Schild's Ladder (2 page)

A circular tunnel, slightly wider than her height, connected her spartan quarters to a chamber where she could interact with the software she'd brought from Earth, and through it the Mimosans themselves. She bounced down the borehole, slapping the wall with her hands and feet, bumping her head and elbows deliberately.

As she entered the chamber, she seemed to emerge from the mouth of a burrow to float above a lush, wide meadow beneath a cloud-dappled sky. The illusion was purely audiovisual—the sounds encoded in radio waves—but with no weight to hold her against the ceramic hidden beneath the meadow, the force of detail was eerily compelling. It only took a few blades of grass and some chirping insects to make her half-believe that she could smell the late-summer air.

Would it really have been an act of self-betrayal, if this landscape had stretched all the way inside her—right down to the sensations of inhabiting her old, two-meter body, gorging on a breakfast of fruit and oats after swimming across Chalmers Lake? If she could drift in and out of this soothing work of art without losing her grip on reality, why couldn't she take the process a few steps further?

She pushed the argument aside, though she was glad that it never stopped nagging at her. When the means existed to transform yourself, instantly and effortlessly, into anything at all, the only way to maintain an identity was to draw your own boundaries. But once you lost the urge to keep on asking whether or not you'd drawn them in the right place, you might as well have been born
Homo sapiens
, with no real choices at all.

A short distance from the burrow stood a marble statue of Rainzi, arms folded, smiling slightly. Cass gestured at the messenger and it came to life, the white stone taking on the hue and texture of skin. Rainzi himself was several generations removed from anyone who'd bothered to simulate a living dermis, let alone possess one, but Cass was not equipped to make sense of the Mimosans' own communications protocols, so she'd chosen to have everything translated into the visual dialect used back on Earth.

“We'll give you our decision at nine o'clock, as promised,” the messenger assured her. “But we hope you won't mind if we precede this with a final review session. Some of us feel that there are matters that have yet to be entirely resolved. We'll begin at half past seven.” The messenger bowed, then froze again, expecting no reply.

Cass tried not to read too much into the sudden change of plan. It was unnerving to discover that her hosts still hadn't been able to reach a verdict, but at least they weren't going to keep her waiting any longer than she'd expected. The fact that she'd alread briefed them in detail on every aspect of the experiment that had crossed her mind during three decades of preparation, and they now hoped to hear something new and decisive from her in twenty minutes' time, was no reason to panic. Whatever loose ends they'd found in her analysis, they were giving her the chance to put things right.

Her confidence was shaken, though, and she couldn't stop thinking about the prospect of failure. After a month here, she still wasn't lonely, or homesick; that was the price she'd pay upon returning. Even at the leisurely pace of the embodied, seven hundred and forty years cut a deep rift. It would be millennia before the changes that her friends on Earth had lived through together would cease to set her apart from them. Millennia, if ever.

She still believed that she could come to terms with that loss, so long as she had something to weigh against it. Being a singleton meant accepting that every decision had its cost, but once you understood that this state of affairs was a hard-won prize, not a plight to rail against, it gave some dignity to all but the most foolish choices.

If the Mimosans turned her down, though? Maybe there was something daring and romantic in the mere act of traveling hundreds of light-years, inhabiting the body of a vacuum-dwelling insect, and alienating herself from the world where she belonged, all in the hope of seeing her ideas tested as rapidly as possible. But for how long would she be able to take comfort from the sheer audacity of what she'd done, once that hope had come to nothing?

She curled into a ball and tried to weep. She could not shed tears, and the sobs rebounding against her membrance-sealed mouth were like the drone of a mosquito. But the shuddering as she worked her vestigial lungs still provided some sense of release. She had not entirely erased the map of her Earthly body from her mind; too much of the way she experienced emotions was bound up in its specific form. So everything she'd amputated lingered as a kind of phantom—nowhere near as convincing as a true simulation, but still compelling enough to make a difference.

