Anne transmitted her coordinates and flight plan.
“We confirm your location, please identify yourself.”
“My name is Anne. I come from another star.”
There was a long pause, then a different voice answered. “If you are from Ghahar, please explain your intentions.”
“I am not from Ghahar.”
“Why should I believe that? Show yourself.”
“I’ve taken the same shape as your people, in the hope of living among you for a while.” Anne opened a video channel and showed them her unremarkable Noudah face. “But there’s a signal being transmitted from these coordinates that might persuade you that I’m telling the truth.” She gave the location of the decoy node, twenty light years away, and specified a frequency. The signal coming from the node contained an image of the very same face.
This time, the silence stretched out for several minutes. It would take a while for the Tirans to confirm the true distance of the radio source.
“You do not have permission to land. Please enter this orbit, and we will rendezvous and board your ship.”
Parameters for the orbit came through on the data channel. Anne said, “As you wish.”
Minutes later, Joan’s instruments picked up three fusion ships being launched from Tiran bases. When Anne reached the prescribed orbit, Joan listened anxiously to the instructions the Tirans issued. Their tone sounded wary, but they were entitled to treat this stranger with caution, all the more so if they believed Anne’s claim.
Joan was accustomed to a very different kind of reception, but then the members of the Amalgam had spent hundreds of millennia establishing a framework of trust. They also benefited from a milieu in which most kinds of force had been rendered ineffectual; when everyone had backups of themselves scattered around the galaxy, it required a vastly disproportionate effort to inconvenience someone, let alone kill them. By any reasonable measure, honesty and cooperation yielded far richer rewards than subterfuge and slaughter.
Nonetheless, each individual culture had its roots in a biological heritage that gave rise to behavior governed more by ancient urges than contemporary realities, and even when they mastered the technology to choose their own nature, the precise set of traits they preserved was up to them. In the worst case, a species still saddled with inappropriate drives but empowered by advanced technology could wreak havoc. The Noudah deserved to be treated with courtesy and respect, but they did not yet belong in the Amalgam.
The Tirans’ own exchanges were not on open channels, so once they had entered Anne’s ship Joan could only guess what was happening. She waited until two of the ships had returned to the surface, then sent her own message to Ghahar’s traffic control.
“I come in peace from another star. I seek permission to land.”
3
The Ghahari allowed Joan to fly her ship straight down to the surface. She wasn’t sure if this was because they were more trusting, or if they were afraid that the Tirans might try to interfere if she lingered in orbit.
The landing site was a bare plain of chocolate colored sand. The air shimmered in the heat, the distortions intensified by the thickness of the atmosphere, making the horizon waver as if seen through molten glass. Joan waited in the cockpit as three trucks approached; they all came to a halt some twenty meters away. A voice over the radio instructed her to leave the ship; she complied, and after she’d stood in the open for a minute, a lone Noudah left one of the trucks and walked toward her.
“I’m Pirit,” she said. “Welcome to Ghahar.” Her gestures were courteous but restrained.
“I’m Joan. Thank you for your hospitality.”
“Your impersonation of our biology is impeccable.” There was a trace of skepticism in Pirit’s tone; Joan had pointed the Ghahari to her own portrait being broadcast from the decoy node, but she had to admit that in the context her lack of exotic technology and traits would make it harder to accept the implications of that transmission.
“In my culture, it’s a matter of courtesy to imitate one’s hosts as closely as possible.”
Pirit hesitated, as if pondering whether to debate the merits of such a custom, but then rather than quibbling over the niceties of interspecies etiquette she chose to confront the real issue head on. “If you’re a Tiran spy, or a defector, the sooner you admit that the better.”
“That’s very sensible advice, but I’m neither.”
The Noudah wore no clothing as such, but Pirit had a belt with a number of pouches. She took a hand-held scanner from one and ran it over Joan’s body. Joan’s briefing suggested that it was probably only checking for metal, volatile explosives and radiation; the technology to image her body or search for pathogens would not be so portable. In any case, she was a healthy, unarmed Noudah down to the molecular level.
