Diaspora

Paolo said decisively, “What comes next is the Forge. You helped design it, didn’t you?”

“I wouldn’t go that far. I played a minor role.”

Paolo grinned. “Success has a thousand parents, but failure is an orphan.”

Yatima rolled vis eyes. “The Forge was not a failure. But the Transmuters won’t want to hear about my towering contribution to analytic methods in relativistic electron plasma modeling.”

“No? Well, I was never an insider at all, so whatever we tell them will have to come from you.”

Yatima thought it over. “I knew the two people who really mattered.” Ve smiled. “You could say it’s a love story.”

“Blanca and Gabriel?”

“Maybe I should have said ’triangle.'”

Paolo was baffled. “Who else was involved?”

“I never met her myself. But I think you can guess who I mean.”

7. KOZUCH’S LEGACY

Carter-Zimmerman polis, Earth

24 667 274 153 236 CST

10 December 3015, 3:49:10.390 UT

Gabriel asked the Carter-Zimmerman library to show him every scheme on record for building a traversable wormhole. The problem had been studied long before the necessary technology was remotely within reach, both as an exercise in theoretical physics and as an attempt to map out the possibilities for future civilizations. It had seemed like an act of ingratitude, as well as a waste of resources, to discard the fruits of all this ancient labor and start again from scratch, so Gabriel had volunteered to sort through all the methods and machines advocated in the past and select the ten most promising candidates for detailed feasibility studies.

The library promptly constructed an indexscape with 3,017 different blueprints, laid out in a conceptual evolutionary tree which stretched across the scape’s imaginary vacuum for hundreds of kilodelta. Gabriel was taken aback for a moment; he’d been aware of the numbers, but the visible history of the subject was still an intimidating sight. People had been contemplating wormhole travel for almost a millennium; longer, counting the early designs based on classical General Relativity, but it was with the advent of Kozuch Theory that the field had truly flourished.

In Kozuch Theory, wormholes were everything. Even the vacuum was a froth of short-lived wormholes when examined at the Planck-Wheeler length of ten-to-the-minus-thirty-five meters. As early as 1955, John Wheeler had suggested that the apparently smooth space-time of General Relativity would turn out to be a tangled maze of quantum wormholes at this scale, but it was another idea of Wheeler’s—finally made to work, with spectacular success, by Renata Kozuch a hundred years later—that had transformed these wormholes from arcane curiosities far beyond the limits of detection into the most important structures in physics. The elementary particles themselves were the mouths of wormholes. Electrons, quarks, neutrinos, photons, W-Z bosons, gravitons, and gluons were all just the mouths of longer-lived versions of the fleeting wormholes of the vacuum.

Kozuch had labored for more than twenty years to refine this hypothesis, drawing together tantalizing but partial results from dozens of other specialties, cannibalizing everything from Penrose spin networks to the compactified extra dimensions of string theory. By including six sub-microscopic dimensions along with the usual four of space-time, she had shown how wormholes with different topologies could account for the properties of all the known particles. No one had directly observed a Kozuch-Wheeler wormhole, but after surviving a millennium of experimental tests the model was widely accepted, not as the best tool for most practical calculations, but as the definitive expression of the underlying order of the physical world.

Gabriel had learned Kozuch Theory in the womb, and it had always seemed to him to be the deepest, clearest picture of reality available. The mass of a particle was a consequence of the disruption it caused to a certain class of vacuum wormholes: those with virtual gravitons at both ends. Disturbing the usual pattern of connections between these wormholes made space-time effectively curved, much as a change in the weave of a basket could force the surface to bend by bringing parallel threads together. It also created a few loose threads: other wormholes squeezed out of the vacuum by the “tighter weave” wherever space-time was curved, giving rise to both Hawking radiation from black holes and the even fainter Unruh radiation of ordinary objects.

Charge, color, and flavor arose from similar effects, but with virtual photons, gluons, and W-Z bosons as the mouths of the vacuum wormholes involved, and the six rolled-up dimensions, to which gravitons were impervious, now playing a crucial role. Spin measured the presence of a certain kind of extra-dimensional twist in the wormhole mouth; each half-twist contributed half a unit of spin. Fermions, particles such as electrons with an odd number of half-twists, had wormholes which could themselves become twisted like ribbons; if an electron was rotated 360 degrees, its wormhole would gain or lose a definite twist, with measurable consequences. Bosons, such as photons, had full twists in their wormhole mouths, but a 360-degree rotation left them unchanged because the kinks in their wormholes canceled themselves out. A single boson could be “self-linked,” the only opening into a wormhole which looped back on itself, or any number of identical bosons could share a wormhole. Fermions were always joined in even numbers; the simplest case was a particle at one end of the wormhole, with its antiparticle at the other.

Under the extreme space-rime curvature of the early universe, countless vacuum wormholes had been “squeezed from the weave” to take on a more tangible existence. Most had formed particle-antiparticle pairs like electrons and positrons, but more rarely they’d created less symmetric combinations, such as an electron at one end of the wormhole with a three-pronged branching into a triplet of quarks, making up a proton, at the other.

This was the origin of all matter. By sheer chance, the vacuum had shed slightly more electron-proton wormholes than their antimatter equivalent, positrons linked to antiprotons, before expanding and cooling to the point where particle production ceased. Without that tiny random excess, every last electron and proton would have been annihilated by a matching antiparticle, and there would have been nothing in the universe but the microwave background, reverberating through empty space.

Kozuch herself had pointed out in 2059 that if this version of Big Bang cosmology was correct, it meant that every surviving electron was linked to a proton, somewhere. Brand new wormholes with known endpoints could be manufactured at will, simply by creating pairs of electrons and positrons, but existing wormholes already crisscrossed interstellar space. After twenty billion years drifting through an evolving and expanding universe, many particles torn from the vacuum side-by-side would have ended up thousands of light years apart. Chances were, every grain of sand, every drop of water on Earth, contained gateways to each of the hundreds of billions of stars in the galaxy, and some that reached far beyond.

The catch was: nothing in the universe could pass through the wormhole mouth of an elementary particle. All the known particles possessed a single quantum unit of surface area, and the probability of any of them passing through another’s wormhole was precisely zero.

This problem was not insurmountable. When an electron and a positron collided, their wormholes were spliced together end-to-end, making the two colliding mouths vanish. In that case two gamma-ray photons were produced, but if the wormholes could be spliced, not electron-end to positron-end but electron-end to electron-end, the energy normally lost as gamma rays would be trapped, and would go into making the new, spliced wormhole wider.

Achieving this union would require concentrating a modest amount of energy—two gigajoules, enough to melt a six-ton block of ice—into a volume as much smaller than that ice block as an atom was smaller than the observable universe. Wormholes produced by electron-electron splicing would be traversable only by fundamental particles, but splicing together a few billion of them would further widen the resulting wormhole, rather than lengthening it, enabling a moderately sophisticated nanomachine to pass through.

