Diaspora

Orlando cut him off sharply. "You don't have to talk things up for me. I'm in no danger of repeating the act." They stood on the lawn, facing each other. Paolo composed a dozen different combinations of mood to communicate, but none of them felt right. He could have granted his father perfect knowledge of everything he was feeling—but what exactly would that knowledge have conveyed? In the end, there was fusion, or separateness. There was nothing in between.

Orlando said, "Kill myself—and leave the fate of the Coalition in your hands? You must he out of your fucking mind."

They walked on together, laughing.

Karpal seemed barely able to gather his thoughts enough to speak. Paolo would have offered him a mind graft promoting tranquillity and concentration—distilled from his own most focused moments—but he was sure that Karpal would never have accepted it. He said, "Why don't you just start wherever you want to? I'll stop you if you're not making sense."

Karpal looked around the white dodecahedron with an expression of disbelief. "You live here?"

"Some of the time."

"But this is your homescape? No trees? No sky? No furniture?"

Paolo refrained from repeating any of Hermann's naive-robot jokes. "I add them when I want them. You know, like… music. Look, don't let my taste in decor distract you—"

Karpal made a chair and sat down heavily.

He said, "Hao Wang proved a powerful theorem, twenty-three hundred years ago. Think of a row of Wang Tiles as being like the data tape of a Turing Machine." Paolo had the library grant him knowledge of the term; it was the original conceptual form of a generalized computing device, an imaginary machine which moved back and forth along a limitless one-dimensional data tape, reading and writing symbols according to a given set of rules.

"With the right set of tiles, to force the right pattern, the next row of the tiling will look like the data tape after the Turing Machine has performed one step of its computation. And the row after that will be the data tape after two steps, and so on. For any given Turing Machine, there's a set of Wang Tiles that can imitate it."

Paolo nodded amiably. He hadn't heard of this particular quaint result, but it was hardly surprising. "The carpets must be carrying out billions of acts of computation every second… but then, so are the water molecules around them. There are no physical processes that don't perform arithmetic of some kind."

"True. But with the carpets, it's not quite the same as random molecular motion."

"Maybe not."

Karpal smiled, but said nothing.

"What? You've found a pattern? Don't tell me: our set of twenty thousand polysaccharide Wang Tiles just happens to form the Turing Machine for calculating pi."

"No. What they form is a universal Turing Machine. They can calculate anything at all—depending on the data they start with. Every daughter fragment is like a program being fed to a chemical computer. Growth executes the program."

"Ah." Paolo's curiosity was roused—but he was having some trouble picturing where the hypothetical Turing Machine put its read/write head. "Are you telling me only one tile changes between any two rows, where the 'machine' leaves its mark on the 'data tape'… The mosaics he'd seen were a riot of complexity, with no two rows remotely the same.

Karpal said, "No, no. Wang's original example worked exactly like a standard Turing Machine, to simplify the argument… but the carpets are more like an arbitrary number of different computers with overlapping data, all working in parallel. This is biology, not a designed machine—it's as messy and wild as, say, a mammalian genome. In fact, there are mathematical similarities with gene regulation: I've identified Kauffman networks at every level, from the tiling rules up; the whole system's poised on the hyperadaptive edge between frozen and chaotic behavior."

Paolo absorbed that, with the library's help. Like Earth life, the carpets seemed to have evolved a combination of robustness and flexibility which would have maximized their power to take advantage of natural selection. Thousands of different autocatalytic chemical networks must have arisen soon after the formation of Orpheus, but as the ocean chemistry and the climate changed in the Vegan system's early traumatic millennia, the ability to respond to selection pressure had itself been selected for, and the carpets were the result. Their complexity seemed redundant, now, after a hundred million years of relative stability—and no predators or competition in sight—but the legacy remained.

"So if the carpets have ended up as universal computers… with no real need anymore to respond to their surroundings… what are they doing with all that computing power?"

Karpal said solemnly, "I'll show you."