his thought in a more productive direction. He kicked at the sand at his feet, barely missing another shaft of ornately carved metal.
“Abel, what are these things?” he called out to the commander of the warriors. “Half of the oases we have visited seem to have them protruding from the ground.”
One of the warriors looked up from where he had been conversing quietly with two others over the small portable table covered with the maps of the nodes. His complexion was slate gray like the rest, but streaks of black ran through his hair. His eyes were steady and unblinking in a face not creased by either smile or frown.
“They are the devices of the chronoids,” Abel said with disgust in his voice, “the machines of beings of another realm—another realm just the same as yours. In our haste, we do not bury them as we might. They are a violation of the protocols.”
“Another realm.” Astron looked up from the scroll he had been studying intently. “We are not the only visitors you have seen?”
“Indeed not,” Abel said. “Ever since the reflectives seized the origin, the visits have been most frequent. The chronoids look much as we do and they engage in some great struggle not so very different from our own. But their weapons are not similar in the least and they are difficult for us to understand.”
“What kind of weapons?” Kestrel said, suddenly interested. “Something that would give you an advantage if you had them instead? Do they by chance involve the use of fire?”
“We would not use the devices of the chronoids.” Abel pursed his lips. “The reflectives do so only at great peril, since they work so imperfectly in a realm different from which they were intended.” The commander stopped and looked at Kestrel intently. “More importantly, they are not part of the tradition that stretches back to the memories of our creation. Only the reflectives would think of trying something so base to gain advantage.”
“But where are—”
“Perhaps it is worth the effort to show you one of the foul things,” Abel said. “Then you might better understand.” He gestured to one of the other gray warriors. The second began to protest but Abel’s stare cut short the words. The warrior spat at the ground at his feet and then b
egan digging into the sand. Shortly he retrieved an oblong box of metal and brought it forward for the others to see.
“Why, it looks like a clock,” Astron exclaimed as the object drew closer. “A device for measuring the passage of time. See the three ornate bands of metal pivoted at the center of the circular face with symbols about the rim.”
“These devices do much more than merely count the swings of a pendulum,” Abel said. “Just as our realm is governed by the symmetries of space, so is that of the chronoids ruled by the symmetries of time. With these clocks, as you call them, they manipulate the order of events in strange ways.
“Here, in the realm of the reticulates, the devices behave in manners even more bizarre. The manipulations of time are somehow transformed to ones of space instead. In battles where the reflectives possess them, I have seen entire moves undone against our wills, even though we held the advantage—whole squads of men exchanged with those of our enemy so that we were outnumbered, rather than the other way around.”
“How did this clock come to be here?” Kestrel asked,
“Somehow the reflectives have found a way to communicate between the realms, exchanging men with the chronoids for weapons that aid their own cause. Recently the reflectives seem to have increased the frequency of their contacts. The artifacts are more and more abundant. Ten thousand moves ago, we would find them only at one node in a score; now we see them at virtually half.”
“And the rotators choose not to use those clocks?” Astron asked.
“They disturb the protocols.” Abel again puckered his lips. “Their very presence somehow has changed the third and fourth laws so that they no longer operate as they should. And in our realm, strange things happen with them that even the chronoids never intended. Who knows when they will affect the first, second, and fifth laws?”
Abel looked out over the sands and shuddered. “Besides the forced transport of bodies to other nodes, I have heard of things happening inside as well.” He paused and seemed to chew on his tongue. “I cannot totally explain, but the transformations of the clocks in the realm of reticulates can change more than just the physical. No, despite any possible advantage, we prefer to bury what we find in the sands.”
One of the warriors from another of the subnodes called to Abel. The commander abruptly turned away without another word and resumed his duties. The abruptness of the rotator did not bother Kestrel. He had come to realize that there was little need for courtesy in a realm such as this. But the information he had learned had been most interesting. Perhaps there was something in what Abel had said that would help them in their plight. Kestrel looked at Astron, trying to draw out the significance of what he had heard, but the demon was again fully occupied by the parchment in his lap.
Kestrel saw a flash of color at another of the subnodes and immediately his attention was drawn away. Something was happening that he had not seen before. A giant sling had been strung between two of the trees. While he watched, a roll of brilliant red cloth was launched in a high arc into the sky. Like a streaking comet, the material unfolded into an eye-catching arch that could be seen far over the horizon. After it had plummeted back to the ground, several of the warriors raced out onto the desert to retrieve the cloth and roll it back up into a coil.
Kestrel saw four of the warriors at one of the subnodes scanning the horizon, three looking out along paths that ran to adjacent nodes, and two others at angles in between. Almost as soon as the signal bolt was retrieved, Kestrel noticed a flash of motion down the line of sight that was farthest to the left. Another banner of red soared up into the sky in answer to the signal.
Then in a clockwise direction from the first, just barely above the horizon and far more distant, four more banners answered as well. All eyes turned to the rightmost path, the last of the six, but the sky remained calm; there was no arch of color sailing into the sky.
