The Way of the Wizard

Counting the Shapes Yoon Ha Lee

How many shapes of pain are there?

Are any topologically equivalent?

And is one of them death?

Biantha woke to a heavy knocking on the door and found her face pressed against a book’s musty pages. She sat up and brushed her pale hair out of her face, trying to discern a pattern to the knocking and finding that the simplest one was impatience. Then she got to her feet and opened the door, since her warding spell had given her no warning of an unfriendly presence outside. Besides, it would be a little longer before the demons reached Evergard.

“Took your time answering the door, didn’t you, Lady Biantha?” Evergard’s gray-haired lord, Vathré, scowled at her. Without asking for permission, which he never did anyway, he strode past her to sweep his eyes over the flurry of papers that covered her desk. “You’d think that, after years of glancing at your work, I’d understand it.”

“Some of the conjectures are probably gibberish anyway.” She smiled at him, guessing that what frustrated him had little to do with her or the theorems that made her spells possible. Vathré visited her when he needed an ear detached from court intrigues. “What troubles you this time, my lord?”

He appropriated her one extra chair and gestured for her to sit at the desk, which she did, letting her smile fade. “We haven’t much longer, Biantha. The demons have already overrun Rix Pass. No one agrees on when they’ll get here. The astrologer refused to consult the stars, which is a first — claimed he didn’t want to see even an iffy prediction—” Vathré looked away from her. “My best guess is that the demons will be here within a month. They still have to march, overwhelming army or no.”

Biantha nodded. Horses barely tolerated demon-scent and went mad if forced to carry demons. “And you came to me for battle spells?” She could not keep the bitterness from her voice. The one time she had killed with a spell had been for a child’s sake. It had not helped the child, as far as she knew.

“Do you have any battle spells?” he asked gravely.

“Not many.” She leaned over and tapped the nearest pile of paper. “I was in the middle of this proof when I discovered that I’d have to review one of Yverry’s theorems. I fell asleep trying to find it. Give me a few days and I can set up a battle spell that will kill any demons you’ve already managed to wound.” Biantha saw the weariness in the lord’s green eyes and flushed. “It isn’t much, I know.”

“That helps, but it isn’t what I came for.”

Dread opened at the pit of her stomach. “The Prophecy.”

Vathré inclined his head.

“I’ve tried to pry some sense out of it ever since I learned of it, you know.” She rubbed her eyes. “The poetry translates into shapes and equations that are simply intractable. I’ve tried every kind of analysis and transformation I know. If there’s any hope in the rhymes, the rhythms, the ambiguities, don’t ask me to show you where it is. You’d do better consulting the minstrels for a lecture on symbolism.”

“I don’t trust the minstrels.” His brows drew together. “And any time I consult the other magicians, I get too many uncertainties to untangle. The seers and healers are hopeless. The astrologer gets headaches trying to determine where to start. The cartomancer gives me a dozen different possibilities each time she casts the cards. As far as the Prophecy is concerned, yours is the only kind of magic I can trust.”

Biantha smiled wanly. “Which is why, of course, it’s so limited.” Sometimes she envied the astrologer, the cartomancer, the enchanters, the healers, the seers — magicians whose powers were less reliable but more versatile. “I’ll work on it, my lord.”

“A month,” he reminded her.

She hesitated. “Have you declared your heir yet?”

Vathré eyed her. “Not you, too?”

She swallowed. “If you die, my lord, someone must carry on. Don’t leave the succession in doubt. A problem may have several solutions, but some solutions can still be wrong.”

“We’ve been over this before,” he said. “Considering the current state of affairs, I’d have to declare a chain of succession down to the apprentice cook. If anyone survives, they can argue over it. My advisors can rule by council until then.”

Biantha bowed her head and watched him leave.

Usually Biantha avoided Evergard’s great hall. It reminded her of her former home, the demon emperor’s palace, though the scents of lavender and lilacs drifted through the air, not the smell of blood; people smiled at her instead of bowing or curtsying rigidly. Musicians played softly while nobles chattered, idle soldiers gambled for pittances, and children scampered in and out, oblivious to the adults’ strained voices. A few of the boys were fair-haired, like herself. Biantha closed her eyes briefly before turning along the walls, partly to avoid thinking about a particular fair-haired boy, partly because she had come to study the tapestries for inspiration.

The tapestries’ colors remained as vibrant as they had been when she first swore fealty to Lord Vathré upon the Blade Fidora. Biantha had long ago determined the logic by which the tapestries had been arranged, and did not concern herself with it now. Instead, she inspected the scenes of the Nightbreak War.

Here was the Battle of Noiren Field, where webs of starlight blinded a thousand soldiers and angular silhouettes soared above, ready for the massacre. Here was General Vian on a blood bay destrier, leading a charge against a phalanx of demons. Here was amber-eyed Lady Chandal weeping over a fallen young man whose closed eyes might also have been amber, flowers springing up where her tears splashed onto the battlefield. Biantha swallowed and quickened her steps. One by one she passed the tapestries until she found what she sought.