When she was spent, Cass stretched out her limbs and drifted over the meadow like a dandelion seed, as calm and lucid as she'd been at any time since her arrival.

She knew what she knew about Quantum Graph Theory, backward. Whatever insights she was capable of extracting from that body of knowledge, she'd extracted long ago. But if the Mimosans had found a question she couldn't answer, a doubt she couldn't assuage, that in itself would be a chance to learn something more.

Even if they sent her home with nothing else, she would not be leaving empty-handed.

It was Livia who asked the first question, and it was far simpler than anything Cass had anticipated.

“Do you believe that the Sarumpaet rules are correct?”

Cass hesitated longer than she needed to, a calculated attempt to imbue her response with appropriate gravity.

“I'm not certain that they are, but the likelihood seems overwhelming to me.”

“Your experiment would test them more rigorously than anything that's been tried before,” Livia observed.

Cass nodded. “I do see that as a benefit, but only a minor one. I don't believe that merely testing the rules one more time would justify the experiment. I'm more interested in what the rules imply, given that they're almost certainly correct.”

Where was this heading
? She glanced around at the others, seated in a ring in the meadow: Yann, Bakim, Darsono, Ilene, Zulkifli, and Rainzi. Her Mediator had chosen appearances for all of them, since they offered none themselves, but at least their facial expressions and body language were modulated by their own intentional signals. By choice, they all looked politely interested, but were giving nothing away.

“You have a lot of confidence in QGT?” Clearly, Livia did realize just how strange her questions sounded; her tone was that of someone begging to be indulged until her purpose became apparent.

Cass said, “Yes, I do. It's simple, it's elegant, and it's consistent with all observations to date.” That handful of words sounded glib, but other people had quantified all of these criteria long ago. QGT as a description of the dynamics of the universe with the minimum possible algorithmic complexity. QGT as a topological redescription of some basic results in category theory—a mathematical setting in which the Sarumpaet rules appeared as natural and inevitable as the rules of arithmetic. QGT as the most probable underlying system of physical laws, given any substantial database of experimental results that spanned both nuclear physics and cosmology.

Darsono leaned toward her and interjected, “But why, in your heart”—he thumped his chest with an imaginary fist—“are you convinced that it's true?” Cass smiled. That was not a gesture in the staid vocabulary her Mediator used by default; Darsono must have requested it explicitly.

“In part, it's the history,” she admitted, relaxing slightly. “The lineage of the ideas. If some alien civilization had handed us Quantum Graph Theory on a stone tablet—out of the blue, in the eighteenth or nineteenth century—I might not feel the same way about it. But
general relativity
and
quantum mechanics
were among the most beautiful things the ancients created, and they're still the best practical approximations we have for most of the universe. QGT is their union. If general relativity is so close to the truth that only the tiniest fragment can be missing, and quantum mechanics is the same...how much freedom can there be to encompass all of the successes of both, and still be wrong?”

Kusnanto Sarumpaet had lived on Earth at the turn of the third millennium, when a group of physicists and mathematicians scattered across the planet—now known universally as the Sultans of Spin—had produced the first viable offspring of general relativity and quantum mechanics. To merge the two descriptions of nature, you needed to replace the precise, unequivocal geometry of classical space-time with a quantum state that assigned amplitudes to a whole range of possible geometries. One way to do this was to imagine carrying a particle such as an electron around a loop, and computing the amplitude for its direction of spin being the same at the end of the journey as when it first set out. In flat space, the spins would always agree, but in curved space the result would depend on the detailed geometry of the region through which the particle had traveled. Generalizing this idea, crisscrossing space with a whole network of paths taken by particles of various spins, and comparing them all at the junctions where they met, led to the notion of a
spin network
. Like the harmonics of a wave, these networks comprised a set of building blocks from which all quantum states of geometry could be constructed.

