Permutation City

physiological model—the most radical stage of the project, by far. In comparison, tinkering with a few of the model’s parameters should have seemed trivial.

Durham appeared on the terminal—which was otherwise still dysfunctional. Paul was already beginning to think of him as a bossy little djinn trapped inside the screen—rather than a vast, omnipotent deity striding the halls of Reality, pulling all the strings. The pitch of his voice was enough to deflate any aura of power and grandeur.

Squeak. “Experiment one, trial zero. Baseline data. Time resolution one millisecond—system standard. Just count to ten, at one-second intervals, as near as you can judge it. Okay?”

“I think I can manage that.” He’d planned all this himself, he didn’t need step-by-step instructions. Durham’s image vanished; during the experiments, there could be no cues from real time.

Paul counted to ten. The djinn returned. Staring at the face on the screen, Paul realized that he had no inclination to think of it as “his own.” Perhaps that was a legacy of distancing himself from the earlier Copies. Or perhaps his mental image of himself had never been much like his true appearance—and now, in defense of sanity, was moving even further away.

Squeak. “Okay. Experiment one, trial number one. Time resolution five milliseconds. Are you ready?”

“Yes.”

The djinn vanished. Paul counted: “One. Two. Three. Four. Five. Six. Seven. Eight. Nine. Ten.”

Squeak. “Anything to report?”

“No. I mean, I can’t help feeling slightly apprehensive, just knowing that you’re screwing around with my… infrastructure. But apart from that, nothing.”

Durham’s eyes no longer glazed over while he was waiting for the speeded-up reply; either he’d gained a degree of self-discipline, or—more likely—he’d interposed some smart editing software to conceal his boredom.

Squeak. “Don’t worry about apprehension. We’re running a control, remember?”

Paul would have preferred not to have been reminded. He’d known that Durham must have cloned him, and would be feeding exactly the same sensorium to both Copies—while only making changes in the model’s time resolution for one of them. It was an essential part of the experiment—but he didn’t want to dwell on it. A third self, shadowing his thoughts, was too much to acknowledge on top of everything else.

Squeak. “Trial number two. Time resolution ten milliseconds.”

Paul counted. The easiest thing in the world, he thought, when you’re made of flesh, when you’re made of matter, when the quarks and the electrons just do what comes naturally. Human beings were embodied, ultimately, in fields of fundamental particles—incapable, surely, of being anything other than themselves. Copies were embodied in computer memories as vast sets of numbers. Numbers which certainly could be interpreted as describing a human body sitting in a room… but it was hard to see that meaning as intrinsic, as necessary, when tens of thousands of arbitrary choices had been made about the way in which the model had been coded. Is this my blood sugar here… or my testosterone level? Is this the firing rate of a motor neuron as I raise my right hand… or a signal coming in from my retina as I watch myself doing it? Anybody given access to the raw data, but unaware of the conventions, could spend a lifetime sifting through the numbers without deciphering what any of it meant.

And yet no Copy buried in the data itself—ignorant of the details or not—could have the slightest trouble making sense of it all in an instant.

Squeak. “Trial number three. Time resolution twenty milliseconds.”

“One. Two. Three.”

For time to pass for a Copy, the numbers which defined it had to change from moment to moment. Recomputed over and over again, a Copy was a sequence of snapshots, frames of a movie—or frames of computer animation.

But… when, exactly, did these snapshots give rise to conscious thought? While they were being computed? Or in the brief interludes when they sat in the computer’s memory, unchanging, doing nothing but representing one static instant of the Copy’s life? When both stages were taking place a thousand times per subjective second, it hardly seemed to matter, but very soon—

Squeak. “Trial number four. Time resolution fifty milliseconds.”

What am I? The data? The process that generates it? The relationships between the numbers?

All of the above?

“One hundred milliseconds.”

“One. Two. Three.”

Paul listened to his voice as he counted—as if half expecting to begin to notice the encroachment of silence, to start perceiving the gaps in himself.

“Two hundred milliseconds.”

A fifth of a second. “One. Two.” Was he strobing in and out of existence now, at five subjective hertz? The crudest of celluloid movies had never flickered at this rate. “Three. Four.” He waved his hand in front of his face; the motion looked perfectly smooth, perfectly normal. And of course it did; he wasn’t watching from the outside. “Five. Six. Seven.” A sudden, intense wave of nausea passed through him but he fought it down, and continued. “Eight. Nine. Ten.”

The djinn reappeared and emitted a brief, solicitous squeak. “What’s wrong? Do you want to stop for a while?”

“No, I’m fine.” Paul glanced around the innocent, sun-dappled room, and laughed. How would Durham handle it if the control and the subject had just given two different replies? He tried to recall his plans for such a contingency, but couldn’t remember them—and didn’t much care. It wasn’t his problem any more.

Squeak. “Trial number seven. Time resolution five hundred milliseconds.”

Paul counted—and the truth was, he felt no different. A little uneasy, yes—but factoring out any squeamishness, everything about his experience seemed to remain the same. And that made sense, at least in the long run—because nothing was being omitted, in the long run. His model-of-a-brain was only being fully described at half-second (model time) intervals—but each description still included the results of everything that “would have happened” in between. Every half-second, his brain was ending up in exactly the state it would have been in if nothing had been left out.

“One thousand milliseconds.”

But… what was going on, in between? The equations controlling the model were far too complex to solve in a single step. In the process of calculating the solutions, vast arrays of partial results were being generated and discarded along the way. In a sense, these partial results implied—even if they didn’t directly represent—events taking place within the gaps between successive complete descriptions. And when the whole model was arbitrary, who was to say that these implied events, buried a little more deeply in the torrent of data, were any “less real” than those which were directly described?

“Two thousand milliseconds.”

“One. Two. Three. Four.”

If he seemed to speak (and hear himself speak) every number, it was because the effects of having said “three” (and having heard himself say it) were implicit in the details of calculating how his brain evolved from the time when he’d just said “two” to the time when he’d just said “four.”

“Five thousand milliseconds.”

“One. Two. Three. Four. Five.”

Besides, hearing words that he’d never “really” spoken wasn’t much stranger than a Copy hearing anything at all. Even the standard millisecond clock rate of this world was far too coarse to resolve the full range of audible tones. Sound wasn’t represented in the model by fluctuations in air pressure values—which couldn’t change fast enough—but in terms of audio power spectra: profiles of intensity versus frequency. Twenty kilohertz was just a number here, a label; nothing could actually oscillate at that rate. Real ears analyzed