"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."