Gabriel had heard it rumored that the gleisners had considered the wormhole option, but elected to put it aside for the next few millennia. Building conventional interstellar spacecraft must have seemed trivial compared to the kind of technology it would take to tear open the portals to the stars scattered at their feet. Still, with 3,017 designs to choose from there had to be one within Carter-Zimmerman’s reach, even if it took a thousand years to bring to fruition. Gabriel was undaunted by the time scale; he had long hoped for a grand scheme like this to make sense of his longevity. Without a purpose that spanned the centuries, he could only drift between interests and aesthetics, friends and lovers, triumphs and disappointments. He could only live a new life every gigatau or two, until there was no difference between his continued existence and his replacement by someone new.

Full of hope, he moved across the scape toward the first blueprint.

8. SHORT CUTS

Carter-Zimmerman polis, Earth

51 479 998 754 659 CST

7 August 3865, 14:52:31.813 UT

Blanca floated through the latest world ve’d grown from a novel symmetry group and a handful of recursion formulae. Giant inverted pyramids floated above ver, sprouting luminous outgrowths like rococo chandeliers. Feathery planar crystals swirled and grew around ver, then began to collide and merge into strange new objects, random acts of origami performed with diamond and emerald films. Below ver, a vast terrain of mountains and canyons was eroding in fast motion, carved by a blizzard of diffusion laws into glistening green and blue mesas, impossible overhangs, towering stratified sculptures veined with minerals unknown to chemistry.

In Konishi, ve would probably have called this “mathematics.” In C-Z, it was necessary to call it “art,” since anything else suggested a virtual universe in direct competition with the real one. Blanca had been dismayed to see the other polises sink back into complacency after the initial shock of carnevale, but ve still chafed against C-Z’s growing orthodoxy when it proclaimed that to explore any system of rules that failed to illuminate the physics of reality amounted to pernicious solipsism. The beauty of the physical world had nothing to do with its power to harm that was just the dogma of the dead statics in another guise and everything to do with the simplicity and consistency of its laws. Blanca was unimpressed by claims that C-Z’s physicists and engineers toiled only in the service of protecting the Coalition from the next dangerous cosmic surprise. It was the elegance of Kozuch Theory and the grandeur of the Forge itself that had kept them going; if either the guiding principles or the design had been the slightest bit uglier, they would have packed it in long ago.

Gabriel appeared beside ver, his fur dusted immediately with tiny crystals. Blanca reached over and brushed his shoulders affectionately; he responded by pressing a hand into the darkness of vis chest, inducing a gentle warmth throughout the whole invaded space. The places where Blanca’s icon seemed to lose its tangible boundary were the most sensitive by far; they could be touched in three dimensions.

“We’ve had a neutralization in one ring.” Gabriel seemed pleased, but nothing in his voice or gestalt betrayed the fact that the whole Forge group had been working toward this moment for the last eight centuries. Blanca nodded slightly, a gesture packed with warmth that only vis lover could have decoded.

Gabriel said, “Will you rush with me? Until confirmation?” He sounded slightly guilty to be asking.

The news would have just reached Earth that a positron in one of the Forge’s magnetic storage rings had lost its charge and escaped into the surrounding laser trap, 65 hours ago. But it would take almost three more hours—ten megatau—for the crucial matching result from the second ring at the opposite end of the accelerator to arrive. Gabriel had lived through every similar delay tau-by-tau until now, patiently accepting the glacial slowness of manipulating matter on the hundred-terameter scale, but Blanca had certainly never seen it as some great moral principle.

“Why not?” They held hands in a cobalt blue snowdrift while their exoselves synched and slowed; the scape was synched directly to Blanca’s mind, so it appeared to carry on at the same rate.

Ve watched Gabriel’s face as they waited, cheating the time by a mere factor of a million instead of jumping the gap in a single bound. Even if it wasn’t a moral issue, relating to the physical world could be a delicate balancing act. Should you dart from significant event to significant event, creating a life devoid of everything else? Probably not—but exactly how much subjective time should you endure between the moments you were, in all honesty, desperately waiting for? Gabriel had passed the time at the standard Coalition rate, mostly by immersing himself in elaborate schemes for the eventual deployment of the wormholes, in between his sparse contacts with the machinery of the Forge as it was constructed and tested. But he’d almost run out of future to plan; the last Blanca had heard, he’d mapped out a detailed strategy for the—careful, non-exponential—exploration of the entire universe. Local wormholes probably didn’t lead everywhere, since the mouths could only have traveled a certain distance since the time they were formed, but the closed, finite universe ought further than a few hundred million light years, there’d he wormholes in the galaxies at that distance which would reach as far again.

Gabriel’s mildly preoccupied expression changed to one of satisfaction, though nothing as dramatic as relief. “The other ring’s confirmed. We’ve grabbed both ends.”

Blanca swung his arm, dislodging a flurry of blue crystals from his fur. “Congratulations.” If the second neutralized positron had slipped out into space, it would have been impossible to find. With luck, they’d soon confirm that photons could pass through the wormhole, but a bombardment of either tiny mouth would only produce a trickle from the other.

Gabriel mused, “I keep wondering if we could have failed. I mean… we made a few mistakes in the design that we only discovered centuries later. And we hit those chaotic modes in the electron beams where the simulations broke down, so we had to map the whole state space empirically and find a way through by trial-and-error. We did a hundred thousand small things wrong, wasting time, making it harder. But could we ever have failed completely, beyond recovery? Beyond repair?”

“Isn’t that question slightly premature?” Blanca inclined vis head skeptically. “Assuming this isn’t a false alarm, you’ve just linked the two ends of the Forge. That’s a start, but you’re not quite staring down the runnel to Procyon yet.”

Gabriel smiled airily. “We’ve proved the basic principle; the rest is just a matter of persistence. Until the neutralization of those positrons, Kozuch-Wheeler wormholes might have turned out to be nothing but a useful fiction: just another metaphor that gave the right predictions at low energies, but fell apart under closer scrutiny.” He paused for a moment, looking slightly scandalized by his own words; it was a risk that the Forge group had rarely mentioned. “But now we’ve shown that they’re real, and that we understand how to manipulate them. So what can go wrong from here?”

“I don’t know. When it comes to interstellar wormholes, it might take longer than you think to find one that doesn’t lead straight into the heart of a star, or the core of a planet.”

“That’s true. But a certain amount of matter in every system has to he in the form of small asteroids, or interplanetary dust—somewhere we can burrow out from easily. And even if our estimates are wrong by a factor of a thousand, it would still only take a year or two to find and enlarge each new usable wormhole. Would you call that failure? When the gleisners are exploring a new system every century and calling it success?”

