Count to a Trillion

13

Philosophical Language

1. Her Champion

The hollering of the crowd, and the Princess smiling and waving down to them went on and on. Even though he was being photographed by those flying bugs, and his image was projected titan-sized on to the clouds above the castle, Menelaus got bored of smiling, as his face was not built for it. So he rolled a cigarette, slouched against a nearby statue, struck a match against the statue’s buttocks, and had a smoke. He examined his huge picture overhead. You know, his handmade buckskins really did look rather shabby, come to think on it, especially next to this princess.

Montrose was lost in thought, looking down at the shining coiffeur of her hair, jeweled and elaborate. Her scent, warm and feminine with a hint of lavender, was like a half-heard note of music, seductive as spring air. He noticed that the top of her head did not reach his chin: she might be too short to dance with. Not that the people of this day danced proper dances, woman in a man’s arms. They bowed and swayed in lines and figures. How could something like the waltz, Mankind’s greatest invention, simply pass away? Menelaus told himself he would have to reintroduce the custom. Otherwise there would be no chance to take this little golden woman in his arms.

He did not notice when her vast face vanished from the clouds above, and the cheers changed into sea-wave sounds of more ordinary mirth; but suddenly it was dim on the balcony again. She tilted up her finely-boned chin. He could not help but look at the red arc of her full lower lip, the tiny crease between chin and lip. What was that line called? Did it have a name?

“Isn’t it beautiful?” she asked gaily, waving her gloved hand to the winter midnight horizon, the houses and fields below aflame with fireworks and colored torches.

Since he did not know what she was talking about, he nodded and said, “Very.”

Rania said, “I was told by my fathers, the men who raised me, that my mother died bringing me into the world—my world, what you call a ship. Madalena, they said her name was. One memento I had from my mother was a picture of the Virgin Mary, crowned in stars, and with the moon beneath her feet. I did not know what it was, so I thought it was a picture of ‘Mother Earth’ of which the crew so often spoke, the world that once beamed a whole library of messages to us, and then fell silent. You see, I did not know your world was a globe. I had never seen a living globe. And so I loved this world because I pictured her as a beautiful mother, crowned in stars. Can you say, in truth, my picture is worse than those who think this world is merely a rock in space, coated with a thin film of water and air?”

She looked dreamy, thoughtful and melancholy, yet the shadow of a smile touched her scarlet lips. Menelaus decided now was not the time to tell her that her mother was a Petrie dish.

Menelaus shrugged with one shoulder. “I like the world just fine, mountains and trees, all that good stuff. Plague, I even like the Alaska wastes where I was snowed in not long back—hunting and ice-fishing. I just don’t like the people, mostly. You got a rotten set-up here, Princess, and it sounds like you were the setter-upper, not Blackie.”

“Perhaps the people of the world have not been as kind to you as they have to me. It would be ungrateful of me to feel less than love, after all the warmth this world has shown. A world of wonder! Do you ever smell the air, feel the flowing wind, and simply marvel at it? You have breathed bottled air, I know. But you were not born breathing it.”

Menelaus had seen simple joy shining on the faces of children; but this was different. This was intelligent joy, adult and profound. It was a strange thing to see. In his life, the people he met did not rejoice—if that was the word for it—in the simple act of breathing.

“I was born breathing free, alright. I would prefer to live in a Democracy.”

“If the people also preferred it, so should we all be. I was not born in a crown, or surrounded by fine things—these were pressed upon me by a grateful world, relieved from the endless tears and horrors of war. You know, I did not even know what war was at first, or murder? I lived among elderly scientists.”

Montrose thought now was not the time to tell her that those elderly scientists were very well-acquainted with murder indeed, having killed the Captain and more than half the crew.

Instead he said, “I don’t believe people don’t want to be free.”

“Nor do I, but there are two kinds of freedom: license to indulge any desire, base or noble, natural or unnatural, provided no one and nothing hinders you is the first kind, and it is deadly to men. The second kind is the freedom that comes of fulfilling or completing the work of nature that is half-formed in us. Men who are free in the first sense of the word will freely vote their freedom away, in return for lucre, prestige, and safety. In the early days, the Senior Del Azarchel simply bought the elections he needed, until the free nations of the world had prime ministers and parliaments composed of his creatures, who joined the Concordat willingly.”

A strange look came into her eyes, which Montrose did not know how to interpret. Nostalgia? Sorrow?

