Complete Stories

by Rudy Rucker

  As the fire heated the water for Pythagoras’s morning ablutions, the philosopher pondered his dream of the Crooked Beetle and the vast new pattern gained at such costs from his dreamworld familiar. The new number-form corresponded to some object or quality to be found in the mundane world—the peras—in which Pythagoras was now once more firmly enmeshed. But the crucial identity of the pattern would remain a mystery until he actually experienced the shock of recognizing the physical form to which the number was attached in the higher realms. Pythagoras had learned patience, and was content for the time being simply to revolve the number in his powerful mind.

  Soon Pythagoras had finished washing and was intent on assembling, like any common hermit, his simple breakfast of honey, dates and almonds. How useful it would have been, Pythagoras thought as he enjoyed his meal, to have the numbers for these staples. But the creatures of the Unlimited granted their gifts capriciously, and when for his second gift he’d asked the Tangled Tree for the signifier for Honey, he’d instead received a Sheepskin Number.

  No sooner had Pythagoras brought the last fingerful of honey to his bearded lips than he espied his prize student, Archytas, eagerly ascending the slope to his teacher’s cave. Pythagoras sighed, daunted by the zeal of the young man.

  Archytas began talking excitedly before he’d even reached the ledge. Something involving the golden ratio and a new ruler-compass method for inscribing a regular pentagon within a circle. Pythagoras let the words flow past him undigested. He found his young acolyte’s modernistic geometric constructions overly refined.

  “O, why not just use trial and error till you find something that’s reasonably close to cutting the circle in five?” said Pythagoras. He would have despised such a thought a year ago, but his escalating traffic with the demons of the apeiron had corrupted the asceticism of his taste.

  Hoisting himself level with Pythagoras, Archytas gave a short, braying laugh, assuming his mentor to be joking. “Indeed. And why not jump headlong into the pit of impiety and say that integral numbers are not the basis of all things? Why not maintain that the apeiron is the very warp and woof of our world?”

  “Will Eurythoë be coming for her lesson today?”

  Taken aback by the abrupt change in topic, Archytas made a face as if he had bitten down on an olive stone. His demeanor grew stiff and somewhat remote. “My mother, the gods save her, indeed persists in her uncommon thirst for knowledge. Echoing my father Glaucas’s complaints, the other wives look askance at Eurythoë’s unbecoming philosophical ardor, wondering why she cannot content herself with simple domestic pursuits. But I quash all such talk by defending your virtues, both as a citizen and as a wise man.” Archytas stared grimly at his teacher. “I hope my faith in you is fully justified.”

  Pythagoras felt a smidgen of shame. He disguised the feeling with a peremptory manner. “Of course, of course. But you still haven’t answered my question.”

  Archytas forced out the reply: “Yes, my mother plans to visit you in the late afternoon.”

  This matter settled, the two men picked up their dialogue not from Archytas’s revolutionary construction, but from the point where Pythagoras’s discourses had ended yesterday. As the sun rose higher, they were joined by other young scholars from Tarentum, until finally Pythagoras sat at the center of a stellated polygon of questing minds. The topic for today was Pythagoras’s wonderful geometric proof of his great theorem that in a right triangle, the square on the hypotenuse equals the sum of the squares on the sides. To illustrate his argument, Pythagoras drew a diagram in a flat patch of sand; it was his “whirling squares” image, showing a square inscribed at an angle within a larger square.

  Though Pythagoras’s belief in his original worldview was all but shattered, he still enjoyed the verbal puppet-show of his ideas. He taught with a craft and a grace that come from long experience; he could make dry magnitudes and geometries sing like the notes of a fine musician’s lyre.

  When the sun was high overhead, rumbling stomachs dictated a break, and the living polygon of scholars fell apart into its component points. Taking advantage of the shade in the mouth of the cave, the town-dwellers broke out food from their wallets, eagerly vying to offer Pythagoras the choicest morsels of flatbread and feta. Their teacher accepted with the stern good nature that chose no favorites. Gourds of cool water from Pythagoras’s personal spring complemented their simple fare.