“No.” Blanca tried harder. “Okay, what about this? You’ve just proved that you can splice two identical, electron-positron wormholes together, at the electron ends. What if it doesn’t work when you substitute a proton for one of the positrons?” Only primordial electron-proton wormholes offered the chance of an instant short-cut to the stars; the current experiment was using freshly created electron-positron pairs merely for the sake of having both ends of each wormhole accessible. Working exclusively with electron-proton wormholes might have been simpler in theory, but new ones with known endpoints couldn’t be created at useful rate under anything less than Big Bang conditions. Gabriel hesitated, and for a moment Blanca wondered if he’d taken the scenario to heart.

“That would be a setback,” he conceded. “But Kozuch Theory clearly predicts that when you hit an electron linked to a proton with another one linked to a positron, the proton will decay into a neutron, the positron will neutralize… and the final wormhole will be even wider than the one we’ve just made. And there’s no room left, now, for idle speculation about Kozuch Theory being wrong. So—“ He thumbed his nose at ver, then jumped to the Forge scape.

Blanca followed. The schematic ahead of them showed a wire-thin cylinder; the thickness was not remotely to scale, but the length was correctly portrayed, stretching more than ten times wider than Pluto’s orbit. All the planetary orbits were drawn in, but the inner four, Mercury to Mars, were lost in the glare of the tiny sun.

The Forge was a giant particle accelerator, consisting of over fourteen trillion free-flying components. Each one used a small light-sail to balance the sun’s slight gravitational pull and keep itself locked onto a rigid straight line 140 billion kilometers long. The sails worked off beams sent fanning out from a network of solar-powered UV lasers, orbiting the sun closer than Mercury; they also extracted the energy needed to power the accelerator.

Most of the components were individual PASER units, lined up one after the other at ten-meter intervals. They re-focused the electron beams, then boosted the energy of each particle passing through them by about 140 microjoules. That didn’t sound like much, but for one electron it was equivalent to 900 trillion volts. PASERs used the Schachter effect: a suitable material was bathed in laser light, raising its atoms into high-energy states, and when a charged particle passed along a narrow channel drilled through the material, its electric field triggered the surrounding atoms into giving up their energy. It was as if the laser primed countless tiny electronic catapults, and then the particle came along and sprung them all, one after the other, getting a small kick forward from each one.

The energy density maintained within each PASER was enormous, and Blanca had seen a recording of an early test model bursting from radiation pressure. There hadn’t been much of an explosion, though; the PASERs were tiny garnet-like crystals, each one massing less than a gram. Substantial asteroids, hundreds of meters wide, had been mined for the tens of millions of tons of raw materials needed to make the Forge, but even Carter-Zimmerman’s most gung-ho astrophysical engineers would have vetoed any design that required gutting Ceres or Vesta or Pallas.

Blanca jumped to one end of the Forge, where the scape showed a “live” image of the real equipment, albeit delayed by the 65 hours it took for the signal to reach Earth. At both ends of the linear accelerator, electron-positron pairs were created in small cyclotrons; the positrons were retained in storage rings, while the electrons were fed straight into the main accelerator. The opposing beams met in the center of the Forge, and if two electrons collided head-on, fast enough to overcome electrostatic repulsion, Kozuch Theory predicted that they’d splice wormholes. The electrons themselves would disappear without a trace—locally violating conservation of both charge and energy—but the negative charge lost would be balanced by the neutralization of the positrons at the new wormhole’s far ends, and the energy of the missing electrons would manifest itself as the mass of the two neutral particles which the positrons had become, dubbed “femtomouths” or “FMs” by the Forge group’s theorists, since they were expected to be about a femtometer wide.

Blanca was remaining cautiously skeptical, but it seemed that the predicted sequence of events had finally taken place. No instruments had witnessed the vanishing act at the center of the Forge; tracking the torrent of electrons and looking for one perfect collision among all the near misses would have been impossible. But neutral particles of exactly the right mass, heavy as specks of dust but smaller than atomic nuclei, had been caught in the laser traps surrounding both storage rings at exactly the same time.

Gabriel had followed ver, and now they moved together through the hull of the storage ring facility and hovered above the laser trap. The scape merged a camera-based view of the equipment with schematics generated from instrument readings; most unrealistically, they could see the putative FM—a black dot radiating self-important tags—being gently shuffled through the trap by the shifting gradients of luminosity, scattering UV photons just enough to let the lasers nudge it along.

It would take over an hour for the FM to be delivered from the trap into the next stage. They rushed, though not as quickly as before.

“Aren’t the rest of the Forge group watching this?” They’d entered the scape privately, invisible and oblivious to any other users; Gabriel had inflected the address that way.

“Probably.”

“Don’t you want to be with them at the moment of proof?”

“Apparently not.” Gabriel pressed his hand inside ver again, deeper this time; pulses of warmth spread our from the center of vis torso. Blanca turned toward him and stroked his back, reaching for the place where the fur became, if he chose, almost unbearably sensitive. C-Z culture had its problems, but in Konishi a simple exchange of pleasure phrased in this manner would have been unthinkable. The two of them were not slavishly embodied; harm remained impossible, coercion remained impossible. But Konishi had sanctified autonomy in the same absurd fashion as the statics had sanctified the pitfalls of the flesh.

The FM arrived in the gamma-ray chamber, and a series of intense pulsed bombardments began. The gamma-ray photons had wavelengths of around ten-to-the-minus-fifteen meters, roughly the same as the FM’s diameter. A photon’s wavelength had nothing to do with the size of its wormhole mouth, but it did measure how precisely you could constrain its location and aim it at a chosen target.

Blanca protested, half-seriously, “Why couldn’t you have positioned the Forge so the time lags were equal?” Gamma rays should have been emerging instantaneously from the wormhole’s other mouth, but the far end of the accelerator was three billion kilometers further from Earth than the near end, so it would be another three hours before they’d know what had happened there, 68 hours earlier.

Gabriel defended himself almost absent-mindedly “It was a compromise. Comets to avoid, gravitational effects to balance…” Blanca followed his gaze into the flickering gamma-ray glow, and knew at once what he was thinking. What they were witnessing here opened up some very strange possibilities. According to a hypothetical observer flying along the axis of the Forge toward the far end, these photons, transported faster than light, would be coming out of the wormhole before they went in. That peculiar ordering of events was largely academic—the traveler wouldn’t even know about it until photons from both ends had had time to reach ver—but if ve also happened to be carrying a wormhole mouth of vis own, linked to one in the hands of an accomplice in a second spacecraft following behind, then as the traveler flew past the far end of the Forge ve could signal the accomplice to destroy the gamma-ray source at this end… before the photons ve’d just seen emerging had ever been sent.

Once they had a second wormhole, the Forge group would be able to make this ancient thought experiment a reality. The most likely solution to the paradox involved virtual particles—the mouths of vacuum wormholes—traveling in a loop that included both the Forge wormhole and the ship-borne one. Virtual particles were constantly streaming along every available path through space-time, and though crossing ordinary space between the mouths of the two wormholes would take them a certain amount of time, moving through the ship-borne wormhole would carry them back into the past, reducing the total time needed to go around the loop. As the two spacecraft neared the point where signaling from future to past became possible, the transit time for the loop would approach zero, and each virtual particle would find an exponentially growing army of doppelgangers hard on its heels: future versions of itself which had already made the trip. As they slipped into perfect phase with each other, their rapidly increasing energy density would make the wormhole mouths implode into tiny black holes, which would then vanish in puffs of Hawking radiation.

Apart from ruling out time travel, this would have serious practical consequences: once the galaxy was crisscrossed with wormholes, there’d be loops of virtual particles threading them all, and any careless manipulation of the mouths could see the whole network annihilated.

Gabriel said, “It’s almost time. Shall we…?”

They jumped to the far end of the Forge, where the scape was showing the most recent data available: still a few minutes before the gamma-ray bombardment had begun. The second FM sat in an observation chamber, under the scrutiny of a cylindrical array of gamma-ray detectors, nudged occasionally by UV lasers to keep it perfectly centered. The faint scatter from the lasers was the only sign that the thing was really there; with no electric charge or magnetic moment, it was a far more elusive object than a single atom.

“Don’t you think we should be with the others?” Blanca had lived with the distant promises of the Forge for so long now that it was hard to be moved by this first, microscopic hint of what lay ahead. But if they really were on the threshold of a change that would shape the history of the Coalition for the next ten thousand years, it seemed like a fair excuse for public celebration.

“I thought you’d be pleased.” Gabriel laughed curtly, offended. “At the end of eight centuries, we’re together for this moment. Doesn’t that mean anything to you?”

Blanca stroked his hack. “I’m deeply touched. But don’t you think you owe your colleagues—”

He disengaged from ver angrily. “All right. Have it your way. We’ll join the crowd.”

He jumped. Blanca followed. As they re-entered the scape in public mode it seemed to expand dramatically; half of Carter-Zimmerman was hovering in the space above the observation chamber, and the image had been re-scaled to fit them all in.

People recognized Gabriel at once, and flocked around to congratulate him. Blanca moved aside and listened to the excited well-wishers.

“This is it! Can you imagine the gleisners’ reaction, when they arrive at the next star and find that we’ve beaten them to it?” The citizen’s icon was an ape-shaped cage full of tiny yellow birds in constant flight.

Gabriel replied diplomatically, “We’ll be avoiding their targets. That was always the plan.”

“I don’t mean we should explore the system in competition with them. Just leave an unmistakable sign.” Blanca considered interjecting that the first few thousand wormholes they widened would be most unlikely to include any of the gleisners’ immediate destinations, but then thought better of it.

On jumping to the scape, they’d synched by default to the average rate of its inhabitants, a rush of about a hundred thousand. It was fluctuating, though; some people were growing impatient, while others were trying to prolong the suspense. Blanca let verself drift with the average, enjoying the sense of being jostled through time by the whims of the crowd. Ve wandered through the scape, exchanging pleasantries with strangers, finding it hard to take the vast machinery of the observation chamber seriously so soon after experiencing it all on a scale where there’d barely been room to spread vis arms. Ve spotted Yatima in the distance, deep in conversation with other members of the Forge group, and felt an amusing surge of quasi-parental pride—even if most of the skills ve’d taught the orphan would have been more use to a Konishi Miner than a C-Z physicist.

As the moment approached, people started chanting a countdown. Blanca searched for Gabriel; he was surrounded by demonstrative strangers, but when he saw ver approaching he broke away.

“Five!”

Gabriel took vis hand. “I’m sorry.”

“Four!”

He said, “I didn’t want to be with the others. I didn’t want to be with anyone but you.”

“Three!”

Fear flashed in his eyes. “My outlook’s programmed to cushion me, but I don’t know how I’ll take this.”

“Two!”

“One traversable wormhole, and then the rest is mass-production. I’ve made this my whole life. I’ve made this my whole purpose.”

“ONE!”

“I cap, find another goal, choose another goal, but then who will I be?”

Blanca reached up and touched his cheek, not knowing what to say. Vis own outlook was much less focused; ve’d never faced a sharp transition like this.

“ZERO!”

The crowd fell silent. Blanca waited for the uproar, the cheers, the screams of triumph. Nothing. Gabriel looked down, then Blanca did too. The femtomouth was scattering the lasers’ ultraviolet, as ever, but no gamma rays were emerging.

Blanca said, “The other mouth must have drifted out of the focus.”

Gabriel laughed nervously. “But it didn’t. We were there, and the instruments said nothing.” People around them were whispering their own theories discreetly, but their gestalt seemed more tolerantly amused than derisive. After eight centuries of setbacks, it would have been too good to be true if the Forge had delivered the definitive proof of its success at the first opportunity.

“Then there must be a calibration error. If the mouth drifted, but the instruments thought it was still at the focus, then the whole system needs to be recalibrated.”

“Yes.” Gabriel ran his hands through the fur of his face, then laughed. “Here I am expecting to fall off the edge of the world, and one more thing goes wrong to save me.”

“One final screw-up to smooth the transition. What more could you ask for?”

“Yeah.”

“And then what?”

He shrugged, suddenly embarrassed by the whole question. “You said it yourself: linking the Forge is only the start. We haven’t wrapped the universe in wormholes yet. And at this rate, there’ll he screw-ups to smooth the transition for another eight hundred years.”

Blanca spent half a gigatau exploring vis new imaginary world, fine-tuning the parameters and starting again a thousand times, but never intervening and sculpting the landscape directly. That was wicked—it made it less artful, and more mock-physical—but no one had to know. When ve opened it up to the public, people would marvel at its perfect blend of consistency and spontaneity.

Ve was sitting on the edge of a deep canyon, watching leaf-green dust clouds flow in around ver like a vivid but ethereal waterfall, when Gabriel appeared. Blanca had spent some time worrying about the problems with the Forge, but within the first megatau it had slipped from vis thoughts completely. Ve knew they’d sort it out, the way they’d sorted out every other obstacle. It was always just a matter of perseverance.

Gabriel said calmly, “Gamma rays are coming through the far end now.”

“That’s wonderful! What was the problem? A misaligned laser?”

“There was no problem. We haven’t carried out any repairs. We haven’t changed a thing.”

“What, the mouth just drifted back into the focus? Is it oscillating back and forth in the trap?”

Gabriel dipped his hands into the green flow. He was always sitting at the Locus, perfectly positioned. “The gamma rays we’re seeing now are the ones that went in at the start. We coded all the pulses with a time stamp, remember? Well, the first pulses to emerge had the time stamp for the gamma rays sent in five and a half days ago. They’ve taken as long to come out as if they’d crossed the ordinary space between the mouths. Exactly, down to the picosecond. The wormhole is traversable, but it isn’t a short cut. It’s a hundred and forty billion kilometers long.”

Blanca absorbed this in silence. Asking if he was sure didn’t seem like a good idea; the Forge group would have spent the last few megatau searching frantically for a more palatable conclusion.

