Anthology of Speculative Fiction, Volume Two

by Short Story Anthology

  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 sombre 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 towards 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 armour 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, grey 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 towards 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.

  The Planck Dive, by Greg Egan

  Hugo Nomination for Best Novelette 1999

  Gisela was contemplating the advantages of being crushed — almost certainly to death, albeit as slowly as possible — when the messenger appeared in her homescape. She noted its presence but instructed it to wait, a sleek golden courier with winged sandals stretching out a hand impatiently, frozen in mid-stride twenty delta away.

  The scape was currently an expanse of yellow dunes beneath a pale blue sky, neither too stark nor too distracting. Gisela, reclining on the cool sand, was intent on a giant, scruffy triangle hovering at an incline over the dunes, each edge resembling a loose bundle of straw. The triangle was a collection of Feynman diagrams, showing just a few of the many ways a particle could move between three events in spacetime. A quantum particle could not be pinned down to any one path, but it could be treated as a sum of localised components, each following a different trajectory and taking part in a different set of interactions along the way.

  In “empty” spacetime, interactions with virtual particles caused each component’s phase to rotate constantly, like the hand of a clock. But the time measured by any kind of clock travelling between two events in flat spacetime was greatest when the route taken was a straight line — any detours caused time dilation, shortening the trip — and so a plot of phase shift versus detour size also reached its peak for a straight line. Since this peak was smooth and flat, a group of nearly straight paths clustered around it all had similar phase shifts, and these paths allowed many more components to arrive in phase with each other, reinforcing each other, than any equivalent group on the slopes. Three straight lines, glowing red through the centre of each “bundle of straw”, illustrated the result: the classical paths, the paths of highest probability, were straight lines.

  In the presence of matter, all the same processes became slightly skewed. Gisela added a couple of nanograms of lead to the model — a few trillion atoms, their world lines running vertically through the centre of the triangle, sprouting their own thicket of virtual particles. Atoms were neutral in charge and colour, but their individual electrons and quarks still scattered virtual photons and gluons. Every kind of matter interfered with some part of the virtual swarm, and the initial disturbance spread out through spacetime by scattering virtual particles itself, rapidly obliterating any difference between the effect of a tonne of rock or a tonne of neutrinos, growing weaker with distance according to a roughly inverse square law. With the rain of virtual particles — and the phase shifts they created — varying from place to place, the paths of highest probability ceased obeying the geometry of flat spacetime. The luminous red triangle of most-probable trajectories was now visibly curved.

  The key idea dated back to Sakharov: gravity was nothing but the residue of the imperfect cancellation of other forces; squeeze the quantum vacuum hard enough and Einstein’s equations fell out. But since Einstein, every theory of gravity was also a theory oftime. Relativity demanded that a free-falling particle’s rotating phase agree with every other clock that travelled the same path, and once gravitational time dilation was linked to changes in virtual particle density, every measure of time — from the half-life of a radioisotope’s decay (stimulated by vacuum fluctuations) to the vibrational modes of a sliver of quartz (ultimately due to the same phase effects as those giving rise to classical paths) — could be reinterpreted as a count of interactions with virtual particles.

  It was this line of reasoning that had led Kumar — a century after Sakharov, building on work by Penrose, Smolin and Rovelli — to devise a model of spacetime as a quantum sum of every possible network of particle world lines, with classical “time” arising from the number of intersections along a given strand of the net. This model had been an unqualified success, surviving theoretical scrutiny and experimental tests for centuries. But it had never been validated at the smallest length scales, accessible only at absurdly high energies, and it made no attempt to explain the basic structure of the nets, or the rules that governed them. Gisela wanted to know where those details came from. She wanted to understand the universe at its deepest level, to touch the beauty and simplicity that lay beneath it all.

  That was why she was taking the Planck Dive.

  The messenger caught her eye again. It was radiating tags indicating that it represented Cartan’s mayor: non-sentient software that dealt with the maintenance of good relations with other polises, observing formal niceties and smoothing away minor points of conflict in those cases where no real citizen-to-citizen connections existed. Since Cartan had been in orbit around Chandrasekhar, ninety-seven light years from Earth, for almost three centuries — and was currently even further from all the other spacefaring polises — Gisela was at a loss to imagine what urgent diplomatic tasks the mayor could be engaged i
n, let alone why it would want to consult her.

  She sent the messenger an activation tag. Deferring to the scape’s aesthetic of continuity, it sprinted across the dunes, coming to a halt in front of her in a cloud of fine dust. “We’re in the process of receiving two visitors from Earth.”

  Gisela was astonished. “Earth? Which polis?”

  “Athena. The first one has just arrived; the second will be in transit for another ninety minutes.”

  Gisela had never heard of Athena, but ninety minutes per person sounded ominous. Everything meaningful about an individual citizen could be packed into less than an exabyte, and sent as a gamma-ray burst a few milliseconds long. If you wanted to simulate an entire flesher body — cell by cell, redundant viscera and all — that was a harmless enough eccentricity, but lugging the microscopic details of your “very own” small intestine ninety-seven light years was just being precious.

  “What do you know about Athena? In brief.”

  “It was founded in 2312, with a charter expressing the goal of ‘regaining the lost flesher virtues.’ In public fora, its citizens have shown little interest in exopolitan reality — other than flesher history and artforms — but they do participate in some contemporary interpolis cultural activities.”

  “So why have these two come here?” Gisela laughed. “If they’re refugees from boredom, surely they could have sought asylum a little closer to home?”

  The mayor took her literally. “They haven’t adopted Cartan citizenship; they’ve entered the polis with only visitor privileges. In their transmission preamble they stated that their purpose in coming was to witness the Planck Dive.”

  “Witness — not take part in?”

  “That’s what they said.”

  They could have witnessed as much from home as any non-participant here in Cartan. The Dive team had been broadcasting everything — studies, schematics, simulations, technical arguments, metaphysical debates — from the moment the idea had coalesced out of little more than jokes and thought experiments, a few years after they’d gone into orbit around the black hole. But at least Gisela now knew why the mayor had picked on her; she’d volunteered to respond to any requests for information about the Dive that couldn’t be answered automatically from public sources. No one seemed to have found their reports to be lacking a single worthwhile detail, though, until now.