by Rudy Rucker
“That our house,” remarked Jewelle, noticing my glance. “Unger sleep there too.”
“Come on, don’t be shy, I’m Tanya,” said one of the cockroach aliens, stretching out her pale purple hand. “Welcome to the Nanonesia level of La Hampa.” Her faceted deep-green eyes were familiar from my Ratvale mirror. Her narrow lips bent upwards in a welcoming U, revealing yellow, unthreatening teeth.
Tanya helped me up the steps onto a kind of patio, smooth as marble and patterned with intricate pastel scrolls. Her hands were soft and sticky, vaguely unpleasant to the touch. She had a pungent smell like ammonia. I took a step back from her, feeling vulnerable.
“One ground rule,” said Tanya. “If any of you humans plays rough with us, you’re all outta here. You want to pass that word on to Roland Haut. We like it peaceful in Nanonesia, and any species wants to fight, they’re eighty-sixed.”
“Two to the eighty-sixth is the largest power of two that doesn’t have any zeros when you write it out in decimal,” said the other cockroach, who’d flopped down on his belly to goggle at Paul, still lying on his board. “Lemme ask you this. What’s the biggest Mersenne prime you got? I’m only asking for the lizards' sake, mind you. My name’s Osckar, and I’m a hierophantic logician from—whaddaya, whaddaya, call it Galaxy Z.” Galaxy Z or not, Osckar and Tanya talked like New Yorkers.
“The biggest Mersenne prime that I heard of lately is two to the 25,964,951 minus one,” said Paul, math robot that he was. I would have liked to ask Tanya what she knew about Haut— how had he ended up with a ray gun on an island in the world below? But it was hard to get a word in edgewise with all the alien mathematicians here.
“My condolences,” the female member of the lizard couple was saying to Paul, ironically drawing out the word. She fixed him with one of her large, golden eyes. “Your puny Mersenne prime is only enough to make a fourteen-million-digit perfect number. In our world, googol-digit perfect numbers are a commonplace. And we’ve proved there are infinitely many bigger ones, as well.” She gestured delicately towards herself and the other lizard. “I’m Vulma and this is Mulvane. We’re number theorists.” She tossed her head and twitched her colorfully ridged tail. She had meaty rear limbs like those of a T. rex.
“Charmed,” chimed in Mulvane, baring his long rows of teeth in a smile. A whiff of carrion rode upon his lukewarm breath. Even so, he seemed no more menacing than the average European math professor.
“Number theory’s a baby pool,” said Osckar the cockroach dismissively. “Logic’s the open sea. Hey, speaking of logic, whaddaya got for provably unsolvable systems of Diophantine equations back on Earth? I’m talking clean and simple here. None of those furshlugginer Godel numbers.” His wing covers twitched as if he were shrugging.
Paul answered something I won’t bore you with, and Vulma one-upped him again, and Osckar said something nasty about number theory again, and Mulvane got mad.
“Logic is for unstable, disorganized individuals who don’t know their own minds,” said the lizard number theorist, angrily fluttering his little wings.
“Space shape more important,” put in Jewelle. “Number and logic just game.”
“And don’t, ah, forget infinity,” came another voice. “Listen to Unger.” At first I couldn’t tell where the voice came from, and then I realized the nudibranch was making sounds by vibrating his upper surface. An orange band around his edge rippled as he talked. Although he had no eyes, those soft ivory branches upon his back were sensitive to the motions of our bodies.
“Hi there, Unger,” said Alma, waving at him. “Don’t tell me you’re a mathematician, too?”
“Unger is a point-set topologist turned transfinite set theorist,” said Unger. "He can’t tell a raven from a writing desk.” Pause. “That’s a joke. The raven’s, ah, digestive tract and two beak-nostrils being homotopic to the three holes formed by the desk’s, ah, four legs and three cross-bars? Stay awhile and Unger can educate you about Cantor’s Continuum Problem. The true power of the, ah, continuum is alef-two. And the next cardinal in the beth power-hierarchy is alef-seven. Big, ah, surprise. To enjoy the proof, amathematical Alma, you might get Rowena to load you up with a conotoxin sting for mind expansion. Like your Dad. Or the Nataraja can make you some, ah, pot. I’ll pace you by eating grork.”
“Don’t make fun of my father,” said Alma, confused. “How do you weirdos know so much about us? For that matter, how do you know English?”
