Spherical Harmonic

by Catherine Asaro

  I held back my smile. “You should indeed honor us,” I agreed. “But why should we rule?”

  “I can’t believe you have to ask.”

  “Humor me.”

  “The Houses are better fit to do it than the common people.” She spoke as if that were obvious and universally accepted, rather than one of the most controversial debates of our time.

  “Not everyone feels that way,” I said.

  “Not everyone deserves a voice.”

  Well, Majda certainly hadn’t lost her arrogance. I had the approval of the people now, but if Naaj started talking this way in public, I would lose support fast. My ascendance was already going to create trouble in exactly those circles she was most likely to offend. I frowned at her. “That many nobles among the Houses feel as you do is one reason the rule of the Ruby Dynasty will be controversial in certain groups.”

  “Then those groups need ‘reeducation.’”

  “Lése majesté,” I said. “That’s what you want.”

  She tilted her head. “What language is that?”

  “French. From Earth. It means a crime against the sovereign of a realm. The punishment could be severe.”

  “As it should be.” Surprise trickled past her mental barriers. “I wouldn’t have expected the Allieds to be so sensible.”

  Sensible depended on your point of view. “They no longer support that attitude. They long ago chose to govern through elected representatives.”

  She waved her hand in dismissal. “Which is why they are weak.”

  I didn’t believe she actually had that narrow a view. She hadn’t risen so high in the treacherous seas of political intrigue by ignoring reality. “Or it could be that we simply happened to be here first and had longer to build our power base.”

  She refused to relent. “It doesn’t matter, Dehya. The Allieds aren’t strong enough to deal with the situation. You must be firm now, both with the Allieds and with your ‘certain groups.’”

  Firm, yes. But with whom remained to be seen.

  I expected the clink of gems to stop when the bodyguards ushered me into Kelric’s study. He looked up as I entered, his hand poised over a tower of playing pieces. A ruby ball sparkled in his hand. Setting it down, he rose to his feet.

  “My greetings, Dehya.” He motioned at a chair. “Please join me.”

  “My greetings.” I sat with him at the table.

  Instead of putting his jewels back into his pouch, this time he left them out: diamond polyhedrons, sapphire disks, emerald rods, opal rings, gold cubes, and more. I had come to discuss our impending public appearance, but I couldn’t pass up this opportunity. He had steadfastly refused to let anyone watch his games.

  I studied the structure. “These are beautiful gems.”

  “Dice.”

  I looked up at him. “They’re dice?”

  He watched me intently from across the table. “Yes.”

  “You’re gambling then?”

  “No.” His gaze never wavered. “You must learn to play.”

  “Why me?” I asked, intrigued.

  “Who more appropriate?” He indicated the lustrous tower. It had an amethyst cube as its base. A seven-sided sapphire polyhedron sat on top of the cube. An emerald octahedron balanced on the sapphire, held in place by a small emerald ring. The tower continued with a nine-sided green-yellow gem, a ten-sided yellow gem, an eleven-sided topaz, and a twelve-sided bronze die. He had found ingenious ways to balance them, using rings and small cups. The room lights glittered off the gems.

  “It is called a queen’s spectrum” He considered the tower. “Actually, this would be a queen’s gamble.”

  “What is the difference?” I asked.

  “A gamble is any structure built with great risk but substantial potential payoff.” He balanced the ruby ball on the top, within a diamond ring.

  “Shouldn’t you have put a ruby with thirteen sides there?”

  Kelric gave me an approving glance. “You’re fast. But the highest ranked polyhedron is the dodecahedron. None have more than twelve sides.” He indicated the ruby. “Unless you consider a sphere a polyhedron with an infinite number of sides.”

  “Clever. But that isn’t a sphere. It’s a ball.”

  He laughed. “True. A sphere is hollow. Surely our highest-ranking piece must be solid.”

  Possibilities swirled in my mind, tantalizing. “It’s more than a game, isn’t it?”

  “That depends on how you play.” He shrugged. “Most people gamble.”

  “But you don’t?” I had forgotten how hard it could be to converse with Kelric. He had never been talkative, and the last nineteen years had intensified his taciturn inclinations.

