by Rudy Rucker
The infernal machine hovered over us, flattening the waves around us, its loudspeaker broadcasting commands. A woman’s voice. “Please return to the beach immediately. Bela! