Cordelia said, “What would make it worthwhile, then? What’s the most you could hope for?”
Vikram sketched a Feynman diagram in the air between them. “If you take spacetime for granted, rotational symmetry plus quantum mechanics gives you a set of rules for dealing with a particle’s spin. Penrose turned this inside out, and showed that the whole concept of ‘the angle between two directions’ can be created from scratch in a network of world lines, so long as they obey those spin rules. Suppose a system of particles with a certain total spin throws an electron to another system, and in the process the first system’s spin decreases. If you knew the angle between the two spin vectors, you could calculate the probability that the second spin was increased rather than decreased … but if the concept of ‘angle’ doesn’t even exist yet, you can work backwards and define itfrom the probability you get by looking at all the networks for which the second spin is increased.
“Kumar and others extended this idea to cover more abstract symmetries. From a list of rules about what constitutes a valid network, and how to assign a phase to each one, we can now derive all known physics. But I want to know if there’s a deeper explanation for those rules. Are spin and the other quantum numbers truly elementary, or are they the product of something more fundamental? And when networks reinforce or cancel each other according to the phase difference between them, is that something basic we just have to accept, or is there hidden machinery beneath the mathematics?”
Timon appeared in the scape, and drew Gisela aside. “I’ve committed a small infraction — and knowing you, you’ll find out anyway. So this is a confession in the hope of leniency.”
“What have you done?”
Timon regarded her nervously. “Prospero was rambling on about flesher culture as the route to all knowledge.” He morphed into a perfect imitation, and replayed Prospero’s voice: “‘The key to astronomy lies in the study of the great Egyptian astrologers, and the heart of mathematics is revealed in the rituals of the Pythagorean mystics … ’”
Gisela put her face in her hands; she would have been hard-pressed not to respond herself. “And you said — ?”
“I told him that if he was ever embodied in a space-suit, floating among the stars, he ought to try sneezing on the face plate to improve the view.”
Gisela cracked up laughing. Timon asked hopefully, “Does that mean I’m forgiven?”
“No. How did he take it?”
“Hard to tell.” Timon frowned. “I’m not sure that he’s capable of grasping insults. It would require imagining that someone could believe that he’s less than essential to the future of civilisation.”
Gisela said sternly, “Two more days. Try harder.”
“Try harder yourself. It’s your turn now.”
“What?”
“Prospero wants to see you.” Timon grinned with malicious pleasure. “Time to have your own mythic essence extracted.”
Gisela glanced towards Cordelia; she was talking animatedly with Vikram. Athena, and Prospero, had suffocated her; it was only away from both that she came to life. The decision to migrate was hers alone, but Gisela would never forgive herself if she did anything to diminish the opportunity.
Timon said, “Be nice.”
***
The Dive team had decided against any parting of the clones; their frozen snapshots would be incorporated into the blueprint for Cartan Null without ever being run outside Chandrasekhar. When Gisela had told Prospero this, he’d been appalled, but he’d cheered up almost immediately; it left him all the more room to invent some ritual farewell for the travellers, without being distracted by the truth.
The whole team did gather in the control scape, though, along with Prospero and Cordelia, and a few dozen friends. Gisela stood apart from the crowd as Vikram counted down to the deadline. On “ten”, she instructed her exoself to clone her. On “nine”, she sent the snapshot to the address being broadcast by an icon for the Cartan Null file — a stylised set of counter-rotating light beams — hovering in the middle of the scape. When the tag came back confirming the transaction, she felt a surge of loss; the Dive was no longer part of her own linear future, even if she thought of the clone as a component of her extended self.
Vikram shouted exuberantly, “Three! Two! One!” He picked up the Cartan Null icon and tossed it into a map of the spacetime around Chandrasekhar. This triggered a gamma-ray burst from the polis to a probe with an eight-M orbit; there, the data was coded into nanomachines designed to recreate it in active, photonic form — and those nanomachines joined the stream cascading into the hole.