“Siddown already,” chirped Tanya. “Then we’ll talk. Don’t listen to Unger. Mollusks are—let’s face facts—slimy. Why get high when you got hierophantics?”
We folded our wetsuits for cushions and settled onto the rocks.
“What do you mean by hierophantics?” I asked, intrigued by the word.
“The Hierophant is a Tarot card,” volunteered my knowledgeable Alma. “A trump of the Major Arcana. It shows a wise woman who explains mysteries. At least I think she’s a woman. Hiero + phant is mystery + show, it’s like hiero + glyph is mystery + symbol.”
“Just so,” said Mulvane, turning his scaly, clawed hands upward. “And hierophantics is an advanced style of thought that one absorbs in La Hampa. The human race’s adoption of language and of writing were first steps towards hierophantics.” “Osckar and me have taken a zillion steps more,” bragged Tanya.
“Maybe our Morphic Classification Theorem is hierophan- tic,” put in Paul.
“I think so,” said Rowena. “Hierophantic mean speed-up. Long story short.”
“Oh stop it with the math,” said Alma, toying with her X-eyed smiley face necklace. “I thought this was supposed to be a luau. Back home that means a party?”
“Eat, eat, eat! Drink, drink, drink!” said Tanya. “That’s the way you learn hierophantics.” She tugged over a clear crystal basin that was filled with—really big worms. Or snakes. Or, no, they were sea cucumbers, white with dark brown leopard spots; they had stubby leg bumps and little fans of feelers at their front ends; each of them was roughly the size of a salami. “Ice cream? Nxgan? Pizza? Grork?” said Osckar, picking up a pair of the heavy, drooping invertebrates and offering them around. “Whaddaya, whaddaya, the Nataraja sea cukes give it to ya just the way you want it, red-cold or ice-hot.”
“You inverted the thermal intensifies,” said Mulvane in a supercilious tone.
Alma shied away from the sea cucumbers. “Ick! Won’t any of you tell me how you learned English? How about it Tanya? You’re all different kinds of aliens, right?”
“We’re as diverse as it gets,” said the lively female cockroach. “Our races emigrated to La Hampa forever ago. We came from planets scattered all over the infinite multiverse.”
“It’s not infinite,” said scaly Mulvane, his wings standing out for emphasis. “And it’s not a multiverse. It’s one exceedingly large but finite global universe with a complicated indexing system to pick out the local universes and the hyperverse stacks. Like a Library of Babel that has all the possible books. And there’s no quantum mechanics required, I might append. Don't be sneaking in those spurious assumptions, Tanya.”
“The Library of Babel is infinite if there’s no upper bound to, ah, the size of a book,” put in Unger, gently waving the ivory tree of sensors upon his back. “The fear of infinity is a kind of blindness. A disability. The fear of infinity destroys the possibility of, ah, seeing the real. It’s quite obvious that infinity in its highest form has created and sustains us. Infinity is in every cell of your body and in each of your, ah, thoughts.”
“You’re an expert at being blind,” sneered Vulma with a dismissive flick of her tail. “Light-blind, blind to logic, and blind drunk every night.”
“Number theory is as cowardly as studying fish names instead of swimming in the sea!” exclaimed Unger. His body surface was heaving violently, making his voice quite loud. “Number theory is like looking at sex pictures instead of finding a mate! I pity you, lizard-thing.”
“I’m not the
one who’s a self-fertilizing hermaphrodite,” said Vulma, her long mouth wide-open in a grin. The aliens seemed to enjoy arguing with each other.
“Enough buffoonery,” said Unger to change the subject. “I will, ah, answer Alma’s question. The way we learned your language and your cultural history, Alma, was by looking at or by electrically sensing the, ah, patterns within the flesh of a Nataraja jellyfish that intersects a lake on the other side of that hill. We know your world in the limited fashion of peeping, timid number theorists. But now you’re here in person. We exult to share our, ah, corporeal vibrations in depth. Thus this welcoming luau.”
“You did more than watch us,” I said to the aliens. “You reached into our world. We saw you in mirrors.”
“Your jellyfish’s body is like, whaddaya, an interactive vlog,” said Osckar. “And, yeah, when we reach in, we come as mirror images to reduce the disruption. It’s like our wave functions are ninety degrees out of phase.”
“What is this jellyfish you keep talking about?” interjected Paul.
