Metria and the three Princesses looked as blank as Cube felt. "How do you extend it?" Cube asked. "I mean, what other dimension is there?"
"The fourth dimension is time, of course. Backwards, forward, sidewise, above, and below. It increases the volume of the figure enormously, without adding to any of the three spacial dimensions. A tesseract would be a perfect four-dimensional square: eighty-one similar cubes in the same space."
"Time," Cube said, clinging to that sliver she could understand. "You mean a cube before this one is another cube, and one after this one is still another?"
"That depends on how you see it, but that is approximately it. The fourth dimension can add infinitely to the three spacial dimensions."
"But it still looks like a cube," Cube said.
"Yes, just as any even cross section of a cube looks like a square. Of course if you get into tilted slices, like conic sections--"
"So this world-sized cube we're inside of is a cross section of a world-sized tesseract."
"Yes. Wasn't that obvious?"
"Not at first. What do you make of the walls?"
Karia inspected the nearest wall. "I believe this shows one of the other aspects of the hypercube. Unfortunately it has been imploded, so is not serviceable at the moment. See, it is not a picture; it has perspective."
"It has what?" Cube asked.
"This is a special kind of magic that makes distant objects change position with respect to close ones," the centaur explained. "See, if you walk along the wall, you can see things shift behind others."
Cube and the others walked along the wall, looking. It was true; distant mountains seemed to shift, so as to be behind different trees or houses. Yet when she touched the wall, it remained impenetrable.
"You mean that everything in the walls is real, too?" Cube asked. "Just flattened?"
"Because of the compression of the tesseract into a simple cube," Karia agreed. "It is not functioning, any more than we would be if we were squeezed into two dimensions."
"What would make this cube serviceable?" Cube asked.
"Restoration of the proper tesseract. Then the inhabitants could resume motion."
"The statues are real people?" Metria asked. "Frozen in time?"
"Yes. A population with no temporal dimension is unable to function properly."
"So we need to restore time," Cube said carefully. "Then they'll return to life, and the world of Tesseract will be whole again."
"Who could implode a tesseract?" Metria asked.
"A Demon," Karia said.
"Fornax!" the three Princesses said together.
"She's still trying to mess up the Quest," Cube said, as the fog in her head cleared.
"Figuring the Demon Xanth wouldn't notice a tiny spot like this," Metria agreed. "The fifteenth derivative of Ida's little moon."
"She must have been right," Cube said. "Because she got away with it."
"And now we have to fix it," Karia said.
"If we just can figure out how," Cube said.
There was half a silence. None of them knew how.
"Maybe one of the others will know," Karia said, timing her comment to come exactly as the half silence ended.
"Who?" Cube asked, her hand poised near the pouch.
"Maybe Ryver," Melody said. "He's handsome."
"Or Drek," Harmony added. "He's big."
"Or Cory and Tessa," Rhythm concluded. "They sidestep."
Cube put her hand in. "All remaining Companions," she said. The four of them slid out.
There was a tangle of explanations. Then Cory spoke. "Tessa must hold the key, because her full name is Tesseract."
Cube's jaw dropped. "The same as this world!"
"Well, it's too big a name for me," Tessa said. "It's downright ungainly, so I don't use it."
"Still, you must be the key. I came here, and it's a cube; maybe you can make it return to tesseract form. Names relate."
Tessa smiled. "I wonder how Cory's relates? Her full name is Corybant. It means a wild dancing spirit."
"I'm too awkward to dance," Cory said, embarrassed.
"But you know, names do relate," Ryver said. "Cube found this cube, and she had to gather nine Companions. There must be some reason for all of us. Tessa must be part of the key, but she can't do it alone. Maybe Cory is another part of the key."
"Wild dancing won't help," Cory said sourly.
"How do you know?"
There was most of another silence, which Karia again managed to catch just as it ended. "Perhaps it is so. We don't know the rules of magic here; they could be anything. Maybe dancing would cause the tesseract to be restored."