  “No.” He gathered up the pieces and put them in his pouch, but instead of tying it on his belt, he offered it to me. “You must have copies made.”

  Stunned, I took the pouch. No one had ever seen him part with it. “Are you certain you want me to take this?”

  “Yes.” He shifted his weight. “Return them soon.”

  “I will.” I knew he could have had his console do a holo-scan of the dice and transmit the results to my jewelers, who could make them without the originals. This was a deliberate gesture of trust. “Thank you.”

  “When you have your own set, we will play Quis.”

  “Is that what you call the game?”

  “Yes. It means ‘influence.’”

  “Literally?” My neural nodes sifted through language bases, trying to find a match for the word Quis. If I could narrow down the language, it might provide a clue about where Kelric had been all these years. Most people accepted that he had been with the Traders, but I didn’t believe it.

  Quis sounded like keys in Earth English. In Earth Latin, quis meant “who,” and in the language of the Topólo people on the world Metropoli, keez meant “rebirth.” None of those fit with places that it made any sense for Kelric to have been all these years.

  “The literal translation is ‘resurrection,’” he said. “But Quis gives influence if you play well. You plan with it, analyze, tell tales.”

  “It sounds fascinating.” My nodes came up with kuxel for resurrection and kux for “come back to life,” both ancient Mayan words. But that didn’t help much, either, given that all our languages derived in part from ancient Mesoamerican tongues.

  “You must learn Quis.” Kelric was studying me with his gold gaze. “No other person will play it like you.”

  Who could resist a pitch like this? “All right. But why won’t you teach anyone else?”

  “They don’t have my oath.”

  “Your oath?”

  He spoke quietly, not in our modern tongue, but in classical Iotic, a language over five thousand years old. “For Skolia and the Ruby Dynasty, I come to your Circle to give my Oath. I swear to hold your Estate above all else, as I hold the future of Skolia in my mind and hands. I swear, on penalty of my life, that my loyalty is to the House of Skolia, only to Skolia, and completely to Skolia.”

  I stared at him, stunned. He had repeated the ancient oath Naaj Majda had given me in the Hall of Chambers. But it wasn’t identical. Where did his version come from? And how did it relate to Quis? I was certain it did, somehow.

  “You honor me with your oath,” I said. “And I give you mine in return.”

  He nodded, apparently satisfied with my response.

  An image formed in my mind:

  lm

  The l was dark purple and three-dimensional, like a plum, but polished and smooth, almost reflective. The m looked similar, except with a bluer hue. Those two letters could mean anything, but to me, in that font, they referred to the quantum numbers that defined a spherical harmonic wave.

  The letters suddenly morphed into spherical harmonic orbitals.

  They shimmered in my mind, glistening blue, violet, rose, and lavender.

  “They’re us,” I sudddenly stated.

  Kelric blinked. “The Quis dice?”

  “Not your gem
s. Spherical harmonics. They’re us. The Rhon.” His dice had prodded my thoughts. The way he built with them, their beauty… an idea hovered at the edges of my mind, if I could only catch the thought.

  “Spherical harmonics as the Rhon.” Kelric smiled. “The idea has a certain symmetry.”

  I laughed, tickled by his humor. Our bodyguards exuded bafflement. I supposed the joke wasn’t that funny unless you liked to play with the symmetry properties of spherical harmonics. I had forgotten this side of Kelric, the way he and I used to talk in math puns. The rest of the family had thought us strange, but we enjoyed ourselves.

  “A Rhon psion is an orbital in Kyle space,” I said. The orbitals continued to glimmer in my thoughts. Some resembled Kelric’s round Quis dice. “They’re made from spherical harmonics.”

  “Orbitals of thought” Kelric tilted his head. “But spherical harmonics give only the angular dependence. It’s like saying the Rhon only goes around a center. Nothing takes us out of that center.”

  More puzzlement came from our guards: They wondered if we were talking in code.

  “You’re still missing something,” Kelric said. “The radial extent.”

