"I suppose that is possible," Cube agreed dubiously.
"Where does your thread lead?"
Now Cube saw it. "To your moon."
"That confirms it. Go on to Cone, unhampered."
"Thank you." Cube went out, got in the dogsled, and urged it onward. It zoomed along the thread toward Ida"s head, and soon was arriving at the growing cone-shaped world.
Thereafter, things blurred as Cube followed the thread through world after world, seeking the Ida on each and going to her moon. Cone was filled with water, and Ida lived at the bottom of the pointed sea; somehow breathing wasn"t a problem. Her moon was Dumbbell, where everyone constantly exercised. Then Pincushion, where everyone lived on huge long pins, and Spiral, like a little galaxy, Tangle, like knots in spaghetti, Motes, which seemed to be a swarm of particles, Trapezoid, which was not exactly cubic, and Shoe. Every old woman lived in Shoe, with myriads of children, so that none of them knew what to do. Then Implosion, Puzzle, and Octopus, which had to be seen to be believed. Then Tesseract--and the thread stopped.
The dogsled came to a halt inside a hollow cube the size of a world. The mountains, forests, lakes, and houses were all on the six great walls of it. And there was no way out.
Cube looked around. The dogsled rested on the floor of the giant box, beside a river and a hill, near a wall. Everything seemed normal, except that the thread stopped. That was why she knew there was no way out; the thread ended.
Well, not exactly. As she peered more closely, she saw that the thread actually turned and went into the wall to the right. But the wall was a picture, a painting, a mural, and the thread became a diminishing line on it, until it disappeared behind a painted house.
She got out of the dogsled. "Wait here," she told it, and the dog eyes closed for another snooze. It was a very obliging sled. Not the company Diamond was, but useful. As an afterthought she set the pacifier on the seat, so that it would not affect her exploration of this situation.
She walked up to the wall and tapped its surface. It was rock hard. She rubbed a finger across it, and it was mirror smooth. She squatted and traced the ground up to the wall; there was a faint path there, that became part of the picture so neatly that it looked real from any distance. She stood and reached high, verifying that the sky was painted too, and the clouds.
This was one giant picture, with only the square ground being real. But what was the point of it?
She traced the thread back the way they had come. She discovered that she was in a corner, and the thread came from another wall. She had come from another mural.
She walked out of the corner, toward a house that seemed to be in the real section. There was a man hoeing his garden beside it. But as she approached him, she discovered that he was frozen in place. This was odd in more than one way: not only was he absolutely still, not even breathing, he was off-balance, and should have fallen. But he remained as he was, slightly tilted.
"h.e.l.lo," she said. But of course there was no answer. She touched his elbow, and it was as hard as stone. She pushed him, at first lightly, then strongly. He remained fixed in place.
She realized that the man must be a realistic statue, fastened to the ground at a slight angle, immobile. All the vegetables growing in the garden were fixed too; she could not bend so much as a lettuce leaf. All part of the crafted scene.
She went to a nearby tree. All its leaves were fixed in place. There was no breath of wind. She checked the farmstead"s pitcher pump. A drop of water was falling from the spout. It was in mid air, frozen too, but not cold, just locked in place. All part of the scene.
Cube was beginning to feel nervous. She had thought this was a world inside a huge cube, but it was actually a lifeless model. She was the only thing moving within it. The only thing alive.
She explored further, using the whisk broom to get around faster, but only confirmed what she had discovered. All the trees, rivers, houses, and people were statuary, part of one encompa.s.sing artificial scene, marvelously made. She was alone in a three-dimensional picture.
"I think I need help," she murmured to herself.
She returned to the dogsled. Then she reached into the pouch. "Metria."
The demoness caught her hand and slid out. She looked around. "Oh, my! What fine mess have you gotten us into this time?"
"A three-dimensional painting," Cube said. "I was riding the dogsled along the thread, into the world of Tesseract, and found myself alone in this cube."
"Cube! That"s fitting," the demoness laughed. "Cube in a cube."
Cube hadn"t thought of that. "Names are seldom entirely coincidental, in Xanth. Could I have been drawn to this world for a reason?"
Metria got serious. "But you said the world was Tesseract."
"Yes. But it seems to be a cube."
"Let me check this out. I"ll just pop off for a moment." The demoness disappeared with a sharp pop, leaving a dissipating wisp of smoke behind.
Cube, alone again, tried something else. She summoned a nickelpede. The creature appeared, looked around, and glanced curiously at her.
"I don"t understand it any better than you do," she said, and banished it. She had merely been verifying her talent. She felt safer, knowing that she still had her nickelpedes.
Metria reappeared. "It"s a cube, all right. Outside it"s a cubic moon in orbit about Ida"s head, featureless. Inside it"s just this decorated sh.e.l.l. Could this be the end of the line?"
"I don"t think so. The thread goes into the wall. I just can"t follow it."
"Maybe the thread has given out. How many moons has it traversed?"
"I believe this is the fifteenth. But if it"s the end, what am I supposed to do here?"
"I just remembered: it"s not the end, because there"s Zombie World on down the line. So it must be a tired thread."
"I"ll bring out the Princesses," Cube said. She put her hand into the pouch. "Princesses."
Three hands caught hers. The three slid out together, and landed before her. "Wow!" Melody said, looking around.
"A square world," Harmony added, looking asquare.
"A cubic world," Rhythm said, looking acube.
"Cube"s world," Metria said.
"But it"s supposed to be Tesseract," Cube said. "Whatever that is."
"We"d better look it up," Melody said.
"I"ll get the big dictionary," Harmony agreed.
"Ooof!" Rhythm grunted as a huge tome landed in her arms.
They put the dictionary on the ground and turned the pages, poring over it.
"Tesseract," Melody said, finding the word.
"A cube generalized to four dimensions," Harmony read.
"A four-dimensional hypercube," Rhythm read.
"A structure consisting of eighty-one identical cubes occupying the same s.p.a.ce," Metria read over their shoulders. "That"s three to the fourth power."
"We"re only three to the third power," Melody said.
"You mean three cubed," Harmony said.
"That"s wrong," Rhythm said. "We are really only one Sorceress cubed."
Cube was having difficulty following this, but doubted that the little Princesses knew exactly what they were talking about. "Do you mean that however you figure it, the tesseract is beyond your power?"
"That"s what they mean," Metria said. "They can"t fix it."
"Then who can fix it?"
"Maybe one of the others," Melody said hopefully.
"Like Karia," Harmony said. "She"s smart."
"All centaurs are," Rhythm said.
Cube brought out the centaur, and explained the situation. "Do you know what a tesseract is?"
"Of course. It"s a hypercube. A four-dimensional structure."
Cube"s head was thickening. "Can you explain that from the ground up?"
The centaur smiled. "I"ll go into didactic mode." She reached behind her to draw an arrow from her quiver. She used the tip to make a dent in the sand before her. "A dimension is a measurement. This is a point--a no-dimensional object." She scratched a line. "This is a line, a one-dimensional object. It has length, nothing else." She scratched a square. "This is a two-dimensional figure, length and breadth. Infinitely greater than the prior figure, but still limited." She glanced at the Princesses. "Eight sticks, please." They appeared in a bundle, and she continued her lessen. She stood four sticks at the corners of the square, and connected them with four more. "This is a cube, a three-dimensional figure, with length, breadth, and height. Now if we extend it another dimension, we"ll have a hypercube. A tesseract. It"s elementary."
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 s.p.a.cial dimensions. A tesseract would be a perfect four-dimensional square: eighty-one similar cubes in the same s.p.a.ce."
"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 s.p.a.cial 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."