A sudden babble of excitement erupted from the rotators. Even though they had not yet eaten, shield straps were tightened and a dozen or more began practicing stylized jumps and feints with their swords.
“What is happening?” Kestrel asked Astron.
The demon stopped tracing his finger across a copy of the node network and listened to the rush of voices that Kestrel could not quite follow.
“The prospect for battle is high.” Astron looked up from the map. “Imagine that this node is one vertex of a hexagon, just like one of the fruit trees around the oasis. The rotators also occupy the one on the left and then, on the far side of the center, three more as well.” The demon pointed down the path to the right. “A contingent of reflectives just vacated this node before we arrived; they must be one adjacent move away, most probably at the last node of the six.”
“So the warriors here arm for a fight against an enemy they have not even seen,” Kestrel said. “The node on the right may be occupied by twice as many—or they might run before the battle can be engaged.”
“That is not the way it is done in the realm of reticulates,” Astron said. “After some study, I think I understand better how the moves are made.” The demon stabbed at the map. “The rotators occupy five of the six vertices of a hexagon; simultaneously they will all move to the node at the very center of them all. The forces of symmetry will be enormous; the reflectives at the sixth node will be drawn in as well. They will be unable to resist. And with the warriors from five nodes against those of one, the outcome of the battle should be quite favorable.”
Kestrel studied the parchment on Astron’s lap with the cryptic squiggles, trying to make sense of what the demon was saying.
“Besides,” Astron continued, “it is a good move for us as well. It is in the right direction.”
“What do you mean?” Kestrel brought his attention back to the demon.
“It places us one vertex closer to the origin,” the demon said. “Look, I have been studying these maps and identified this one point as the center of all the others. All the symmetries pivot about it. Just like the center of the hexagon to which we will be moving, there is one vertex that is the origin of the entire realm.”
Kestrel shook his head. He still did not understand.
“The origin is least bound by the forces of symmetries,” Astron continued. “There is no other node which must have the same activities in order for things to balance. There the unusual is more likely to occur. It is the one node where we have some hope—some hope of performing wizardry and building a fire.”
Kestrel felt his spirits lift. “Yes,” he exclaimed, “you just might be right. How else could the reflectives communicate with the chronoids if not through the flame. And Abel said that since they have captured the origin, the contacts have become more intense.” He looked at Astron’s map with far keener interest.
“After the battle, we will press on to this origin?” Kestrel asked.
“Not necessarily. If the reflectives do not see such moves as part of their overall plan, they will travel elsewhere, and it will be difficult for us to resist being carried along.”
“Then they will need a little convincing.” Kestrel smiled and rubbed his hands together. His thoughts began to jump as he looked back to Abel with calculating eyes.
“What about a trap?” he asked. “Now that I think of it, this move to the center of the hexagon seems very obvious. Suppose it is part of some greater symmetry that is being planned by the reflectives.”
“I had not thought of that,” Astron exclaimed. The demon looked at Kestrel and wrinkled his nose. “Another example of the kind of thinking you were talking about as we returned from the glen of the harebell, I suppose. But yes, if I can understand the strategy of the move with such little exposure, how subtle indeed can it be? Why would the reflectives move to the node that completes the hexagon, rather than choose another oasis that does not impress symmetry so strongly upon them?”
Kestrel did not bother to hear the rest of what Astron said. He sprang to his feet and walked to the subnode that was occupied by the co
mmander. Fortunately the rotators had so carefully distributed everyone about the oasis that the resistance of maintaining symmetry could almost totally be ignored.
“Commander,” he said, “how cunning have the reflectives proven to be in the past?”
Abel looked up from the map he was studying and pursed his lips. “The reflectives do not act with cunning. If they did, I would grant them a small token of respect. Instead, they employ any methods to enforce advantage—poisoning oases just as they leave or imitating our signal flares with messages of deception.”
“And you?” Kestrel smiled. “The rotators do not engage in such tactics when the alternative would be a defeat?”
“Certainly not.” Abel glowered. “It is the fundamental difference between the two of us. We wish to rid this realm of the reflectives, it is true; but for the rotators, the end does not justify all means.”
Kestrel looked to the horizon and rubbed his chin. “Suppose I can provide you a method that will result in substantial advantage,” he said, “something that might tip the struggle permanently in your favor.”
“I do not know the customs of your realm,” Abel said. “What you judge to be of no consequence might be totally out of concert with what we rotators believe.”
“It is more a matter of cunning than the poisoning of wells,” Kestrel said.
“Speak and I shall judge,” Abel said. “If what you say has merit, then I will pledge my token to your command and all of those who can be communicated with by sky-ribbon as well.”
Kestrel looked into the cold gray eyes and hesitated. Among men, he had seen such an expression only in the most steadfast of wizards. “I do not seek your command,” he said quickly. “I propose only to offer advice. If it is accepted, then the results will be compensation enough for those who travel with me.”