The Labyrinth

Icarus looked up in the pale gloom all around him, glancing at the inky mouths of several tunnels which opened into the chamber he and his father were sitting in. A shaft of light from high above through an opening in the ceiling illuminated his face, creased gravely with fear. He coughed a little on the ambient dust, and having already broken his pained silence, faintly murmured: "Do you know the way out?"

Daedalus, for his part, was racking his peerless mind, too lost in the depths of his thoughts to answer even his own son. He mumbled to himself and scratched lines in the floor with a finger, elaborating on some drawings, spitefully wiping out others. At last he nodded to himself, apparently convinced of his own reasoning now. The internal struggle being won, he drifted back to the grim reality of the Labyrinth, where the two of them were slated to die.

"I do not," he replied finally.

"But...the Labyr---," Icarus started incredulously, wanting desperately to believe his father's intellect would save them.

"Yes, I built the Labyrinth," Daedalus acknowledged, his voice still tinged with pride, "but who could remember every single detail of a place like this? Not even I."

Icarus slumped despondently into the darkness at the edge of the chamber. But a sly grin persisted on the face of the architect. He laughed in spite of their fate. "The Minotaur is coming soon," he added, idly watching a spider amble by.

"You're mad," Icarus sputtered. An undertone of contempt in his voice echoed faintly from the walls. "The Minotaur has long since perished at the hands of Perseus."

Daedalus could hear the anger in his son's voice, but was not angry himself. Nothing could upset his confidence now: he had mastered his plight.

"Your education has not progressed far enough, my son," he answered reposefully, "if you really believe the Minotaur was begotten of a divine bull and a mortal woman."

Icarus fell silent. Motes of dust danced unperturbed in the light as Daedalus watched his son try to come to terms with the truth, bemused.

Icarus shook his head slightly, still unable to believe his father. "Wh-what is it then?"

"Use your reason, son! Do you accept that everything is either natural or artificial?"

"The gods..." Icarus started to object.

"The gods care nothing for our world," Daedalus spat. "Forget about them."

"Fair enough," Icarus admitted sheepishly.

"Then you accept that everything is either natural or artificial," Daedalus persisted.

"It cannot be otherwise," Icarus agreed.

Daedalus led his son further into the logic of his argument. "A bull siring a woman's child: is it not unfeasible? Have you seen anything of the sort before?"

"I hesitate to ask," Icarus remarked wryly, "whether such a thing has ever been tried."

A gale of laughter overwhelmed Daedalus. "Unions of this kind have taken place before. They were all fruitless, however." He stroked his beard thoughtfully, adding, "...though the sire was usually a man." He resumed his argument: "You will then agree that a cross between a bull and human woman does not exist in nature."

"Certainly," Icarus replied, beginning to see where this argument was leading.

Daedalus concluded his argument: "Not being natural, the Minotaur is necessarily artificial, is it not?"

Icarus paused again. Hope glimmered in his eyes. "Indeed."

"The Minotaur, my son, is a machine, like the smiths of Hephaestus. It is not proper to say that Theseus killed the Minotaur, he rather destroyed it. Another Minotaur was built to take the place of the first. And both were built directly from my designs, which no one else fully understands."

Icarus had caught on. "That can only mean that you know the mind of this machine intimately, down to the last nuance."

"Exactly. And the truth is that there isn't much to understand. The Minotaur is unrivaled in both strength and stupidity. But it does understand one thing that no man understands, that is," Daedalus boasted, "almost no man other than myself."

Puzzled, Icarus questioned him. "And what is that?"

Daedalus peered keenly into the light, as if the Minotaur were there before them and he were commenting on its innards in detail. "Just as geometry illuminates shape as we usually know it, there is a body of knowledge I have discovered which illuminates things which are interconnected, to put it briefly. Like geometry, it is axiomatic in nature, and also concerns the shapes of things, although its subject matter is subtly different: rather than examining the exact dimensions of the roads, for example, one is only concerned with which roads end in which cities, and so on. Indeed, I noticed the patterns of this new science first in the roads of Greece, and in the architecture of Crete, but started to see them in many other places. The Labyrinth is the culmination of my labors and..."

"Would you speak to the point?" Daedalus interjected, "You said the Minotaur would come soon."

"Oh, yes. The Minotaur understands the outlines of this science and so it can navigate the many winding passages of the Labyrinth with great efficiency. Or, to put it more accurately," Daedalus explained with such mischievous glee that Icarus wondered how his father lived through his youth, "the Minotaur can navigate the Labyrinth so long as no one confounds the signs left out for it."