Unlike the other Nightbreak tapestries, its border had been woven in rust rather than Evergard’s colors, blue and black: rust for betrayal. She stared at the dispassionate face of Lord Mière, enchanter and traitor to Evergard. His had been a simpler magic than her own, drawing upon ritual and incantation. With it he had almost defeated the Watchlanders; only his daughter’s knife had saved them.

Symmetry, she sighed. The one thing she had pried from the Prophecy was that it possessed a twisted symmetry. It hinted at two wars between the demons’ empire and the Watchlands, and because records of the first war — the Nightbreak War — were scant, Biantha had yet to understood certain cantos, certain equations, that dealt with it. Hours with Evergard’s minstrels and historians hadn’t helped. Other than herself, only Vathré knew that there might be a second traitor among them.

Or that, because they had won the first war, they might lose the second, in a cruel mirroring transformation of history.

“Lady Biantha?”

She turned. “Yes?”

The captain — she did not know his name — bowed slightly. “It isn’t often that we see you down here, my lady.”

Biantha smiled wryly. “A bit too much noise for my work, and on occasion I test spells that might go wrong, sometimes fatally so. My chambers are shielded, but out here… ”

In the demon emperor’s court, her words would have been a veiled threat. Here, the captain nodded thoughtfully and gestured at the tapestry. “I was wondering why you were looking at this. Most people avoid it.”

“I was thinking about the Prophecy,” she said, retracing the intractable equations in her mind. There had to be a way to balance term against term, solve the system and read Evergard’s future, but it continued to escape her. “I’m worried.”

“We all are.”

Biantha paused. “You said ‘most people.’ Does that include yourself?”

His mouth twisted. “No. It’s a useful reminder. Do you ever wish you had stayed at the demon emperor’s palace?”

She read honest curiosity in the captain’s expression, not innuendo. “Never.” She breathed deeply. “I started learning mathemagic there because magicians, even human magicians, are protected unless they do something foolish. Otherwise I would have been a slave or a soldier; I had no wish for the former and no heart, no talent, for the latter.”

Such a small word, foolish, when the penalty it carried had given Biantha nightmares for years. She had seen the demon emperor touch his serpent-eyed scepter to a courtesan’s perfumed shoulder, as if in blessing; had been unable to avert her gaze before she saw the woman’s eyes boiling away and splinters of bone erupting through the rouged skin.

The captain looked down. “I’m sorry to have reminded you, my lady.”

“A useful reminder,” she echoed. “And what does this portrait of Lord Mière remind you of, if I may ask?”

“Honor, and those who lose it,” he said. “Lord Mière was my great-grandfather.”

Biantha blinked and saw that there was, indeed, a resemblance in the structure of his face. Her eyes moved to the tapestry’s rust border. What had driven Mière to betrayal? It occurred to her, not for the first time, that she herself had fled the demon emperor’s court — but the symmetry here seemed incomplete. “Do you think there’s hope for us?” she asked the captain.

He spread his hands, studying Biantha’s face as she had his just a moment before. “There are those of us who say we must have a chance, or you would have returned to the demons.”

She felt herself flush — and then laughed, though that laughter came perilously close to tears. “I have rarely known demons to forgive. Neither have they forgiven Evergard their defeat in the Nightbreak War.”

“More’s the pity,” said the captain, frowning thoughtfully, and took his leave.

For us or the demons? Biantha thought.

Symmetry. The word haunted Biantha through the days and nights as she struggled with the Prophecy. She had wondered, after meeting the captain, if it meant something as simple as her flight from the demons, the fact that one of Lord Mière’s descendants survived here. The ballads said Mière had but a single daughter, named Paienne, but they made no mention of her after she saved the Watchlands.

The secret eluded her, slipped away from her, sent her into dreams where dizzying shifts in perspective finally drove her to awaken. Biantha turned to her tomes, seeking clues in others’ mathemagical speculations; when she tired of that, she memorized her battle spells, bowing to the heartless logic of war. And went back to the tomes, their treasury of axioms and theorems, diagrams and discussions.

She was leafing through Athique’s Transformations when someone imitated thunder on her door. Biantha put down the book and opened the door. “Yes?”

The herald bowed elaborately. “A meeting of the court, my lady. Lord Vathré wishes you to attend.”

“I’ll be there.” Firmly, she shut the door and changed into her formal robes as swiftly as she could. Biantha had attended few court meetings: at first, because Vathré had been uncertain of her loyalties, then because of her awkwardness as a foreigner, and finally because she rarely had anything to contribute to matters of state and found her time better spent working on her magic. That Vathré should summon her now was unusual.

