by Greg Egan
Hamilton laughed humorlessly. “You can’t deceive me. I saw through you from the start.”
“Do you think X-rays are Satanic? Penicillin?”
“Don’t treat me like a fool. There’s no comparison.”
“Why not? Everything I’ve helped develop is part of the same continuum. I’ve read some of your writing on medieval culture, and you’re always berating modern commentators for presenting it as unsophisticated. No one really thought the Earth was flat. No one really treated every novelty as witchcraft. So why view any of my work any differently than a fourteenth-century man would view twentieth-century medicine?”
Hamilton replied, “If a fourteenth-century man was suddenly faced with twentieth-century medicine, don’t you think he’d be entitled to wonder how it had been revealed to his contemporaries?”
Robert shifted uneasily on his chair. Helen hadn’t sworn him to secrecy, but he’d agreed with her view: it was better to wait, to spread the knowledge that would ground an understanding of what had happened, before revealing any details of the contact between branches.
But this man’s wife was dying, needlessly. And Robert was tired of keeping secrets. Some wars required it, but others were better won with honesty.
He said, “I know you hate H.G. Wells. But what if he was right, about one little thing?”
Robert told him everything, glossing over the technicalities but leaving out nothing substantial. Hamilton listened without interrupting, gripped by a kind of unwilling fascination. His expression shifted from hostile to incredulous, but there were also hints of begrudging amazement, as if he could at least appreciate some of the beauty and complexity of the picture Robert was painting.
But when Robert had finished, Hamilton said merely, “You’re a grand liar, Stoney. But what else should I expect, from the King of Lies?”
#
Robert was in a somber mood on the drive back to Cambridge. The encounter with Hamilton had depressed him, and the question of who’d swayed the nation in the debate seemed remote and abstract in comparison.
Helen had taken a house in the suburbs, rather than inviting scandal by cohabiting with him, though her frequent visits to his rooms seemed to have had almost the same effect. Robert walked her to the door.
“I think it went well, don’t you?” she said.
“I suppose so.”
“I’m leaving tonight,” she added casually. “This is goodbye.”
“What?” Robert was staggered. “Everything’s still up in the air! I still need you!”
She shook her head. “You have all the tools you need, all the clues. And plenty of local allies. There’s nothing truly urgent I could tell you, now, that you couldn’t find out just as quickly on your own.”
Robert pleaded with her, but her mind was made up. The driver beeped the horn; Robert gestured to him impatiently.
“You know, my breath’s frosting visibly,” he said, “and you’re producing nothing. You really ought to be more careful.”
She laughed. “It’s a bit late to worry about that.”
“Where will you go? Back home? Or off to twist another branch?”
“Another branch. But there’s something I’m planning to do on the way.”
“What’s that?”
“Do you remember once, you wrote about an Oracle? A machine that could solve the halting problem?”
“Of course.” Given a device that could tell you in advance whether a given computer program would halt, or go on running forever, you’d be able to prove or disprove any theorem whatsoever about the integers: the Goldbach conjecture, Fermat’s Last Theorem, anything. You’d simply show this “Oracle” a program that would loop through all the integers, testing every possible set of values and only halting if it came to a set that violated the conjecture. You’d never need to run the program itself; the Oracle’s verdict on whether or not it halted would be enough.
Such a device might or might not be possible, but Robert had proved more than twenty years before that no ordinary computer, however ingeniously programmed, would suffice. If program H could always tell you in a finite time whether or not program X would halt, you could tack on a small addition to H to create program Z, which perversely and deliberately went into an infinite loop whenever it examined a program that halted. If Z examined itself, it would either halt eventually, or run forever. But either possibility contradicted the alleged powers of program H: if Z actually ran forever, it would be because H had claimed that it wouldn’t, and vice versa. Program H could not exist.
“Time travel,” Helen said, “gives me a chance to become an Oracle. There’s a way to exploit the inability to change your own past, a way to squeeze an infinite number of timelike paths – none of them closed, but some of them arbitrarily near to it – into a finite physical system. Once you do that, you can solve the halting problem.”
“How?” Robert’s mind was racing. “And once you’ve done that … what about higher cardinalities? An Oracle for Oracles, able to test conjectures about the real numbers?”
Helen smiled enigmatically. “The first problem should only take you forty or fifty years to solve. As for the rest,” she pulled away from him, moving into the darkness of the hallway, “what makes you think I know the answer myself?” She blew him a kiss, then vanished from sight.
Robert took a step toward her, but the hallway was empty.
He walked back to the car, sad and exalted, his heart pounding.
The driver asked wearily, “Where to now, sir?”
Robert said, “Further up, and further in.”
4
The night after the funeral, Jack paced the house until three a.m. When would it be bearable? When? She’d shown more strength and courage, dying, than he felt within himself right now. But she’d share it with him, in the weeks to come. She’d share it with them all.
In bed, in the darkness, he tried to sense her presence around him. But it was forced, it was premature. It was one thing to have faith that she was watching over him, but quite another to expect to be spared every trace of grief, every trace of pain.
