“—Old? The portrait was painted last year. We are somewhat apart in age, out of synch, as her body, born in space, could not adjust properly to earth-normal conditions, and years she spent in ageless slumber while a cure was sought. We call it ‘Earthsickness.’ Do not think I am too old to admire her charms, nor to father a dynasty on her, since I learned the secret of—”

“—hell, Blackie! You can’t hold a brain-damaged man responsible for what might come out of his mouth! Did I say something I shouldn’t’ve to her?”

But Del Azarchel was not listening. He was staring at the glass table. He put his hand down and froze the image. The counter read 113. “What is that? What are they looking at?”

Montrose looked.

3. Opening Statement

The input angle was almost directly above the naked figure crouched in the cold room. An image of the Monument was glowing darkly in the floor, distorted only where cables and squat cylindrical units stood here and there in the space.

Montrose stared at the freeze-frame.

There was something hypnotically regular about the alien hieroglyphs. The center of the image showed a slightly off-center ellipse of concentric lines-within-lines, each line composed of circles and triangles, of crooked lines, angles acute and obtuse, and sine curves, hypnotically repeating patterns like the ripples seen at low tide. Circumscribing the oval was a central triangle composed of more symbols, and at the corners of the triangle were three shapes: a triangle, a circle, a parabola.

It was a maddening thing to stare at, because the mind’s eye kept seeing patterns in the chaos, like seeing faces in the clouds. Surely those four dots there were meant to form a square? The three overlapping circles—what could it be but the alien version of a simple Venn diagram? And didn’t that set of glyphs look something like the Bohr model of the atom? Or maybe the rings of Saturn? On the other hand, that cluster of squiggles in the northeast quadrant looked like the coastline of Norway, and that set of hooked sine waves looked like his Aunt Bertholda’s nose.

Montrose said meditatively, “The main figure in the main statement is an isosceles triangle, but what does it stand for? And the oval that surrounds it—could mean anything. Look at the symbols the Monument Builders put at the two foci. See? That value is the difference between the hydrogen atom and hydroxyl molecule natural-emission frequencies, 21 centimeters and 18 centimeters multiplied to twelve values by the Fibonacci sequence, forms the ratio between the foci and the major axis of the figure. It is the kind of mathematical nicety any technological civilization expecting to make contact with any other technological civilization would expect us to know. I mean, if we are not listening on the Cold Hydrogen radio-frequency, we are not animals curious enough to be interesting in talking, I guess. And if we don’t have the math for the Fibonacci sequence, well, then, we are too dumb to talk to. So that part is pretty obvious, which is why that put it in the alpha group, the opening statement cartouche.”

“No, I know that,” said Del Azarchel impatiently. “The opening sequence was the first thing we translated. It sets up the basic logic signs, affirmative and negative, A is A, all that. The two legs of the triangle represent their symbol for a binary choice. Either-or. That is not what I am talking about. This equation here. It only flickered into the floorscreens for a moment, at the sixty-eight-minute mark. They—the other version of you and the other version of me—derived this expression from folding the image like an origami, getting the Eta and the Epsilon sequence to overlap…”

Montrose could not take his eyes from the opening sequence. Filled circle meant “is” and empty circle meant “is not,” and that capital-V-looking doo-dad meant “either-or.” The symbols at the corner of the main equilateral triangle of script each stood for a principle of formal logic. The law of identity, or “is” is “is”; the law of noncontradiction, or “is” is not “is not”; and the law of mutual exclusion, or “either-or.”

The Beta Sequence sprang directly out of the Alpha Sequence. Here were transformations topologically identical to Venn diagrams and Tables of Oppositions. Logic and then mathematics. Dash stood for the number two, isosceles triangles for three, hexagon meant nine, nine-sided polygon meant eighty-one. Like the ancient Greeks, the Monument Builders did not seem to have a letter for one or zero, but instead used a complex expression for the concepts: two divided by two and two minus two. Radiating from the Beta Sequence in order were certain irrational numbers like pi and the square root of two that any mathematician would find fascinating. Then was the Pythagorean theorem. Next was some theorem human geometry never stumbled across. Then, like old friends, were the Euclidean solids, but written out as Cartesian algorithms.

“The Monument is a No Trespassing sign,” said Menelaus.

“What?” Del Azarchel asked. His voice was tense.

Menelaus noticed Del Azarchel’s eyes were swiveling slowly in their sockets, not able to focus on Menelaus’s eyes. It seemed an odd phenomenon.

Montrose spoke slowly enough to match Del Azarchel’s biological frame of reference. “It does not say: Welcome to the stars. It says: You belong to us.”

4. Intelligence Test

Montrose saw his own face in the tabletop glass turn toward him, turn toward the camera, turn as if he knew the sleepwalker version of himself would see this scene from this angle.

The lips moved. It was gibberish. Somehow, whether from memory or inspiration or some quirk of his own mind, he recognized it as an invented, impromptu thirty-six-tonal language with several parallel channels of communication:

The Diamond Star is an intelligence test as well as a trap. It is a watering hole. Their voyage from Epsilon Tauri will take eight thousand, six hundred years. Assuming they launched immediately when we began star-mining in earnest, we have untilA.D.10917 in the Eleventh Millennium.…

There was also a pain in his head, an ache behind his eyes, as if his nervous system recalled the strain it had just been under, and was rebelling against attempting such strains again.

By mining the Diamond Star we proved our race was smart enough to be useful slaves to the hegemony of machine intelligences swarming through the Hyades Cluster one hundred fifty-one lightyears from Earth. The relative difference in racial intelligence means that energy expenditures to launch the Earth-Conquering Armada will be minimized: They cannot afford to accelerate their World Armada past point zero one eight percent of the speed of light, some five million meters per second. The calculations shown here describe the energy expense to conquer us will be below detectable threshold values: In military terms, the equation puts their war coffer amounts at near zero. This is due to the steepness of the negative power imbalance, which stands as near-vertical. Because of our relative worthlessness as a slave-race, but because of the relative cheapness of transport costs, they intend to use the human race as a form of …

Click. Del Azarchel had shut off the table. It was like a spell being broken. The look in the eyes staring up at him from the glass was gone. The strange notes of music, the eerie song, went silent.

Intend to use the human race as a form of … what? But it was gone.

Menelaus rubbed his temples. His mouth was dry. “The Earth is in someone else’s backyard. Our civilization, everything we have, our smarts, our accomplishments, the natural resources of the solar system, our future, our golden future … they own it.”