Complete Stories (80 page)

The citizens pressed forward, each carrying a stone, a few of them leaning close to hiss curses of execration, bur surprisingly many whispering words of comfort. The rebellious Alcibedes was missing from the line of citizens, but Eurythoë and Archytas were there, forced forward by a soldier with a drawn sword. Their stones were no larger than hens’ eggs, yet they of all the weights felt the heaviest of all.

Breathing was quickly becoming an impossible task for the old man’s frail chest. Letting the air out was easy, but drawing the air back in—ah, there was the bring-down, there was the drag. The sun blazed in Pythagoras’s eyes and a buzzing filled his ears. Something shiny came at him—a fat beetle, landing on his chin. The citizens filed by, still placing their rocks. The omen of a glistening insect upon the tortured man’s face was so inauspicious that each of them felt impelled to look away.

The beetle gave a modulated buzz, and Pythagoras let himself imagine he could hear it as words. “Use the number I gave you, fool,” the beetle seemed to say. “Focus!”

Another stone descended, followed by yet another, and that one by a third and fourth. Pythagoras felt his ribs compress and snap, pain flooding him like liquor from Hades. Into his blood-buzzing ears came the noises from the crowd of watchers: taunts and shouts and a lone female sob.

“Enough now,” yodeled Glaucas, who’d been closely watching the torture from one side. “The man is broken. Remove the rocks. You three slaves over there, carry him to the riverside midden to expire. It will be fitting for Pythagoras to exhale his soul into the fumes of human waste. That should be
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enough for him.” Glaucas raised his voice to a yet higher pitch. “Let this be a warning to any who would challenge my might! I am as a God, and all must bow down before me.”

Far from prostrating themselves, the citizens simply stared at Glaucas. This unpleasant execution seemed to be doing the King’s popularity no good. And many were the hands that reached out to remove the rocks and the door from Pythagoras.

When the weight went away, Pythagoras’s punctured lungs snatched whistling breaths of sweet air. At some far remove he witnessed himself lying uncovered in the forum, saw the weeping Eurythoë and Archytas bid him farewell, and saw his bloody form tossed onto a rude cart and trundled through the streets by three slaves. He was beyond pain now, well into the tunnel to the Elysium. He was ready for the end.

Yet his progress into the final ecstasy kept being thwarted by something nipping at him, buzzing, tickling. Either it was the bug upon his face, or it was a vision of the Crooked Beetle. At this point inside and outside were the same.

“You did well to speak for us, Pythagoras,” said the bug or the Beetle. “You are a worthy man. Now use my number.”

“Hhhhhow,” came Pythagoras’s faint sigh.

Emerging from within the Crooked Beetle’s very mandibles, the Bristle Cat said, “We can’t tell you what the number means, because if you don’t know it yourself you don’t know yourself to know nohow. Contrariwise if I tell you to know there’s no you knowing, you know?” The Beetle pinched irritably at the smirking Cat, but the protean beast drew its head down into its body, sending a commensurately-sized pink bulge out from its rear.

The shock of Pythagoras’s body landing in the dump caused his eyes to flicker open. He was fully anaesthetized and paralyzed by his body’s collapse. His filmed eyes stared dully upwards. The slaves who’d had brought his corpse thither walked away, laughing at the lot of the only citizen worse off than themselves.

Pythagoras tried to inventory his pitiful condition. He lay beneath a dead tree of bare polished wood beside a sparkling filth-choked rivulet worming through the dump. A swarm of glistening flies buzzed around his chest wounds, tasting of the fresh blood. And there was a beetle crawling on his nose; from the corner of one eye he could see it. A tufted yellow cat came ambling up, leaning over to taste, like the flies, of his hot, sticky blood.

His vision grew fainter; his heart beat as weakly and erratically as an infant drummer; his lungs drew in only the most shallow of painful draughts; his broken bones jabbed like a thousand daggers. From these incredible wounds, he would never heal. This was the end.