“It was proud and stubborn kings and warlords of small or backward nations, which had returned to a more personal and less bureaucratic form of government, that held out against him. They had the second type of freedom, not the first: They were not dehumanized. Bad as they were, those kings regarded their subjects as their children, not as their customers or patients or wards or subjects of their latest experiments in sociopolitical engineering. But they lacked the first type of freedom, and those subjects were not free enough to resist us.”

Montrose wondered where the Princess had gotten her notion of what princesses acted like. Where else? From the royalty she defeated, the princes who treated their subjects like children. The strange look was one of admiration.

“What did you offer them?” he asked.

“Honors and offices—the Copts and Manchurians and Boers form the backbone of our officer cadre, and they are allowed forms of dress and address denied other men, and in the wild areas of the world, they rule unchecked. The Concordat allows them indulgences the Church denies to others, such as divorce and contraception: They do not replace their numbers, and in a generation their vestige must find another fate. Much evil is done in my name that I abhor. If I were free to be ungrateful, I would flee my post. As it is, here I am chained as if with chains of gold, fair and gleaming, and only the terrible voice of a stronger duty can call me away.”

Montrose said, “What’s this talk of chains? Aren’t you in charge?”

“I have all the power a Captain might have over her ship, if her sails were in darkness.”

For a moment, he thought she meant a seagoing ship, sailing at night. But, no: in her world there was no night, only the darkness between stars. “A lightship out of her guiding lightbeam is in free fall, Princess,” he said.

Rania nodded. “Exactly so. Such a Captain is merely trapped in an elaborate construction of steel, and merely carried along. The power of the Sovereign rests on the consent, tacit or open, of her subjects. Either they love her, or she does not lead. You know that. I was not born of this world: Every breeze and breath of air is a gift to me, not something I made for my own. I must repay as best I may, not counting the cost.”

He squinted at her. This sounded like the kind of thing men facing danger told themselves.

“What cost are we talking about? You said you wanted my help. Are you in trouble?”

“I expect you to be fearless, in any of your aspects or avatars.”

He was taken aback. “What does that mean? What exactly are you aiming I can do for you?”

“Learned Montrose, you surprise me! You know where you excel.” Her tone seemed playful. Or perhaps he was imagining it.

“My jobs, in no particular order, were weaponsmith, pony-soldier, duelist, lawyer, a short stint as a spacehand, and a shorter stint as a xenomathematician. Oh, and human guinea pig for self-inflicted brain experimentation. I am not a failure at two of them.”

“I have no need for your counsel as an attorney, being well-supplied with staff in that regard. It is your other professions that interest me.”

“Great! Who do you want me to kill?”

“There is a dragon, O my champion, I require you to slay.”

“What? I mean, begging your pardon? Did you say you wanted me to kill what again?”

“Come. Walk with me.”

Rania merely tucked her shoulder under his arm, and wound her slender hand around his, so that he found himself half-embracing her as he had just been imagining.

The sensation of her silken glove on his hand sent a curious ripple up his arm.

This is it. He thought. I am falling in love. Or I got the stomach flu.

He breathed deeply. Her loveliness was an aura around her, a warmth, a perfume. He walked, feeling like a bull being led by the nose-ring by some slender farm girl. The strength in her arm surprised him: there was lioness muscle under that soft skin.

And she was another man’s girl! He hated himself, at least a little bit, at the thought of being a poacher, and he hated himself again for not hating himself more. But in the back of his mind, he thought it as clear as day that Blackie did not deserve her.

But the strength of his own infatuation puzzled him. He had seen pretty women before—no one fell in love that fast, just in the twinkling of an eye. But she had been in his mind since first he saw her portrait at Blackie’s. Why did she look so … familiar? He felt in his heart as if he already knew her.

She was not leading him back into the ballroom, but down the balcony to a smaller door to one side. The half-invisible soldiers softly opened the door for them. The soldiers did not enter, but stayed behind.

Beyond was a corridor, one he had not seen coming in, wainscoted in highly polished wood up to waist-high, and above that, an intricate wallpaper in blue with gold highlights, a motif of lianas, leaves, and lilies.

