A Calculus of Angels

by J. Gregory Keyes

  Frisk was frowning deeply. “But there are kings in the Bible, called as such. King David. King Solomon—”

  “Whose position and fame rested equally on the backs of birth and accomplishment. Ah, our beer.”

  He lifted the mug up. “To such as us, gentlemen, who are the future of the world.”

  Frisk hesitated an instant, shrugged, and raised the glass in toast. He did not, however, drink. “In any event,” he said, “our debate has interrupted my question. If you cannot read the Mosaic script, how certain are you that you got the right book?”

  “Well, I can read a bit. And I have this …” He fumbled out the slip of paper with the name of the book scrawled in Newton’s sloppy Hebrew.

  “You see,” Ben began, and then stopped abruptly. He had read the first word correctly enough—Sepher. But with a deep sinking in his chest he knew that last word was not Razim.

  He had been given the wrong book.

  2.

  The Monochord

  For Adrienne, the next two days were uneventful, though there was a considerable bustle all around her as servants and soldiers prepared for the long march east. They got news that the Muscovite camps were still more than twenty miles away and stationary. Less dependable sources spoke of pitched battles near Paris, and d’Argenson speculated that the Russians were delaying their siege of Nancy to reinforce the more important thrust toward the French capital.

  “Why not aid the French defense?” Adrienne asked d’Argenson, as they picked their way amongst the vine-fettered statues of a neglected garden.

  D’Argenson grinned a bit ruefully and brushed back his thin brown hair. “Paris will fall, if not to armies, from within. You can only fight so many wars and build so many grand chateaux on the bellies of the poor before they go mad, like starved dogs. The king, begging your pardon, never really understood that.”

  He rubbed his chin. “We cannot even hold Lorraine, with only twice a thousand men. With that number and some good fortune, we might reach Prague. Myself, I would rather march down to Tuscany, for I hear that even a man with a small army can make much of himself there. But the duke—well, he dreams of the Holy Roman Empire. He fancies himself an emperor one day, I think.”

  “He has some claim?”

  “No. But Emperor Karl has two young daughters, and he has had them named his heirs, since he has no sons.”

  “I see. And his men will follow him, this young duke?”

  D’Argenson pulled at the facings of his burgundy coat and nodded thoughtfully. “Those with weak loyalties are long gone. Those remaining believe that the old days will return, and throw their lot with one who might be emperor.”

  “I take it you disagree with such sentiments.”

  D’Argenson leaned against the marble column of a small pavilion and folded his arms. “Know you something of history? How in the dark days after the fall of Rome, barbarians ruled? How from them came a few strong men, like Carolus Magnus, who founded empires and brought order?”

  “Yes, of course.”

  D’Argenson smiled. “The kings of today make fine lineages for themselves, don’t they? Pretending that their ancestors were once Roman senators or Trojans or what have you. And yet the discerning student of history can see that even the great Charlemagne was really just the strongest and ablest of the barbarians, of as mean a birth as anyone. That is, I believe, our sort of epoch. Rome is falling. History is killing old, diluted lines to make way for younger, cleaner blood.”

  Adrienne eyed him doubtfully. “Do you fancy your blood clean, Hercule d’Argenson?”

  “Me? Bah! What need have I of an empire, of enemies on every front, of sons squabbling over my gains and shredding them in the process? As I said, Mademoiselle, I have read altogether too much history.”

  “What then?”

  “Oh—enough to eat, and good food rather than slop. Entertainments that divert and surprise me. Able companions to make my days and nights memorable.” His eyes sparkled devilishly at her, and she found that there was a certain charm to his broken nose, if not beauty.

  “Even those things require a modicum of affluence,” Adrienne remarked.

  “Indeed. I never said I wanted nothing, Mademoiselle, nor to live contemptibly like a monk. No, I am content to watch for those who might be king, to wait my chance, to serve them, and then ask my reward. Nothing extravagant—a small duchy, an estate in the country.”

