Paolo watched the mosaic extending itself, following the tiling rules perfectly—an orderly mathematical process, here: no chance collisions of radicals with catalylytic sites, no mismatched borders between two newgrown neighboring "tiles" triggering the disintegration of both. Just the distillation of the higher-level consequences of all that random motion.
Karpal led Paolo up to a height where he could see subtle patterns being woven, overlapping multiplexed periodicities drifting across the growing edge, meeting and sometimes interacting, sometimes passing right through each other. Mobile pseudo-attractors, quasi-stable waveforms in a one-dimensional universe. The carpet's second dimension was more like time than space, a permanent record of the history of the edge.
Karpal seemed to read his mind. "One dimensional. Worse than flatland. No connectivity, no complexity What can possibly happen in a system like that? Nothing of interest, right?" He clapped his hands and the scape exploded around Paolo. Trails of color streaked across his sensorium, entwining, then disintegrating into luminous smoke.
"Wrong. Everything goes on in a multidimensional frequency space. I've Fourier-transformed the edge into over a thousand components, and there's independent information in all of them. We're only in a narrow cross section here, a sixteen-dimensional slice—but it's oriented to show the principal components, the maximum detail."
Paolo spun in a blur of meaningless color, utterly lost, his surroundings beyond comprehension. "You're a gleisner robot, Karpal! Only sixteen dimensions! How can you have done this?"
Karpal sounded hurt, wherever he was. "Why do you think I came to C-Z? I thought you people were flexible!"
"What you're doing is…" What? Heresy? There was no such thing. Officially. "Have you shown this to anyone else?"
"Of course not. Who did you have in mind? Liesl? Hermann?"
"Good. I know how to keep my mouth shut." Paolo jumped back to the dodecahedron; Karpal followed. "How can I put this? The physical universe has three spatial dimensions, plus time. Citizens of Carter-Zimmerman inhabit the physical universe. The false promises of Kozuch Theory kept us from the stars for a thousand years. Higher-dimensional mind games are strictly for the solipsists." Even as he said it, he realized how pompous he sounded.
Karpal replied, more bemused than offended, "It's the only way to see what's going on. The only sensible, way to apprehend it. Don't you want to know what the carpets are actually like?"
Paolo felt himself being tempted. Inhabit a sixteen dimensional slice of a thousand-dimensional frequency space? But it was in the service of understanding a real physical system—not a novel experience for its own sake.
And nobody had to find out.
He ran a quick self-predictive model. There was a ninety-three percent chance that he'd give in, after a kilotau spent agonizing over the decision. It hardly seemed fair to keep Karpal waiting that long.
He said, "You'll have to loan me your mind-shaping algorithm. My exoself wouldn't know where to begin.
When it was done, he steeled himself, and jumped back into Karpal's scape. For a moment, there was nothing but the same meaningless blur as before.
Then everything suddenly crystallized.
Creatures swain around them, elaborately branched tubes like mobile coral, vividly colored in all the hues of Paolo's mental palette—Karpal's attempt to cram in some of the information that a mere sixteen dimensions couldn't show. Paolo glanced down at his own body; nothing was missing, but he could see around it in all the thirteen dimensions in which it was nothing but a pinprick. He quickly looked away. The "coral" seemed far more natural to his altered sensory map, occupying space in all directions, and shaded with hints that it occupied much more. Paolo had no doubt that it was "alive"; it looked more organic than the carpets themselves, by far.
Karpal said, "Every point in this space encodes some kind of quasi-periodic pattern in the tiles. Each dimension represents a different characteristic size—like a wavelength, although the analogy's not precise. The position of each dimension represents other attributes of the pattern, relating to the particular tiles it employs. So the localized systems you see around you are clusters of a few billion patterns with broadly similar attributes at similar wavelengths."
They moved away from the swimming coral, into a swarm of something like jellyfish: floppy hyperspheres waving wispy tendrils (each one of them more substantial than Paolo). Tiny jewel-like creatures darted among them. Paolo was just beginning to notice that nothing moved here like a solid object drifting through normal space; motion seemed to entail a shimmering deformation at the leading hypersurface, a visible process of disassembly and reconstruction.
Karpal led him on through the secret ocean. There were helical worms, coiled together in groups of indeterminate number—each single creature breaking up into a dozen or more wriggling slivers, and then recombining… although not always from the same parts. There were dazzling multicolored stemless flowers, intricate hypercones of "gossamer-thin" fifteen-dimensional petals—each one a hypnotic fractal labyrinth of crevices and capillaries. There were clawed monstrosities, writhing knots of sharp insectile parts like an orgy of decapitated scorpions.
Paolo said, uncertainly, "You could give people a glimpse of this in just three dimensions. Enough to make it clear that there's… life in here. This is going to shake them up badly, though." Life-embedded in the accidental computations of Wang's Carpets, with no possibility of ever relating to the world outside. This was an affront to Carter-Zimmerman's whole philosophy: if nature had evolved "organisms" as divorced from reality as the inhabitants of the most inward-looking polis, where was the privileged status of the physical universe, the clear distinction between reality and illusion? And after three hundred years of waiting for good news from the Diaspora, how would they respond to this back on Earth?
Karpal said, "There's one more thing I have to show you "
He'd named the creatures squid, for obvious reasons. They were prodding each other with their tentacles in a way that looked thoroughly carnal. Karpal explained, "There's no analogue of light here. We're viewing all this according to ad hoc rules which have nothing to do with the native physics. All the creatures here gather information about each other by contact alone-which is actually quite a rich means of exchanging data, with so many dimensions. What you're seeing is communication by touch."
"Communication about what?"
"Just gossip, I expect. Social relationships."
Paolo stared at the writhing mass of tentacles.
"You think they're conscious?"
Karpal, point-like, grinned broadly. "They have a central control structure, with more connectivity than a citizen's brain, which correlates data gathered from the skin. I've mapped that organ, and I've started to analyze its function."
He led Paolo into another scape, a representation of the data structures in the "brain" of one of the squid. It was—mercifully—three-dimensional, and highly stylized, with translucent colored blocks to represent mental symbols, linked by broad lines indicating the major connections between them. Paolo had seen similar diagrams of citizens' minds; this was far less elaborate, but eerily familiar nonetheless.
Karpal said, "Here's the sensory map of its surroundings. Full of other squid's bodies, and vague data on the last known positions of a few smaller creatures. But you'll see that the symbols activated by the physical presence of the other squid are linked to these" —he traced the connection with one finger— "representations. Which are crude miniatures of this whole structure here."