Finally, ve said, “Why? Do you have any ideas?'

He shrugged. “The only thing we can come up with that makes any sense is this: the total energy of the wormhole depends almost entirely on the size and shape of the mouths. It’s the mouths that interact with virtual gravitons; the wormhole tunnel can be as long or short as you like, and the mouths will still have exactly the same mass.”

“Yes, but that’s no reason for the tunnel to grow longer, just because the mouths are moved apart in external space.”

“Wait. There’s a tiny correction to the total energy that does depend on length. If the wormhole is shorter than the path through external space, then the energy of the virtual particles passing through it will be slightly higher than the normal vacuum energy. So if the wormhole is free to adjust its length to minimize that energy, the internal distance between the mouths will end up the same as the external distance.”

“But the wormhole isn’t free to do that! Kozuch Theory won’t allow it to grow longer than ten-to-the-minus-thirty-five meters; in the six extra dimensions, the whole universe is no wider than that!”

Gabriel said dryly, “It seems Kozuch Theory has a few problems. First Lacerta, still unexplained. Now this.” The gleisners had put a non-sentient probe into orbit around the Lacerta black hole, but it had revealed nothing about the cause of the neutron stars’ collision.

They sat in silence for a while, legs hanging over the canyon’s edge, watching the green mist cascading down. In terms of a pure intellectual challenge, Gabriel couldn’t have hoped for more: Kozuch Theory would have to be completely re-assessed, or even replaced, and the instrument he’d spent the last eight hundred years helping to build would be at the center of the transformation.

It was only as a short cut to the stars that the Forge had turned out to be a complete waste of time.

Blanca said, “You’ve brought us closer to the truth. That’s never a defeat.”

Gabriel laughed bitterly. “No? There’s already talk of cloning a thousand copies of Carter-Zimmerman and dispatching them all in different directions, to help us catch up with the gleisners. If the wormholes had been instantly traversable they would have bound the whole galaxy together; we could have moved from star to star as easily as we jump from scape to scape. But now we’re destined for fragmentation. A few clones of C-Z will fly off to the stars, centuries will pass… and by the time any news comes back the other polises will be past caring. We’ll all drift apart.” He scooped a handful of dust forward, speeding its fall over the precipice. “I was going to build a network spanning the universe. That’s who I was: the citizen who’d put it all in the palms of our hands. Who am I now?”

“Instigator of the next scientific revolution.”

“No.” He shook his head slowly. “I can’t turn that corner. I can live with failure. I can live with humiliation. I can meekly follow the gleisners into space, slower than light, accepting that there’s no better way after all. But don’t expect me to take the thing that’s poisoned my dreams and embrace it as some kind of triumphant revelation.”

Blanca watched him staring morosely into the distance. Ve’d been wrong, for all these centuries: the elegance of Kozuch Theory had never been enough for Gabriel. So the chance to uncover and remove its flaws was no consolation to him at all.

Blanca stood. “Come on.”

“What?”

Ve reached down and took his hand. “Jump with me.”

“Where?”

“Not to another scape. Here. Over the edge.”

Gabriel regarded ver dubiously, but he rose to his feet. “Why?”

“It will make you feel better.”

“I doubt it.”

“Then do it for me.”

He smiled ruefully. “All right.”

They stood on the edge of the rock, feeling the dust swirl down around their feet. Gabriel said, surprised, “It makes me uneasy, just knowing that I’m going to give tip control of my icon. Must be something vestigial. You know even winged exuberants had a strong reaction against free fall? Diving was often a useful maneuver for them, but they retained an instinctive desire to put an end to it as soon as possible.”

“Well, don’t panic and fly off, or I’ll never forgive you. Ready?”

“No.” Gabriel craned his neck forward. “I really don’t like this.”

Blanca squeezed his hand and stepped forward, and the laws of the imaginary world sent them tumbling down.

9. DEGREES OF FREEDOM

Carter-Zimmerman polis, interstellar space

58 315 855 965 866 CST

21 March 4082, 8:06:03.020 UT

Blanca felt obliged to visit the Hull at least once a year. Everyone in Carter-Zimmerman knew that ve’d chosen to experience some subjective time on the trip to Fomalhaut—despite Gabriel’s decision to remain frozen for the duration—and there was really only one acceptable reason for doing that.

“Blanca! You’re awake!” Enif had spotted ver already, and he bounded toward ver on all fours across the micrometeorite-pitted ceramic, sure-footed as ever. Alnath and Merak followed, at a slightly more prudent velocity. Most of the Osvalds used embodiment software to simulate hypothetical vacuum-adapted fleshers, complete with airtight, thermally insulating hides, infrared communication, variably adhesive palms and soles, and simulated repair of simulated radiation damage. The design was perfectly functional, but since each space-going clone of Carter-Zimmerman polis was barely larger than one of these Star Puppies, having the real things as passengers was out of the question. The Hull was just a plausible fiction, a synthetic scape melding the real sky with an imaginary spacecraft hundreds of meters long; thousands of times heavier than the polis, it could only have been real if they’d postponed the Diaspora for a few millennia in order to manufacture enough antihydrogen to fuel it.

Enif almost collided with ver, but he swerved aside just in time, barely maintaining his grip. He was always showing off his finely honed Hull-skills, but Blanca wondered what the others would have done if he’d misjudged the adhesion and launched himself into space. Would they have violated the carefully simulated physics and magicked him back down? Or would they have mounted a somber rescue mission?

“You’re awake! Exactly one year later!”

“That’s right. I’ve decided to become your vernal equinox, keeping you in touch with the rhythms of the home world.” Blanca couldn’t help verself; ever since ve’d discovered that the Osvalds’ outlook made them lap up any old astrobabble like this as if it was dazzlingly profound, ve’d been pushing the envelope in search of whatever vestigial sense of irony might have survived their perfect accommodation to the mental rigors of interstellar travel.

Enif sighed happily, “You’ll be our dark sun rising, a nostalgic afterimage on our collective retina!” The others had caught up, and the three of them began earnestly discussing the importance of remaining in synch with the Earth’s ancient cycles. The fact that they were all fifth generation C-Z homeborn who’d never been remotely affected by the seasons didn’t seem to rate a mention. When Carter-Zimmerman polis was cloned a thousand times and the clones launched toward a thousand destinations, the vast majority of citizens taking part in the Diaspora had sensibly decided to keep all their snapshots frozen until they arrived, side-stepping both tedium and risk. If a snapshot file was destroyed en route without having been run since the instant of cloning, that would constitute no loss, no death, at all. Many citizens had also programmed their exoselves to restart them only at target systems that turned out to be sufficiently interesting, eliminating even the risk of disappointment.

At the other extreme, ninety-two citizens had chosen to experience every one of the thousand journeys, and though some were rushing fast enough to shrink each trip to a few megatau, the rest subscribed to the curious belief that flesher-equivalent subjective time was the only “honest” rate at which to engage with the physical world. They were the ones who required the most heavy-handed outlooks to keep them from going insane.