  “King Glaucas spoke of you again last night, master,” said the sinewy, wolfish Alcibedes. Unlike the other pupils, he wore a short sword at his belt. “At dusk in the forum. He told the Senators and the slow-witted priests of Apollo that you are a sorcerer. The icosahedral ball you gave Eurythoë—Glaucas terms it a magic amulet. He claims the mere sight of it caused the goats to give sour milk.”

  “My father is troubled,” said Archytas. “He fears the people tire of his rule. The unity of our little band disturbs him. He fears you may foment a revolution, Pythagoras. Now that you’ve won his wife and son as pupils, who else might not follow you?”

  “A tyrant’s bed is most uneasy,” murmured Alcibedes, staring down at his sword.

  “What of the common citizens, then?” said Pythagoras. “Do they speak well of me?”

  “The farmers are happy to have their fields well-surveyed,” said Meno. “And the innkeepers rejoice to have so many of your students lodging in Tarentum.”

  “Pythagoras’s knowledge of the heavens has even helped the priests in their computations of our calendar,” chimed in Dascylus. “After all, was our teacher not the first to reveal the identity of the Evening Star and the Morning Star?”

  “Even so, Glaucas can inflame the rabble to hate me,” said Pythagoras. “At times I fear for my life.”

  “Perhaps Glaucas fears for his life as well,” said Alcibedes. “Who knows what the future might bring? It seems unlikely that both you and he can live here forever, O Master. What if you really were to die? You should prepare us. Can you not lift the injunction of secrecy from your great teachings? We long to spread your wisdom far and wide. Indeed no man is immortal, and when you pass into the Elysian world, it will be our lot to inculcate your noble truths. Were it not better that we begin to practice at it even now?”

  For the second time today, Pythagoras felt a twinge of shame. His reasons for making his teachings secret were simply that he did not want to give away that which he could sell to students. “I will ponder upon your suggestion, Alcibedes,” he said slowly. “But now, my children, let us return to our studies. If some day you are to farm these plants, you must learn their foliage well.”

  After several more hours of vibrant discourse, Pythagoras abruptly called a halt to the day’s lesson. “My faculties are waning, lads. We shall delve further into the consequences of my great theorem tomorrow.”

  As he watched the sturdy youths rollick down the slope toward Tarentum, Pythagoras realized he had told them only half the truth. While his intellectual powers were indeed spent for the day, the energies of his loins had reached an almost painful peak as he anticipated the arrival of Eurythoë.

  Pythagoras barely had time to clean and curl his beard before he spotted Eurythoë on his side of the river, her delicate, sandal-clad feet scribing a clean curve across the rocky slopes, a curve designed to intersect the vertex of his soul.

  She arrived, flushed from her hike and infinitely desirable. Black curls lay pinned by a sheen of sweat to her brow. Her bosom fluttered beneath the white fabric of her robe. A subtle musk as of some wild animal rose from her pleasing form.

  Eurythoë’s deep gray eyes met the gaze of the philosopher, yet her manner was skittish. Rather than immediately accept Pythagoras’s embrace as was her wont, she looked nervously back toward Tarentum.

  “What troubles you, dear Eurythoë?”

  “I am consumed by fear that our illicit love will be discovered. I saw a most evil omen this morn.”

  “What manner of omen?”

  “One of the slaves returned from the ma
rket bearing a pannier of fish, and atop the wet pile lay one with a dark, muddy tail! You’ve often inveighed against those very creatures! Eat not fish whose tails are black.”

  Pythagoras made a dismissive gesture. “My reference to the evil nature of such creatures was but an allegorical warning against those who draw strength from muck. Do not trouble yourself any further, Eurythoë. You didn’t eat of the fish, did you? Very well then, we’ve nothing to fear. Let us hie ourselves to my soft, warm pile of sheepskins.”

  Conducting the wife of Glaucas, the mother of Archytas, into his cave, Pythagoras soon reveled in the sight of her naked charms. Quickly doffing his own clothing, Pythagoras caught her up in his embrace. As she always did, Eurythoë began their lovemaking by stroking his golden thigh.

  Marvel of marvels, an extensive, irregular patch of Pythagoras’s inner left thigh was some substance other than flesh. The stuff was utterly impermeable, too hard to cut with a knife or even to scratch with the noblest gem, yet it was also like the thinnest leaf of beaten metal, flexibly mimicking the architecture of his muscles and tendons and veins, the bright patch merging imperceptibly with his skin. Though the inadequacy of language forced Pythagoras to call it “adamantine gold,” the thigh seemed really to be of a substance quite other than anything seen upon Earth.