As she crossed the threshold, she touched the ruby that rested between her breasts. It must have been a control surface, because up from her coiffeur, glittering like dragonflies, rose a swarm of tiny, winged machines. Her hair came undone, and formed a momentary cloud of scented gold around her face. It was not that the strands were weightless in the night-breeze around her, but Menelaus had a ghost of a memory in his mind that it should have looked that way.

She shook her face to clear it, and Menelaus found the sight adorable, like a surfacing mermaid shaking spray free from her features.

Or like a sorceress. Her twinkling Tinkerbell-sized fliers were darting here and there in midair, destroying camera ladybugs, or driving them out of the slowly-closing door. He did not even mind that she plucked the half-consumed cigarette from his hand and had her dragonflies carry it out the door for her, and toss it away.

“Ventilation performance,” she said.

“We’re aground,” he said. “Air is free on Earth.”

“But why fall into bad habits? No tobacco is allowed aloft.”

The door shut, the night-breeze stilled. Menelaus then and there decided the prettiest sight on earth was that of a girl tucking her hair behind her ear.

“Are you talking about going into space again?” A strange, a wild hope rose in his breast even as he said it. But then he shook his head, doubting. “I read some of Blackie’s books. He daren’t let the Hermetic leave the system, since it is his pistol pointed between the eyes of the world. And he daren’t let another manned expedition go the Diamond Star, because that expedition, when it returned, would come back with another pistol as large. They’d pay back his heirs in his own ugly coin—with enough money to buy or bomb the world, a world where all they knew and loved would be long dead. As for the Bellerophon, right now she’s got canisters strapped like bananas to the main keel for the construction crew, but that is going to all be stripped off and fall back home once the machine installation is complete. But no people are invited on that vessel. Men are too dangerous to trust going to go fetch the dangerous stuff in the Diamond Star.”

She just shook her head. “I will not think that way, and shall not understand those who do. Should two mites on the ear of an elephant bite each other to death, when the elephant is plunging off a cliff’s brink? You asked of me what I wanted killed. Are you willing to enter the lists?”

“Fight a duel? My dad would have approved. He thought womenfolk should talk that way. But you—you’re not serious.”

“I am.”

“You got armies. And a ship. You’re a princess.”

“I am a woman, and a young woman, and armies cannot grapple this foe of mine. My enemy is not a thing of flesh and blood. The mystery of that Monument is my dragon. It will devour me if I am not saved.”

“The Monument?”

“Can you read it?”

It was the moment he had been waiting for his whole life.

Menelaus was astonished at how evenly and calmly the words rolled off his tongue, “Ma’am, I can read that damn Monument for you, if anyone on Earth can.”

2. The Logic Behind Logic

The corridor was lit, but was not exactly bright. Candles, good old-fashioned pre-Edison candles, stood on small tables every ten paces or so, between antique suits of gold-chased armor, or glass cases containing china curios or silver cups. Behind each candle was a dark drape, evidently meant to preserve the wallpaper from smoke stains. The buttery-gold light breathed and lived, and made the hallway into an elfin place, alive with shadows.

Without a further word, she reached over and tapped one of the mirrors facing the corridor. It was smartglass, just as back in Blackie’s chalet, and an image of the Xi Segment of the Monument came up in the view.

The right window showed differential equations from the Divarication Theory; the left showed the symbol-groups of the Xi-wave function-group being organized into a matrix. This left window was connected by little red threads to show which symbol in the matrix represented which Monument sign. More than one information view of the process was displayed: one was a branching tree, one was a rippling set of Venn diagrams, like a rainy pond, one was a polar axis view, one was a Cartesian diagram, one was a basic-grammar theory spiderweb.

When the matrix was entirely filled in, the information began to sequence itself. One pattern after another was superimposed on the various trees and ponds and spiderwebs, and where there were partial matches, the letters to the right lit up with colors, matching a color-coded version of the Monument symbols.

“I know that sequence,” said Montrose. “I designed it. That is what I had the Zurich computer use to go through the alien math, to make the codes to establish the nerve-channels in my brain.”

“But what does the Xi Segment express?”

“I don’t know. I just copied it.”

“Compare the table results. Everything the Monument says, it says in repeating patterns. Logic in the Opening Statements underpins mathematics according to the Russell-Whitehead meta-language, which is in the Gamma Segment. Mathematics in the Alpha Segment underpins geometry and physics, the sections labeled Alpha 357 to Beta 120. Game-theory in Eta underpins economics in Theta. So then, what underpins the basic statements of logic? You see? Compare this here to those untranslated expressions in the first two bands of the Monument pole. They come before the scientific statements, the periodic table, or the Maxwell equations. Assume these are metaphysical expressions, needed to explain and justify the basic physics here, symbols written in a pattern we humans cannot grasp, because the physical roots of the laws of physics are unknown to us.”

