Permutation City

"Eight. Nine. Ten." Another imperceptible leap into the future, and the djinn reappeared.

Squeak. "Trial number two. Odd numbered states, then even."

In external terms: he would count to ten, skipping every second model-time moment . . . then forget having done so, and count again, going back and filling in the gaps.

And from his own point of view? As he counted, once only, the external world -- even if he couldn't see it -- was flickering back and forth between two separate regions of time, which had been chopped up into seventeen-millisecond portions, and interleaved.

So . . . who was right? Paul thought it over, half seriously. Maybe both, descriptions were equally valid; after all, relativity had abolished absolute time. Everybody was entitled to their own frame of reference; crossing deep space at close to lightspeed, or skimming the event horizon of a black hole. Why shouldn't a Copy's experience of time be as sacrosanct as that of any astronaut?

The analogy was flawed, though. Relativistic transformations were smooth -- possibly extreme, but always continuous. One observer's space-time could be stretched and deformed in the eyes of another -- but it couldn't be sliced like a loaf of bread and then shuffled like a deck of cards.

"Every tenth state, in ten sets."

Paul counted -- and for argument's sake, tried to defend his own perspective, tried to imagine the outside world actually cycling through fragments of time drawn from ten distinct periods. The trouble was . . . this allegedly shuddering universe contained the computer which ran the whole model, the infrastructure upon which everything else depended. If its orderly chronology had been torn to shreds, what was keeping him together, enabling him to ponder the question?

"Every twentieth state, in twenty sets."

Nineteen episodes of amnesia, nineteen new beginnings.

(Unless, of course, he was the control.)

"Every hundredth state, in one hundred sets."

He'd lost any real feeling for what was happening. He just counted.

"Pseudo-random ordering of states."

"One. Two. Three."

Now he was . . . dust. To an outside observer, these ten seconds had been ground up into ten thousand uncorrelated moments and scattered throughout real time -- and in model time, the outside world had suffered an equivalent fate. Yet the pattern of his awareness remained perfectly intact: somehow he found himself, "assembled himself from these scrambled fragments. He'd been taken apart like a jigsaw puzzle -- but his dissection and shuffling were transparent to him. Somehow -- on their own terms -- the pieces remained connected.

"Eight. Nine. Ten."

Squeak. "You're sweating."

"Both of me?"

Squeak. The djinn laughed. "What do you think?"

Paul said, "Do me one small favor. The experiment is over. Shut down one of me -- control or subject, I don't care."

Squeak. "Done."

"Now there's no need to conceal anything, is there? So run the pseudo-random effect on me again -- and stay on-line. This time, you count to ten."

Squeak. Durham shook his head. "Can't do it, Paul. Think about it: you can't be computed non-sequentially when past perceptions aren't known."

Of course; the broken vase problem all over again.

Paul said, "Record yourself, then, and use that."

The djinn seemed to find the request amusing, but he agreed; he even slowed down the recording so it lasted ten model-time seconds. Paul watched the blurred lips and jaws intently, listened carefully to the drone of white noise.

Squeak. "Happy now?"

"You did scramble me, and not the recording?"

Squeak. "Of course. Your wish is my command."

"Yeah? Then do it again."

Durham grimaced, but obliged.

Paul said, "Now, scramble the recording."

It looked just the same. Of course.

"Again."

Squeak. "What's the point of all this?"

"Just do it."

Paul watched, the hairs on the back of his neck rising, convinced that he was on the verge of . . . what? Finally confronting the "obvious" fact that the wildest permutations in the relationship between model time and real time would be undetectable to an isolated Copy? He'd accepted the near certainty of that, tacitly, for almost twenty years . . . but the firsthand experience of having his mind literally scrambled -- to absolutely no effect -- was still provocative in a way that the abstract understanding had never been.

He said, "When do we move on to the next stage?"

Squeak. "Why so keen all of a sudden?"

"Nothing's changed. I just want to get it over and done with."

Squeak. "Lining up all the other machines is taking some delicate negotiations. The network allocation software isn't designed to accommodate whims about geography. It's a bit like going to a bank and asking to deposit some money . . . at a certain location in a particular computer's memory. Basically, people think I'm crazy."