  “So you think the duke might be emperor after all.”

  “He will at least take me nearer those who might be. And I have little better to do.” He shrugged. “Francis has the makings of a good king, I think, and it will be some few years before all credit of noble blood is bankrupted.” He smirked again. “As to my pleasures and companions, I take them where and when I may. I will not forfeit the living of my life until it is secure.”

  “I am sure you will not, Monsieur,” Adrienne answered, reflecting that once such a bold remark would have brought a blush. No longer; the virgin hue was long gone from her cheeks. “I was wondering …”

  “Yes?” He arched his brows.

  “Wondering if there is any good I might do in these preparations.”

  “But of course! You could ease the suffering of one who labors mightily in that cause.”

  She smiled primly. “I had rather thought to be of some use in packing necessities.”

  D’Argenson heaved an extravagant sigh. “It seems I will have no surcease from my sorrows.”

  “I am sure consolation awaits you within these walls,” Adrienne said dryly, “for there are maids and cooks aplenty. If I can be of some other use …”

  “As a matter of fact, you can be,” d’Argenson said, more seriously. “The duke has a library of some size. He wishes certain volumes selected to travel with us. I am aware that you were schooled at Saint Cyr—”

  “I would be glad to do that,” Adrienne assured him. “Could you show me the way?”

  “Now?”

  “If you please.”

  “Other things would please me better”—he leered playfully—“but it shall be, as in all things, as you wish.”

  “You are a gentleman, sir.”

  “And see how you repay my kindness with an indictment! Ah, well, such is life and such are women.”

  They retraced their steps through the ruined garden to the manse, and both were silent.

  “And your son?” he ventured. “How is he taking to life out of the rain?”

  “Well enough. It is all confusing for him, I think.”

  “I have not heard him speak,” d’Argenson said. “He is a quiet little fellow.”

  “He has not yet spoken,” Adrienne replied.

  “Not yet? My girl was babbling at his age.”

  “You’ve a child?”

  He raised his hands helplessly. “I pray I do. God willing I will see her again someday. Another reason I would prefer Tuscany, for her mother is a Florentine. She should be thirteen, this year.”

  “And she spoke at just over a year?”

  “It is the usual time, I think. But children differ.”

  Adrienne nodded, a bit disturbed. She had assumed it only natural that Nicolas had not formed words. He seemed too young for it. But what did she know about raising children? Only what she had learned by experimenting thus far. She resolved to have a long conversation with the nurse. Or perhaps it would be best for Nico if she …

  No. Nico was her child, no one else’s. She had learned calculus and optics. She would learn this, too.

  The library occupied a large and windowless room on the second story, but it was cheerfully illumined by an alchemical lanthorn which—considering the rarity of such devices these days—told her this was a library that saw some use. It was an extensive one, too, and she noted that many of the volumes were well worn. This was no nobleman’s “show” library of immaculate and unread volumes. Someone had treasured this room.

  “How many books and what sort?” she asked.

  �
��The duke has esoteric tastes. Begin with the scientific and occult volumes. We should not carry more than half again a hundred, I should think, so be selective. Do you know enough of such matters to be selective?”

  “Yes,” Adrienne replied, tasting a secret irony, “I believe that I do.”

  “Well, then, I shall leave you to it. I will send a servant later to package them.”

  Adrienne nodded distractedly as she perused the spines, savoring a quickening that she had not known in years. They were here, her old loves.

  There was the Horologium Oscillatorium and Cosmotheoros of Christiaan Huygens; the Arithemetica Infinitorum, La Geometric De Analysi—books she had secretly devoured as a little girl at Saint Cyr. And there, too, were the texts from her older years, chief among them works of Isaac Newton, including the Principia Mathematica, its binding still new and unmarred. In less than half an hour, she took down thirty books of science, opened them to their title pages, remembered. Remembered an earlier woman with her name and face.