She was right. For once the attendants and servants had been cleared out, and the court had arrayed itself along the sides of the throne room while Vathré and his advisers sat at the head. She took her place between the astrologer and Lady Iastre. The astrologer wore his habitual frown, while the lady’s face was cool and composed, revealing nothing. Biantha knew better, after playing draughts or rithmomachia against Iastre once a week in less hectic times: Iastre’s face only went blank when she anticipated trouble.

“We have a guest today,” said Vathré at his driest. His eyes might have flicked to Biantha, too briefly for her to tell for certain.

On cue, the guards led in a man who wore black and red and gold, stripped of his sword — she knew there had been a sword, by the uniform. The style of his clothing spoke of the demons’ realm, and the only one besides the emperor who dared appear in those colors was his champion. The emperor’s champion, her son.

A challenge? Biantha thought, clenching her hands so they would not shake. Has Marten come to challenge Vathré? But surely the emperor knew Evergard held different customs and would hardly surrender the Watchlands’ fate to a duel’s outcome.

Hopelessly, she studied the man who had so suddenly disrupted her memories of the child who hid flowers and leaves between the pages of her books, who climbed onto her desk to look out the window at the soldiers drilling. He had her pale hair, a face very like hers. His hands, relaxed at his sides, were also hers, though deadlier; Biantha knew of the training an emperor’s champion underwent and had little faith that the guards could stop him from killing Vathré if he wished. But Marten’s eyes belonged to a man Biantha had tried to forget, who had died attempting to keep her from leaving the palace with their child.

Silence descended upon the throne room. Vathré’s court noted the resemblance, though Marten had yet to spot his mother. He looked straight ahead at Evergard’s lord.

Vathré stood and drew the Blade Fidora from its sheath. It glimmered like crystal, like the first light of morning, like tears. The lords and ladies glanced at each other, but did not set whispers spinning through the room. Biantha, too, kept silent: a word spoken false in the unsheathed sword’s presence would cause it to weep or bleed; the magic had driven men and women mad, and no lord of Evergard used it lightly.

“I am trying to decide whether you are very thoughtless or very clever,” Vathré said softly. “Who are you and why are you here?”

“I was the sword at the emperor’s side,” he answered, “and that sword was nameless.” The pale-haired man closed his eyes, opened them. “My name is Marten. I came because the emperor has thousands of swords now, to do his bidding; and I no longer found that bidding to my taste.”

Vathré glanced down at the Blade Fidora. Its color remained clear and true. “An interesting time to change your loyalties — if, indeed, they’ve changed. You might have found a better way to leave than by showing up here in full uniform, scaring the guards out of their wits.”

“I left when the demons were… subduing a village,” Marten said flatly. “I don’t know the village’s name. I hardly had time to find more suitable attire, my lord, and on campaign one dresses in uniform as a matter of course. To do otherwise would have aroused suspicion.”

“And you weren’t afraid of being caught and killed on the spot?” one of the advisers demanded.

He shrugged. “I was taught three spells in my training. One allowed me to walk unharmed through the palace wards. One calls fire from blood. And the last lets me pass by like the dream of a ghost.”

Biantha glanced at the Blade Fidora and its unwavering light.

Lady Iastre coughed. “Forgive me if I’m less well-informed than I ought to be,” she said, “and slow to react as well — but you mentioned being ‘on campaign.’ Is this a common thing, that ‘the sword at the emperor’s side’ should be out in the field?”

Marten’s eyes moved toward the source of the voice, and so he caught sight of Biantha. He inhaled sharply. Biantha felt her face freeze, though she longed to smile at the stranger her son had become. Answer, she wished him. Say you’ve come to me after so many years—

Marten gathered himself and said, “I came to warn you, if nothing else; death is a price I have taken from many.” His voice shook, but he continued to face Vathré squarely. “The demon emperor has come, and your battles will be the harder for it.” Then the whispers began, and even Iastre cast troubled eyes toward Biantha; the light of the Blade Fidora reflected all the shades of fear, all the colors of despair, that were voiced. “Please,” Marten said, raising his voice but slightly, “let me help. My lord, I may be slow in learning that there is more to war than following orders. That there are people who die for their homes or their families—”

“Families,” Biantha repeated, tasting bitterness. So calm, his face, like polished metal. She felt Iastre’s hand on her arm and forced a smile.

The whispers had died down, and Marten faltered. “I know how the emperor thinks,” he said at last. “Let me help you there, my lord, or have me killed. Either way, you will have taken the emperor’s champion from him.”

So pale, his face, like Fidora’s light. Biantha caught her breath, waiting for Vathré to speak.

Lines of strain etched the lord’s face as he left the throne to stand before Marten. “Will you swear fealty to the Watchlands and their lord, then?”

Marten did not flinch. “Yes.”