He waited for sleep. He needed to get some rest before dawn, or how would he face her children in the morning?
Gradually, he became aware of someone standing in the darkness at the foot of the bed. As he examined and reexamined the shadows, he formed a clear image of the apparition’s face.
It was his own. Younger, happier, surer of himself.
Jack sat up. “What do you want?”
“I want you to come with me.” The figure approached; Jack recoiled, and it halted.
“Come with you, where?” Jack demanded.
“To a place where she’s waiting.”
Jack shook his head. “No. I don’t believe you. She said she’d come for me herself, when it was time. She said she’d guide me.”
“She didn’t understand, then,” the apparition insisted gently. “She didn’t know I could fetch you myself. Do you think I’d send her in my place? Do you think I’d shirk the task?”
Jack searched the smiling, supplicatory face. “Who are you?” His own soul, in Heaven, remade? Was this a gift God offered everyone? To meet, before death, the very thing you would become – if you so chose? So that even this would be an act of free will?
The apparition said, “Stoney persuaded me to let his friend treat Joyce. We lived on, together. More than a century has passed. And now we want you to join us.”
Jack choked with horror. “No! This is a trick! You’re the Devil!”
The thing replied mildly, “There is no Devil. And no God, either. Just people. But I promise you: people with the powers of gods are kinder than any god we ever imagined.”
Jack covered his face. “Leave me be.” He whispered fervent prayers, and waited. It was a test, a moment of vulnerability, but God wouldn’t leave him naked like this, face-to-face with the Enemy, for longer than he could endure.
He uncovered his face. The thing was still with him.
>
It said, “Do you remember, when your faith came to you? The sense of a shield around you melting away, like armor you’d worn to keep God at bay?”
“Yes.” Jack acknowledged the truth defiantly; he wasn’t frightened that this abomination could see into his past, into his heart.
“That took strength: to admit that you needed God. But it takes the same kind of strength, again, to understand that some needs can never be met. I can’t promise you Heaven. We have no disease, we have no war, we have no poverty. But we have to find our own love, our own goodness. There is no final word of comfort. We only have each other.”
Jack didn’t reply; this blasphemous fantasy wasn’t even worth challenging. He said, “I know you’re lying. Do you really imagine that I’d leave the boys alone here?”
“They’d go back to America, back to their father. How many years do you think you’d have with them, if you stay? They’ve already lost their mother. It would be easier for them now, a single clean break.”
Jack shouted angrily, “Get out of my house!”
The thing came closer, and sat on the bed. It put a hand on his shoulder. Jack sobbed, “Help me!” But he didn’t know whose aid he was invoking any more.
“Do you remember the scene in The Seat of Oak? When the Harpy traps everyone in her cave underground, and tries to convince them that there is no Nescia? Only this drab underworld is real, she tells them. Everything else they think they’ve seen was just make-believe.” Jack’s own young face smiled nostalgically. “And we had dear old Shrugweight reply: he didn’t think much of this so-called ‘real world’ of hers. And even if she was right, since four little children could make up a better world, he’d rather go on pretending that their imaginary one was real.
“But we had it all upside down! The real world is richer, and stranger, and more beautiful than anything ever imagined. Milton, Dante, John the Divine are the ones who trapped you in a drab, gray underworld. That’s where you are now. But if you give me your hand, I can pull you out.”
Jack’s chest was bursting. He couldn’t lose his faith. He’d kept it through worse than this. He’d kept it through every torture and indignity God had inflicted on his wife’s frail body. No one could take it from him now. He crooned to himself, “In my time of trouble, He will find me.”
The cool hand tightened its grip on his shoulder. “You can be with her, now. Just say the word, and you will become a part of me. I will take you inside me, and you will see through my eyes, and we will travel back to the world where she still lives.”
Jack wept openly. “Leave me in peace! Just leave me to mourn her!”
The thing nodded sadly. “If that’s what you want.”
“I do! Go!”
“When I’m sure.”
Suddenly, Jack thought back to the long rant Stoney had delivered in the studio. Every choice went every way, Stoney had claimed. No decision could ever be final.
“Now I know you’re lying!” he shouted triumphantly. “If you believed everything Stoney told you, how could my choice ever mean a thing? I would always say yes to you, and I would always say no! It would all be the same!”
The apparition replied solemnly, “While I’m here with you, touching you, you can’t be divided. Your choice will count.”
Jack wiped his eyes, and gazed into its face. It seemed to believe every word it was speaking. What if this truly was his metaphysical twin, speaking as honestly as he could, and not merely the Devil in a mask? Perhaps there was a grain of truth in Stoney’s awful vision; perhaps this was another version of himself, a living person who honestly believed that the two of them shared a history.
Then it was a visitor sent by God, to humble him. To teach him compassion toward Stoney. To show Jack that he too, with a little less faith, and a little more pride, might have been damned forever.
Jack stretched out a hand and touched the face of this poor lost soul. There, but for the grace of God, go I.
He said, “I’ve made my choice. Now leave me.”