“I don’t follow you.”

“We have yet to deduce a logical system proving the physical constants of the universe must be those of our cosmos, and none other. Obviously these are matters physics cannot address, since empiricism can only examine the universe we have before us. So, the physics of before physics: I would call it meta-physics, but the word is taken. Let us call it Axiomatics, the justification of fundamental physical constants.”

“So they know the basic rules for why the universe is the way it is and not some other way. So what?”

“So I suggest the symmetry is maintained for the Mu-Nu Group over here. I suggest to you that these groups of expressions are, as the Monument Builders are great lovers of symmetry, the meta-logical expression: a symbolic code for the expression that would justify the basic rules of logic. The basic rules for why the mind is as it is and not some other way.”

“That makes no sense. You cannot use logic to justify logic. Either you assume the rule work, or you’re an ass. Um, pardon my…”

“The meta-logic rules, I am saying, do not use logic to justify the axioms of logic logically—as you correctly point out, that would be a paradox. But what is the underpinning for logic in the ultimate sense?”

“It works.”

She smiled graciously. “Many philosophers believe this indicates an intimate connection between the laws of physics, the laws of mathematics, and the way the human mind works. Odd, is it not? In an infinite universe, why would we just so happen to evolve brains that could comprehend the laws that just so happen to underpin the physical universe?”

“Not so odd. I’ll tell you why. Natural selection and the damn fool common sense God gave a goose. Lookit here: Animals who thought is was the same as is not might think a predator what is about to eat them up, is not about to dine so fine, and then the natural difference between is and is not would be clear as either-or: namely either you vamoose out from those sharp teeth, or you’ll be an is not in no time.”

“Nicely spoken, but you are familiar with Divarication theory. You are one of its primary authors, are you not? Put any information value you wish into the expression for whatever gene controls the organism’s logic. Somewhere in the little bits of matter that make us up, is something written in our DNA—think of it as a symphony written in a chemical code of four notes—somewhere is the arpeggio that programs us to believe A is A. Estimate the volume needed to carry that abstraction forward between all the generations of organisms possessing neural systems since the pre-Cambrian. Look at how the figure falls out.”

He ran his finger on the mirror surface, and drew out a few calculations. “It’s impossible,” he said at last. “If there was a gene for logic, it would have mutated by now, and cropped up. There would be other creatures with other rules for other types of logic—which is something I can’t imagine, anyhow. I mean, even a mama bird counting her eggs don’t make twice two equal to five.”

“To me, this suggests a simpler and more universal structure to thought,” Rania said. “The laws of optics form a limiting set to the divarication for the principles of how to evolve an eye. Likewise, other laws must form a limit to how logic, language, and thought can evolve. The basic rules of the universe make it so that no organism can evolved into a rational creature for whom A equals not-A.”

“What are you saying?”

She pointed at the mirror: “That! The rules of meta-logic, my champion, is what you have in your brain. A set of neural logic gates which allow you to see meta-logical patterns, and recognize those patterns where they appear. It is your lance to slay my dragon. Because those patterns appear in the Monument: it is written in nothing but patterns.”

“Lady, I still don’t understand, and that is something I am not used to saying.”

“Remember the oldest problem in Sign Theory: How do you communicate with a species so alien that nothing in your psychology or culture is the same? How do you refer to things with no shared references? And I am suggesting we are looking at the handiwork of some race that solved that problem. The mere fact that the Monument exists proves that a universal language is possible, which means that the relation of field theory to physics to molecular chemistry to DNA to brain to brain structures to thought to logic to symbol cannot be arbitrary—despite that our Earthly theories hold them to be.”

“Math, logic, and physics are universal. So I guess that is the only thing aliens can talk with us about.”

“But they are only the beginning of the Monument message. What of other universals? But how do you make a symbol for honesty, for justice, for beauty, for love, for any abstraction?”

“Maybe those things come out of genetic adaptation to game-theory: organisms that don’t play fair enough to cooperate with natural allies can’t compete with mutual foes.”