Sarumpaet's quantum graphs were the children of spin networks, moving one step further away from general relativity by taking their own parents' best qualities at face value. They abandoned the idea of any preexisting space in which the network could be embedded, and defined everything—space, time, geometry, and matter—entirely on their own terms. Particles were loops of altered valence woven into the graph. The area of any surface was due to the number of edges of the graph that pierced it, the volume of any region to the number of nodes it contained. And every measure of time, from planetary orbits to the vibrations of nuclei, could ultimately be rephrased as a count of the changes between the graphs describing space at two different moments.

Sarumpaet had struggled for decades to breathe life into this vision, by finding the correct laws that governed the probability of any one graph evolving into another. In the end, he'd been blessed by a lack of choices; there had only been one set of rules that could make everything work. The two grandparents of his theory, imperfect as they were, could not be very far wrong: both had yielded predictions in their respective domains that had been verified to hair's-breadth accuracy. Doing justice to both had left no room for errors.

Livia said, “Conceptually, that argument is very appealing. But there could still be deviations from the rules—far too small to have been detected so far—that would change the outcome of your experiment completely.”

“So it's a sensitive test,” Cass agreed. “But that's not why I've proposed it.” They were talking in circles. “If the rules hold, the graph I've designed should be stable for almost six-trillionths of a second. That's long enough to give us a wealth of observations of a space-time utterly different from our own. If it doesn't last that long, I'll be disappointed. I'm not doing this in the hope of proving Sarumpaet wrong!”

Cass turned to Darsono, seeking some hint that he might share her exasperation, but before she could gauge his mood, Livia spoke again.

“What if it lasts much longer?”

Finally, Cass understood. “This is about
safety
? I've addressed the potential risks, very thoroughly—”

“On the basis that the Sarumpaet rules are correct.”

“Yes. What other basis should I have used?”
Phoenician astrology? Californian lithomancy
? Cass resisted the urge to lapse into sarcasm; there was too much at stake. “I've admitted that there's no certainty that the rules hold in every last untested circumstance. But I have nothing better to put in their place.”

“Nor do I,” Livia said gently. “My point is, we mustn't over-interpret the success of the Sarumpaet rules. General relativity and quantum field theory confessed from the start that they were just approximations: pushed to extremes, they both yielded obvious nonsense. But the fact that QGT doesn't—the fact that there is no fundamental reason why it can't be universally applicable—is no guarantee that it really does stretch that far.”

Cass gritted her teeth. “I concede that. But where does it leave us? Refusing to perform any experiment that hasn't been tried before?”

Rainzi said, “Of course not. Livia is proposing a staged approach. Before attempting to construct your graph, we'd move toward it in a series of experiments, gradually bridging the gap.”

Cass fell silent. Compared to outright rejection this was a trivial obstacle, but it still stung: she'd worked for thirty years to refine her own proposal, and she resented the implication that she'd been reckless.

“How many stages?”

“Fifteen,” Livia replied. She swept a hand through the vacuum in front of her, and a sequence of target graphs appeared. Cass studied them, taking her time.

They'd been well chosen. At first one by one, then in pairs, then triples, the features that conspired to render her own target stable were introduced. If there
was
some undiscovered flaw in the rules that would make the final graph dangerous, there could be no more systematic way to detect it in advance.

“It's your choice,” Rainzi said. “We'll vote on whichever proposal you endorse.”

Cass met his eyes. The openness of his face was an act of puppetry, but that didn't mean he was insincere. This wasn't a threat, an attempt to bully her into agreeing. It was a mark of respect that they were letting her decide, letting her weigh up her own costs, her own fears, before they voted.

She said, “Fifteen experiments. How long would that take?”

Ilene answered, “Perhaps three years. Perhaps five.” Conditions varied, and the Quietener wasn't perfect. Planning an experiment in QGT was like waiting for a stretch of ocean to grow sufficiently calm that a few flimsy barriers could block the waves and keep out the wildlife long enough to let you test some subtle principle of fluid dynamics. There was no equivalent of a laboratory water tank; space-time was all ocean, indivisible.