by Carl Sagan
“It seems to be the same everywhere. In our case, we emerged a long time ago on many different worlds in the Milky Way. The first of us developed interstellar space-flight, and eventually chanced on one of the transit stations. Of course, we didn’t know what it was. We weren’t even sore it was artificial until the first of us were brave enough to slide down.”
“Who’s ‘we’? You mean the ancestors of your…race, your species?”
“No, no. We’re many species from many worlds. Eventually we found a large number of subways—various ages, various styles of ornamentation, and all abandoned. Most were still in good working condition. All we did was make some repairs and improvements.”
“No other artifacts? No dead cities? No records of what happened? No subway builders left?”
He shook his head.
“No industrialized, abandoned planets?”
He repeated the gesture.
“There was a Galaxy-wide civilization that picked up and left without leaving a trace—except for the stations?”
“That’s more or less right. And it’s the same in other galaxies also. Billions of years ago, they all went somewhere. We haven’t the slightest idea where.”
“But where could they go?”
He shook his head for the third time, but now very slowly.
“So then you’re not…”
“No, we’re just caretakers,” he said. “Maybe someday they’ll come back.”
“Okay, just one more,” she pleaded, holding her index finger up before her as, probably, had been her practice at age two. “One more question.”
“All right,” he answered tolerantly. “But we only have a few minutes left.”
She glanced at the doorway again, and suppressed a tremor as a small, almost transparent crab sidled by.
• • •
“I want to know about your myths, your religions. What fills you with awe? Or are those who make the numinous unable to feel it?”
“You make the numinous also. No, I know what you’re asking. Certainly we feel it. You recognize that some of this is hard for me to communicate to you. But I’ll give yon an example of what you’re asking for. I don’t say this is it exactly, but it’ll give you a…”
He paused momentarily and again she felt a tingle, this time in her left occipital lobe. She entertained the notion that he was rifling through her neurons. Had he missed something last night? If so, she was glad. It meant they weren’t perfect.
“…flavor of our numinous. It concerns pi, the ratio of the circumference of a circle to its diameter. You know 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 hear 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…help me, 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 have 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 construction 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 dutifully 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.<
br />
“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 π 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 π? The Stationmasters, 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 powerful, 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 black hole transit system. There would be five independent, mutually corroborative stories supported by compelling physical evidence. This one was fact, not hearsay and hocus-pocus.
She turned toward him and dropped the frond. Wordlessly, he stooped and returned it to her.
“You’ve been very generous in answering all my questions. Can I answer any for you?”
“Thanks. You answered all our questions last night.”
“That’s it? No commandments? No instructions for the provincials?”
“It doesn’t work that way, Presh. You’re grown up now. You’re on your own.” He tilted his head, gave her that grin, and she flew into his arms, her eyes again filling with tears. It was a long embrace. Eventually, she felt him gently disengage her arms. It was time to go to bed. She imagined holding up her index finger and asking for still one more minute. But she did not want to disappoint him.
“Bye, Presh,” he said. “Give your mother my love.”
“Take care,” she replied in a small voice. She took one last look at the seashore at the center of the Galaxy. A pair of seabirds, petrels perhaps, were suspended on some rising column of air. They remained aloft with hardly a beat of their wings. Just at the entrance to the airlock, she turned and called to him.
“What does your Message say? The one in pi?”
“We don’t know,” he replied a little sadly, taking a few steps toward her. “Maybe it’s a kind of statistical accident. We’re still working on it.”
The breeze stirred up, tousling her hair once again.
“Well, give us a call when you figure it out,” she said.
CHAPTER 21
Causality
As flies to wanton boys are we to the gods—They kill us for their sport.
—WILLIAM SHAKESPEARE
King Lear, IV, i, 36
Who is all-powerful should fear everything.
—PIERRE CORNEILLE
Cinna (1640), Act IV, Scene II
THEY WERE overjoyed to be back. They whooped it up, giddy with excitement. They climbed over the chairs. They hugged and patted erne another on the back. All of them were close to tears. They had succeeded—but not only that, they had returned, safely negotiating all the tunnels. Abruptly, amidst a bail of static, the radio began blaring out the Machine status report. All three benzels were decelerating. The built-up electrical charge was dissipating. From the commentary, it was clear that Project had no idea of what had happened.
Ellie wondered how much time had passed. She glanced at her watch. It had been a day at least, which would bring them well into the year 2000. Appropriate enough. Oh, wait till they hear what we have to tell them, she thought. Reassuringly, she patted the compartment where the dozens of video microcassettes were stored. How the world would change when these films were released!
The space between and around the benzels had been repressurized. The airlock doors were being opened. Now there were radio inquiries about their well-being.
“We’re fine!” she shouted back into her microphone. “Let us out. You won’t believe what happened to us.”
The Five emerged from the airlock happy, effusively greeting their comrades who had helped build and operate the Machine. The Japanese technicians saluted them. Project officials surged toward them.
Devi said quietly to Ellie, “As far as I can tell, everyone’s wearing exactly the same clothing they did yesterday. Look at that ghastly yellow tie on Peter Valerian.”
“Oh, he wears that old thing all the time,” Ellie replied. “His wife gave it to him.” The clocks read 15:20. Activation had occurred close to three o’clock the previous afternoon. So they had been gone just a little over twenty-four…
“What day is it?” she asked. They looked at her uncomprehendingly. Something was wrong.
“Peter, for heaven’s sake, what day is it?”
“How do you mean?” Valerian answered. “It’s today. Friday, December 31, 1999. It’s New Year’s Eve. Is that what you mean? Ellie, are you all right?”
Vaygay was telling Arkhangelsky to let him begin at the beginning, but only after his cigarettes were produced. Project officials and representatives of the Machine Consortium were converging around them. She saw der Heer wedging his way to her through the crowd.
“From your perspective, what happened?” she asked as finally he came within conversational range.
“Nothing. The vacuum system worked, the benzels spun up, they accumulated quite an electrical charg
e, they reached the prescribed speed, and then everything reversed.”
“What do you mean, ‘everything reversed’?”
“The benzels slowed down and the charge dissipated. The system was repressurized, the benzels stopped, and all of you came out. The whole thing took maybe twenty minutes, and we couldn’t talk to you while the benzels were spinning. Did you experience anything at all?”
She laughed. “Ken, my boy,” she said, “have I got a story for you.”
• • •
There was a party for project personnel to celebrate Machine Activation and the momentous New Year. Ellie and her traveling companions did not attend. The television stations were full of celebrations, parades, exhibits, retrospectives, prognostications and optimistic addresses by national leaders. She caught a glimpse of remarks by the Abbot Utsumi, beatific as ever. But she could not dawdle. Project Directorate had quickly concluded, from the fragments of their adventures that the Five had time to recount, that something had gone wrong. They found themselves hustled away from the milling crowds of government and Consortium officials for a preliminary interrogation. It was thought prudent, project officials explained, for each of the Five to be questioned separately.
Der Heer and Valerian conducted her debriefing in a small conference room. There were other project officials present, including Vaygay’s former student Anatoly Goldmann. She understood that Bobby Bui, who spoke Russian, was sitting in for the Americans during Vaygay’s interrogation.
They listened politely, and Peter was encouraging now and again. But they had difficulty understanding the sequence of events. Much of what she related somehow worried them. Her excitement was noncontagious. It was hard for them to grasp that the dodecahedron had been gone for twenty minutes, much less a day, because the armada of instruments exterior to the benzels had filmed and recorded the event, and reported nothing extraordinary. All that had happened. Valerian explained, was that the benzels had reached their prescribed speed, several instruments of unknown purpose had the equivalent of their needles move, the benzels slowed down and stopped, and the Five emerged in a state of great excitement. He didn’t exactly say “babbling nonsense,” but she could sense his concern. They treated her with deference, but she knew what they were thinking: The only function of the Machine was in twenty minutes to produce a memorable illusion, or—just possibly—to drive the Five of them mad.