Cantor’s Dragon, by Craig DeLancey

Georg Cantor waits while his wife Vally pulls at the heavy door to the Nervenklinik. The crisp air smells of leaves and wood smoke, but as they pass into the white-tiled halls disinfectant envelops them.

The nurse comes and introduces herself. Cantor says nothing. He has not spoken in a month. He rarely even focuses his eyes. The nurse leads them down long passages. Their shoes snap at the marble floor. After many turns, they stop at a white door that opens to his room: a narrow bed covered with taut white sheets, a comfortable chair facing a window that looks out onto a lawn edged by waving oaks, a round rug on the cherry floor.

Vally seats him in the chair. “You need rest, Georg,” she whispers.

Cantor looks out at the oaks. They hold tenaciously to their last few leaves.

To the nurse Vally says, “We lost our dear son Rudolf. That was hard. And my husband is a professor. A mathematician. He has achieved great things. But the strain is great. And then, that wretched Kronecker in Berlin. It’s all too much.”

The nurse nods, professionally sympathetic as she straightens the room. The name means nothing to her, but the point is clear: the cruelty of other men.

Vally leaves, followed by the nurse, whose soft shoes squeak as she backs out and pulls the door till its lock clicks. Cantor holds his breath and listens. The rustle of scales against plaster is faintly audible. He expected this. The dragon is here already, coiled in the walls of the clinic.

Cantor stands and presses his cheek to the cool plaster by the window. “I hear you, wyrm,” he says.

The dragon rustles in response, contracting.

“Wyrm,” Cantor whispers, to provoke, to invoke.

Cantor kissed his son’s forehead after the boy coughed blood one last time and stopped breathing. Vally gasped and held her breath. The doctor backed into a corner, ashamed. And Cantor heard, distinctly, an eager rustling in the walls.

dragonTwo days later, when Cantor finally collapsed into sleep, he had the nightmare that silenced him and led him to the brittle quiet of the Nervenklinik.

He sees a rising narrow stair. It stretches up and up. Beyond its peak a golden light glows, pale and weak with distance. Children sit and stand on the stair. Most of them weep as they peer at the impossible summit, wishing they could catch some sliver of its meager warmth. Others have collapsed with despair, their backs turned on the light.

“Climb!” Cantor cries to them. But his voice is a choked moan. It moves no one.

That’s when the horrible thought comes to him: Rudolf is on that slope. With his weak lungs, his throat choked with blood, and without his father, Rudolf will give up. He is halted on the way, in the half darkness.

“Climb!” Cantor tries to howl. The effort does nothing but wake him.

The second night in the clinic, after the nurse leaves with the dinner plates under silver lids, clucking disapproval because Herr Doktor has merely tasted his food, the dragon folds the wall aside. Cantor is surprised. He did not know the dragon had this trick. He half expected the dragon did not exist.

It pulls at a corner, and the plaster bends neatly away. Someone will prove that kind of folding is possible, Cantor realizes. He sees in an instant how it works: sets of uncountably many points can be rearranged into new, smaller spaces.

But Cantor has other, more pressing thoughts. He beholds the dragon’s black head, its black shining scales, the smooth and sensitive circular membrane of each ear, vibrating behind a black eye. Cantor cannot discern the dragon’s tongue from the flames that churn in the cup of its jaw. Fire rattles in its throat, a sound like Rudolf’s failing lungs.

The dragon is waiting on his words. It too expects him to speak.

Cantor frowns, silent and furious. Outside, strong winds turn the last leaves of the oaks over, flashing white. Black clouds speed over the bending trees and weep rain on the windows. Thunder rumbles so close that the glass rattles in the sash. Finally, Cantor can hold back his anger no longer. He hisses, “Wyrm, did you kill my son?”

Cantor knows his son died of consumption. He knows that black spots ate the boy’s lungs. But he asks again, “Wyrm, was that you, coiled in the bottom of his breath, weighing down his every gasp?”

