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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 which 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 computa-tion every second ... but then, so are the water molecules
around them. There are no physical processes which 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 Or-pheus 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
competi-tion 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?"
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Karpal said solemnly, "I'll show you."
Paolo followed him into an environment where they drifted above a schematic
of a carpet, an abstract landscape stretching far into the distance,
elaborately wrin-kled like the real thing, but otherwise heavily stylized,
with each of the polysaccha-ride building blocks portrayed as a square tile
with four different colored edges. The adjoining edges of neighboring tiles
bore complementary colors to represent the complementary, interlocking
shapes of the borders of the building blocks.
"One group of microprobes finally managed to sequence an entire daughter
fragment," Karpal explained, "although the exact edges it started life with
are largely guesswork, since the thing was growing while they were trying
to map it." He gestured impatiently, and all the wrinkles and folds were
smoothed away, an irrelevant distraction. They moved to one border of the
ragged-edged carpet, and Karpal started the simulation running.
Paolo watched the mosaic extending itself, following the tiling rules
perfectly an orderly mathematical process, here: no chance collisions of
radicals with catalytic sites, no mismatched borders between two new-grown [ Pobierz całość w formacie PDF ]