by Carl Sagan
“It’s like the search you did for the Message. With these radio telescopes.”
“Yes; in both cases we were looking for a signal that’s well out of the noise, something that can’t be just a statistical fluke.”
“But it doesn’t have to be a hundred fours—is that right? It could speak to us?”
“Sure. Imagine after a while we get a long sequence of just zeros and ones. Then, just as we did with the Message, we could pull a picture out, if there’s one in there. You understand, it could be anything.”
“You mean you could decode a picture hiding in pi and it would be a mess of Hebrew letters?”
“Sure. Big blade letters, carved in stone.”
He looked at her quizzically.
“Forgive me, Eleanor, but don’t you think you’re being a mite too…indirect? You don’t belong to a silent order of Buddhist nuns. Why don’t you just tell your story?”
“Palmer, if I had hard evidence, I’d speak up. But if I don’t have any, people like Kitz will say that I’m lying. Or hallucinating. That’s why that manuscript’s in your inside pocket. You’re going to seal it, date it, notarize it, and put it in a safety-deposit box. If anything happens to me, you can release it to the world. I give you full authority to do anything you want with it.”
“And if nothing happens to you?”
“If nothing happens to me? Then, when we find what we’re looking for, that manuscript will confirm our story. If we find evidence of a double black hole at the Galactic Center, or some huge artificial construction in Cygnus A, or a message hiding inside pi, this”—she tapped him lightly on the chest—“will be my evidence. Then I’ll speak out… Meantime, don’t lose it.”
“I still don’t understand,” he confessed. “We know there’s a mathematical order to the universe. The law of gravity and all that. How is this different? So there’s order inside the digits of pi. So what?”
“No, don’t you see? This would be different. This isn’t just starting the universe out with some precise mathematical laws that determine physics and chemistry. This is a message. Whoever makes the universe hides messages in transcendental numbers so they’ll be read fifteen billion years later when intelligent life finally evolves. I criticized you and Rankin the time we first met for not understanding this. ‘If God wanted us to know that he existed, why didn’t he send us an unambiguous message?’ I asked. Remember?”
“I remember very well. You think God is a mathematician.”
“Something like that. If what we’re told is true. If this isn’t a wild-goose chase. If there’s a message hiding in pi and not one of the infinity of other transcendental numbers. That’s a lot of ifs.”
“You’re looking for Revelation in arithmetic. I know a better way.”
“Palmer, this is the only way. This is the only thing that would convince a skeptic. Imagine we find something. It doesn’t have to be tremendously complicated. Just something more orderly than could accumulate by chance that many digits into pi That’s all we need. Then mathematicians all over the world can find exactly the same pattern or message or whatever it proves to be. Then there are no sectarian divisions. Everybody begins reading the same Scripture. No one could then argue that the key miracle in the religion was some conjurer’s trick, or that later historians had falsified the record, or that it’s just hysteria or delusion or a substitute parent for when we grow up. Everyone could be a believer.”
“You can’t be sure you’ll find anything. You can hide here and compute till the cows come home. Or you can go out and tell your story to the world. Sooner or later you’ll have to choose.”
“I’m hoping I won’t have to choose. Palmer. First the physical evidence, then the public announcements. Otherwise… Don’t you see how vulnerable we’d be? I don’t mean for myself, but…”
He shook his head almost imperceptibly. A smile was playing at the corners of his lips. He had detected a certain irony in their circumstances.
“Why are you so eager for me to tell my story?” she asked.
Perhaps he took it for a rhetorical question. At any rate he did not respond, and she continued.
“Don’t you think there’s been a strange…reversal of our positions? Here I am, the bearer of the profound religious experience I can’t prove—really, Palmer, I can barely fathom it. And here you are, the hardened skeptic trying—more successfully than I ever did—to be kind to the credulous.”
“Oh no, Eleanor,” he said, “I’m not a skeptic. I’m a believer.”