Pirit escorted her to one of the trucks, and invited her to recline in a section at the back. Another Noudah drove while Pirit watched over Joan. They soon arrived at a small complex of buildings a couple of kilometers from where the ship had touched down. The walls, roofs and floors of the buildings were all made from the local sand, cemented with an adhesive that the Noudah secreted from their own bodies.
Inside, Joan was given a thorough medical examination, including three kinds of full-body scan. The Noudah who examined her treated her with a kind of detached efficiency devoid of any pleasantries; she wasn’t sure if that was their standard bedside manner, or a kind of glazed shock at having been told of her claimed origins.
Pirit took her to an adjoining room and offered her a couch. The Noudah anatomy did not allow for sitting, but they liked to recline.
Pirit remained standing. “How did you come here?” she asked.
“You’ve seen my ship. I flew it from Baneth.”
“And how did you reach Baneth?”
“I’m not free to discuss that,” Joan replied cheerfully.
“Not free?” Pirit’s face clouded with silver, as if she was genuinely perplexed.
Joan said, “You understand me perfectly. Please don’t tell me there’s nothing you’re not free to discuss with me.”
“You certainly didn’t fly that ship twenty light years.”
“No, I certainly didn’t.”
Pirit hesitated. “Did you come through the Cataract?” The Cataract was a black hole, a remote partner to the Noudah’s sun; they orbited each other at a distance of about eighty billion kilometers. The name came from its telescopic appearance: a dark circle ringed by a distortion in the background of stars, like some kind of visual aberration. The Tirans and Ghahari were in a race to be the first to visit this extraordinary neighbor, but as yet neither of them were quite up to the task.
“Through the Cataract? I think your scientists have already proven that black holes aren’t shortcuts to anywhere.”
“Our scientists aren’t always right.”
“Neither are ours,” Joan admitted, “but all the evidence points in one direction: black holes aren’t doorways, they’re shredding machines.”
“So you traveled the whole twenty light years?”
“More than that,” Joan said truthfully, “from my original home. I’ve spent half my life traveling.”
“Faster than light?” Pirit suggested hopefully.
“No. That’s impossible.”
They circled around the question a dozen more times, before Pirit finally changed her tune from how to why?
“I’m a xenomathematician,” Joan said. “I’ve come here in the hope of collaborating with your archaeologists in their study of Niah artifacts.”
Pirit was stunned. “What do you know about the Niah?”
“Not as much as I’d like to.” Joan gestured at her Noudah body. “As I’m sure you’ve already surmised, we’ve listened to your broadcasts for some time, so we know pretty much what an ordinary Noudah knows. That includes the basic facts about the Niah. Historically they’ve been referred to as your ancestors, though the latest studies suggest that you and
they really just have an earlier common ancestor. They died out about a million years ago, but there’s evidence that they might have had a sophisticated culture for as long as three million years. There’s no indication that they ever developed space flight. Basically, once they achieved material comfort, they seem to have devoted themselves to various artforms, including mathematics.”
“So you’ve traveled twenty light years just to look at Niah tablets?” Pirit was incredulous.
“Any culture that spent three million years doing mathematics must have something to teach us.”
“Really?” Pirit’s face became blue with disgust. “In the ten thousand years since we discovered the wheel, we’ve already reached halfway to the Cataract. They wasted their time on useless abstractions.”
Joan said, “I come from a culture of spacefarers myself, so I respect your achievements. But I don’t think anyone really knows what the Niah achieved. I’d like to find out, with the help of your people.”
Pirit was silent for a while. “What if we say no?”
“Then I’ll leave empty-handed.”
“What if we insist that you remain with us?”
“Then I’ll die here, empty-handed.” On her command, this body would expire in an instant; she could not be held and tortured.
Pirit said angrily, “You must be willing to trade something for the privilege you’re demanding!”