“No,” she said, “I don’t believe it is merely game-theory. Or, I should say, what is game-theory based on? How do we teach our own children abstractions like truth and justice? Toddlers learn about right and wrong, about yes and no, forbidden and permitted, the basics of law and mercy, long before they learn to count. We do not teach them biology, then genetics, then the theory of the selfish Gene, then the theory of the natural harmony of self-interest, and then tell them it is not in their self-interest not to fib to their fathers. When a child is caught lying, what do you do?”

He straightened up and stepped away from the mirror, partly because the nearness was driving him mad, partly because he wanted to look at her face.

“Lecture ’em good, and take a strap to ’em, so to help remember them the lecture.”

“And what does that suggest?”

“Well—I reckon our kids learn universal concepts the way a baby bird learns birdsongs,” Montrose said. “Pain and pleasure mean ‘yes’ and ‘no.’ The signs we show them, simple things at first, like a swat on the rump, match like lock and key to something in their nervous system. Swat on the rump stimulates the pain centers wired to signal an avoid this behavior. Smiles and touches linked to ganglia wired up to express pleasure. Lock fits key.”

“Then how is it possible to talk to aliens?”

“I am not sure it is. No alien creature, things whose bodies are made of silicon rocks or methane soup or intelligent clouds of smog, things we can’t imagine, they are not going to have any locks in their brains—or whatever part of them does their thinking and fretting—that can possibly fit our keys. Our notions of justice and truth and beauty don’t mean spittle to them. How could you make a language to express things like that? Ideas that only make sense in a certain context? Except…” Menelaus frowned thoughtfully. “Same way we teach our babies, I guess. Teach them in context. Point and grunt. Swat then on the rump. Give a petting and a smile. But you would have to give them our nervous system first.”

“You think as I do. Go on.”

“Go on to what?” He said, exasperated. “You can’t send the context of the message before you send the message! What would that even mean? A language that deciphers itself? How do you do it?”

She smiled, and it was like the sun coming out.

“Simple. You encode the lock and the key both,” she continued. “The human brain is not really a lump of hydrogen and carbon, is it? It is a pattern of information. Anything that you grew in a tank that followed the code-pattern of the human genome would be human, would it not? A human brain made of another substance, provided the nerve cells operated in the same way, or in a way parallel to ours, would be human, would it not?”

“Ghost Del Azarchel thinks so, or so he told me.”

“And what is the human genome but a language, a code of information, a song of four notes, which could be recompiled into any system of other notes, the way a number line can be expressed in base two or base ten?”

He nodded. “I guess so. If you were intelligent, and you wanted to send a message, and the only thing you knew about the recipient was that he occupied the same universe with the same natural laws as you, you’d send the message with the messenger. The messenger would be coded up, expressed as a series of numbers, or logic signs, or something else universal. You show him how to build the lock, tumbler by tumbler, and then you show him where to put all the ridges on the key, tooth by tooth. Is that what you are getting at with all this weird talk of logic and meta-logic? The Monument is instructions on how to build a system that can read the Monument.”

“Not a system to read the Monument. A system to build a person who can learn to read it.”

“A messenger!” He smacked his fist into his palm and grinned. “Listen, we can build this messenger, this message-reading machine. You must know that Del Azarchel has made a breakthrough in brain emulation. He has got a perfect replica of himself, I mean perfect, talks like him, and over the phone Alan Turing couldn’t tell it weren’t him. If you have enough wealth, Princess, then you can afford to get me the computer space needed to build a second one…”

“It is not necessary.”

“No, no, listen! It’s a great idea. All you do is string up the models the same way the human brain is strung up, using the universal life-code here, translated into human DNA, and making the hardwiring of the brain follow those DNA instructions … Don’t make a model of Blackie, make a model of the brain that can read the Monument, based on the Monument’s own negative image of…”

“I am saying it is not necessary.”

“… unlike a real brain, there is no upper limit to … Wait. Why ain’t it necessary?”

“It’s been done.”

Such a wild hope entered his heart at that moment, he wondered if he were going mad. The key to the Monument was what this conversation was about! The key to the future of Mankind, and, yes, to the future of Menelaus as well. If his soul had been music, it would have roared into a crescendo at that moment.

He understood what she was saying.

“It’s you, Princess, isn’t it? You are the key. You, the starry messenger!” Menelaus pointed at the Monument. “Where and how exactly were you born, Princess? What part of that describes your code?”