“One particular jellyfish make your world,” said Rowena. “Your jellyfish’s cable generates one after another of your parallel universes,” added Tanya. “And the series of universes is what we call a hyperverse. It’s like successive drafts of a novel.”
“Or like the output of a sculptor who finds successively lovelier images within a quarry’s stones,” said Unger. “Forms that approach the beauty of, ah, Alma.”
“Why thank you,” said Alma.
I was beginning to understand the meaning of the gnarled connector cord I’d seen running through the hypertunnel from Earth to La Hampa. Some godlike jellyfish was in physical contact with our universe. According to Tanya, the jellyfish was feeding in a series of information seeds that specified successive versions of our world, thereby constructing or connecting to an ever-changing series of Earths, each of them somewhat similar to ours, and each of them supposedly a bit better than the ones before. My mind felt very clear as I formed these ideas.
“Look at Bela thinking!” said Osckar the cockroach mathematician from Galaxy Z. “I can see the mysto steam coming outta his ears. That’s the hierophantics taking hold. You’ve been drinking the water, right?” He flopped two of those leopard-spotted invertebrates down in front of me. “Eat these and get even smarter,” he added. The sea cucumbers pointed their palps at me, as if waiting for me to speak to them. But I wasn’t ready for that yet.
“Maybe you want to poison us,” said Alma as Osckar laid a pair of the fat, spotted sea cukes in front of her. “I still don’t like the way that Rowena ate Owen and spat his bones in my backyard.”
“Eating the first member of a race that we physically contact is typical of Rowena and her sister,” sneered Vulma, filliping her tail towards the cone shells. “They’re so literal-minded.”
"Maybe Rowena was hoping to taste a human soul when she chowed down on that bodyguard schnook,” said Osckar with a sarcastic laugh. “She’s a real romantic, you bet.”
“No taste soul,” said Rowena. “Those humans predictable.” “How can a complex computation like thought be predictable?” said Paul. “Even if there is an axiom system for a human mind, deriving future mental states should take a really long time.”
“Your world docile; your people docile,” said Rowena. “Other world, other humans maybe not. Computation landscape always different. Like geology. Not docile everywhere.”
Mulvane glared over at the cone shells. “Those two would be a bit more bearable if they’d speak properly.”
“Unger would like to point out that Rowena and Jewelle use their, ah, special rhetoric by deliberate choice,” put in Unger.
“Deep talk big block,” said Jewelle. “Like hierophantic.” Which was sort of what I’d been telling Alma about Asian versus Western styles of speech. Not that I could figure out what the hell Rowena had been talking about just now. What did she mean by docile?
By now Osckar and Tanya had set a couple of those nasty- looking sea cucumbers down beside each of us. The cockroaches were gesturing with their spindly arms to encourage us to eat.
“Notice that our sun’s getting darker?” said Tanya. “Its brightness cycles up and down once a day.” The dimmed sun looked a bit splotchy. “Dark means suppertime,” added Tanya. “Eat!”
“Let’s see you bite into one of those gross things, Tanya,” said Paul, gazing down at his sea cucumbers.
The cockroach woman picked up a sea cucumber and sang to it. “I got a yen for nxgan! As if you didn’t know, cukie-pie.” The creature morphed into a crisp brown packet like a giant deep-fried egg roll, glistening with fat and nicely folded. Tanya crunched down on it, spilling out lumpy orange liquid from its interior. “Scrumptious nxgan,” she said, her voice sweet with saliva. She used one of her spare legs to push a gobbet of the orange stuff into her mouth.
My two sea cucumbers stretched comfortably, like a pair of starlets by a swimming-pool, turning their fans of sensors towards my face as if worshipping the sun. They really and truly wanted to be eaten. I was almost hungry enough to try.
“Maybe some baked tofu in a pita bread with pickled bok choy?” murmured Alma to her sea cucumbers. “And a big bottle of Beck’s.” Instantly the creatures morphed into a pita pouch and a damp green bottle of beer. Alma raised her eyebrows, but didn’t touch the food. Meanwhile Paul asked his sea cukes to be a pork chop with French-fried yams next to a tall glass of orange soda. And I told mine to form roast rabbit, black rice with carrot puree, and a glass of red wine.
“I don’t know,” said Alma. “What if the food’s full of sick eggs that’ll hatch larvae inside us that eat our flesh and burst out—yuuugh?” She made a rapid gesture to mime something erupting through the wall of her abdomen.
