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.