“So, what’s new? What have I missed?” Blanca showed verself on the Hull no more than once or twice a year, letting the Osvalds assume that ve was spending the rest of the time frozen. Since ve’d chosen to wake at all only on this, the shortest of the journeys, such a watered-down approach to the Diaspora Experience must have struck vis fellow passengers as consistent, if not exactly laudable.

Merak rose up on her hind legs, frowning amiably, the veins in her throat beneath her violet hide still pulsing visibly after her sprint. “You really can’t tell! Procyon’s shifted almost a sixth of a degree since you were last here! And Alpha Centauri more than twice as much!” She closed her eyes, for a moment too blissed-out to continue. “Don’t you feel it, Blanca? You must! That exquisite sense of parallax, of moving through the stars in three dimensions…”

Blanca had privately dubbed the citizens who used this outlook—most, but not all of them Star Puppies—“The Osvalds,” after the character in Ibsen’s Ghosts who ends the play repeating senselessly, “The sun. The sun.” The stars. The stars. When they weren’t speechless with joy over parallax shifts, they were mesmerized by the fluctuations of variable stars, or the slow orbits of a few easily resolved binaries. The polis was too small to be equipped with serious astronomical facilities, and in any case the Star Puppies stuck slavishly to their limited, mock-biological vision. But they basked in the starlight, and reveled in the sheer distance and time scales of the journey, because they’d reshaped their minds to render every detail of the experience endlessly pleasurable, endlessly fascinating, and endlessly significant.

Blanca stayed for a few kilotau, allowing Enif, Alnath, and Merak to lead ver all the way around the imaginary ship, pointing out hundreds of tiny changes in the sky and explaining what they meant, stopping now and then to show ver off to their friends. When ve finally hinted that vis time was almost up, they took ver to the nose and gazed reverently at their destination. In a year, Fomalhaut hadn’t brightened noticeably, and there were no close stars to be seen streaming away from it, so even Merak had to admit that there was nothing much to single it out.

Blanca didn’t have the heart to remind them that they’d deliberately blinded themselves to the most spectacular sign of the polis’s motion: at eight percent of lightspeed, the Doppler-shift starbow centered on Fomalhaut was far too subtle for them to detect. The scape itself was based on data from cameras with single-photon sensitivity and sub-Angstrom wavelength resolution, so the sight was there for the asking, but the idea of cheating their embodiment to absorb this information directly, or even just constructing a false-color sky to exaggerate the Doppler effect to the point of visibility, would have filled them with horror. They were experiencing the trip through the raw senses of plausible space faring fleshers; any embellishments could only detract from that authenticity, and risk leading them into the madness of abstractionism.

Ve bid them farewell until next time. They gamboled around ver, protesting noisily and pleading with ver to stay, but Blanca knew they wouldn’t miss ver for long.

Back in vis homescape, Blanca admitted to verself that ve’d actually enjoyed the visit. A brief dose of the Puppies’ relentless enthusiasm always helped shake up vis perspective on vis own obsession.

Vis current homescape was a fissured, vitreous plain beneath a deep orange sky. Mercurial silver clouds just a few delta from the ground rose in updrafts, sublimated into invisible vapor, then re-condensed abruptly and sank again. The ground suffered quakes induced by forces from the clouds that had no analogue in real-world physics; Blanca was beginning to get a feel for the patterns in the sky that presaged the big ones, but the precise rules, complex emergent properties of the lower-level deterministic laws, remained elusive. This world and its seismology were just decoration and diversion, though. The reason ve’d elected to experience time on the voyage at all zig-zagged for kilodelta across the scape—and the trail of discarded Kozuch diagrams, failed attempts to solve the Distance Problem, would soon constitute the most significant feature of the plain, out-classing the fissures produced by even the strongest quakes.

Blanca hovered at the fresh end of the trail, taking stock of vis recent dismal efforts. Ve’d spent the last few megatau trying to patch an ugly system of “higher-order corrections” onto Kozuch’s original model, infinite regresses of wormholes-within-wormholes which ve’d hoped might sum to arbitrarily large, but finite, lengths, hundred-billion-kilometer fractals packed into a space twenty orders of magnitude smaller than a proton. Before that, ve’d tinkered with the process of vacuum creation and annihilation, trying to get the space-time in the wormhole to expand and contract on cue as the mouths were repositioned. Neither approach had worked, and in retrospect ve was glad that they hadn’t; these ad hoc modifications were far too clumsy to deserve to be true.

After being used to create the antihydrogen to fuel the Diaspora, the Forge had been reclaimed by the small group of particle physicists in Earth C-Z not terminally disillusioned by the failure of its original purpose. Their experiments had now probed every known species of particle down to the Planck-Wheeler length, and so long as no traversable wormholes were produced the results remained perfectly consistent with Kozuch Theory. To Blanca, this strongly suggested that Kozuch’s original identification between particle types and wormhole mouths was correct, and whatever else needed to he overhauled or thrown out, that basic idea should remain intact as the core of a revised theory.

On Earth, though, there was a growing consensus that Kozuch’s whole model had to be abandoned. The six extra dimensions which allowed the wormhole mouths their diversity were already being described as “the mathematical fiction that misled physicists for two thousand years,” and theorists were urging each other to adopt a more “realistic” approach with all the puritanical vigor of scourge-wielding penitents.

Blanca accepted that it was possible that all of Kozuch Theory’s successful predictions were due to nothing but the “mirroring” of the logical structure of wormhole topology in another system altogether. The motion under gravity of an object dropped down a borehole passing through the center of an asteroid obeyed essentially the same mathematics as the motion of an object tied to the free end of an idealized anchored spring—but pushing either model too far as a metaphor for the other generated nonsense. The success of Kozuch’s model could be due to the fact that it was just an extremely good metaphor, most of the time, for some deeper physical process which was actually as different from extra-dimensional wormholes as a spring was different from an asteroid.

The trouble was, this conclusion fitted the prevailing mood in C-Z far too well: the recriminations over the failure of wormhole travel, the backlash against the other polises’ continuing retreat from the physical world, and the increasingly popular doctrine that the only way to avoid following them was to anchor C-Z culture firmly to the rock of direct ancestral experience, and dismiss everything else as metaphysical indulgence. In that climate, Kozuch’s six extra dimensions could never be more than the product of a temporary misunderstanding of what was really going on.

Blanca had originally planned to spend no more than twenty or thirty megatau on the problem, then sleep for the rest of the voyage, satisfied that ve’d struggled long and hard enough to understand exactly how difficult it would be to find a solution. Ve’d guarded against investing too much hope in the prospect of helping Gabriel out of his post-Forge depression, despite fanciful visions of greeting him when he woke with the news that his soul-destroying “failure” had been transformed into the key to the physics of the next two thousand years. But the fact remained that Renata Kozuch had invented a universe of unsurpassed elegance, ruled by a set of economical and harmonious laws—and the bulletins from Earth were beginning to portray this marvelous creation as some kind of hideous mistake, as disastrous as the Ptolemaic epicycles, as wrong-headed as phlogiston and the aether. Blanca felt that ve owed Kozuch herself a spirited defense.