  That younger Adrienne had devoted her whole life to the love of unmasking the subtle harmonies of God and Nature. Her ambition had been to continue such studies for the length of her life, and yet even as a girl she understood the absurd constraints inhering to the female sex that must be overcome to do so. Other women, in the past, had risen beyond their circumscribed roles of wife and mother—some boldly, like Ninon de Lenclos—others in secret.

  Of those two ways, she had timidly chosen the second, or perhaps, looking back, it had been chosen for her. Chosen that day when one of her teachers at Saint Cyr found her puzzling at an algebra problem and had slipped her—with index finger pressed tight to her lips—a book on the subject. Nourishing her with secret knowledge, that teacher in time brought her to the attention of the Korai.

  How long the Korai had existed, none could say, though they claimed since antiquity. A secret cabal, all female, they abetted one another in the quest for knowledge. They were her friends, her secret mothers and sisters, her peers and judges. They discussed things scientific, published books and treatises under the names of men, and thought themselves clever. With them, Adrienne had been happy.

  And then, one day, they vanished. Her old friend, the teacher, would not speak to her, the letters in cipher ceased arriving; her own letters—first quizzical and then pleading—returned unanswered. At the age of seventeen, she was alone in a way that she had never been.

  In that state she was taken to court at wondrous and terrible Versailles. While the girls at Saint Cyr were discouraged from studying mathematics and science, they were well educated in other things, and the greatest prize that a Black—a girl in the senior class—could hope for was to be selected by the queen, Madame de Maintenon, to be her secretary. In the midst of her despondency, Adrienne was dully surprised to find herself selected.

  Without the Korai, Maintenon became her friend, her confidante, nearly her mother. But Maintenon was a devout, even puritanical woman. For her, science was a distraction from salvation; the only purpose for educating a woman was to make her a better Christian, wife, and mother. Adrienne could not tell Maintenon of the Korai or speak to her of her interests. Instead, she lived as Maintenon did, defending herself from the debauchery of the court with virtue and faith. But in her heart she could not give up her first love, science. When the queen died, she was again alone, confused, wishing for one thing but now hampered by the cumbersome morality of Madame de Maintenon.

  Gazing at the pages of mathematical symbols, she cursed that younger Adrienne, who could have been everything she wanted. She could have become the mistress of some wealthy, married man who would support her and not care how she spent her private time. She could have spurned convention and simply done as she pleased, the way the great Ninon did. Instead, she had merely dug herself a grave and dragged half the world into it with her. It was her timidity that had brought a comet to bruise the Earth, which had murdered Nicolas, Torcy, the king.…

  She tightened her lips. Enough of that.

  Cohabiting with the scientific books were a number of more dubious titles. For instance, De Occulta Philosophia and Natural Magick—prescientific compendiums of nonsense that she would hardly place beside the Principia—nevertheless seemed to her to have seen much use, and d’Argenson had been specific in his mention of the occult. Better was Robert Fludd’s History of the Macrocosm and Microcosm, which contained some good—though somewhat naïve—work on the harmonic affinity. She shuffled through its pages, musing at the quaint diagrams. One she remembered fondly, for she had first seen it at the age of ten, and by it she had begun to understand the harmonic relationships of the universe.

  It depicted a sort of cosmic violin, a monochord, its scrolled head high above heaven, single string descending through the realms of angels, planets, elements, and finally to Earth. Two octaves were marked along its length, demonstrating that the ratios between the spheres were the same as those between the notes of the musical scale. It was simplistic, but for a young girl already acquainted with music it had been a revelation, an analogical doorway to the science of affinity.

  Now, however, something bothered her about the picture. She looked it over again, reading each Latin inscription, searching for the cause of her disquiet.

  And then, suddenly, she saw it. At the head of the “violin” was a tuning key, by which the cosmic wire might be tightened or loosened. Grasping the key was a hand reaching out from a cloud. The hand of God, of course, the master tuner of the cosmic instrument. But it was not God that it reminded her of.