“Are you? The story I have to tell isn’t exactly about Punishment and Reward. It’s not exactly Advent and Rapture. There’s not a word in it about Jesus. Part of my message is that we’re not central to the purpose of the Cosmos. What happened to me makes us all seem very small.”
“It does. But it also makes God very big.”
She glanced at him for a moment and rushed on.
“Yon know, as the Earth races around the Sun, the powers of this world—the religious powers, the secular powers—once pretended the Earth wasn’t moving at all. They were in the business of being powerful. Or at least pretending to be powerful And the truth made them feel too small. The truth frightened them; it undermined their power. So they suppressed it. Those people found the truth dangerous. You’re sure you know what believing me entails?”
“I’ve been searching, Eleanor. After all these years, believe me, I know the truth when I see it. Any faith that admires truth, that strives to know God, must be brave enough to accommodate the universe. I mean the real universe. All those light-years. All those worlds. I think of the scope of your universe, the opportunities it affords the Creator, and it takes my breath away. It’s much better than bottling Him up in one small world. I never liked the idea of Earth as God’s green footstool. It was too reassuring, like a children’s story…like a tranquilizer. But your universe has room enough, and time enough, for the kind of God I believe in.
“I say you don’t need any more proof. There are proofs enough already. Cygnus A and all that are just for the scientists. You think it’ll be hard to convince ordinary people that you’re telling the truth. I think it’ll be easy as pie. You think your story is too peculiar, too alien. But I’ve heard it before. I know it well. And I bet you do too.”
He closed his eyes and, after a moment, recited:
He dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven: and behold the angels of God ascending and descending on it… Surely the Lord is in this place; and I knew it not… This is none other but the House of God, and this is the gate of heaven.
He had been a little carried away, as if preaching to the multitudes from the pulpit of a great cathedral, and when he opened his eyes it was with a small self-deprecatory smile. They walked down a vast avenue, flanked left and right by enormous whitewashed radio telescopes straining at the sky, and after a moment he spoke in a more conversational tone:
“Your story has been foretold. It’s happened before. Somewhere inside of you, you must have known. None of your details are in the Book of Genesis. Of course not. How could they be? The Genesis account was right for the time of Jacob. Just as your witness is right for this time, for our time.
“People are going to believe you, Eleanor. Millions of them. All over the world. I know it for certain…”
She shook her head, and they walked on for another moment in silence before he continued.
“All right, then. I understand. You take as much time as you have to. But if there’s any way to hurry it up, do it—for my sake. We have less than a year to the Millennium.”
“I understand also. Bear with me a few more months. If we haven’t found something in pi by then, I’ll consider going public with what happened up there. Before January 1. Maybe Eda and the others would be willing to speak out also. Okay?”
They walked in silence back toward the Argus administration building. The sprinklers were watering the meager lawn, and they stepped around a pud
dle that, on this parched earth, seemed alien, out of place.
“Have you ever been married?” he asked.
“No, I never have. I guess I’ve been too busy.”
“Ever been in love?” The question was direct, matter-of-fact.
“Halfway, half a dozen times. But”—she glanced at the nearest telescope—“there was always so much noise, the signal was hard to find. And you?”
“Never,” he replied flatly. There was a pause, and then he added with a faint smile, “But I have faith.”
She decided not to pursue this ambiguity just yet, and they mounted the short flight of stairs to examine the Argus mainframe computer.
CHAPTER 24
The Artist’s Signature
Behold, I tell you a mystery; we shall not all sleep, but we shall all be changed.
—I CORINTHIANS 15: 51
The universe seems…to have been determined and ordered in accordance with number, by the forethought and the mind of the creator of all things; for the pattern was fixed, like a preliminary sketch, by the domination of number preexistent in the mind of the world-creating God.