“I am infinite,” the dragon whispers, goaded to answer, “but not everywhere.”

They are silent together a long while. Wet gusts lash the glass. Then Cantor tells the dragon, “Kronecker says I am mad: that no such thing as infinity exists, and I am a fool to claim to have tamed it. And: I talk to a dragon. The dragon cannot exist. Hence, I talk to something that does not exist. Ergo, I am mad. But about the infinite, I don’t believe I am mad. The infinite exists. Endless infinities, each larger than another.”

The dragon shifts and scratches at a scale with a single stony toenail. “How do we know if something exists?”

“If a thing would spawn no contradiction, then that thing exists.”

The dragon stretches out its neck and lifts its wings as best it can in its parallel confines. The delicate black skin hisses over the coarse, unfinished wood slats that make the back of the wall.

“And what of the dragon?” it says. “Can there be a dragon? A beast that ate too, too much? That feasted on human hopes? Count my scales. They are as numerous as numbers. My dragon brain lies folded in my scaly tail. And my tail stretches forever.” The dragon blows twin streams of pale smoke from its nostrils: dragon laughter. The gray fumes smell of coal heavy with sulfur. “But I contradict nothing: no hope, no faith, no prayer. Thus the dragon exists.”

“Quod erat demonstratum,” Cantor whispers.

There were days when his son stopped coughing blood. One April morning they went out to the park. They sat in the grass, with Rudolf wrapped in a blanket. Crocuses thrust up through the cold, damp soil. Rudolf picked them, and Cantor did not stop him, did not ask that he wait till the blooms opened. Rudolf might not live till the blooms opened.

“You take three, father,” the boy said. He always whispered, not wanting to start a coughing fit, not wanting to punctuate his words with blood. “And I’ll take three. Six is all there are.”

“Others will grow,” Cantor told him.

“For how long?”

Cantor considered this. “For so long, that it might as well be forever.”

The boy nodded. “Time enough, then.”

Vally brings Cantor a letter from a priest in Italy. The Pater writes to ask if the infinities of Cantor contradict the finitudes that Saint Thomas Aquinas demanded of the pious. Cantor is excited. He sees in an instant how the church needs his wisdom.

“I shall abandon mathematics,” he says. “And dedicate myself to philosophy and God. Theology. The Church.”

Vally smiles with hope and relief. Georg is talking to her! Like his old self!

She clutches his hands. “Yes,” she says. “You have your inheritance. We shall be fine. Come home to us. Don’t worry about those men who spurned you. They’ll be forgotten. We miss you at home. You’re such a fine father and husband. The doctor will let you come home soon, I’m sure.”

Even the dragon has seen Cantor’s kindness. At dinner every night Cantor had asked each of his children in turn to tell the story of his or her day, before he looked to his wife and said, “Thank you for this meal.”

Every day the same. The precision of a mathematician in attending to these cares: axioms of love.

“You’ll leave before the winter,” the dragon says one gray afternoon. Cantor is surprised. He thought the dragon could speak only if spoken to.

“Before the winter,” Cantor says.

“And I will curse you.”

“What empowers you to curse, wyrm?”

“I curse everyone who wonders.”

“On such a foundation I too might have this power, and curse you in kind.”

The dragon smiles, the corners of its lizard mouth curling. “My curse comes first. Soon you’ll die…”

“Soon each mortal dies,” Cantor says impatiently. “That is no curse.”

“That is not the curse,” the dragon says. “Soon you’ll die. Then you must decide between heaven and hell. Hell is near and crowded. God is infinitely far away. If you are to ascend into heaven, you must take the Dragon’s Stair. This is my curse.” The dragon shifts his head to reveal, in the dark behind his vast bulk, a narrow stair of stone.

“The first step on the stair is carved with a name,” the dragon says.

“The second step is carved with a name.

“The third step too is so carved.

“Yes, on each step is cut a name.”

