Permutation City (25 page)

So the two subjective histories remained as one. Paul
had been
a visitor believing he was a Copy. And he'd
also been
the Copy itself. The patterns had merged seamlessly; there could be no way of saying that one history was true and the other false. Both explanations were equally valid.

Once, preparing to be scanned, he'd had two futures.

Now he had two pasts.

+ + +

Paul woke in darkness, confused for a moment, then pulled his cramped left arm out from under the pillow and glanced at his watch. Low power infrared sensors in the watch face detected his gaze, and flashed up the time -- followed by a reminder:
due at landau
7
a.m.
It was barely after five, but it hardly seemed worth going back to sleep.

Memories of the night before came back to him. Elizabeth had finally confronted him, asking what decision he'd reached: to abandon his life's work, or to forge ahead, now that he knew, firsthand, what was involved.

His answer seemed to have disappointed her. He didn't expect to see her again.

How could he give up?
He knew he could never be sure that he'd discovered the truth -- but that didn't mean that nobody else could.

If he made a Copy, ran it for a few virtual days, then terminated it abruptly . . . then at least
that
Copy would know if its own pattern of experience continued.

And if another Paul Durham in one of the countless billions of alternative worlds could provide a future for the terminated Copy -- a pattern into which it could merge -- then perhaps that flesh-and-blood Durham would repeat the whole process

And so on, again and again.

And although the seams would always be perfect, the "explanation" for the flesh-and-blood human believing that he had a second past as a Copy would necessarily grow ever more "contrived," less convincing . . . and the dust theory would become ever more compelling.

Paul lay in bed in the darkness, waiting for sunrise, staring into the future down this corridor of mirrors.

One thing nagged at him. He could have sworn he'd had a dream, just before he woke: an elaborate fable, conveying some kind of insight. That's all he knew -- or thought he knew. The details hovered maddeningly on the verge of recollection.

His dreams were evanescent, though, and he didn't expect to remember anything more.

17

(Remit not paucity)

APRIL 2051

Maria shifted in her seat to try to get her circulation flowing, then realized it wasn't enough. She stood up and limped around the room, bending down to massage her cramped right calf.

She said, "And you claim you're the
twenty-third
?"
She was almost afraid to sound too skeptical; not because she believed that Durham would take offence, but because the story was so strangely entrancing that she wasn't sure she wanted to deflate it, yet. One hint of mockery and the floodgates would open. "You're the
twenty-third
flesh-and-blood Paul Durham whose past includes all those who came before?"

Durham said, "I may be wrong about the exact number. I may have counted this last version more than once; if I'm capable of believing in twenty-three incarnations, some of them might be false. The whole nature of the delusions I suffered contributes to the uncertainty."

"Contributes.
Isn't that a bit of an understatement?"

Durham was unflappable. "I'm cured now. The nanosurgery worked. The doctors pronounced me sane, and I have no reason to question their judgement. They've scanned my brain; it's functioning impeccably. I've seen the data, before and after. Activity in the prefrontal cortex --"

"But don't you see how absurd that is? You acknowledge that you
were
deluded. You insist that you're cured now. But you claim that your delusions weren't delusions --"

Durham said patiently, "I've admitted from the outset: my condition
explains
everything. I believed -- because I was mentally ill -- that I was the twenty-third-generation Copy of another Paul Durham, from another world."

"Because you were mentally ill!
End of story."

"No. Because I'm certifiably rational now -- and the logic of the dust theory makes as much sense to me as ever. And it makes no difference whether my memories are true, false, or both."

Maria groaned.
"Logic of the dust theory!
It's
not
a
theory.
It can't be tested."

"Can't be tested by whom?"

"By anyone! I mean . . . even assuming that everything you believe is the truth: you've 'been through' twenty-three separate experiments, and you still don't know what you've proved or disproved! As you say: your condition accounts for everything. Haven't you heard of Occam's razor: once you have a perfectly simple explanation for something, you don't go looking for ever more complicated ways of explaining the very same thing? No
dust theory
is required." Her words reverberated in the near-empty room. She said, "I need some fresh air."

Durham said firmly, "After twenty-three ambiguous results, I know how to get it right this time. A Copy plus a virtual environment is a patchwork, a mess. A system like that isn't rich enough, detailed enough, or consistent enough, to be self-sustaining. If it was, when I was shut down,
the entire VR world I was in
would have persisted. That never happened. Instead -- every time -- I found a flesh-and-blood human with a reason to believe he shared my past.
That
explained my pattern of experience far better than VR -- even to the point of insanity.

"What I have to do now is construct a consistent pattern which can only have
one
past."

Maria took a few deep breaths. It was almost too much to bear: Durham's sad flat, his cosmic visions, his relentless, mechanical logic, grinding away trying to make sense of the legacy of his disease. The doctors
had
cured him, he
was
sane. He just didn't want to disown his delusional past -- so he'd invented a flawlessly logical, utterly irrefutable, reason to hang on to it.

If he'd really told the cops all this, why were they still hounding him? They should have seen that he was harmless and left him alone -- and left his moronic clients to fend for themselves. The man wasn't even a danger to himself. And if he could ever harness a fraction of the energy and intelligence he'd put into this "project" and direct it towards something worthwhile --

Durham said, "Do you know what a Garden-of-Eden configuration is?"