  The golden thigh was an uncanny scar from Pythagoras’s very first dream-meeting with the creatures of the apeiron, the thigh an ever-present reminder that the creatures were indeed more than dreams. In that first meeting the Braided Worm and the Crooked Beetle had appeared to him, the Worm a loquacious and foully knotted creature whose form so defied all definition that Pythagoras could never determine if its component strands numbered two, or three, or four. The worm had offered Pythagoras the magical power of the River Number, and when Pythagoras had greedily accepted the offer, the Beetle had bitten deeply into his thigh, turning a part of it into adamantine gold. The Beetle had laughingly termed the change a “memory upgrade,” and then somehow the Worm had transferred the River Number into the enhanced Pythagoras. He’d woken from that dream irrevocably changed.

  At first, Eurythoë had been frightened and repelled by Pythagoras’s gleaming thigh. But when he told her the alteration was a sign of the gods’ favor—and why not believe this?—she learned to find it erotically stimulating.

  She drew her fingertips across the eerily sensitive surface of the golden thigh, and soon the dust rose from Pythagoras’s mound of sheepskins as he bisected Eurythoë’s triangle and became the radius to her sphere. The even and the odd blended into the One. And then, all passion slaked, the couple lay loosely embracing, smiling full into each other’s eyes.

  Trying, as always, to mentally encompass the wonder of Eurythoë, Pythagoras mused that she herself must embody a number form, as did every woman and man. Women were even numbers, and men odd. But what a large number it would take to adequately represent Eurythoë, to capture in a net of notational dots this woman’s scent, the curved surfaces of her honey-colored skin, the soothing tones of her normal speech and her sharp cries of ecstasy.

  Suddenly there was a clatter from the lip of the cave. Falling stones? Pythagoras sprang nimbly to the arched opening, feeling himself lithe and wise. A well-aimed rock whizzed past his head and shattered against the cliff beside the cave’s mouth. All at once he felt himself nude, middle-aged and absurd.

  “Against the advice of your own maxim, you have poked fire with the sword, O Pythagoras,” sang a mocking voice. “All the town will hear of it.”

  His tormentor was an open-mouthed, fat-bellied little figure in a white toga that revealed bare, thickly tufted legs. At first glance he looked like—a vengeful fish with a black tail. Evidently he’d come to spy on Eurythoë’s lovemaking. He made the insulting gesture of the fig, and raced down the slope like a homing pigeon.

  “Senator Pemptus!” exclaimed Eurythoë. “One of my husband’s spies. O, Pythagoras, you must flee. I’ll hurry down and try to salve my husband’s wounded pride. But I fear the worst for you.” She began weeping.

  “Must I run from an innumerate, bean-eating tyrant like a common slave?” said Pythagoras. “And what of my pupils? What of our love? I’d rather remain here in my cave, aloof with my music.” Pythagoras gestured at his beloved monochord, a one-stringed instrument that had taught him much. “I’ve not told you this, Eurythoë, but the gods have granted me certain miraculous powers in addition to my golden thigh.”

  Eurythoë hugged him, dried her eyes, and began trying to repair the disarray of her hair with ivory pins. She succeeded only in making it appear that she wore a lopsided bird’s nest atop her head. Finally she spoke again.

  “There are too many of them, Pythagoras, and they will come for you. Humble yourself and flee. For what does anything matter if you or both of us are dead? Save yourself, and let me do what I can to salvage my own position. Think of your own maxim, Pythagoras: Give way to the flock!”

  “You are right, my dear,” said Pythagoras, quietly pulling on his robe. “The flying dust survives the storm. I leave on the instant. Spare me one last kiss.”

  Smooth lips met bearded ones, and then Eurythoë was light-footedly gone. Pythagoras dallied in the cave long enough only to pack a wallet with food. All other necessaries were kept within the confines of his skull.