Yes, echoed Biantha, doubt biting her heart. She had not known, when she first came to Evergard, what powers the Blade Fidora possessed. A magician-smith had died in its forging, that there might never again be a traitor like Lord Mière. Vathré had questioned Biantha, as he had just questioned Marten, and the first part of the sword’s virtue had been plain to her, a mirror of spoken minds.

Only later had Vathré told her the second part, that a false oath sworn upon the sword killed the oath-taker. Once an heir to Evergard had sworn guardianship to the Watchlands and their people and fallen dead. Once a weary soldier had woken Evergard’s lady three hours before dawn to confess a betrayal planned, and then committed suicide. Biantha had no desire to find her son the subject of another story, another song. How had Paienne felt, she wondered suddenly, when her father’s treachery became part of the Nightbreak War’s history?

Marten laid his hand upon the glass-clear blade. “I swear it.” Then, swallowing, he looked directly at Biantha.

She could not bring herself to trust him, even after the long years, when he wore a uniform like his father’s. This time, she did turn away.

“There’s something sinful,” said Iastre, fingers running round and round a captured draughts piece, “in sitting here playing a game when our world is falling apart.”

Biantha smiled uncertainly and considered her options. “If I stayed in my room and fretted about it all the time, I should go mad.” She nudged one of her pieces to a new square, musing on how the symmetry of the game — red on black, black on black — had soon been spoiled by their moves.

“I hear it was Marten’s planning that kept the demons from overrunning Silverbridge so far.”

She looked up and saw Iastre’s worried expression. “A good thing, I suppose — especially considering that the emperor now has a personal reason for wanting to humble the Watchlands.”

“Surely you don’t think he should have stayed in the emperor’s service,” Iastre protested.

Oh, but he did once, Biantha did not say. “It’s your move.”

A snort. “Don’t change the subject on me now. You fled the emperor’s palace too, if you’ll recall.”

“Too well,” she agreed. She had slept poorly the first few years at Evergard, hearing danger in the footfalls that passed by her door and dreaming of the emperor’s serpent-eyed scepter upon her own shoulder. “But I left in a time of peace, and as terrible a crime as I had committed, I was only a human mathemagician. Besides,”—and Biantha drew in a shaky breath—“they knew they had my son: punishment enough.”

Iastre shook her head and finally made her move. “He’s here now, and he may be our only hope.”

“That,” she said, “is what worries me.”

Even here, playing draughts, Biantha found no escape from Marten. She had spotted him once in the courtyard, sparring against Evergard’s best soldiers while a healer and several enchanters looked on, lest the former champion seek a life instead of a touch. At mealtimes in the great hall she took to eating at the far end of the high table; yet over the clinking glasses and silverware, the tense voices and rustling clothes, Biantha heard Marten and Vathré speaking easily with each other. Evergard’s lord trusted Marten — they all trusted Marten now, while she dared not.

Like a pendulum, her thoughts swung between her son and Paienne, her son and Lord Mière. Late at night, when she walked the battlements listening vainly for the footfalls of marching soldiers, feeling betrayal’s cold hand in every tremor of the wind, she remembered tales of the Nightbreak War. Biantha had never put much faith in the minstrels’ embellished ballads, but the poetry preyed upon her fears.

Working with fragments of history and the military reports that came in daily, she attempted to map past onto future, battle onto battle… betrayal onto betrayal. And failed, over and over. And cursed the Prophecy, staring at the worn and inscrutable pages, alone in her room. It was during one of those bouts that a familiar knocking startled her from her work.

Marten? thought Biantha involuntarily. But she had learned the rhythm of Vathré’s tread, and when she opened the door she knew who waited behind it. The twin edges of relief and disappointment cut her heart.

The gray-haired man looked her up and down, and scowled. “I thought you might be overworking yourself again.”

She essayed a smile, stepping aside so he could enter. “Overwork, my lord? Tell that to the soldiers who train, and fight, and die for it, or see their friends die for it. Tell that to the cook or the servants in the keep.”

“There are ways and ways of work, my dear.” He paced around the chamber, casting a curious eye over her bookcase and her cluttered desk, then rested a hand on her shoulder. “Perhaps I should come back later, when you’ve rested — and I do mean rest, not sitting in bed to read your books rather than sitting at your desk.”

Biantha craned her head back to glance at him. “At least tell me why you came.”

“Marten,” he said bluntly, releasing her shoulder.

She flinched.

“You’re hurting the boy,” Vathré said. “He’s been here quite a while and you haven’t said a word to him.”

She arched an eyebrow. “He’s not the boy I left behind, my lord.” Her voice nearly broke.

“I’m old enough to call you a girl, Lady Biantha. Don’t quibble. Even I can’t find cause to mistrust him, and the years have made me paranoid.”