"Maybe by all of us," Ryver said. "Maybe that's why all of us are here. To be part of the magic dance."
"I can't dance," Cory said. "I ruin any dance I try."
"So do I," Ryver said. "I'm all feet."
"We don't know any dances," Melody said.
"We haven't learned the steps," Harmony agreed.
"So we just make the music," Rhythm concluded.
"Nobody ever wants to dance with me," Cube said.
"And how is Drek supposed to dance?" Metria asked. "He doesn't have any feet."
"So that's out," Ryver said.
"Perhaps not," Karia said. "There is a kind of dance that does not require intricate or beautiful body motions, or memory of patterns. All it needs is following directives as they come. It's called square dancing."
"Square--as in cube?" Ryver asked. "As in tesseract?"
The centaur nodded. "Perhaps that does relate." She sent a glance around to the others. "Shall we try it?"
Cube shrugged. She wasn't at all sure this would work, but she had no better idea.
"A square dance requires four couples," Karia said. "Four men and four women. Since we have eight females and only two males, and one of the latter can't dance, we shall have to make do with some substitutions. Shall I make assignments?"
"Girls have to play boys?" Melody demanded.
"Some will," the centaur agreed.
"Not us!" Harmony protested.
"But for the purpose of the dance--"
"Yuck!" Harmony concluded.
Karia rolled her eyes so sweepingly they almost fell out of her head. "You three will be girls," she conceded. Then she turned to the others. "You are amenable?"
The others nodded.
"Cube, you will be a male," Karia said. "Dance with Melody. Metria, dance with Harmony. Ryver, dance with Rhythm. She will enchant your feet just enough to enable you to do it." She sent the little Princess a look that required agreement. "Cory, dance with Tessa. Form your couples."
The three Princesses ran to join their partners, and Cory and Tessa were already together. Cube had known she would not be cast as a woman and was resigned. She suspected that Cory was similarly resigned; she was the tallest member of their party, and not pretty. Metria seemed to be handling it well enough; maybe her sense of mischief sufficed. She had assumed the aspect of a portly middle-aged gentleman.
"I will direct the dance," Karia said. "Drek will watch the thread and seek to follow it. The moment he makes it, we will follow, for the way will be open. The rest of you must focus on the dance, for if it is to be effective, it must be accurate. Keep dancing, whatever happens, until I say it has ended."
The centaur did seem to know what she was doing. Cube almost found a modicum of confidence. Half a modicum, anyway.
"Couples form a square, facing each other," Karia said, and made spot adjustments so that they got it right. Cube and Melody faced Metria and Harmony, with the other couples forming the sides of the square.
"Now there are certain basic actions, which we will rehearse first," the centaur continued. "When the dance starts, you will do them when I call them out. The important thing is that they be done together; a square dance is a pattern, most esthetic when performed precisely. You need have no concern for what is past or what is coming; it is ongoing. Simply listen to my calls and it will
go well. Now the first action is 'swing your partner.'" She directed them in that, and soon Cube was swinging Melody competently. Other actions were do-si-do, promenade, and balancing. When they had these straight, Karia asked for music. The Princesses got together and generated loud square dance music from a spot in the air above the square. Now they were ready to dance.
"Set in order," Karia said. "Balance to your corner." Cube turned and did the leg swinging motion facing her corner, who was Rhythm. As they finished, she faced the girl's partner Ryver briefly. He was dancing competently, his partner having enchanted his clumsy feet as directed. Cube smiled at him, beginning to enjoy this. To her surprise, he smiled back. Then she really enjoyed it.
"Swing your partner." Cube turned back to swing Melody.
"Gee this is fun," the girl said.
"Promenade." Cube and Melody linked arms the prescribed way and stepped around in a circle, in time with the others. She could see that it did form a pattern, an artistic whole. There was pleasure in that too.