“Requesting, not demanding,” Joan insisted gently. “And what I’m willing to offer is my own culture’s perspective on Niah mathematics. If you ask your archaeologists and mathematicians, I’m sure they’ll tell you that there are many things written in the Niah tablets that they don’t yet understand. My colleague and I—” neither of them had mentioned Anne before, but Joan was sure that Pirit knew all about her “— simply want to shed as much light as we can on this subject.”
Pirit said bitterly, “You won’t even tell us how you came to our world. Why should we trust you to share whatever you discover about the Niah?”
“Interstellar travel is no great mystery,” Joan countered. “You know all the basic science already; making it work is just a matter of persistence. If you’re left to develop your own technology, you might even come up with better methods than we have.”
“So we’re expected to be patient, to discover these things for ourselves ... but you can’t wait a few centuries for us to decipher the Niah artifacts?”
Joan said bluntly, “The present Noudah culture, both here and in Tira, seems to hold the Niah in contempt. Dozens of partially excavated sites containing Niah artifacts are under threat from irrigation projects and other developments. That’s the reason we couldn’t wait. We needed to come here and offer our assistance, before the last traces of the Niah disappeared forever.”
Pirit did not reply, but Joan hoped she knew what her interrogator was thinking: Nobody would cross twenty light years for a few worthless scribblings. Perhaps we’ve underestimated the Niah. Perhaps our ancestors have left us a great secret, a great legacy. And perhaps the fastest – perhaps the only – way to uncover it is to give this impertinent, irritating alien exactly what she wants.
4
The sun was rising ahead of them as they reached the top of the hill. Sando turned to Joan, and his face became green with pleasure. “Look behind you,” he said.
Joan did as he asked. The valley below was hidden in fog, and it had settled so evenly that she could see their shadows in the dawn light, stretched out across the top of the fog layer. Around the shadow of her head was a circular halo like a small rainbow.
“We call it the Niah’s light,” Sando said. “In the old days, people used to say that the halo proved that the Niah blood was strong in you.”
Joan said, “The only trouble with that hypothesis being that you see it around your head ... and I see it around mine.” On Earth, the phenomenon was known as a “glory”. The particles of fog were scattering the sunlight back toward them, turning it one hundred and eighty degrees. To look at the shadow of your own head was to face directly away from the sun, so the halo always appeared around the observer’s shadow.
“I suppose you’re the final proof that Niah blood has nothing to do with it,” Sando mused.
“That’s assuming I’m telling you the truth, and I really can see it around my own head.”
“And assuming,” Sando added, “that the Niah really did stay at home, and didn’t wander around the galaxy spreading their progeny.”
They came over the top of the hill and looked down into the adjoining riverine valley. The sparse brown grass of the hillside gave way to a lush violet growth closer to the water. Joan’s arrival had delayed the flooding of the valley, but even alien interest in the Niah had only bought the archaeologists an extra year. The dam was part of a long-planned agricultural development, and however tantalizing the possibility that Joan might reveal some priceless insight hidden among the Niah’s “useless abstractions”, that vague promise could only compete with more tangible considerations for a limited time.
Part of the hill had fallen away in a landslide a few centuries before, revealing more than a dozen beautifully preserved strata. When Joan and Sando reached the excavation site, Rali and Surat were already at work, clearing away soft sedimentary rock from a layer that Sando had dated as belonging to the Niah’s “twilight” period.
Pirit had insisted that only Sando, the senior archaeologist, be told about Joan’s true nature; Joan refused to lie to anyone, but had agreed to tell her colleagues only that she was a mathematician and that she was not permitted to discuss her past. At first this had made them guarded and resentful, no doubt because they assumed that she was some kind of spy sent by the authorities to watch over them. Later it had dawned on them that she was genuinely interested in their work, and that the absurd restrictions on her topics of conversation were not of her own choosing. Nothing about the Noudah’s language or appearance correlated strongly with their recent division into nations – with no oceans to cross, and a long history of migration they were more or less geographically homogeneous – but Joan’s odd name and occasional faux pas could still be ascribed to some mysterious exoticism. Rali and Surat seemed content to assume that she was a defector from one of the smaller nations, and that her history could not be made explicit for obscure political reasons.