On the map, the falling icon veered into a “motionless” vertical world line as it approached the two-M shell. Successive slices of constant time in the static frame outside the hole never crossed the horizon, they merely clung to it; by one definition, the nanomachines would take forever to enter Chandrasekhar.
By another definition, the Dive was over. In their own frame, the nanomachines would have taken less than one-and-a-half milliseconds to fall from the probe to the horizon, and not much longer to reach the point where Cartan Null was launched. And however much subjective time the Divers had experienced, however much computing had been done along the way, the entire region of space containing Cartan Null would have been crushed into the singularity a few microseconds later.
“If the Divers tunnelled out of the hole, there’d be a paradox, wouldn’t there?” Gisela turned; she hadn’t noticed Cordelia behind her. “Whenever they emerged, they wouldn’t have fallen in yet — so they could swoop down and grab the nanomachines, preventing their own births.” The idea seemed to disturb her.
Gisela said, “Only if they tunnelled out close to the horizon. If they appeared further away — say here in Cartan, right now — they’d already be too late. The nanomachines have had too much of a head start; the fact that they’re almost standing still in our reference frame doesn’t make them an easy target if you’re actually chasing after them. Even at lightspeed, nothing could catch them from here.”
Cordelia appeared to take heart from this. “So escape isn’t impossible?”
“Well … ” Gisela thought of listing some of the other hurdles, but then she began to wonder if the question was about something else entirely. “No. It’s not impossible.”
Cordelia gave her a conspiratorial smile. “Good.”
Prospero cried out, “Gather round! Gather round now and hear The Ballad of Cartan Null!” He created a podium, rising beneath his feet. Timon sidled up to Gisela and whispered, “If this involves a lute, I’m sending my senses elsewhere.”
It didn’t; the blank verse was delivered without musical accompaniment. The content, though, was even worse than Gisela had feared. Prospero had ignored everything she and the others had told him. In his version of events, “Charon’s passengers” entered “gravity’s abyss” for reasons he’d invented out of thin air: to escape, respectively, a failed romance/vengeance for an unspeakable crime/the ennui of longevity; to resurrect a lost flesher ancestor; to seek contact with “the gods.” The universal questions the Divers had actually hoped to answer — the structure of spacetime at the Planck scale, the underpinnings of quantum mechanics — didn’t rate a mention.
Gisela glanced at Timon, but he seemed to be taking the news that his sole version had just fled into Chandrasekhar to avoid punishment for an unnamed atrocity extremely well; there was disbelief on his face, but no anger. He said softly, “This man lives in Hell. Mucus on the face plate is all he’ll ever see.”
The audience stood in silence as Prospero began to “describe” the Dive itself. Timon stared at the floor with a bemused smile. Tiet wore an expression of detached boredom. Vikram kept peeking at a display behind him, to see if the faint gravitational radiation emitted by the inflowing nanomachines was still conforming to his predictions.
It was Sachio who finally lost control and interjected angrily, “Cartan Null is some ghostly image of a scape, full of ghostly icons, floatin
g through the vacuum, down into the hole?”
Prospero seemed more startled than outraged by the interruption. “It is a city of light. Translucent, ethereal … ”
The owl in Sachio’s skull puffed its feathers out. “No photon state would look like that. What you describe could never exist, and even if it could it would never be conscious.” Sachio had worked for decades on the problem of giving Cartan Null the freedom to process data without disrupting the geometry around it.
Prospero spread his arms in a conciliatory gesture. “An archetypal quest narrative must be kept simple. To burden it withtechnicalities — ”
Sachio inclined his head briefly, fingertips to forehead, downloading information from the polis library. “Do you have any idea what archetypal narratives are?”