Meanwhile she saw that Drek was elongating along the nearby thread, getting close to it, facing its entry into the wall. If, somehow, this dance made it possible to enter the realm of that wall, he would be ready.
The dance intensified. Not only was Cube getting into it, she saw that the others were too. There was something about the music, the beat, the pattern, and the participation that was exhilarating. She had never been a great dancer, but she could follow directions, and the basic forms were easy. She saw that this was true for Ryver, who did not need fancy footwork, and Cory, who did not need to be short, and of course the girls. Even Metria in her jolly coachman guise was smiling. There was pleasure in unity, and doing things together, making the patterns. They were being melded into an artistic whole. Too bad they didn't have an audience!
Something happened. At first Cube thought it was merely her joy of the dance; she was feeling giddy as she moved through the forms. For one thing, she even got to do-si-do with Ryver on occasion, though both had male parts; not everything was male-female. The dance seemed to be transcending itself, becoming something larger, more significant. But soon she realized that it was something beyond it. The very air seemed to be coming alive.
Drek was disappearing into the wall.
"Promenade!" Karia cried. "Along the thread!"
They followed the thread--right through the wall and into the adjacent cube. Along a path, until they came to a broader section. They formed the square again, bowed to their partners, and ended it.
There was a burst of applause. Startled, Cube looked. People were all around them. The folk of this realm had come alive! The bad spell had been broken, and the tesseract had been restored. All through the magic of the dance.
They broke it up, breathlessly congratulating each other. Suddenly Cube was being hugged--and realized with amazement that it was by Ryver. "We did it!" he said. "We danced and won."
They had indeed. But for the moment all Cube could think of was being held by Ryver. What absolute joy!
Chapter 13
Amber Dawn
Of course the good folk of Tesseract World insisted on feting them all with a great party, and they insisted on learning how this marvelous magic square dance was performed. It turned out that they had been aware of their predicament, but unable to do anything about it. The collapse of their four-dimensional reality into three dimensions had happened in less than an instant, rendering them helplessly timeless. Until they were restored by the dance troupe, and they were duly grateful.
First the group repeated the dance they had done, which was easy, because Karia remembered the calls. Then they became instructors, each taking a Tesseract partner to guide through it, forming two squares. The natives were good at multiplying squares; it was their nature. Cube got to dance as a woman, with a handsome male partner; she loved that. Even Drek Dragon got to dance with a slinky lady dragon, in their fashion, and she loved his perfume.
At last they were able to proceed. The others slid into the pouch, and Cube followed the thread to Princess Ida, whose moon looked like a stylized bug. It seemed that the tour of the moons was not over, because the thread led to it.
"This is Fractal," Ida said. "Much of it is invisible from here, but when you go to it you will find that it is surrounded by one or two myriads of threadlike patterns, leading to ever-smaller similar worlds. My next self resides on one of those worlds. I'm sure she will help you."
"Is there no limit to these moons?" Cube asked. "Is every one different?"
"The answer seems to be no and yes. We have discovered no limit, and no two worlds similar in shape. Perhaps it is your destiny to reach the end of the line, as it were, and fathom the last of the chain."
"I don't know," Cube said doubtfully.
"Neither do I," Ida agreed.
Cube thanked her, and rode the dogsled to Fractal World. It was as described, replete with many sprouting threads, twisting into intricate diminishing patterns. Her own thread followed the fractal thread from the nose-point and came to a tiny bug-world hidden there. But of course it seemed full world size when she got there. The Ida there was hospitable, and helped her on her way to the next moon.
And the next, and the next. It became a blur, and Cube regretted that she could not linger to admire the truly different worlds she saw in passing. But she had somewhere to go, and she wanted to get there.
Then she came to Zombie World. It looked like a moldy apple, and she hoped she would not remain there long. But as fate would have it, this was the one she had to explore.
The thread did not lead her to a zombie Princess Ida, but past rotten trees and decaying people to a crumbling castle surrounded by a stinking moat. "Oh, no!" Cube breathed. "Castle Zombie."