  Instead she stared at her own hand, remembering the sensation when she had touched Crecy, a sensation that had been somehow familiar. Now she realized it had been like grasping a vibrating wire, as if it were her hand on the cosmic monochord.

  Still gazing at the drawing, she no longer saw it. Instead she saw an equation, the one from her dream, which had somehow made her hand from nothingness.

  They were harmonic equations.

  Her skin creeping as with fever, she stumbled about the room. Searching a small desk she found ink and quill, but no paper, though she emptied its drawers onto the floor. She pushed books this way and that, searching for some hidden scrap of vellum, anything to write upon, and in her desperation noticed a book—Femmes Illustres, a romance by Scudéry. Smiling grimly, she opened it, tore out pages which had space on them, and began to write. When she ran out of room, she found another useless book—Polexandre—and cannibalized it, too. And all the while her heart beat faster, like notes rising on a scale; and it was passion, like the time she and Nicolas had loved, like a wonderful symphony, and at times she wept, remembering how it felt to see, to discover, to understand.

  The servant came in and Adrienne nearly shouted her away. The nurse came later, asking if she wanted to see her son, but she dismissed her, too. The window darkened with night, and at last a knock came on the door she had finally closed against intruders.

  Rubbing her eyes, she answered it. It was d’Argenson.

  “You are beginning to frighten the servants,” he said, peering around her.

  “My apologies. I became quite absorbed, I fear.”

  “Ah. I had not thought that choosing a few books would present such complications, but then I know little of science. If it is too onerous a task …”

  “No, it was nothing of that nature,” Adrienne replied. “I merely had a thought on one of the books and wished to write it down while it was still clear.”

  “A scientifical thought?” he asked, seeming surprised but not shocked.

  “Indeed.” She paused only for the barest instant, and then she did what she should have done in a different age. “It is an interest of mine, science.”

  “Really?” d’Argenson replied. “I’ve never been able to comprehend much of it myself. I stand in awe of you if you understand but a hundredth of what these books contain.” He tilted his head. “In any case, I hope my interruption has done no permanent damage to the cause of science,
but I had good reason. The demoiselle Crecy has asked for you.”

  “Veronique? Awake?”

  “Even so, I am delighted to say.”

  “Well,” Adrienne said. “I thank you very much for the news.” He hadn’t even blinked at her announcement. It did not upset him, her interest, even when laid plainly at his feet. On impulse, she leaned up and kissed the blunted point of his nose, and was rewarded by his furious blush.

  “My lady!” he choked, after a heartbeat or so. “To what does my nose owe this honor?”

  She turned to gather her papers and cap the ink. “Perhaps I will tell you, someday. For now, just know I thank you.”

  “You are much welcome, and my nose thanks you. Almost, you rendered it straight again. If you ever feel the desire to perform a similar service in other anatomical—”

  “Hush,” Adrienne said. “Do not make me regret myself.”

  He smiled, somehow boyishly despite his very unchildlike face. “Never would I that,” he replied, bowed, and gracefully retreated from the room.

  A moment later she followed, winding through the dark passages of the house until she found Crecy’s sickroom. As promised, the redhead was awake, head propped on a pillow.

  “Hello,” she said, sounding stronger than she looked.

  “I’m glad to see you improved, Veronique. I was worried about you.”

  “Were you?” Crecy said.

  “I am happy to see you wakeful. You know our situation?”

  “Roughly. D’Argenson explained much to me. A good man, a friend of Nicolas.”

  “Veronique …”

  “Yes?”

  Adrienne knelt at her side and found her hand. It was warm and gripped hers feebly when she took it with her left hand, not her strange right one.

  “Veronique, I love you. You and I, we have survived much together. I do not know your heart—I don’t think I will ever know it—but I tell you plainly that I love you.”

  “Thank you. It is good to hear that, stepping back from the grave.” Her lips almost seemed to tremble.