“Oh?” She ran her fingers over her copy of the Prophecy, worn smooth by years of on-and-off study. By all accounts, Marten’s advice was sound — but the demons kept coming.

“I’m sending him to command at Silverbridge.” Vathré shook his head. “We’ve held out as long as we can, but it looks like our efforts have been no more than a delaying action. I haven’t told the council yet, but we’re going to have to withdraw to Aultgard.” He exhaled softly. “Marten will keep the demons occupied while the bulk of the army retreats.”

Biantha stared at him.

“The soldiers are coming to trust him, you know,” he remarked. “He’s perhaps the best tactician Evergard has seen in the past couple generations, and I want to see if that trust is justified.”

She closed her eyes and said, “A gamble, my lord. Wouldn’t you do better to put someone else in charge?”

Vathré ignored her question. “I thought you should know before I announce it.”

“Thank you, my lord.” Biantha paused, then added, “Do you know where Marten might be at the moment?”

He smiled sadly. “Haunting the battlements, hoping you will stop by.”

She bowed her head and, after he had left, went to search for her son. Biantha found him by the southern tower, a sword sheathed at his back. Even now it disconcerted her to see him in the dress of Evergard’s soldiers, as if her mind refused to surrender that first image of Marten standing before the court in red and black and gold.

“Mother,” he said, clasping his hands behind his back.

Slowly, reluctantly, she faced him. “I’m here.”

Moonlight pooled in his eyes and glittered in the tears that streaked his face. “I remember,” he said without accusation. “I was seven years old and you told me to pack. You were arguing with Father.”

Biantha nodded. Marten had nearly reached the age where he would have to begin training as either a magician or a soldier, or forfeit what little protection his parents’ status gave him. Over the years, as their son grew older, she spoke to her husband of leaving the demons’ empire to seek refuge in the Watchlands or the realms further east. He always treated her kindly, without ever turning an eye to the courtesans — demon and human both — who served those the emperor favored.

Yet Biantha had never forgotten her husband’s puzzlement, molting slowly into anger, that she should wish to leave a court that sheltered them, though it did nothing to shelter others. She could not reconcile herself to the demons’ casual cruelty: one of the emperor’s nieces sent, after an ill-advised duel, to redeem her honor by riding a horse to the mines of Sarmont and back, five days and back forcing a terrified beast to carry her. The pale-eyed assassin who had fallen from favor after killing the rebellious lady of Reis Keep, solely because he had left evidence of his work. Children drowned after a plague blinded them and clouded their wits. If anything, the demons were as cruel to each other as to the humans who lived among and below them, but Biantha had found less and less comfort in that knowledge.

“I stood in the doorway,” Marten went on, “trying to understand. Then Father was weeping—”

She had said to her husband, If you will not come, then I must go without you.

“—and he drew his sword against you.”

“And I killed him,” Biantha said, dry-mouthed. “I tried to get you to come with me, but you wouldn’t leave him. You started to cry. I had little time, and there were ever guards nearby, listening for anything amiss. So I went alone. It would have been my death to stay after murdering one of the emperor’s officers. In the end, the emperor’s trust meant more to him than you or I.”

“Please don’t leave me again,” Marten whispered. He stood straight-backed in the darkness, the hilt of the sword at his back peering over his shoulder like a sleepy eye, but his face was taut. “I am leaving for Silverbridge tomorrow.”

“Will you be at the forefront?”

“It would be unwise.” His mouth tightened for a moment. “I will be giving orders.”

“To kill.” And, perhaps, be killed, she wanted to say, but the words fluttered in her throat.

Marten met her gaze calmly. “It is war, Mother.”

“It is now,” she agreed, “but it wasn’t before. I know what it is to be the emperor’s champion. ‘The sword at the emperor’s side,’ you said. The others heard the words only; they have never lain awake and sleepless for memory of bloodstains on a pale rug, or because of the sudden, silenced cries at night. How many fell to your blade, Marten?”

“I came to follow you when I started losing count.” His eyes were dry, now, though Biantha saw the shapes of pain stirring behind them. “When the numbers started slipping out of my grasp.”

Biantha held silence before her like a skein of threads that wanted words to untangle it.

He lifted a hand, hesitated, let it drop. “I wanted to talk to you once, if never again. Before I go to Silverbridge where the demons await.”

She smiled at him, then. But always the suspicion remained that he had some way of breaking his oath to Vathré, that the demon emperor had sent him to ensure the Watchlands’ downfall through some subtle plan — or, more simply, that he had come to betray the mother he had abandoned, who had abandoned him; she no longer knew which.

“Go, then,” said Biantha, neither promise nor peril in her voice, and left him to await dawn alone.