  The idea suddenly coalesced in my mind. Just as his Quis dice formed individual balls or rings, symmetric about their centers, so spherical harmonics built up the mind of a Rhon psion in Kyle space, symmetric about our mental center of being. But a spherical harmonic had only angular dependence; it only described how a shape varied around a central point. It had no radial dependence. It didn’t tell how a shape varied as we moved into or away from that center.

  I saw the problem now. It was obvious. A Rhon psion could exist in Kyle space, but only in isolation. We were complete with respect to our own centers, but we couldn’t reach out.

  I spoke slowly. “When the Rhon make the psiberweb, we link our minds with the minds of many others. Those links radiate out from our centers. The web takes us out of ourselves. Without it, we can exist, but we are cut off from humanity.” I paused, uncomfortable. “If we want to be truly human, we need those links.”

  “Do you think we are truly human?”

  Gods. What a question. I thought of Taquinil. The waveform I had used to describe Taquinil’s existence in Kyle space had come from my impression of my son. It included radial as well as angular dependence, which made me think he wasn’t ready yet to completely shed his humanity. We had the ability within ourselves to reach out, if we wished. What we did with that ability depended on us. “Perhaps we each have to make that choice.”

  He regarded me curiously. “What made you think of all this?”

  I indicated his dice pouch of gems. “They remind me of spherical harmonics. All those colors.”

  “You see mathematical functions in color?”

  “Always. Texture, too. Even music.” I chuckled. “Spin is more frivolous than angular momentum.”

  “I should enjoy hearing more about it.” Kelric rested his elbow on the table and his chin on his knuckles. It pulled down his shirt cuff, uncovering his wrist guard. Intricate hieroglyphs were engraved in the gold. Intrigued, I tried to decipher the language. It had a faint resemblance to Iotic, but I couldn’t be sure without a closer look.

  Following my gaze, he glanced down. Then he lowered his arm and pulled down his cuff.

  “They’re marriage guards,” I said. Almost no one wore them anymore, not even among the most conservative Houses. They looked too much like Trader slave restraints. That resemblance had destroyed a tradition with a five-thousand-year history among our people. At one time, the giving of such guards had been an expression of love.

  “Dehya, don’t ask.” He paused. “There is Jeejon. My wife.”

  I knew Jeejon hadn’t given him the guards. Perhaps he was protecting a former wife. Children? Given the current turmoil in the Imperialate, he had reason for caution. And he obviously loved Jeejon, as unlikely a pair as they seemed.

  I didn’t push. When he was ready, if ever, he would talk about it. Instead I said, “I like your wife.”

  Kelric grinned, his teeth bright against his gold skin. “So do I.”

  My breath caught at his smile. I was no more immune to his beauty than anyone else. But more had changed than the gray in his hair or the lines around his eyes. Nineteen years ago, he had often let a woman’s physical appearance dazzle him, sometimes to his detriment. He had also tended to prefer women from the noble Houses. Jeejon came from a background so different from his, she had almost no overlap with his previous life.

  “I wonder, though, how she will survive the Imperial court,” I said.

  “She is my consort. She can do whatever she wants.”

  “Well, yes.” I could just imagine how that would fit Naaj’s ideas of nobility and lèse majesté. “But the Imperial court won’t go easy on her.”

  “Then forget the Imperial court.” His face relaxed. “I love her, Dehya. And if the noble Houses have a problem with that, tough.”

  “Well. Good.” I liked this new Kelric more and more. He had also given me a valuable insight.

  I thought of his ruby ball, which resembled an orbital. By itself, the ball meant little. It took meaning only as part of a Quis structure. So it was with my mind in Kyle space: the psiberweb gave it meaning. Kyle space formed another aspect of human existence. It deepened our humanity by creating an alternate reality out of the sum total of human thought. The Rhon could open portals to it, but those gates went nowhere without the rest of humanity to give structure to that mental universe.

  Only a short time remained before the shuttle took Kelric and me from Roca’s Pride down to Parthonia for our speech, which would be broadcast to all the settled worlds. Before we could leave, one visit remained to be made. So I walked with Jinn Opsister and my bodyguards, my heart heavy.