Ve ran vis Kozuch avatar; an image of the long-dead flesher appeared in the scape beside ver. Kozuch had been a dark-haired woman, shorter than most, sixty-two years old when she’d published her masterpiece—an anomalous age for spectacular achievement in the sciences, in that era. The avatar wasn’t sentient, let alone a faithful re-creation of Kozuch’s mind; she’d died in the early years of the Introdus, and no one really knew why she’d declined to be scanned. But the software had access to her published views on a wide range of topics, and it could read between the lines to some degree and extract a limited amount of implicit information. Blanca asked, for the thirty-seventh time, “How long can a wormhole he?”

“Half the circumference of the standard fiber.” The avatar, not unreasonably, injected a hint of impatience into Kozuch’s voice. And though it paraphrased inventively, the answer was always the same: about five time ten-to-the-minus-thirty-five meters.

“The standard fiber?” The avatar gave ver something approaching a look of exasperation, but Blanca pleaded stubbornly, “Remind me.” Ve had to go back to the foundations; ve had to re-examine the model’s basic assumptions and find a way to modify them that made sense of the Distance Problem, but left the fundamental symmetries of the wormhole mouths intact.

The avatar relented; in the end it always cooperated, whether Kozuch herself would have or not. “Let’s start with a two-dimensional spacelike slice through a Minkowski universe—flat and static, the simplest possible toy to play with.” It created a translucent rectangle, about a delta long and half a delta wide, then bent it around so that the two halves were parallel, a hand’s width apart, one above the other. “The curvature here means nothing, of course; it’s necessary in order to construct the diagram, but physically it has no significance at all.” Blanca nodded, feeling slightly embarrassed; this was like asking Carl Friedrich Gauss to recite multiplication tables.

The avatar cut two small disks out of the diagram. one in the top plane and the other directly beneath it. “If we want to connect these circles with a wormhole, there are two ways of doing it.” It pasted a thin rectangular strip into the diagram, joining a small part of the top hole’s rim to the matching segment of the bottom rim. Then it extended this tentative bridge all the way around both holes, spinning it out into a complete tunnel. The tunnel assumed an hourglass shape, tapering to a waist but never pinching closed. “According to General Relativity, this solution would appear to have negative energy in some reference frames, especially if it was traversable. The two mouths could still have positive mass, though, so I pursued some tentative quantum-gravity versions of this for a while, but in the end I could never make it work as a model for stable particles.”

It erased the hourglass-shaped tunnel, leaving the two holes disconnected again, then pasted a narrow strip between the left-hand side of the top rim and the right hand side of the bottom rim. As before, it extended the strip all the way around both circles, always connecting opposite sides of the rims, creating a pair of cones meeting at a point between the wormhole mouths. “This solution has positive mass. In fact, if GR held true at this scale, it would just be a pair of black holes sharing a singularity. Of course, even for the heaviest elementary particles the Schwarzschild radius is far smaller than the Planck-Wheeler length, so quantum uncertainty would disrupt any potential event horizons, and perhaps even smooth away the singularity as well. But I wanted to find a simple, geometrical model underlying that uncertainty.”

“So you expressed it by adding extra dimensions. If Einstein’s equations in four dimensions can’t pin down the structure of space-time on the smallest scale, then every 'fixed point’ in the classical model must have some extra degrees of freedom.”

“Exactly.” The avatar gestured at the diagram, and it was subtly transformed: the translucent sheet became a mass of tiny bubbles, each one an identical perfect sphere. This was a heavily stylized view—rather like drawing a cylinder as a long line of adjoining circles—but Blanca understood the convention: every point in the diagram, though fixed in the two dimensions of the sheet, was now considered to be free to position itself anywhere on the surface of its own tiny sphere. “The extra space each point can occupy is called the ’standard fiber’ of the model; it’s not long and fibrous, I know, but the term is a legacy of mathematical history, so we’re stuck with it. I started with a 2-sphere for the standard fiber; I only changed it to a 6-sphere when it became clear that six dimensions were needed to account for all the particles.”

The avatar created a fist-sized sphere floating above the main diagram, and covered it with a palette of colors that varied smoothly over the whole surface. “How does giving every point a 2-sphere to move in get around the singularity? Suppose we approach the center of the wormhole from a certain angle, and let the extra dimensions change like this.” The avatar drew a white line down the sphere from the north pole toward the equator, and a colored line appeared simultaneously on the main diagram: a path leading straight into the top cone of the wormhole. The path’s colors came from the line being sketched on the sphere; they signified the values of the two extra dimensions being assigned to each point.

As the line on the sphere crossed the equator, the path crossed between the two cones. “That would have been the singularity, but in a moment I’ll show you what’s become of it.” The avatar extended the meridian toward the south pole, and the path through the worm hole continued on through the lower cone, and emerged in the bottom region of ordinary space.

“Okay, that’s one geodesic. And in the classical version, all geodesics from one wormhole mouth to the other would converge on the singularity. But now…” It drew a second meridian on the sphere, starting again from the north pole, but heading for a point on the equator 180 degrees away. This time, the colored path that appeared on the wormhole diagram approached the top mouth from the opposite side.

As before, when the meridian crossed the equator of the sphere, the path through the wormhole crossed between the two cones. Since the tips of the cones only touched at a single point, the second path had to pass through the same point as the first—but the avatar produced a magnifying glass and held it up to that point’s standard fiber for Blanca to see. The tiny sphere had two colored dots on opposite sides of its equator. The two paths never actually collided; the extra dimensions gave them room to avoid each other, even though they converged on the same point of ordinary space.

The avatar gestured at the diagram, and suddenly the whole surface was color-coded for the extra dimensions. Far from the wormhole mouths the space was uniformly white—indicating that the extra dimensions were unconstrained, and there was no way of knowing any point’s position on the standard fiber. Within each cone, though, the space gradually took on a definite hue—red in the top cone, violet in the bottom—and then, close to the meeting point, the color began to vary strikingly with the angle of approach: vivid green on one side of the top cone, sweeping round to magenta 180 degrees away—a pattern that emerged inverted on the cone below, before melding smoothly into the surrounding violet, which in turn faded to white. It was as if every radial path through the wormhole had been lifted “up” out of the plane of this two-dimensional space to a slightly different “height” as it approached, allowing them all to “cross over” at the center without fear of colliding. The only real difference was that the extra-dimensional equivalent of “height above the plane” had to occur in a space that looped back on itself, so that a line rotated through 360 degrees could change “height” smoothly all the way, and still end up exactly where it began.