Four days later, Biantha stood before her bookcase, eyes roaming aimlessly over her collection of mathemagical works, some in the tight, angular script of the demon empire, others in the ornate writing common to the Watchlands’ scholars. There has to be something useful, she told herself, even after having scoured everything that looked remotely relevant. Now, more than ever, she wished she had talent for another of the magical disciplines, which did not rely on memorized proofs or the vagaries of inspiration, though none of them had ever seemed to get far with the Prophecy.

Would that it were a straightforward problem—

Biantha froze. The Prophecy did not describe the idealized spaces with which she had grown accustomed to dealing, but the tangles of truth, the interactions of demons and humans, the snarls of cause and effect and relation. Even the astrologer admitted privately that his predictions, on occasion, failed spectacularly where people were involved. She had been trying to linearize the cantos: the wrong approach.

Evergard’s treasurer had once teased her about the cost of paper, though she took care to waste as little as possible. She located a pile of empty sheets in a drawer and set them on her desk, opening her copy of the Prophecy to the first page. After a moment, Biantha also retrieved Sarielle’s Speculations, Spells and Stranger Sets, sparing a glance for the 400-line poem in the back; Sarielle of Rix had fancied herself a poet. She had passed evenings lingering over the book’s carefully engraved figures and diagrams, curves that Sarielle had labeled “pathological” for their peculiarities.

Symmetry. That which remained changeless. Red pieces upon black and black upon black at the start of a draughts match. A ballad that began and ended with the same sequence of measures; and now that Biantha turned her thoughts in this direction, she remembered a song that traveling minstrels had performed before the court, voice after voice braiding into a whole that imitated each part. Her image in the mirror. And now, Sarielle’s pathological curves, where a segment of the proper proportion spawned yet more such segments.

Methodically, she went through the Prophecy, searching for these other symmetries, for the solution that had eluded her for so long. Late into the night, throat parched because she had drained her pitcher and dared not break her concentration by fetching another or calling a servant, Biantha placed Speculations, Spells and Stranger Sets to one side and thumbed through the appendix to Athique’s Infinities. Athique and Sarielle, contemporaries, had been opposites as far as titles went. She reached the approximations of various shapes, sieves and flowers, ferns and laces, that no mortal hand could craft.

One page in particular struck her: shapes built from varying polygons with various “pathologies,” as Athique dubbed them in what Biantha suspected had been a jab at Sarielle’s would-be wordsmithing, repeating a procedure to the borders of infinity. The Prophecy harbored greater complexities, but she wondered if her solution might be one of many algorithms, many possibilities. Her eyes flooded: a lifetime’s work that she had uncovered, explored briefly by mathemagicians before her, and she had little time in which to seek a solution that helped the Watchlands.

Even after she had snuffled the lamp and curled into bed, a headache devouring her brain, words still burned before her eyes: Symmetry. Pathologies. Infinity.

Only a few weeks later, Biantha found herself walking aimlessly down a corridor, freeing her mind from the Prophecy’s tyrannous grip, when Lady Iastre shook her shoulder. “They’re back, Biantha,” she said hurriedly. “I thought you’d like to be there to greet them.”

“Who’s back?”

“Your son. And those who survived Silverbridge.”

Those who survived. Biantha closed her eyes, shaking. “If only the demons would leave us alone—”

The other woman nodded sadly. “But it’s not happening. The emperor will soon be at Evergard itself, is the news I’ve been hearing. Come on.”

“I can’t,” she said, and felt as though the keep were spinning around her while pitiless eyes peered through the walls. “Tell him — tell Marten — I’m glad he’s back.” It was all she could think to say, a message for her son — a message that she would not deliver in person, because the urgency of the situation had jarred her thoughts back to the Prophecy.

“Biantha!” Iastre cried, too late to stop her.

In bits and pieces she learned the rest of the story, by eavesdropping benignly on dinner conversations and the servants’ gossip. The emperor had indeed forsaken his court for the battlefield, perhaps because of Evergard’s stubborn resistance. None of this surprised her, except when a curly-haired herald mentioned the serpent-eyed scepter. To her knowledge that scepter had never left the empire — unless, and the thought sickened her, the demons had begun to consider Evergard part of their empire. It had turned Silverbridge, the shining bridge of ballad, into rust and tarnish, and even now the demons advanced.

Vathré gave a few permission to flee further east with their families, those whose presence mattered little to the coming siege. Others prepared to fight, or die, or both; the mock-battles that Biantha sometimes watched between the guards grew more grim, more intent. She and Iastre agreed that the time for draughts and rithmomachia had passed, as much as she would have welcomed the distraction.

As for Marten — she saw almost nothing of him except the terrible weariness that had taken up residence in his face, as though he had survived a torture past bearing. Biantha grieved for him as a mother; as a mathemagician, she had no comfort to offer, for her own helplessness threatened to overwhelm her. Perhaps he in his turn sensed this, and left her alone.