And Cantor can see the names on the risers of the first stone slabs. Falcon Ells. Edgar of Canterbury. Danniston. Ali Quartermain…

“God is at the top,” the dragon says. “You climb toward God. But if you find your name on a step, you must stop there, and wait. You must wait until Judgment Day, both feet on your stone plinth.

“And Judgment Day has never come.

“Judgment Day, like God, is infinitely far away.

“No saint has made it up the stair. The innocent wait, despairing, along the way.

“Heaven is empty.”

Rudolf was usually fearless. But when he last lay down in his bed, never to rise again, he said to Cantor, “I’m scared, Papa.”

Cantor fought his tears with all his strength. He did not want to weep in front of the boy and betray his failing hope. He managed to say, “Our bodies must die. But our minds, our minds can touch the infinite.”

Rudolf nodded his head very slightly, his mouth pressed closed in determination.

“And,” Cantor said, “you must have faith that you cannot fail to find your way to God.”

“But will I be alone?” Rudolf whispered.

“Only ever for a little while. I promise you, only for a very little while.”

Outside the clinic, the leaves on the oaks darken and curl as autumn ages. Cantor scrawls symbols on stolen scraps of paper, working in secret because he has promised to remain at leisure.

dragon2“Wyrm, what is it you do, when you are not haunting me?” Cantor asks.

The dragon folds down the wall. “I sing from rooftops, hidden from view. I paint murals on buried walls. I pen short stories that are printed in little magazines. All to infect dreams.”

“Braggart,” Cantor says. Then he switches direction: “Who decides my name?”

The dragon understands the question immediately. “You do.”

Cantor smiles. “Can I name myself while climbing the stair?”

The dragon thrashes its tail in anger. It growls, and blows smoke, before it answers. “You must start to say your name before stepping upon the way.”

“But I need not finish naming myself before starting on the way?”

The dragon is silent an hour. Cantor listens to the fire fluttering in its lungs. He patiently writes out his proof as he waits for his answer.

“No,” the dragon hisses, leaking flames that cast flickering shadows along the walls. “You need not finish naming yourself before starting on the way.”

“I choose heaven,” Cantor says.

“Do not be hasty. You can wait till death before you choose.”

“I choose heaven,” Cantor repeats. “And I will choose a name for myself, a name to be writ in the Book of Judgment and to which I will answer.

“And the first letter of my name will be the letter in the alphabet that comes after the first letter of the name of the first step of the Dragon’s Stair. If it be A, I will choose B. If it be B, I will choose C. And so on. If it be Z, I will choose A.

“And the second letter of my name will be the letter in the alphabet that follows the second letter on the second stair.

“And so I will make my name, letter by letter, step by step, as I ascend.

“And this name cannot be writ on any step.”

The dragon clamps its trembling eyelids down and squeezes its mouth shut hard, choking on its own fires. Bested.

The wall is straight and white when the dawn comes. Cantor puts both hands on the plaster by the window, and says in a clear voice, “Here is my curse, dragon. You must tell, to all who will hear, this story of how I beat you.”

Before the dragon can answer, Vally pushes open the door. The nurse has brought a key that allows her to open the window. She slides the glass upward. Fresh air stirs in the room. The leaves have all fallen now from the oaks. The trees wait for the sleep of winter.

Vally packs Cantor’s few things. Her hand on his arm, they walk out into the hall and on into sunlight.

“Soon you’ll be dead,” the dragon hisses. No one hears. “Soon you’ll be alone in heaven.” But this is only spite. The dragon well knows that as Cantor rises on the way, he will gather to himself all the children of judgment and show them the way to infinity.

fin

Craig DeLancey is the author of Gods of Earth. He has published stories in Analog, Cosmos, Shimmer, The Mississippi Review Online, Nature Physics, and other places. His short story “Julie is Three” won the Anlab reader’s choice award. He teaches philosophy at Oswego State. Stop by his web site at www.craigdelancey.com.

Craig DeLancey
Craig DeLancey

 

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