“Messages from the gods, or from the depths of the soul; who can say? But they encode the most profound and mysterious — ”
Sachio cut him off impatiently. “They’re the product of a few chance attractors in flesher neurophysiology. Whenever a more complex or subtle story was disseminated through an oral culture, it would eventually degenerate into an archetypal narrative. Once writing was invented, they were only ever created deliberately by fleshers who failed to understand what they were. If all of antiquity’s greatest statues had been dropped into a glacier, they would have been reduced to a predictable spectrum of spheroidal pebbles by now; that does not make the spheroidal pebble the pinnacle of the artform. What you’ve created is not only devoid of truth, it’s devoid of aesthetic merit.”
Prospero was stunned. He looked around the room expectantly, as if waiting for someone to speak up in defence of the Ballad.
No one made a sound.
This was it: the end of diplomacy. Gisela spoke privately to Cordelia, whispering urgently: “Stay in Cartan! No one can force you to leave!”
Cordelia turned to her with an expression of open astonishment. “But I thought — ” She fell silent, reassessing something, hiding her surprise.
Then she said, “I can’t stay.”
“Why not? What is there to stop you? You can’t stay buried in Athena — ” Gisela caught herself; whatever bizarre hold the place had on her, disparaging it wouldn’t help.
Prospero was muttering in disbelief now, “Ingratitude! Base ingratitude!” Cordelia regarded him with forlorn affection. “He’s not ready.” She faced Gisela, and spoke plainly. “Athena won’t last forever. Polises like that form and decay; there are too many real possibilities for people to cling to one arbitrary sanctified culture, century after century. But he’s not prepared for the transition; he doesn’t even realise it’s coming. I can’t abandon him to that. He’s going to need someone to help him through.” She smiled suddenly, mischievously. “But I’ve cut two centuries off the waiting time. If nothing else, the trip did that.”
Gisela was speechless for a moment, shamed by the strength of this child’s love. Then she sent Cordelia a stream of tags. “These are references to the best libraries on Earth. You’ll get the real stuff there, not some watered-down version of flesher physics.”
Prospero was shrinking the podium, descending to ground level. “Cordelia! Come to me now. We’re leaving these barbarians to the obscurity they deserve!”
For all that she admired Cordelia’s loyalty, Gisela was still saddened by her choice. She said numbly, “You belong in Cartan. It should have been possible. We should have been able to find a way.”
Cordelia shook her head: no failure, no regrets. “Don’t worry about me. I’ve survived Athena so far; I think I can see it through to the end. Everything you’ve shown me, everything I’ve done here, will help.” She squeezed Gisela’s hand. “Thank you.”
She joined her father. Prospero created a doorway, opening up onto a yellow brick road through the stars. He stepped through, and Cordelia followed him.
Vikram turned away from the gravitational wave trace and asked mildly, “All right, you can own up now: who threw in the additional exabyte?”
***
“Freeeeee-dom!” Cordelia bounded across Cartan Null’s control scape, a long platform floating in a tunnel of colour-coded Feynman diagrams, streaming through the darkness like the trails of a billion colliding and disintegrating sparks.
Gisela’s first instinct was to corner her and shout in her face: Kill yourself now! End this now! A brief side-branch, cut short before there was time for personality divergence, hardly counted as a real life and a real death. It would be a forgotten dream, nothing more.
That analysis didn’t hold up, though. From the instant she’d become conscious, this Cordelia had been an entirely separate person: the one who’d left Athena forever, the one who’d escaped. Her extended self had invested far too much in this clone to treat it as a mistake and cut its losses. Beyond anything it hoped for itself, the clone knew exactly what its existence meant for the original. To betray that, even if it could never be found out, would be unthinkable.
Tiet said sharply, “You didn’t raise her hopes, did you?”
Gisela thought back over their conversations. “I don’t think so. She must know there’s almost no chance of survival.”
Vikram looked troubled. “I might have put our own case too strongly. She might believe the same discoveries will be enough for her — but I’m not sure they will.”
Timon sighed impatiently. “She’s here. That’s irreversible; there’s no point agonising about it. All we can do is give her the chance to make what she can of the experience.”