Day by day the demons came closer, to the point where she could stand on the battlements and see the baleful lights in the distance: the orange of campfires, the gold and silver of magefires. Day by day the discussions grew more frantic, more resigned.

At last, one morning, the horns blazed high and clear through the air, and the siege of Evergard began. Biantha took her place on the parapets without saying any farewells, though some had been said to her, and watched while archers fired into the demons’ massed ranks. Not long after, magefire rolled over their hastily raised shields, and she prepared her own spells. Only when the demons began to draw back and prepare a second attack did she call upon powers that required meticulous proofs, held in her mind like the memory of a favorite song — or a child in her arms.

She gathered all the shapes of pain that afflicted the demons and twisted them into death. Red mists obscured her vision as the spell wrenched her own soul, sparing her the need to watch the enemy falling. Yet she would have to use the spell again and again before the demons’ mathemagicians shaped a ward against it. Those who shared her art rarely ventured into battle, for this reason: it often took too long to create attacks or adapt to them. A theorem needed for a spell might take years to discover, or turn out to be impossible; and inspiration, while swift, was sometimes unreliable. She had seen mathemagicians die from careless assumptions in spellcasting.

By midday Biantha no longer noticed the newly fallen corpses. She leaned against the wall’s cold stone — and glimpsed black and red and gold in the distance: the demon emperor, carrying the serpent-eyed scepter that she remembered too clearly. For a moment she thought of the Blade Fidora and cursed the Prophecy’s inscrutable symmetry. “No,” she whispered. Only if the emperor were certain of victory would he risk himself in the front lines, and a cold conviction froze her thoughts.

Marten. He’s counting on Marten to help him.

She had to find Vathré and warn him. She knew where he would be and ran, despite the archers’ protests that she endangered herself. “My lord!” she cried, grieving already, because she saw her fair-haired son beside gray-haired Vathré, directing the defense. “My lord! The emperor—” Biantha nearly tripped, caught herself, continued running.

Vathré turned, trusting her, and then it happened.

The emperor raised his scepter, and darkness welled forth to batter Evergard’s walls. In the darkness, colors moved like the fire of dancing prisms; silence reigned for a second, strangely disturbing after the clamor of war. Then the emperor’s spell ended, leaving behind more dead than the eye could count at a glance. Broken shapes, blood, weapons twisted into deadly metal flowers, a wind like the breath of disease.

Biantha stared disbelievingly over the destruction and saw that the demons who had stood in the spell’s path had died as well; saw that the emperor had come forward to spare his own soldiers, not — she hoped not — because he knew he had a traitor in the Watchlanders’ ranks. So much death, and all they had been able to do, she and the other magicians, was watch.

“Mercy,” Vathré breathed.

“The scepter,” Marten said harshly. “Its unspoken name is Decay.”

She looked across at the gates and sneezed, dust stinging her nostrils. Already those who had fallen were rotting, flesh blackening and curling to reveal bone; Evergard’s sturdy walls had become cracked and mottled.

Marten was shouting orders for everyone to abandon that section of wall before it crumbled. Then he looked at her and said, “We have to get down. Before it spreads. You too, my lord.”

Vathré nodded curtly and offered Biantha his arm; Marten led the way down, across footing made newly treacherous. The walls whispered dryly behind them; she flinched at the crash as a crenel broke off and plummeted.

“—use that scepter again?” she heard the lord asking Marten as she concentrated on her footing.

“No,” she and her son both said. Biantha continued, “Not so far from the seat of his power and without the blood sacrifices. Not against wood or stone. But a touch, against living flesh, is another matter.”

They had reached safety of sorts with the others who had fled the crumbling section of wall. “What of the Prophecy?” Vathré asked her, grimacing as he cast his gaze over the morning’s carnage.

“Prophecy?” Marten repeated, looking at them strangely.

Perhaps he had not heard, or failed to understand what he heard, in the brief time he had been at Evergard. Biantha doubted he had spent much time with the minstrels. At least he was not — she prayed not — a traitor, as she had thought at first. Breath coming hard, she looked around, listened to the cries of the wounded, and then, all at once, the answer came to her, one solution of several.

Perspective. Time and again she had brooded over the Prophecy and the second war it foretold. The rhymes, the rhythms, the ambiguities, she had said to Vathré not long ago. She had thought about the strange symmetry, the Nightbreak War’s traitor — but failed to consider that, in the Prophecy’s second war, the corresponding traitor might betray the demons. The demons, not the Watchlands.

Last time, Lord Mière had betrayed the Watchlands, and died at Paienne’s hand — father and daughter, while Biantha and Marten were mother and son. But the mirror was imperfect, as the twisted symmetry already showed her. Marten did not have to die, and there was still hope for victory.

“The emperor is still down there,” said Vathré quietly. “It seems that if someone were to stop him, we could hold the keep. Hold the keep, and have a chance of winning.”