Rania looked at him in puzzlement for a moment, and then mirth began dancing in her eyes, and she threw back her head, and peals of girlish laughter rang and echoed throughout the corridor.

“Oh, dear, no … forgive me for laughing, but … ah! The irony…”

“You’re not the key to the Monument?”

“Would that I were!” And just as suddenly as her joy appeared, sorrow now appeared.

“Well, who else?”

“You are.”

“Me?”

“You, Crewman Fifty-One, you. Don’t you see the connection?”

“Nope.”

“For a genius, you are not very bright.” She pointed back at the mirror. “Compare these two files. Don’t you see those are two different translations of the same thing, defined by the same algorithm?”

The first file was the Zurich run again. He had derived those parameters, of course, from the Monument math itself, manipulating symbols whose meaning he did not know, merely trusting that the unknown “grammar rules” of the aliens would make the conclusion valid if the axioms were valid.

The second file was a snapshot of the Theta sine symbol group of the Monument: a mathematical expression which, when translated into Earthly biochemistry, contained instructions on how to build or emulate a brain to read the Monument.

The two were the same. In using the Monument math to establish which nerve connections to use to become intelligent enough to read the Monument, Menelaus had unwittingly come to the same logic-path as the Monument instructions on how to read the Monument.

She said, “The pattern is an emergent property of the mathematics.”

“Why did they put the same thing in two places? I was not using the symbol-forms from that segment to do my brain-tinkering!”

“The Monument Builders are obsessed with recursions.”

Menelaus understood. The builders were trying to be as clear as possible, and so they repeated themselves. It was a communication strategy: two parts of a redundant message could be checked against each other for accuracy.

She said, “You did not know what you were doing to yourself, but you produced, in part of your cortex, something that follows this same pattern that repeats as a leitmotif in the Monument. Don’t you recall?”

“Recall what?”

“You were reading the Monument, sight-reading it, without notes, at a glance, from before I was born. Once you had the rules for reading symbols out of logic patterns build into your nervous system, you could not help but see them. That was part of what drove you mad.”

“At a glance? But—I thought I was a failure!”

“You were. What you did to your brain was ill-considered, stupidly rash, idiotic.” He liked her smile, sure enough, but he was not sure how much he liked her needling him.

“But I could read the Monument!” he protested.

“It that a tribute to your genius, or theirs? It was built to be read.”

3. Flight of Ideas

Then they were both talking at once. It was one of those conversations where each sentence was only a fragment for the other person to finish, a team conversation, with him and her merely contributing ideas as the stream of thought seemed to rush along under its own effort. For the first time since he laid eyes on her, Menelaus forgot she was gorgeous, and when he talked over her or shouted her down or called some idea of hers stupid, he did not notice it, any more than he noticed her interrupting him, or lashing him with golden laughter for his slow-wittedness.

The conversation theorized that solving the Monument was not a decryption problem; it was an emulation problem. The Monument seemed to contain no symbols beyond the basics. After the opening sequence, it was all meta-symbolism, like a DNA string, meant to produce symbols through a series of logic gates, but the expression would be in terms of game-theory.

That was why a computer emulation of an analog thinking machine was needed. They needed to model the meta-symbols and see them in action to see what they meant: see what came out of the rules of the game written out on the Monument surface.

“Each symbol’s range of meanings could be expressed as a cup-length. Under the Leray-Hirsch Theorem, a cohomology monomorphism could be described to express the all polydimensional vector subspaces involved. The opening sequence of symbols could be manipulated, even if they were not understood, by the game rules described by the Theta Group of symbols.” So spoke the conversation. Menelaus did not realize that it was his side of the conversation speaking, himself, until she interrupted.

She could not shout him down, her voice was too delicate, but she put her gloved fingers on his lips to say something, and the perfumed touch of silken fingertips, fingers slender as a child’s, snapped him out of his trance.

Menelaus was brought up short.

“… cannot overlook the possibility that your own nervous system structure was affected by the same game-theory codes embedded in the Monument. What was the expression you used to program that antique mainframe back in your day? The one that did a pattern recognition on possible nerve reorganization paths?”

Menelaus heard himself answer, but he did not pay attention to his own words. Because he was looking at her face.