#
Author’s note: Where the lives of the fictional characters of this story parallel those of real historical figures, I’ve drawn on biographies by Andrew Hodges and A.N. Wilson. The self-dual formulation of general relativity was discovered by Abhay Ashtekar in 1986, and has since led to ground-breaking developments in quantum gravity, but the implications drawn from it here are fanciful.
BORDER GUARDS
In the early afternoon of his fourth day out of sadness, Jamil was wandering home from the gardens at the center of Noether when he heard shouts from the playing field behind the library. On the spur of the moment, without even asking the city what game was in progress, he decided to join in.
As he rounded the corner and the field came into view, it was clear from the movements of the players that they were in the middle of a quantum soccer match. At Jamil’s request, the city painted the wave function of the hypothetical ball across his vision, and tweaked him to recognize the players as the members of two teams without changing their appearance at all. Maria had once told him that she always chose a literal perception of color-coded clothing instead; she had no desire to use pathways that had evolved for the sake of sorting people into those you defended and those you slaughtered. But almost everything that had been bequeathed to them was stained with blood, and to Jamil it seemed a far sweeter victory to adapt the worst relics to his own ends than to discard them as irretrievably tainted.
The wave function appeared as a vivid auroral light, a quicksilver plasma bright enough to be distinct in the afternoon sunlight, yet unable to dazzle the eye or conceal the players running through it. Bands of color representing the complex phase of the wave swept across the field, parting to wash over separate rising lobes of probability before hitting the boundary and bouncing back again, inverted. The match was being played by the oldest, simplest rules: semi-classical, non-relativistic. The ball was confined to the field by an infinitely high barrier, so there was no question of it tunneling out, leaking away as the match progressed. The players were treated classically: their movements pumped energy into the wave, enabling transitions from the game’s opening state – with the ball spread thinly across the entire field – into the range of higher-energy modes needed to localize it. But localization was fleeting; there was no point forming a nice sharp wave packet in the middle of the field in the hope of kicking it around like a classical object. You had to shape the wave in such a way that all of its modes – cycling at different frequencies, traveling with different velocities – would come into phase with each other, for a fraction of a second, within the goal itself. Achieving that was a matter of energy levels, and timing.
Jamil had noticed that one team was under-strength. The umpire would be skewing the field’s potential to keep the match fair, but a new participant would be especially welcome for the sake of restoring symmetry. He watched the faces of the players, most of them old friends. They were frowning with concentration, but breaking now and then into smiles of delight at their small successes, or their opponents’ ingenuity.
He was badly out of practice, but if he turned out to be dead weight he could always withdraw. And if he misjudged his skills, and lost the match with his incompetence? No one would care. The score was nil all; he could wait for a goal, but that might be an hour or more in coming. Jamil communed with the umpire, and discovered that the players had decided in advance to allow new entries at any time.
Before he could change his mind, he announced himself. The wave froze, and he ran on to the field. People nodded greetings, mostly making no fuss, though Ezequiel shouted, “Welcome back!” Jamil suddenly felt fragile again; though he’d ended his long seclusion four days before, it was well within his power, still, to be dismayed by everything the game would involve. His recovery felt like a finely balanced optical illusion, a figure and ground that could change roles in an instant, a solid cube that could evert into a hollow.
The umpire guided him to his allotted start
ing position, opposite a woman he hadn’t seen before. He offered her a formal bow, and she returned the gesture. This was no time for introductions, but he asked the city if she’d published a name. She had: Margit.
The umpire counted down in their heads. Jamil tensed, regretting his impulsiveness. For seven years he’d been dead to the world. After four days back, what was he good for? His muscles were incapable of atrophy, his reflexes could never be dulled, but he’d chosen to live with an unconstrained will, and at any moment his wavering resolve could desert him.
The umpire said, “Play.” The frozen light around Jamil came to life, and he sprang into motion.
Each player was responsible for a set of modes, particular harmonics of the wave that were theirs to fill, guard, or deplete as necessary. Jamil’s twelve modes cycled at between 1,000 and 1,250 milliHertz. The rules of the game endowed his body with a small, fixed potential energy, which repelled the ball slightly and allowed different modes to push and pull on each other through him, but if he stayed in one spot as the modes cycled, every influence he exerted would eventually be replaced by its opposite, and the effect would simply cancel itself out.
To drive the wave from one mode to another, you needed to move, and to drive it efficiently you needed to exploit the way the modes fell in and out of phase with each other: to take from a 1,000 milliHertz mode and give to a 1,250, you had to act in synch with the quarter-Hertz beat between them. It was like pushing a child’s swing at its natural frequency, but rather than setting a single child in motion, you were standing between two swings and acting more as an intermediary: trying to time your interventions in such a way as to speed up one child at the other’s expense. The way you pushed on the wave at a given time and place was out of your hands completely, but by changing location in just the right way you could gain control over the interaction. Every pair of modes had a spatial beat between them – like the moiré pattern formed by two sheets of woven fabric held up to the light together, shifting from transparent to opaque as the gaps between the threads fell in and out of alignment. Slicing through this cyclic landscape offered the perfect means to match the accompanying chronological beat.