A horrifying thought struck Gisela. “The extra data hasn’t overburdened us, has it? Ruled out access to the full computational domain?” Cordelia had compressed herself down to a far leaner program than the version she’d sent from Earth, but it was still an unexpected load.
Sachio made a sound of indignation. “How badly do you think I did my job? I knew someone would bring in more than they’d promised; I left a hundredfold safety margin. One stowaway changes nothing.”
Timon touched Gisela’s arm. “Look.” Cordelia had finally slowed down enough to start examining her surroundings. The primary beams, the infrastructure for all their computation, had already been blue-shifted to hard gamma rays, and the colliding photons were creating pairs of relativistic electrons and positrons. In addition, a range of experimental beams with shorter wavelengths probed the physics of length scales ten thousand times smaller — physics that would apply to the primary beams about a subjective hour later. Cordelia found the window with the main results from these beams. She turned and called out, “Lots of mesons full of top and bottom quarks ahead, but nothing unexpected!”
“Good!” Gisela felt the knot of guilt and anxiety inside her begin to unwind. Cordelia had chosen the Dive freely, just like the rest of them. The fact that it had been a hard decision for her to make was no reason to assume that she’d regret it.
Timon said, “Well, you were right. I was wrong. She certainly tunnelled out of Athena.”
“Yeah. So much for your theory of closed trapped memetic surfaces.” Gisela laughed. “Pity it was just a metaphor, though.”
“Why? I thought you’d be overjoyed that she made it.”
“I am. It’s just a shame that it says nothing at all about our own chances of escape.”
***
Each orbit gave them thirty minutes of subjective time, while the true length and time scales of Cartan Null shrank a hundredfold. Sachio and Tiet scrutinised the functioning of the polis, checking and rechecking the integrity of the “hardware” as new species of particles entered the pulse trains. Timon reviewed various methods for shunting information into new modes, if the opportunity arose. Gisela struggled to bring Cordelia up to speed, and Vikram, whose main work had been the nanomachines, helped her.
The shortest-wavelength beams were still recapitulating the results of old particle accelerator experiments; the three of them pored over the data together. Gisela summarised as best she could. “Charge and the other quantum numbers generate a kind
of angle between world lines in the networks, just like spin does, but in this case they act like angles in five-dimensional space. At low energies what you see are three separate subspaces, for electromagnetism and the weak and strong forces.”
“Why?”
“An accident in the early universe with Higgs bosons. Let me draw a picture … ”
There was no time to go into all the subtleties of particle physics, but many of the issues that were crucial outside Chandrasekhar were becoming academic for Cartan Null anyway. Broken symmetries were being restored as they spoke, with increasing kinetic energy diluting differences in rest mass into insignificance. The polis was rapidly mutating into a hybrid of every possible particle type; what governed their future would not be the theory of any one force, but the nature of quantum mechanics itself.
“What lies behind the frequency and wavelength of a particle?” Vikram sketched a snapshot of a wave packet on a spacetime diagram. “In its own reference frame, an electron’s phase rotates at a constant rate: about once every ten-to-the-minus-twenty seconds. If it’s moving, we see that rate slowed down by time dilation, but that’s not the whole picture.” He drew a set of components fanning out at different velocities from a single point on the wave, then marked off successive points where the phase came full circle for each one. The locus of these points formed a set of hyperbolic wavefronts in spacetime, like a stack of conical bowls — packed more tightly, in both time and space, where the components’ velocity was greater. “The spacing of the original wave is only reproduced by components with just the right velocity; they trace out identical copies of the wave at later times, all neatly superimposed. Components with the wrong velocity scramble the phase, so their copies all cancel out.” He repeated the entire construction for a hundred points along the wave, and it propagated neatly into the future. “In curved spacetime, the whole process becomes distorted — but given the right symmetries, the shape of the wave can be preserved while the wavelength shrinks and the frequency rises.” Vikram warped the diagram to demonstrate. “Our own situation.”
Anthology of Speculative Fiction, Volume Two Page 289