It was shining. The eyes, green like emeralds in this light, or hazel as amber when she turned her head, were flickering, jumping from point to point, as if the mind behind them could read an encyclopedia of information out of the visual data impinging on her optic nerve. Then the eyes would grow still, staring, motionless, as if fixed on a distant star, a point on the far horizon.

And she was blushing. Her cheeks were pink, her hairline was beaded with sweat, and she had that glow about her that pregnant women were said to have. The look of abundant life.

His own cheeks were burning, too. His heart was pounding. Menelaus felt as if he might faint any moment.

Menelaus stepped back from her, stopping in mid-syllable. She was too excited to notice, but kept talking about Schubert calculus, Grassmann manifolds, fibered subspaces, the E8 supersymmetries.

For a moment his mind reeled. He could not follow what she was saying. How had she jumped to that conclusion? He tried to picture the geometric rotations she rapidly uttered, but found he could not visualize them, not and keep up. He had been following along, sometime leaping ahead of her line of proofs not half a moment ago. But now he was back in his right mind, and the dizzying architecture of speculations, certainties, and guesses was too great to hold in his imagination. The next step … was it correct or not? What was that about astro-algorithmic logic-gate matrices? In what sense was it a specific application of a more general case of emulating a universal virtual machine in n-dimensional coordinates?

Then he noticed she had his ceramic knife in her hand. He did not member handing it to her. She was scratching diagrams and equations in neat rows of Greek and Latin letters, alephs and infinities, as well as the dots and triangles and Celtic knots of Monument hieroglyphs, all along the wallpaper. She was cutting figures into the wood underneath the wallpaper. This was not modern wallpaper, not smart fabric meant to be written on. This was some antique and horribly expensive stuff, probably hand-painted, probably by Leonardo da Vinci and Michelangelo together, then touched up by Rembrandt, using solid gold paintbrushes.

And, of course, right next to her equations, in a larger, rougher handwriting, were his equations and notes. There was a deep scar where he had circled a particularly important multicovariable expression. And there were the slashes where he had put three exclamation points through the gold leaf into the wood paneling.

Next to him in the hallway was a crystal vase with flowers in it, carefully arranged. He plucked the bouquet out, hoisted the crystal jar, and dashed water into his own face.

The shock of the water helped somewhat. He no longer felt faint.

Princess Rania, who had been talking very loudly (for her), and very rapidly in an almost monotone singsong, now stopped. She turned.

All at once she was in his arms, on her tiptoes, and kissing him passionately.

It was like a bolt of lighting traveled up his spine. It was perfect.

And, then, just as suddenly, it was not perfect. She writhed out of his grasp, elusive as starlight, graceful as a sleek lioness, and danced back, her face blank.

He was looking right at her face when it happened: her expression returned to normal. It was like watching a ghost fade out of the body of some possessed person on those old faith healer shows everyone in his family save him used to watch so raptly. Like an actress turning off a character and surfacing. But not like an actress. There was nothing fake about it.

She was not panting, but Rania was breathing a little heavily. Long, slow breaths that made her bosom rise and fall.

“You’re the other one. Ah. Welcome back.”

This time, he understood how she slipped so effortlessly out of his hands: the point at which his two arms could trap her formed a folded set that could be expressed as a Hilbert space. Solving for the shortest vector distance, she leaned on his arm, and when he instinctively tightened it, she had put her center of balance elsewhere at the point of least resistance. It was as perfect as a ballet move. He wondered if the speed of her nerve impulses traveling to her muscles was momentarily increased, it was so smooth, and so rapid.

“Your are possessed, too, ain’t you? You are a Mrs. Hyde!”

Rania stared at him quizzically.

“Miss Hyde, I would prefer. I am a maiden yet.” She showed dimples when she smiled. “Unless you are proposing? I warn you, I am spoken for.”

Menelaus backed up, his arm raised as if to ward off a blow. “You are not in love with Del Azarchel!”

“I don’t recall saying I was.”

“You are in love with me.”

“Define your terms,” she said, favoring him with an arch look. She wiggled the knife at him playfully. He carefully took it from her gloved hand, and slipped it back up his sleeve.

“No normal girl says define your terms when you say you are in love with me.”

She nodded judiciously. “Being normal is a goal oft sought and rarely achieved, but not unenviable for all that. Statistically speaking, it would be unusual if everyone were average.”

“You are in love with the other me. Mr. Hyde. The Daemon. Crewman Fifty-One.”