Pythagoras could feel his densely cultivated mind beginning to disintegrate. Strange, to imagine that such a unique individual as himself could disappear, that a being composed of such hard-won constituents could simply dissolve. His golden thigh began to throb then, as if to remind him of all the ways he differed from other mortals. Focusing on that preternatural portion of himself, Pythagoras was reminded of the great magical numbers that this memory enhancement enabled him to store. The numbers for Sheepskin, River, Fire, Cloud and —

A great revelation struck the dying philosopher with titanic force. The fifth number-form represented the quintessence of Pythagoras. Of course! Summoning all his vaunted powers of concentration and willpower, Pythagoras took mental control of the fifth number, then projected it outward from inside his dying self with explosive force —

He had a moment of dual vision. On the one hand he was dying, moving forward through a tunnel towards an all-encompassing white light. On the other hand, he was standing in the dump, looking down at the tormented form of poor old man.

Pythagoras held up a vigorous, apparently normal arm before his eyes, and laughed heartily. Triumph, even over death! Such were the godly rewards of his brave explorations of the
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. He took a deep breath into easily working lungs, then swung a fist to thump himself on his chest.

Much to Pythagoras’s alarm and surprise, his fist merged with his torso like the obscene bodily involutions of the Bristle Cat! At that moment, a familiar voice rang out. It was an apparition of the Crooked Beetle, floating as a large dusky ghost above the physical beetle that was still perched upon his old body’s face.

“Hail, Pythagoras!” twittered the Beetle, seemingly in ecstasy over the philosopher’s new body. “Welcome to life as a pure mathematical form! I encrypted you rather nicely, don’t you think? I did the basic encoding that night I first bit you. And all along I’ve been updating the Pythagoras number to include your most recent thoughts. That’s what I was doing sitting on your face just now. Keeping your number right up to the minute. You remember everything, don’t you?”

Pythagoras nodded mutely, and pulled his limb from his chest with a queer, unnamable sensation. Ranged around him were also ghostly forms of the Tangled Tree, the Braided Worm, the Bristle Cat, the Swarm of Eyes. Each of them was connected by the finest of tendrils to their earthly instances here in this malodorous dump.

“Your new, numerically defined body still has only a not-quite-life,” explained the Beetle. “It’s unreal in the same way that your number-conjured flames are but colorful tetrahedra until being boosted into full reality by the presence of the elemental Fire within the kindling wood. Your broken old body—it contains
your
kindling.”

Pythagoras looked down at his dying carcass with a feeling of revulsion. It was as uninviting as a soiled, wet toga. “You’re not counseling me to don that same old mortal coil, are you?”

The Crooked Beetle spat, not a number this time, but a viscous dark glob that landed on Pythagoras’s foot with a tingling sensation. It was a tiny, crooked copy of the Beetle itself, connected to the ghostly Beetle by another of the thin, silken strands. The new beetle stretched out its wings, waved them tentatively, then buzzed into the air. “I don’t like to explain everything,” said the great Beetle.

“You need your you to be you,” said the smiling Cat, rubbing against Pythagoras’s ghostly leg, and then passing right through it. “Be your own son and father.”

“Breathe in what you expire,” buzzed the Swarm of Eyes.

The Braided Worm beside the little brook swayed back and forth like a charmed snake. “Don’t fail us, Pythagoras. It still remains for you to prove your greatest result—to prove that we are real.”

“So bend down and breathe in your dying breath!” exhorted the Tangled Tree, gesturing with every one of its innumerable branches.

Of course. Now Pythagoras remembered the custom whereby a child would try to breathe in the last breath of a dying parent. His insubstantial body knelt at the side of his supine flesh. With eyes near-blinded by the light of eternity he stared up at his fresh-minted body. With clear fresh new eyes he stared down at his old self. Now came the dying man’s final breath, the expiration, and Pythagoras’s number-built new body breathed it in.

From the viewpoint of his old self, Pythagoras felt as if he’d been yanked out of paradise. He felt grief and a kind of homesickness at not fully merging with the divine One whose hem he’d only just begun to touch. From the viewpoint of his new self, Pythagoras felt invigorated, renewed and—above all—solid and real. And then he was no longer two, but one. The infinitude of his divine soul had now fulfilled the incarnation of the number-model of his body.

