Грег Иган - Schild’s Ladder

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.