“I figure if they wanted to kill us here, we’d already be dead,” said Paul, prodding his crisp pork-chop with his finger. “Show us how, Bela. You the man.”
“Oh, all right,” I said. I took a sip of my wine and a nibble of my rabbit. Flavors bloomed in my mouth. It was as if I’d never properly tasted anything before. “Yeah, dogs,” I said, digging in. “We’re in heaven.” The sun had turned silvery and spotty, like a moon.
As we ate and drank, the luau grew convivial. Hearing the laughter, the aliens’ children came out from hiding, with several dozen small cone shells emerging from the water, and scores of miniature roaches scuttling down from the ruby-crystal pillbox roach house upon the hill. Mulvane went halfway up the hill and bellowed into a gold-framed mine shaft entrance to call his kids too: a trio of knee-high lizards. Tiny nudibranchs oozed forth from slits in Unger’s skin to scavenge up the spilled scraps of the anemones and sponges that he was eating.
“You never really explained what the Nataraja sea cucumbers are,” said Paul, finishing off a dish of ice cream he was sharing with two of the lizard children. “That word Nataraja, it means—what?”
“La Hampa is a place,” said Mulvane. “This place. The Nataraja is the thing that lives in La Hampa. As it happens, the two are very nearly coextensive. The Nataraja fills every cranny of La Hampa, just as the superorganism Gaia fills every part of your planet Earth. All the levels of La Hampa are filled with the Nataraja: our Nanonesian level, the Subgum level below us, the Paradisio level above us, and so on up and down. Everything you see here is a some part of the Nataraja’s interwoven life cycles. Everything other than us.” He gestured at the seven alien mathematicians and their children. “We, like you, are visitors. Although perhaps our races have been here for so long that we’ve turned a bit Nataraja ourselves.”
“We use the word Nataraja with you because in Earth’s Sanskrit language, nata + raja is dancer + king" said Unger. “Nataraja is another name for dancing Shiva, the creator and destroyer of worlds.”
The island’s trees were swaying in complex rhythms; the patterns in the marble underfoot were slowly changing shape. Everything here—even the rocks, the water, the air—was a living par
t of the Nataraja superorganism that filled La Hampa. The La Hampan animals were as corpuscles in the Nataraja’s blood stream. And my world’s God was a jellyfish that was part of the great Nataraja as well. The ultimate reality was odder than I’d ever imagined.
Turning in on myself, I sensed the richness of my body. I was an ecosystem, a colony. Perhaps, relative to a single-celled bacterium in my gut, I too was a Nataraja of incalculable significance and size.
The children had begun playing a game that Mulvane called centrifugal bumble-puppy, drawing the name from the human database. Responding to the children’s request, the Nataraja had set a little tornado to spinning at the edge of the patio. The little cone shells, lizards, cockroaches, and nudibranchs repeatedly hurled themselves into the tornado and were spewed out—the game of the thing was to try to stay in longer than the others and, if possible, to climb up higher in the tornado’s column. Often as not the children landed in the water, chirping, growling, and fluting with glee.
Mellowed by food and drink, we adults lolled around the dancing fire, talking about math. In a sense mathematics is quite objective: the same deductions can become known to everyone who starts with the same axioms and definitions; the same abstract forms can be universally perceived. So it’s perfectly possible to talk math with a cockroach from Galaxy Z.
This said, there’s also a sense in which mathematics is subjective. If your language is unknown to me, I find your books unreadable; if you paint in colors invisible to me, I avoid your museums; if you travel by carriers I can’t board, your journeys don’t engage me; if your mathematical definitions and axioms seem arbitrary to me, I have little appreciation for your theorems.
Our math conversation with the aliens meandered back and forth across the fuzzy boundary separating information from noise. Generally speaking, the lizards were interested in numbers, the cone shells in space, Unger in infinity, and the cockroaches in logic.
In their home world, the lizard forbearers of Mulvane and Vulma lived underground. Their main concerns were tunnel branchings and family trees. They had very little appreciation for open space, for infinity, or abstract logic. But they were hel-lacious with the integers. They’d long since resolved the Rie- mann hypothesis and Goldbach’s conjecture concerning prime numbers, which was big news for Paul and me. We would have liked to know the proof of the Riemann hypothesis, and they spent a few minutes trying tell it to us, but every concept they mentioned was unknown, requiring explanations that led to yet more arcane background material, with no solid ground in sight. We gave up. Next?