  We paused at a large hatch guarded by more Jagernauts, who unlocked and opened the heavy portal. When my bodyguards started to follow me through the hatchway, I shook my head. “Please wait out here.”

  Jinn didn’t look happy, but this time she didn’t argue. Perhaps she understood.

  I continued on alone and closed the hatch behind me.

  The observation dome curved out from the hull, a transparent bubble of dichromesh glass. The stars blazed outside; ruby, sapphire, emerald, topaz, and diamond. Interstellar Quis dice. Nurseries of interstellar dust filled with hot, newly-born stars spewed through space like impossibly huge fountains frozen for millennia. The aft end of the battle cruiser curved away from the bubble in both directions, huge, its hull gnarled and massive. Far down the curve, the maw of thrusters dwarfed this bubble, but they were quiescent, making the bay safe for now.

  A man stood across the chamber, looking out at the spectacular panorama. The transparent floors, walls, and ceiling made it appear as if he were standing in open space. His hands rested on a waist-high rail.

  I went to stand with him. For a long time we both gazed at space.

  Then he spoke. “How long until you go down to Parthonia?”

  I looked at him. “As soon as you and I finish here.”

  “So.” The First Councilor continued to watch the stars, his face drawn. Prison cuffs glittered on his wrists.

  “Barcala,” I said softly.

  Finally he turned, pain in his gaze. “Must my final view of another human be my executioner?”

  I felt as if were dying inside. “I’m sorry.”

  He looked as if he had aged years. “How long do I have?”

  “A few hours” Gods, I hated this. But unlike as with Jon Casestar, no leeway existed here. The noble Houses, our supporters, ISC—all demanded the deposed leader die. Never mind that Barcala and I had been friends for years or that he had done a good job as First Councilor. Unless we executed him, he would be a constant shadow over the new government.

  He was watching my face. “Did you get what you wanted?”

  “No.” My voice caught. “I don’t want this.”

  “I won’t beg for my life.”
He spoke quietly. “The Assembly has always done what it believes best for our people, Dehya. No, it hasn’t been pretty, what the Ruby Dynasty has endured. But the alternatives were even worse.”

  “‘Hasn’t been pretty?’” My anger stirred. “My father and mother died from ‘not pretty.’ Kurj gave up his peace of mind, his ability to love, and finally his life. Soz died. The Assembly drugged Eldrin and me, threatened and imprisoned us. For what? A son who almost went insane because we should never have had children? What benefit to Skolia was Taquinil’s misery? The Traders tortured Althor for two years. They tortured Eldrin.” I took a deep breath, stunned at the depth of the rage I had suppressed. “My son, husband, mother, father, Soz, Kurj, Althor, Kelric—how long must the list go on? When will we have lived enough hells to satisfy you all?”

  Deep lines were etched his face. “I grieve for your losses. But what is more important? What is best for your family or for human survival?”

  “That’s a cheap shot.”

  “It is a valid question, Dehya.”

  “It doesn’t have to be an either-or question. The Assembly never gave us a chance to find a better way.”

  “And you think you can.”

  I couldn’t evade his question, not when he would soon die because of its answer. I spoke slowly. “This much I know: I can best decide myself how I serve Skolia. As long as the Assembly controls my life, everyone loses. Why must we always have a loser and a winner? A way must exist for both to win.”

  “It isn’t this.” He pushed his hand slowly through his hair, that one motion telling of a deep-seated fatigue beyond physical exhaustion. “You unnerve people. Gods know, none of us can claim to understand how you think. How did you know Kelric Valdoria still lived? That Delos was important? Or about those foster children on Earth? Then there are the webs. You go anywhere. We’ve never found a security system that could stop you. As much as you take that for granted, no one else can do it. Saints only know what else you’ve concluded that you’re telling no one.”

  I froze. What else you’ve concluded. I kept the name Jaibriol III shrouded in my mind. “Barcala, recant your opposition to my government. Go in public and give your support to the Ruby Dynasty. Exhort the former Assembly Councilors to support us. Damn it, let me let you live.”