Blanca gazed at the diagram, trying to see it from a fresh perspective despite the numbing familiarity of the concepts. “And a 6-sphere generates a whole family of particles, because there’s room to avoid the singularity in different ways. But you said you started with a 2-sphere. Do you mean later, when you were working with three-dimensional space?”

“No.” The avatar seemed somewhat bemused by the question. “I started exactly as you see here: with two-dimensional space, and a 2-sphere for the standard fiber.”

“But why a 2-sphere?” Blanca duplicated the diagram, but used a circle as the standard fiber instead of a sphere. Again, no two paths through the wormhole were the same color at the cross-over point; the main difference was that they took on different colors straight from the whiteness of the, surrounding space, because there were no “north and south poles” now from which they could spread out. “In two-dimensional space, you only need one extra dimension to avoid the singularity.”

“That’s true,” the avatar conceded. “But I used a two-dimensional standard fiber because this wormhole possesses two degrees of freedom. One keeps the geodesics from colliding at the center. The other keeps the two mouths of the wormhole itself apart. If I’d used a circle as the standard fiber, then the distance between the mouths would have been fixed at precisely zero—which would have been an absurd constraint, when the whole point of the model was to mimic quantum uncertainty.”

Blanca felt vis infotrope firing up, frustrated but ever hopeful. They’d reached the heart of the Distance Problem. The exaggerated size of the cones in the diagram was misleading; the gravitational curvature of ordinary space around an elementary particle was negligible, and contributed virtually nothing to the length of the wormhole. It was the way paths through the wormhole coiled around the extra dimensions of the standard fiber that allowed them to be slightly longer than they would have been if the two mouths had simply been glued together, rim to rim.

Or in reality, much more than slightly.

“Two degrees of freedom,” Blanca mused. “The width of the wormhole, and its length. But in your model, each dimension shares those two roles from the start—and if they don’t share them equally it gives nonsensical results.” Blanca had tried distorting the standard fiber to allow for longer wormholes, but that had been a disaster. Stretching the 6-sphere into a 6-ellipsoid of astronomical proportions allowed for hundred-billion-kilometer wormholes like the Forge had produced, but it also implied the existence of “electrons” shaped like pieces of string of astronomical length. And changing the topology of the standard fiber, rather than just its shape, would have destroyed the correspondence between wormhole mouths and particles. The avatar responded, somewhat defensively, “Maybe I could have done it your way, starting with a circle to keep the geodesics apart. But then I would have had to introduce a second circle to keep the mouth apart-making the standard fiber a 2-torus. If I’d taken that approach, by the time I worked my way up to matching the particle symmetries I would have found myself lumbered with twelve dimensions: six for each purpose. Which would have worked just as well, but it would have been twice as extravagant. And after the debacle of string theory, it was hard enough selling anyone on six.”

“I can imagine.” Blanca responded automatically, before ve’d fully absorbed what the avatar had said. A moment later, it hit ver.

Twelve dimensions? Ve’d felt so besieged by the realist backlash that ve’d never even considered doing more than defending Kozuch’s six against the charge of “abstractionism.” Twice as extravagant? It certainly would have been in the twenty-first century, when no one knew how long wormholes really were.

But now?

Blanca shut down the avatar and began a fresh set of calculations. Kozuch herself had never said anything so explicit about higher-dimensional alternatives, but the avatar’s educated guess turned out to be perfectly correct. Just as a 2-torus was the result of expanding every point in a circle into another circle perpendicular to the first, turning every point in a 6-sphere into a 6-sphere in its own right created a 12-torus—and a 12-torus as the standard fiber solved everything. The symmetries of the particles, and the Planck-Wheeler size of their wormhole mouths, could arise from one set of six dimensions; the freedom of the wormholes to take on astronomical lengths could then arise from the remaining six.

If the 12-torus was much larger in the six “length” dimensions than the six “width” ones, the two scales became completely independent, the two roles entirely separate. In fact, the easiest way to picture the new model was to split up the whole four-plus-twelve-dimensional universe in much the same way as the ten-dimensional universe of the original Kozuch Theory—but with three levels, instead of two. The smallest six dimensions played the same role as ever: every point in four-dimensional space-time gained six sub-microscopic degrees of freedom. But the six larger dimensions made more sense if the roles were reversed: instead of a separate six-dimensional “macrosphere” for every point in the four-dimensional universe… there was a separate four-dimensional universe for every point in a single, vast, six-dimensional macrosphere.

Blanca returned to the avatar’s wormhole diagram. It was easier to interpret now if the space was unfolded and laid flat; it could then be thought of as one slice of many through a small—and hence approximately flat—part of the macrosphere. One slice through a stack of universes. Blanca replaced the single microsphere at the center of the wormhole with a long chain of microspheres arcing from one mouth to the other, stringing together virtual wormholes from the vacuum of adjacent universes. An elementary particle would be stuck with a constant wormhole length, fixed at the moment of its creation, but a traversable wormhole would be free to tunnel its way into detours of arbitrary size. For the femtomouths produced in the Forge, the verdict was clear: they’d stolen enough vacuum from other universes—they’d snaked out far enough into the macrosphere’s extra dimensions—to equalize their lengths with the external distance between their mouths.

Of course, no one in C-Z would believe a word of this; it was abstractionism run riot. These hypothetical “adjacent universes”—let alone the “macrosphere” they comprised in their totality—would always be impossible to observe. Even if a wormhole could be made wide enough for a tiny robot to fly through, looking to the sides would reveal nothing but a distorted image of the robot itself, as light circled the wormhole’s cross-sectional sphere. The other universes, as ever, would remain 90 degrees away from any direction in which it was possible to look, or travel.

Still, the Distance Problem was solved, with a model that merely extended Renata Kozuch’s work, discarding none of her triumphs. Let them try bettering that in Earth C-Z! Neither ve nor Gabriel were running versions there—they’d left behind snapshots only to be run in the unlikely event that the whole Diaspora was wiped out—but Blanca thought it over and reluctantly dispatched a bulletin homeward, summarizing vis results. That was the correct protocol, after all. Never mind if the work was laughed at and forgotten; ve could argue the case in Fomalhaut C-Z, once there was someone awake worth arguing with.

Blanca watched the silver clouds circulating; there was a big quake coming soon, but ve’d lost interest in seismology. And although there were a thousand things yet to be explored in the extended Kozuch model—how the four-dimensional universes that played “standard fiber” to the macrosphere determined its own strange particle physics, for one—ve wanted to save something for Gabriel. They could map that real but unreachable world together, physicist and scape artist, mathematicians both.

Blanca shut down the glassy plain, the orange sky, the clouds. In the darkness, ve built a hierarchy of luminous spheres and set it spinning beside ver. Then ve instructed vis exoself to freeze ver until the moment they arrived at Fomalhaut.

Ve stared into the light, waiting to see the expression on Gabriel’s face when he heard the news.