it well, of course, and you also know you can never come to the end of pi. There's no creature in the universe, no matter how smart, who could calculate pi to the last digit—because there is no last digit, only an infinite number of digits. Your mathematicians have made an effort to calculate it out to… ”
Again she felt the tingle.
“…none of you seem to know…. Let's say the ten-billionth place. You won't be surprised to bear that other mathematicians have gone further. Well, eventually—let's say it's in the ten-to-the-twentieth-power place— something happens. The randomly varying digits disappear, and for an unbelievably long time there's nothing but ones and zeros.”
Idly, he was tracing a circle out on the sand with his toe. She paused a heartbeat before replying.
“And the zeros and ones finally stop? You get back to a random sequence of digits?” Seeing a faint sign of encouragement from him, she raced on. “And the number of zeros and ones? Is it a product of prime numbers?”
“Yes, eleven of them.”
“You're telling me there's a message in eleven dimensions hidden deep inside the number pi? Someone in the universe communicates by… mathematics? But… helpme, I'm really having trouble understanding you. Mathematics isn't arbitrary. I mean pi has to have the same value everywhere. How can you hide a message inside pi? It's built into the fabric of the universe.”
“Exactly.” She stared at him.
“It's even better than that,” he continued. “Let's assume that only in base-ten arithmetic does the sequence of zeros and ones show up, although you'd recognize that something funny's going on in any other arithmetic. Let's also assume that the beings who first made this discovery had ten fingers. You see how it looks? It's as if pi has been waiting for billions of years for ten-fingered mathematicians with fast computers to come along. You see, the Message was kind of addressed to us.”
“But this is just a metaphor, right? It's not really pi and the ten to the twentieth place? You don't actually nave ten fingers.”
“Not really.” He smiled at her again. “Well, for heaven's sake, what does the Message say?” He paused for a moment, raised an index finger, and then pointed to the door. A small crowd of people was excitedly pouring out of it.
They were in a jovial mood, as if this were a long-delayed picnic outing. Eda was accompanying a stunning young woman in a brightly colored blouse and skirt, her hair neatly covered with the lacy gele favored by Moslem women in Yorubaland; he was clearly overjoyed to see her. From photographs he had shown, Ellie recognized her as Eda's wife. Sukhavati was holding hands with an earnest young man, his eyes large and soulful; she assumed it was Surindar Ghosh, Devi's long-dead medical-student husband. Xi was in animated discourse with a small vigorous man of commanding demeanor, he had drooping wispy mustaches and was garbed in a richly brocaded and beaded gown. Ellie imagined him personally overseeing the constrution of the funerary model of the Middle Kingdom, shouting instructions to those who poured the mercury.
Vaygay ushered over a girl of eleven or twelve, her blond braids bobbing as she walked.
“This is my granddaughter, Nina… more or less. My Grand Duchess. I should have introduced you before. In Moscow.”
Ellie embraced the girl. She was relieved that Vaygay had not appeared with Meera, the ecdysiast. Ellie observed his tenderness toward Nina and decided she liked him more than ever. Over all the years she had known him, he had kept this secret place within his heart well hidden.
“I have not been a good father to her mother,” he confided. “These days, I hardly see Nina at all.”
She looked around her. The Stationmasters had produced for each of the Five what could only be described as their deepest loves. Perhaps it was only to ease the barriers of communication with another, appallingly different species. She was glad none of them were happily chatting with an exact copy of themselves.
What if you could do this back on Earth? she wondered. What if, despite all our pretense and disguise, it was necessary to appear in public with the person we loved most of all? Imagine this a prerequisite for social discourse on Earth. It would change everything. She imagined a phalanx of members of one sex surrounding a solitary member of the other. Or chains of people. Circles. The letters “H” or “Q.” Lazy figure-8s. You could monitor deep affections at a glance, just by looking at the geometry—a kind of general relativity applied to social psychology. The practical difficulties of such an arrangement would be considerable, but no one would be able to lie about love.
The Caretakers were in a polite but determined hurry. There was not much time to talk. The entrance to the air-lock of the dodecahedron was now visible, roughly where it had been when they first arrived. By symmetry, or perhaps because of some interdimensional conservation law, the Magritte doorway had vanished. They introduced everyone. She felt silly, in more ways than one, explaining in English to the Emperor Qin who her father was. But Xi dutiftilly translated, and they all solemnly shook hands as if this were their first encounter, perhaps at a suburban barbecue. Eda's wife was a considerable beauty, and Surindar Ghosh was giving her a more than casual inspection. Devi did not seem to mind; perhaps she was merely gratified at the accuracy of the imposture.
“Where did you go when you stepped through the doorway?” Ellie softly asked her. “Four-sixteen Maidenhall Way,” she answered. Ellie looked at her blankly. “London, 1973. With Surindar.” She nodded her head in his direction. “Before he died.” Ellie wondered what she would have found had she crossed that threshold on the beach. Wisconsin in the late “50s, probably. She hadn't shown up on schedule, so he had come to find her. He had done that in Wisconsin more than once.
Eda had also been told about a message deep inside a transcendental number, but in his story it was not? or e, the base of natural logarithms, but a class of numbers she had never heard of. With an infinity of transcendental numbers, they would never know for sure which number to examine back on Earth.
“I hungered to stay and work on it,” he told Ellie softly, “and I sensed they needed help—some way of thinking about the decipherment that hadn't occurred to them. But I think it's something very personal for them. They don't want to share it with others. And realistically, I suppose we just aren't smart enough to give them a hand.”
They hadn't decrypted the message in?? The Station-masters, the Caretakers, the designers of new galaxies hadn't figured out a message that had been sitting under their thumbs for a galactic rotation or two?
Was the message that difficult, or were they…? “Time to go home,” her father said gently. It was wrenching. She didn't want to go. She tried staring at the palm frond. She tried asking more questions.
“How do you mean “go home'? You mean we're going to emerge somewhere in the solar system? How will we get down to Earth?”
“You'll see,” he answered. “It'll be interesting.” He put his arm around her waist, guiding her toward the open airlock door.
It was like bedtime. You could be cute, you could ask bright questions, and maybe they'd let you stay up a little later. It used to work, at least a little.
“The Earth is linked up now, right? Both ways. If we can go home, you can come down to us in a jiffy.
You know, that makes me awfully nervous. Why don't yon just sever the link? We'll take it from here.”
“Sorry, Presh,” he replied, as if she had already shamelessly prolonged her eight o'clock bedtime. Was he sorry about bedtime, or about being unready to denozzle the tunnel? “For a while at least, it'll be open only to inbound traffic,” he said. “But we don't expect to use it.”
She liked the isolation of the Earth from Vega. She preferred a fifty-two-year-long leeway between unacceptable behavior on Earth and the arrival of a punitive expedition. The black hole link was uncomfortable. They could arrive almost instantaneously, perhaps only in Hokkaido, perhaps anywhere on Earth. It was a transition to what Hadden had called microintervention. No matter what assurances they gave, they would watch us more closely now. No more dropping in for a casual look-see every few million years.
She explored her discomfort further. How… theological… the circumstances had become. Here were beings who live in the sky, beings enormously knowledgeable and pow-erful, beings concerned for our survival, beings with a set of expectations about how we should behave. They disclaim such a role, but they could clearly visit reward and punishment, life and death, on the puny inhabitants of Earth. Now how is this different, she asked herself, from the old-time religion? The answer occurred to her instantly: It was a matter of evidence. In her videotapes, in the data the others had acquired, there would be hard evidence of the existence of the Station, of what went on here, of the blackhole transit system. There would be five independent, mutually corroborative