—NICOMACHUS OF GERASA
Arithmetic I, 6 (ca. A.D. 100)
SHE RUSHED up the steps of the nursing home and, on the newly repainted green veranda, marked off at regular intervals by empty rocking chairs, she saw John Staughton—stooped, immobile, his arms dead weights. In his right hand be clutched a shopping bag in which Ellie could see a translucent shower cap, a flowered makeup case, and two bedroom slippers adorned with pink pom-poms.
“She’s gone,” he said as his eyes focused. “Don’t go in,” he pleaded. “Don’t look at her. She would’ve hated for you to see her like this. You know how much pride she took in her appearance. Anyway, she’s not in there.”
Almost reflexively, out of long practice and still unresolved resentments, Ellie was tempted to turn and enter anyway. Was she prepared, even now, to defy him as a matter of principle? What was the principle, exactly? From the havoc on his face, there was no question about the authenticity of his remorse. He had loved her mother. Maybe, she thought, he loved her more than I did, and a wave of self-reproach swept through her. Her mother had been so frail for so long that Ellie had tested, many times, how she would respond when the moment came. She remembered how beautiful her mother had been in the picture that Staughton had sent her, and suddenly, despite her rehearsals for this moment, she was wracked with sobs.
Startled by her distress, Staughton moved to comfort her. But she put up a hand, and with a visible effort regained her self-control. Even now, she could not bring herself to embrace him. They were strangers, tenuously linked by a corpse. But she had been wrong—she knew it in the depths of her being—to have blamed Staughton for her father’s death.
“I have something for you,” he said as he fumbled in the shopping bag. Some of the contents circulated between top and bottom, and she could see now an imitation-leather wallet and a plastic denture case. She had to look away. At last he straightened up, flourishing a weather-beaten envelope.
“For Eleanor,” it read. Recognizing her mother’s handwriting, she moved to take it. Staughton took a startled step backward, raising the envelope in front of his face as if she had been about to strike him.
“Wait,” he said. “Wait. I know we’ve never gotten along. But do me this one favor: Don’t read the letter until tonight. Okay?”
In his grief, he seemed a decade older.
“Why?” she asked.
“Your favorite question. Just do me this one courtesy. Is it too much to ask?”
“You’re right,” she said. “It’s not too much to ask. I’m sorry.”
He looked her directly in the eye.
“Whatever happened to you in that Machine,” he said, “maybe it changed you.”
“I hope so, John.”
• • •
She called Joss and asked him if he would perform the funeral service. “I don’t have to tell you I’m not religious. But there were times when my mother was. You’re the only person I can think of whom I’d want to do it, and I’m pretty sure my stepfather will approve.” He would be there on the next plane, Joss assured her.
In her hotel room, after an early dinner, she fingered the envelope, caressing every fold and scuff. It was old. Her mother must have written it years ago, carrying it around in some compartment of her purse, debating with herself whether to give it to Ellie. It did not seem newly resealed, and Ellie wondered whether Staughton had read it. Part of her hungered to open it, and part of her hung back with a kind of foreboding. She sat for a long time in the musty armchair thinking, her knees drawn up limberly against her chin.
A chime sounded, and the not quite noiseless carriage of her telefax came to life. It was linked to the Argus computer. Although it reminded her of the old days, there was no real urgency. Whatever the computer had found was not about to go away; π would not set as the Earth turned. If there was a message hiding inside π, it would wait for her forever.
She examined the envelope again, but the echo of the chime intruded. If there was content inside a transcendental number, it could only have been built into the geometry of the universe from the beginning. This new project of hers was in experimental theology. But so is all of science, she thought.
“STAND BY,” the computer printed out on the telefax screen.
