She was silent half a minute. When she spoke, it sounded almost annoyed. “How can you be so sure?”
“Why, it’s obvious,” he answered, surprised. “The radiation from our powerplant ran well ahead of us only during the first year, till we got close to light speed. That wouldn’t give them nearly enough warning, if they set out to meet us when they picked it up. They can’t live close by, or we’d have detected them from the Solar System.”
“Obvious, or smug?” she challenged. “How much do we know? We have barely begun our first tiny venture into deep space. How long have they been exploring? Thousands of years? Millions? What have they discovered, what can they do?”
His smile twisted. “I’m sorry. This is no moment to cast a shadow on.” He sighed. “But I’ve met a great many dreams over the centuries, and most of them turned out to be no more than that. It’s been quite some time since our physicists decided they’d found all the laws of nature, all the possibilities and impossibilities.” He lifted a hand. “I realize that’s a proposition that can never be proven. But the likelihood has come to seem very high, hasn’t it? I’d love to learn the aliens own magic carpets flitting faster than tight; but I don’t expect to.”
Reluctantly, she nodded. “At least, we roust reason on the basis of what we do know. I suspect that’s far less than you think, but— What shall we do?”
“Respond.”
“Of course! But how? I mean, we’re slowing down, but we’re still near light speed. By the tune the, tile machine, any of those machines up ahead receives our signal, won’t we be past it? Won’t its answer take … years to overtake us?”
He squeezed her hand. “Smart girl. You always were.” To the ship: “We want to establish contact as soon as may be. What do you advise?”
The answer jarred them both into bolt uprightness. “That is contingent. The transmission has changed character. It has become considerably more complex.”
“You, you mean they know we’re here? Where are they, anyway?”
“I am refining those figures as I obtain more parallax. The nearest source is approximately a light-year off our path, approximately twice that distance vectorially.”
“Baal! Then they can detect us instantly?”
“No. No, wait, Hanno.” Svoboda’s words came a little unsteadily, but fast. “That needn’t be. Suppose the broadcast is automatic, a cycle. First a simple alert signal, then the message, then the alert signal again, over and over. The message alone—we might not have recognized it for what it is, supposed it was just some natural thing.”
“When I first acquired it,” Pytheas volunteered, “I assumed it was a fluctuation in the background noise, conceivably of interest to astrophysicists but irrelevant to this mission. It was Dopplered and otherwise warped out of identifiability. The low-information transmission that succeeded it made clear that here is no random flux. It also provided unambiguous data by which the warp functions could be determined. I am now compensating for them and thus reconstructing the message proper.”
Hanno sagged back. “How often have they done this,” he whispered, “with how many others?”
“The reconstruction is not yet perfect, but it continually improves as additional data come in,” Pytheas went on. “Since the cycle is short, in shipboard time, I should soon have good definition. The message itself must be fairly brief, with high redundancy, although I anticipate high resolution as well. This is a visual mapping.”
Darkness brimmed in a screen. Suddenly it was full of tiny light-points, uncountably numerous. Their blumness dissipated, they sharpened, minute by minute. Colors appeared in them, and with that help eyes began to make out three-dimensional shapes, self-recurrent in infinite complexity.
“Prime numbers define a coordinate space,” said the ship. “Digital impulses identify points within it, which hi turn are members of fractal sets. Those functions should provide images, but the proper combinations must be found empirically. My mathematical component is running the search. When something intelligible emerges, that should give clues to obtaining further refinement and eventually extracting the entire content.”
“Well,” said Svoboda dazedly, “if the computers on Earth could design you in a single year—”