Looking around the dump, Pythagoras could no longer see the ghostly images of his
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friends—and friends they truly were, not rivals or enemies. Their earthly avatars still here upon the midden remained mute: a tree, a worm of water, a cat, a swarm of flies and a beetle. Pythagoras fully felt how truly these earthly forms did embody the
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, felt more strongly than ever the undivided divinity that is present within all things, whether great or mean.

His new-made body felt strong and sound, though not overly so. The number form was, after all, only that of an old man. But he was no longer an old man who’d been crushed to death by stones. There was one more change as well. The adamantine gold was gone from his thigh, and looking within himself he saw that he’d lost his knowledge of the five magic numbers. He was glad.

So what to do next? Most important was to see Eurythoë. And the Braided Worm had said something very intriguing about Pythagoras having another great result to prove. Perhaps the simplest would be to go back to his cave, receive visitors as always, and continue to think about mathematics. Surely his resurrection would frighten Glaucas into leaving him alone.

But before doing anything else, Pythagoras tended to his soul’s former shell. Gripping the corpse by the shins, Pythagoras bumped it across the slope of the midden and into a patch of trees. He lacked any shovel to dig with, but he used a stick to scrape out a shallow grave, and then gathered a great heap of brush to decently cover the body. It took a long time, several hours in fact, but what did time matter to a man risen from the dead? While he worked, the rudiments of a new and wonderful theorem began coming to him. It hinged, as he’d suspected, on the ratio of a square’s diagonal to its side.

His earlier theorem of the right triangle said that the square on a diagonal is equal to the sum of the squares on the two sides. If the two sides were equal, this meant that the diagonal square was twice the magnitude of each side square. Put differently, a diagonal square and a side square were in proportion two to one. And put differently once again, the ratio of the diagonal to the side could be called the “square root of two”.

For several years now, Pythagoras and his followers had sought for a whole number ratio to represent this curious “square root of two.” The search involved looking for squares that were in a perfect two to one ratio. 49 to 25 was close and 100 to 49 was closer, which meant the square root of two was close to the ratio 7/5 and closer to the ratio 10/7. But the match was never quite perfect, and now that he’d finally let the
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all the way into his heart, Pythagoras fully grasped that the match never would be perfect at all. There was no whole number ratio precisely equal to the square root of two.

He found himself singing a happy tune as he finished up the reverential chores of covering his corpse. Now that he fully understood what he wanted to prove, he would find a way to do it. Mulling over the distinctions between odd and even numbers, Pythagoras set out towards Tarentum. The clever Archytas could help him hone a proper proof.

At the edge of the dump, Pythagoras encountered Eurythoë, her face wet with tears. She was dressed in the black garments of mourning. For him? She didn’t really see him, for she was too busy peering past him, looking for his body on the dump.

“Woman, why are you weeping?” said Pythagoras. “Whom do you seek?”

Eurythoë wiped her face with the black cloth of her veil. “Sir, if you have carried him off, tell me where you have laid him, and I will take him away.”

Pythagoras spoke her name. “Eurythoë.”

She turned and fully saw him at last. “Pythagoras!”

“My dear, even-souled Eurythoë. The
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has saved me. Good as new.” He chuckled and skipped about, executing a little twirl.

“My dear, odd-brained Pythagoras,” sang Eurythoë. “But what of your madness?”

“What madness? Believe this, woman, I’m working on a proof of the reality of the
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! It all has to do with evens and odds.”

“Then I can help you! Let’s go up to your cave.”

“Right now? What about Glaucas and the priests?”

“Glaucas is dead,” said Eurythoë, seemingly not overly saddened by having to deliver this news. “Alcibedes slew him only minutes after they carted your body away. My son Archytas is the new king, and the populace rejoices. The priests of Apollo will do as Archytas says. We already have Turnus’s abject assurances.” She burst out laughing. “Glaucas is the official reason why I’m wearing mourning. But, O Pythagoras, it was only for you.”

“I should speak to Archytas,” said Pythagoras. “About the wonderful new proof.”

“We’ll do that later,” said Eurythoë, kissing him. “After the cave. I want to give you a proper welcome.”

“Very well then,” said Pythagoras. “Let’s take the bridge across the river.”

“No more sorcery?” said Eurythoë.

“No,” said Pythagoras. “Just mathematics.”

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