She thought of her father…well, the simulacrum of her father…about the Caretakers with their network of tunnels through the Galaxy. They had witnessed and perhaps influenced the origin and development of life on millions of worlds. They were building galaxies, closing off sectors of the universe. They could manage at least a limited kind of time travel. They were gods beyond the pious imaginings of almost all religions—all Western religions, anyway. But even they had their limitations. They had not built the tunnels and were unable to do so. They had not inserted the message into the transcendental number, and could not even read it. The Tunnel builders and the π inscribers were somebody else. They didn’t live here anymore. They had left no forwarding address. When the Tunnel builders had departed, she guessed, those who would eventually be the Caretakers had become abandoned children. Like her, like her.
She thought about Eda’s hypothesis that the tunnels were wormholes, distributed at convenient intervals around innumerable stars in this and other galaxies. They resembled black holes, but they had different properties and different origins. They were not exactly massless, because she had seen them leave gravitational wakes in the orbiting debris in the Vega system. And through them beings and ships of many kinds traversed and bound up the Galaxy.
Wormholes. In the revealing jargon of theoretical physics, the universe was their apple and someone had tunneled through, riddling the interior with passageways that criss-crossed the core. For a bacillus who lived on the surface, it was a miracle. But a being standing outside the apple might be less impressed. From that perspective, the Tunnel builders were only an annoyance. But if the Tunnel builders are worms, she thought, who are we?
The Argus computer had gone deep into π, deeper than anyone on Earth, human or machine, had ever gone, although not nearly so deep as the Caretakers had ventured. This was much too soon, she thought, to be the long-undecrypted message about which Theodore Arroway had told her on the shores of that uncharted sea. Maybe this was just a gearing up, a preview of coming attractions, an encouragement to further exploration, a token so humans would not lose heart. Whatever it was, it could not possibly be the message the Caretakers were struggling with. Maybe there were easy messages and hard messages, locked away in the various transcendental cumbers, and the Argus computer had found the easiest. With help.
At the Station, she had learned a kind of humility, a reminder of how little the inhabitants of Earth really knew. There might, she thought, be as many categories of beings more advanced than humans as there are between us and the ants, or maybe even between us and the viruses. But it had not depressed her. Rat
her than a daunting resignation, it had aroused in her a swelling sense of wonder. There was so much more to aspire to now.
It was like the step from high school to college, from everything coming effortlessly to the necessity of making a sustained and disciplined effort to understand at all. In high school, she had grasped her coursework more quickly than almost anybody. In college, she had discovered many people much quicker than she. There had been the same sense of incremental difficulty and challenge when she entered graduate school, and when she became a professional astronomer. At every stage, she had found scientists more accomplished than she, and each stage had been more exciting than the last. Let the revelations roll, she thought, looking at the telefax. She was ready.
“TRANSMISSION PROBLEM. S/N<10. PLEASE STAND BY.”
She was linked to the Argus computer by a communications relay satellite called Defcom Alpha. Perhaps there had been an attitude-control problem, or a programming foul-up. Before she could think about it further, she found she had opened the envelope.
ARROWAY HARDWARE, the letterhead said, and sure enough, the type font was that of the old Royal her father had kept at home to do both business and personal accounts. “June 13, 1964” was typed in the upper right-hand corner. She had been fifteen then. Her father could not have written it; he had been dead for years. A glance at the bottom of the page confirmed the neat hand of her mother.
My sweet Ellie,
Now that I’m dead, I hope you can find it in your heart to forgive me. I know I committed a sin against you, and not just you. I couldn’t bear how you’d hate me if you knew the truth. That’s why I didn’t have the courage to tell you while I was alive. I know how much you loved Ted Arroway, and I want you to know I did, too. I still do. But he wasn’t your real father. Your real father is John Staughton. I did something very wrong. I shouldn’t have and I was weak, but if I hadn’t you wouldn’t be in the world, so please be kind when you think about me. Ted knew and he gave me forgiveness and we said we’d never tell you. But I look out the window right now and I see you in the backyard. You’re sitting there thinking about stars and things that I never could understand and I’m so proud of you. You make such a point about the truth, I thought it was right that you should know this truth about yourself. Your beginning, I mean.