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.