  Emerging into the reddening light of the westering sun, the philosopher paused for a moment’s strategic reflection. Behind him, above his vantage, stretched an impassable wilderness of mountains: easy to lose pursuers there, but dangerous terrain to the hunted one as well. From those treacherous peaks he might never emerge. No, much wiser to head downhill, cross the Nessus, skirt Tarentum slyly while the citizens still organized themselves, then light out for greener pastures. No stranger to travel, Pythagoras had sojourned far and wide, residing for extended stretches in Thebes and Babylon, not to mention Athens, Rhodes, and now the rustic backwater of Tarentum. Surely he would easily find a new home in a land where the people were more understanding of the needs of genius.

  Assuming he could bypass rustic Tarentum with his skull intact.

  For the first time in many months, Pythagoras descended the scree-strewn slope that led from his cave. His golden thigh throbbed, but whether from simple exertion, in warning of some evil to come, or in memory of Eurythoë’s delicate touch, the savant could not say.

  The Nessus was bridged by but a single structure. Though it was too distant to be quite sure, it looked as if the dregs of Tarentum might be massing there. His enemies. To avoid the brutal herd, Pythagoras would need to cross the river Nessus on his own. Though there was no convenient ford, he had no fears about traversing the flood.

  On the weedy banks of the river, well upstream of the bridge, half-concealed amidst some fragrant bushes, Pythagoras halted. Summoning up the Braided Worm’s number of the river, poising the form in his mind, the philosopher dangled his hand into the water.

  At his touch, a pair of liquid lips big as a man’s body cohered on the surface of the gurgling waters, like bas-relief on an Assyrian temple.

  “Greetings, Pythagoras!” said the Nessus, its voice like a pair of fish slapped together. “You have not visited in too long. Shall we resume our discussion of Atlantis?”

  “I haven’t time now, my friend. Enemies are near. Can you bear me safely across your width?”

  “Gladly. Indeed, I can carry you dry for as long a distance as you like.”

  Pythagoras thought for a moment. “Very well, then, bear me downstream past the furthest limits of Tarentum.”

  “Step atop my flow.”

  Continually keeping the River Number in his mind, Pythagoras walked out across the top of the river and seated himself cross-legged upon the surface in midstream.

  The water felt smooth and cool beneath him, a bit like a leathern cushion to the touch. The current swept him downstream towards the bridge.

  Yes, just as he’d feared, a motley mob of the ignorant were gathered there, with Glaucas and Pemptu
s at their head. Armed with sickles, slings, pitchforks and the occasional sword, the citizens watched gawking and gape-mouthed as the reviled philosopher surged toward them. But now Glaucas gave a high cry and the attack began. A stone splashed into the water but one cubit from Pythagoras’s chest, then another, and then a spear.

  Without losing his focus upon the River Number, Pythagoras moved another of his power-numbers into a fresh part of his mind. It was a Cloud Number, the gift of the Swarm of Eyes. He invoked the vast, inchoate magnitude, and was instantly enveloped in a great bank of impenetrable fog. Thus cloaked from view, he got to his feet and walked to a new position upon Nessus’s rushing stream. Cries of fear and anger sounded from above and missiles splashed into the river at random.

  Nessus bore Pythagoras onward, hastening toward the sea. As the river and the philosopher traveled along, they discoursed. “Searching your mind, I see an interesting maxim ascribed to the philosopher Heraclitus,” said Nessus. “No man steps in the same river twice. But is not my form always the same? Do I not ever respond to the same number?”

  “Yes, your essential form remains the same,” answered Pythagoras. “But, as a river, your watery substance is ever-changing. Heraclitus’s teaching has a subtler and more esoteric meaning as well. A man is like a river in that his substance also changes from day to day, not so rapidly as a river’s, but just as ineluctably. One could even say No man kicks the same stone twice. The stone may be fully the same, but the man is not the same, nor is the man-kicking-stone. For a man, as for a river, all is flow. May I ask you a question now, Nessus?”

  “Verily you may,” said the great watery lips that rode the surface at Pythagoras’s side.

  “Last night I received the knowledge of a number from the Crooked Beetle,” said Pythagoras. “The Beetle said this was the last of these magical magnitudes that I shall learn. If hold it up in my mind can you study it and tell me it’s meaning? I need to know how to use it. I feel I will need every arrow in my quiver for the trials to come.”