"Signs?" Icarus wondered aloud.

"Yes. There are signs left at each end of every passage in the Labyrinth which indicate its length." Daedalus was speaking fervently. "By these the Minotaur finds its way quickly, although they were not particularly useful for the many untrained observers who have died here. They are even less useful for the Minotaur, if disturbed. Until now, only you and Theseus have learned my secret. Theseus knew how to trick the Minotaur by corrupting these signs, but they were restored after he escaped. My plan can work again."

Icarus grinned. "Remarkable."

Daedalus then scurried in and out of every passage leading out of their small chamber, deftly changing the shape of unremarkable stone glyphs found at each end, as Icarus looked on inquisitively. His father mentioned something about numbers which are the mirror images of other numbers, and which add to nothing, and how these mirror images of numbers would terminally confuse the Minotaur, but he didn't quite understand. By the time Daedalus finished, the sun had already passed noon. Noticing the direction the shaft of light had taken on the floor, he deduced the points of the compass and bid his son hide in the southern passage, after making some final adjustments to the signs at its two ends: "The Minotaur will approach from the north, and I have made absolutely sure it will not enter this passage."

Safely cloaked in the darkness of the tunnel, they waited as the sunlight crossed the floor and slowly faded. Before long, the light of the full moon took its place. Hours had gone by without a sound. Icarus became impatient: "Where is the Minotaur?"

Just as he spoke, the two heard a faint grinding reverberating through the passages in the north, like the strokes of a saw. The floor shook almost imperceptibly.

Daedalus quickly rose his hand, silencing him. For once he did not want to make his presence known. "The Minotaur can hear and see very well, but as long as we stay absolutely quiet here in the darkness, we will remain safe," he whispered hoarsely. Icarus lifted a hand to his mouth fearfully, as the grinding rose to a terrible clamor, and the floor seemed to thunder.

The Minotaur emerged. From the impenetrable darkness of the northern tunnel facing them, its terrible form came into the pale moonlight of the chamber, filling the mouth of the passage entirely with its bulk. It appraised its surroundings, and sensed something was not quite right. Icarus shrunk in fear as two malevolent eyes set in a bronze horned head swept right past them. As he saw that they had not been noticed, he allowed a strange curiosity to override his fear. What a marvel this Minotaur was! Its workings were in plain view, and he saw a carefully choreographed drama of machinery unfold before his eyes. Gears and levers clattered noisily as the Minotaur turned its head this way and that. Finally, it settled on a passage and stormed out of view.

Icarus relaxed. The apprehension faded in his heart. Daedalus raised his hand again, expecting that his son would believe the Minotaur had left them entirely. Just as soon as the clamor of the Minotaur died out, it started to return. It stomped through the passage it had first entered, and seemed deeply irritated now. A loud, impatient snort resounded from its nostrils. It had never erred like this before! The Minotaur nevertheless chose the same successive passage as before, and returned again. Seeing that its efforts were in vain, but knowing no other way of navigating, it gradually worked itself up into a towering rage, tearing aimlessly through a cycle it could not break out of. The noise was deafening and both father and son winced as they pressed down on their ears tightly.

At last, the great contrivance could no longer carry on. Returning to the chamber before Daedalus and Icarus once more, it tottered to a halt, groaned weakly, and crashed to the earth before the two of them, with a terrible sound like many armored warriors dying together.

Dawn was breaking. Daedalus sneered at his own creation as he ran out to its exhausted frame, which glinted in the first rays of the morning sun. Methodically, he pried its beams loose like ribs and found in the abundant scrap of its innards parts that passed for hammers and wedges, just as he had intended: "I imagined that tyrant Minos might betray me one day," he muttered to himself. Daedalus then beckoned his son to come out and help him and, as the sun rose, the two eagerly sapped the walls of the Labyrinth and wriggled out of the dirt and dim light into the radiance of the Mediterranean day. A light, steady breeze rippled in the grass and in their hair as they drank in, with all their senses, the vivid scenes of lovely, sunny Crete, and their renewed freedom to enjoy them.

Icarus, young as he was, recognized that their troubles were not over as soon as their liberty lost its novelty. "We have escaped the Labyrinth, but we can't hide from Minos forever. What now? To flee on water would be suicide."

Daedalus drew a deep breath of the fresh air, and it seemed to inspire him: "Wax. We need wax," he answered cryptically as they made their way home.

(I hope someone can figure out which branch of math I'm alluding to, and which algorithm of that branch is being used/abused.)