“There are more tablets here, very close to the surface,” Rali announced excitedly. “The acoustics are unmistakable.” Ideally they would have excavated the entire hillside, but they did not have the time or the labor, so they were using acoustic tomography to identify likely deposits of accessible Niah writing, and then concentrating their efforts on those spots.
The Niah had probably had several ephemeral forms of written communication, but when they found something worth publishing, it stayed published: they carved their symbols into a ceramic that made diamond seem like tissue paper. It was almost unheard of for the tablets to be broken, but they were small, and multi-tablet works were sometimes widely dispersed. Niah technology could probably have carved three million years’ worth of knowledge on to the head of a pin – they seemed not to have invented nanomachines, but they were into high quality bulk materials and precision engineering – but for whatever reason they had chosen legibility to the naked eye above other considerations.
Joan made herself useful, taking acoustic readings further along the slope, while Sando watched over his students as they came closer to the buried Niah artifacts. She had learned not to hover around expectantly when a discovery was imminent; she was treated far more warmly if she waited to be summoned. The tomography unit was almost foolproof, using satellite navigation to track its position and software to analyze the signals it gathered; all it really needed was someone to drag it along the rock face at a suitable pace.
Through the corner of her eye, Joan noticed her shadow on the rocks flicker and grow complicated. She looked up to see three dazzling beads of light flying west out of the sun. She might have assumed that th
e fusion ships were doing something useful, but the media was full of talk of “military exercises”, which meant the Tirans and the Ghahari engaging in expensive, belligerent gestures in orbit, trying to convince each other of their superior skills, technology, or sheer strength of numbers. For people with no real differences apart from a few centuries of recent history, they could puff up their minor political disputes into matters of the utmost solemnity. It might almost have been funny, if the idiots hadn’t incinerated hundreds of thousands of each other’s citizens every few decades, not to mention playing callous and often deadly games with the lives of the inhabitants of smaller nations.
“Jown! Jown! Come and look at this!” Surat called to her. Joan switched off the tomography unit and jogged toward the archaeologists, suddenly conscious of her body’s strangeness. Her legs were stumpy but strong, and her balance as she ran came not from arms and shoulders but from the swish of her muscular tail.
“It’s a significant mathematical result,” Rali informed her proudly when she reached them. He’d pressure-washed the sandstone away from the near-indestructible ceramic of the tablet, and it was only a matter of holding the surface at the right angle to the light to see the etched writing stand out as crisply and starkly as it would have a million years before.
Rali was not a mathematician, and he was not offering his own opinion on the theorem the tablet stated; the Niah themselves had a clear set of typographical conventions which they used to distinguish between everything from minor lemmas to the most celebrated theorems. The size and decorations of the symbols labeling the theorem attested to its value in the Niah’s eyes.
Joan read the theorem carefully. The proof was not included on the same tablet, but the Niah had a way of expressing their results that made you believe them as soon as you read them; in this case the definitions of the terms needed to state the theorem were so beautifully chosen that the result seem almost inevitable.
The theorem itself was expressed as a commuting hypercube, one of the Niah’s favorite forms. You could think of a square with four different sets of mathematical objects associated with each of its corners, and a way of mapping one set into another associated with each edge of the square. If the maps commuted, then going across the top of the square, then down, had exactly the same effect as going down the left edge of the square, then across: either way, you mapped each element from the top-left set into the same element of the bottom-right set. A similar kind of result might hold for sets and maps that could naturally be placed at the corners and edges of a cube, or a hypercube of any dimension. It was also possible for the square faces in these structures to stand for relationships that held between the maps between sets, and for cubes to describe relationships between those relationships, and so on.