Mammoth Books presents Wang's Carpets Page 4

  Orlando’s celebration of the microprobe discoveries was a very first-generation affair. The environment was an endless sunlit garden strewn with tables covered in food, and the invitation had politely suggested attendance in fully human form. Paolo politely faked it – simulating most of the physiology, but running the body as a puppet, leaving his mind unshackled.

  Orlando introduced his new lover, Catherine, who presented as a tall, dark-skinned woman. Paolo didn’t recognize her on sight, but checked the identity code she broadcast. It was a small polis, he’d met her once before – as a man called Samuel, one of the physicists who’d worked on the main interstellar fusion drive employed by all the ships of the diaspora. Paolo was amused to think that many of the people here would be seeing his father as a woman. The majority of the citizens of C-Z still practised the conventions of relative gender which had come into fashion in the twenty-third century – and Orlando had wired them into his own son too deeply for Paolo to wish to abandon them – but whenever the paradoxes were revealed so starkly, he wondered how much longer the conventions would endure. Paolo was same-sex to Orlando, and hence saw his father’s lover as a woman, the two close relationships taking precedence over his casual knowledge of Catherine as Samuel. Orlando perceived himself as being male and heterosexual, as his flesh original had been . . . while Samuel saw himself the same way . . . and each perceived the other to be a heterosexual woman. If certain third parties ended up with mixed signals, so be it. It was a typical C-Z compromise: nobody could bear to overturn the old order and do away with gender entirely (as most other polises had done) . . . but nobody could resist the flexibility which being software, not flesh, provided.

  Paolo drifted from table to table, sampling the food to keep up appearances, wishing Elena had come. There was little conversation about the biology of Wang’s Carpets; most of the people here were simply celebrating their win against the opponents of the microprobes – and the humiliation that faction would suffer, now that it was clearer than ever that the “invasive” observations could have done no harm. Liesl’s fears had proved unfounded; there was no other life in the ocean, just Wang’s Carpets of various sizes. Paolo, feeling perversely even-handed after the fact, kept wanting to remind these smug movers and shakers: There might have been anything down there. Strange creatures, delicate and vulnerable in ways we could never have anticipated. We were lucky, that’s all.

  He ended up alone with Orlando almost by chance; they were both fleeing different groups of appalling guests when their paths crossed on the lawn.

  Paolo asked, “How do you think they’ll take this, back home?”

  “It’s first life, isn’t it? Primitive or not. It should at least maintain interest in the diaspora, until the next alien biosphere is discovered.” Orlando seemed subdued; perhaps he was finally coming to terms with the gulf between their modest discovery, and Earth’s longing for world-shaking results. “And at least the chemistry is novel. If it had turned out to be based on DNA and protein, I think half of Earth C-Z would have died of boredom on the spot. Let’s face it, the possibilities of DNA have been simulated to death.”

  Paolo smiled at the heresy. “You think if nature hadn’t managed a little originality, it would have dented people’s faith in the charter? If the solipsist polises had begun to look more inventive than the universe itself . . .”

  “Exactly.”

  They walked on in silence, then Orlando halted, and turned to face him.

  He said, “There’s something I’ve been wanting to tell you. My Earth-self is dead.”

  “What?”

  “Please, don’t make a fuss.”

  “But . . . why? Why would he –?” Dead meant suicide; there was no other cause – unless the sun had turned red giant and swallowed everything out to the orbit of Mars.

  “I don’t know why. Whether it was a vote of confidence in the diaspora” – Orlando had chosen to wake only in the presence of alien life – “or whether he despaired of us sending back good news, and couldn’t face the waiting, and the risk of disappointment. He didn’t give a reason. He just had his exoself send a message, stating what he’d done.”

  Paolo was shaken. If a clone of Orlando had succumbed to pessimism, he couldn’t begin to imagine the state of mind of the rest of Earth C-Z.

  “When did this happen?”

  “About fifty years after the launch.”

  “My Earth-self said nothing.”

  “It was up to me to tell you, not him.”

  “I wouldn’t have seen it that way.”

  “Apparently, you would have.”

  Paolo fell silent, confused. How was he supposed to mourn a distant version of Orlando, in the presence of the one he thought of as real? Death of one clone was a strange half-death, a hard thing to come to terms with. His Earth-self had lost a father; his father had lost an Earth-self. What exactly did that mean to him?

  What Orlando cared most about was Earth C-Z. Paolo said carefully, “Hermann told me there’d been a rise in emigration and suicide – until the spectroscope picked up the Orphean water. Morale has improved a lot since then – and when they hear that it’s more than just water . . .”

  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 transhumanity in your hands? You must be 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 base environment? 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 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 computation 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 c
alculating 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 behaviour.”

  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 any more to respond to their surroundings . . . what are they doing with all that computing power?”

  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 wrinkled like the real thing, but otherwise heavily stylized, with each of the polysaccharide building blocks portrayed as a square tile with four different coloured edges. The adjoining edges of neighbouring tiles bore complementary colours – 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 neighbouring “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 environment exploded around Paolo. Trails of colour 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 colour, 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. Whom did you have in mind? Liesl? Hermann?”

  “Good. I know how to keep my mouth shut.” Paolo invoked his exoself and moved back into the dodecahedron. He addressed the empty room. “How can I put this? The physical universe has three spatial dimensions, plus time. Citizens of Carter-Zimmerman inhabit the physical universe. Higher dimensional mind games are for the solipsists.” Even as he said it, he realized how pompous he sounded. It was an arbitrary doctrine, not some great moral principle.

  But it was the doctrine he’d lived with for twelve hundred years.

  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 – non-sapient – self-predictive model. There was a ninety-three percent chance that he’d give in, after fifteen subjective minutes of 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 moved back into Karpal’s environment. For a moment, there was nothing but the same meaningless blur as before.

  Then everything suddenly crystallized.

  Creatures swam around them, elaborately branched tubes like mobile coral, vividly coloured 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 16-space in all directions, and shaded with hints that it occupied much more. And 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 in 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, all 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 multicoloured 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 truth 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 squids, for obvious reasons. Distant cousins of the jellyfish, perhaps? They were prodding each other with their tentacles in a way which looked thoroughly carnal – but Karpal explained, “There’s no analog 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.