Maria was caught blank for a second, then she said, "Yes, of course. In cellular automaton theory, it's a state of the system that can't be the result of any previous state. No other pattern of cells can give rise to it. If you want a Garden-of-Eden configuration, you have to start with it -- you have to put it in by hand as the system's first state."

Durham grinned at her as if she'd just conceded the whole argument. She said, "What?"

"Isn't it obvious? A cellular automaton isn't like patchwork VR; it's every bit as
consistent
as a physical universe. There's no jumble of
ad hoc
high-level laws; one set of rules applies to every cell. Right?"

"Yes, but --"

"So if I set up a cellular automaton in a Garden-of-Eden configuration, run it through a few trillion clock ticks, then shut it down . . . the pattern will continue to find itself in the dust -- separate from this version of me, separate from this world, but still flowing unambiguously from that initial state. A state which can't be explained by the rules of the automaton. A state which
must
have been constructed in another world -- exactly as I remember it.

"The whole problem, so far, has been that my memories are always entirely explicable
within
the new world. I shut myself down as a Copy -- and find myself in a flesh-and-blood body with flesh-and-blood memories which the laws of physics could have produced from
earlier states
of a flesh-and-blood brain. This world can explain me only as a man whose delusions are unlikely beyond belief -- but there's no denying that I
do
have a complete extra history, here, that's not literally, physically impossible. So whatever I prefer to believe, I have to concede that the outcome of the experiment is still ambiguous. I could, still, be wrong.

"But a cellular automaton can't provide an 'extra history' for a Garden-of-Eden configuration! It's mathematically impossible! If I find myself inside a cellular automaton universe, and I can track my past back to a Garden-of-Eden configuration, that will be conclusive proof that I
did
seed the whole universe in a previous incarnation. The dust theory will be vindicated. And I'll finally know -- beyond any doubt -- that I haven't merely been insane all along."

Maria felt punch-drunk. At one level, she knew she should stop humoring him, stop treating his ideas seriously. On another, it seemed that if Durham was so wrong, she should be able to point out the reasons why. She shouldn't have to call him a madman and refuse to listen to another word.

She said,
"Find yourself in a cellular automaton world?
You don't mean the Autoverse -- ?"

"Of course not. There's no prospect of translating a human into Autoverse biochemistry."

"Then what?"

"There's a cellular automaton called TVC. After Turing, von Neumann and Chiang. Chiang completed it around twenty-ten; it's a souped-up, more elegant version of von Neumann's work from the nineteen fifties."

Maria nodded uncertainly; she'd heard of all this, but it wasn't her field. She did know that John von Neumann and his students had developed a two-dimensional cellular automaton, a simple universe in which you could embed an elaborate pattern of cells -- a rather Lego-like "machine" -- which acted as both a universal constructor and a universal computer. Given the right program -- a string of cells to be interpreted as coded instructions rather than part of the machine -- it could carry out any computation, and build anything at all. Including another copy of itself -- which could build another copy, and so on. Little self-replicating toy computers could blossom into existence without end.

She said, "Chiang's version was three-dimensional, wasn't it?"

"Much better. N-dimensional. Four, five, six, whatever you like. That leaves plenty of room for data within easy reach. In two dimensions, the original von Neumann machine had to reach farther and farther -- and wait longer and longer -- for each successive bit of data. In a six-dimensional TVC automaton, you can have a three-dimensional grid of computers, which keeps on growing indefinitely --
each
with its own three-dimensional memory, which can also grow without bound."

Maria said numbly, "Where are
you
supposed to fit into all of this? If you think translating human biochemistry into
Autoverse
terms is difficult, how are you going to map yourself into a six-dimensional world designed solely to support von Neumann machines?"

"The TVC universe is one big, ever-expanding processor cluster. It runs a Copy of me --"

"I thought the whole point was to do away with Copies!"

"-- in a VR environment which lets me
interact with
the TVC level. Yes, I'll be a patchwork Copy, as always -- there's no alternative to that -- but I'll also be linked to the cellular automaton itself. I'll witness its operation, I'll experience its laws. By observing it, I'll make it a part of what has to be explained.

"And when the simulated TVC universe being run on the physical computer is suddenly shut down, the best explanation for what I've witnessed will be a continuation of that universe -- an extension made out of dust."

Maria could almost see it: a vast lattice of computers, a seed of order in a sea of a random noise, extending itself from moment to moment by sheer force of internal logic, "accreting" the necessary building blocks from the chaos of non-space-time by the very act of
defining
space and time.

Visualizing wasn't believing, though.

She said, "What makes you so sure? Why not another deluded psychiatric patient, who believes he was -- briefly -- a Copy being run on a TVC automaton being run on a processor cluster in another world?"

"You're the one who invoked Occam's razor. Wouldn't you say that a self-contained TVC universe is a simpler explanation, by far?"

"No. It's about the most bizarre thing I can imagine."

"It's a lot less bizarre than yet another version of this universe, containing yet another version of me, with yet another set of convenient delusions."

"How many of your clients believed all this? How many think they're coming along for the ride?"

"Fifteen. And there's a sixteenth who, I think, is tempted."

"They paid -- ?"

"About two million each." He snorted. "It's quite funny, the significance the police have attached to that. Some large sums of money have changed hands, for reasons more complex than usual -- so they assume I must be doing something illegal. I mean, billionaires have been known to make donations larger than that to
the Church of the God Who Makes No Difference.
"
He added hastily, "None of mine."