“A challenge,” Biantha breathed, hardly aware that those around them were listening avidly, for on this hung Evergard’s fate. “Challenge the emperor. He has his honor, strange as it may seem to us. He lost his champion; will he turn down an opportunity to slay, or be slain by, that champion?”

Had there been such a challenge in the Nightbreak War? The ballads, the histories, failed to say. No matter. They were not living a ballad, but writing their own lines to the song.

Vathré nodded, seeing the sense in her words; after all, she had lived in the demons’ realm. Then he unfastened the sheath of his sword from his belt and held it out to Marten. “Take the sword,” he said.

If she was wrong, giving the Blade Fidora to him was unrivaled folly. But they no longer had a choice, if they meant to take advantage of the Prophecy’s tangled possibilities.

He blanched. “I can’t. I don’t even know who the heir is—” probably because Vathré still had not declared the succession. “I haven’t the right.”

Biantha gazed at the gates, now twisted into rusty skeins. The captain of the guard had rallied the remaining troops and was grimly awaiting the demons’ advance.

The lord of Evergard said, exasperated, “I give you the right. This isn’t the time for questions or self-recriminations. Take the sword.”

Resolutely, Marten accepted the Blade Fidora. He grasped the sword’s hilt, and it came clear of the scabbard, shining faintly. “I’m sorry for what I have done in the past,” he whispered, “even though that doesn’t change what was done. Help me now.”

“Hurry,” said Biantha, guessing the battle’s shape. “The emperor will soon come to claim his prize, our home, and you must be there to stop him.” She stood on her toes and kissed him on the cheek: a mother’s kiss, which she had not given him for too many years. She called to mind every protective spell she could think of and forged them together around him despite her exhaustion. “Go with my blessing.” And please come back to me. After losing him once, Biantha did not mean to lose him again.

“And go with mine,” Vathré echoed.

He ducked his head and moved away at a run. Shivering, Biantha tried to gather the strength for more magic against the demons, to influence the Prophecy in their favor. She felt as if she were a formula in an old book, a creature of faded ink and yellowed paper.

As she and Vathré watched, Marten shoved through the soldiers at the gate, pausing only to exchange a few words with some of his comrades. They parted for him, wondering that he and not Vathré held the Blade Fidora; Vathré waved at them in reassurance. Past the gates were the emperor and his elites, dressed in rich colors, standing in near-perfect formation.

“Traitor,” said the emperor to Marten in the cool voice that had never revealed anything but mockery; demon and human both strained to hear him. “Do you think Evergard’s blade will protect you?”

In answer Marten swung the sword toward the emperor’s exposed throat, where veins showed golden through the translucent skin. The elites reacted by moving to surround him while the emperor brought his serpent-eyed scepter up in a parry. The soldiers of Evergard, in their turn, advanced in Marten’s defense. Biantha felt a hysterical laugh forming: the soldiers of both sides looked as though they had choreographed their motions, like dancers.

Now, straining to see what was happening, she realized why the emperor had chosen her son for his champion. Several of the elites saw clearly the blows that would kill them, yet failed to counter in time. Yet her eyes were drawn to the emperor himself, and she sucked in her breath: the emperor appeared to be aiming at a woman who had crippled one of the elites, but Biantha saw the twist in the scepter’s trajectory that would bring it around to strike Marten. Even a traitor champion could not survive a single touch of the scepter; it would weaken him beyond his ability to recover.

“Marten!” she screamed. He was all she had left of her old home and its decadent intrigues; of a man with gentle hands who had loved her within the narrow limits of court life; of her family. The emperor had stolen him from her for so long—

Mathemagical intuition launched her past the meticulous lemmas and lines of a proof, panic giving her thoughts a hawk’s wings. Biantha spun one more spell. Symmetry: the emperor’s attack became Marten’s, in spaces too strange for the mind to imagine. The Blade Fidora went true to its target, while the scepter missed entirely, and it was the emperor’s golden blood that showered Marten’s hands.

I’m sorry for everything, Marten, thought Biantha, and folded out of consciousness.

The minstrels who survived the Siege of Evergard made into song the deaths, the desperation, the duel between the demon emperor and he who was now heir to the Watchlands. Biantha, for her part, listened and grieved in her own way for those who had died… for Mière’s great-grandson. There was more to any story, she had learned, than what the minstrels remembered; and this was as true of herself, her husband, her son.

Biantha wrote only two lines in the margin of an unfinished book — a book of her own theorems.

There are too many shapes of love to be counted.

One of them is forgiveness.

It was a conjecture, not a proof, but Biantha knew its truth nonetheless. After the ink had dried, she left her room with its well-worn books and went to the great hall where Vathré and Iastre, and most especially Marten, expected her for dinner.

for Ch’mera, and for those who teach math