So it was. Cube knew that most of the zombies had retired to their own world, along with the original Zombie Master, and that there was now a replacement couple in Xanth proper. That was all she knew; she had not been curious about the affairs of zombies, preferring only that they be elsewhere. Now it seemed she would be learning more, though not by choice.
The dogsled stopped at the moat. The drawbridge was down, but looked too decrepit to sustain the weight of even one loaded sled. Yet the thread continued on into the sagging castle.
Cube sighed. "You stay here," she told the dogsled. "Maybe my weight won't be too much for it."
The dogsled looked relieved. She wondered how there could be danger, here on the tiniest part of the tiniest world, but it did seem like full size, and she felt as solid as she had on Xanth. Magic didn't have to make sense except on its own terms.
Now what about the pacifier? This time she put it into the pouch. That should stop it from doing anything weird while she was dealing with the Zombie Master.
She put a tentative foot on the derelict bridge. The wood looked rotten, but was actually firm under a squishy surface. She let her weight come down on it, and it held. She took another step, and then walked on out over the moat. It seemed that the rot was mostly for show. If the rest of the castle was that way, it was safe.
Just when she was halfway across, a bilious dripping head rose out of the green soup that was the moat. The moat monster! It opened its festering mouth. It was going to eat her!
Almost without thinking, she put her hand to the pouch. "Drek!" she said.
The dragon emerged so quickly he missed the bridge and dropped down into the moat with a great gooey splash. He wasn't pleased; an absolutely putrid stench wafted up.
The moat monster sniffed, sneezed, and recoiled. It seemed that even a zombie had limits.
Cube held her breath and hurried on across. "I'm okay, Drek!" she called. "Come on back."
The dragon shook his head. She knew why: he didn't want to stink up the pouch.
"Very well; I'll return for you when I'm done in the castle. See if you can find a place to clean up."
Drek nodded. She turned to face the castle, musing how the folk in the pouch always emerged in proper scale for the wor
ld they were in. Maybe her soul management, as she shucked off most of it each time she went to a smaller world, applied to the pouch and its contents, so that the process was automatic. She was just glad that her Companions were still with her, when at one point she had feared they weren't. Their souls had after all come along in the soul pouch. Again, magic was wonderful.
She knocked on the great sagging door, hoping a zombie wouldn't answer. She was in luck: a lovely elderly woman was there. Even old women looked better than Cube did, of course. "Yes?"
"I'm Cube, from Xanth proper. I--I'm here on a Quest, and it led me here."
"Why come in, dear," the woman said. "I am Millie the Ghost."
"A ghost!"
Millie laughed. "So-called because I was a ghost for eight hundred years. I was a restored-to-living woman for more than fifty years before retiring here to Zombie World with my husband, the Zombie Master. I'm so very glad to see you; you're just in time."
"In time?" Cube asked blankly.
"I will fetch her. Meanwhile make yourself comfortable." Millie hurried off.
Fetch who? Cube wasn't sure there wasn't a misunderstanding of some sort. But she saw the thread moving on down the castle hall, so she made herself comfortable by following it. It led to a stairway, which was in good order, as was the hall; there was no trace of zombie rot here.
At the top of the stair was a raised alcove, and in it was a mass of fur or wild hair. The thread stopped at the fur.
Cube picked it up. It seemed to be a cap, or perhaps a wig. She set it on her head, and felt a strange surge of emotion. She had been entirely too nice; it was past time to do something for herself, and to hell with the consequences.
Alarmed by the unaccustomed thought, she swept the wig off her head. It landed back in the alcove, askew. "What is that thing?" she demanded, flustered.
"That is the Hell Toupee," a man's voice answered. "It makes its wearer evil."
That explained it. Cube turned to face the man, who had come along a side hall. He looked cadaverously old, but otherwise healthy. "Hello. I'm, uh, Cube."
"And I am the Zombie Master. My wife said you were here. She is fetching the baby."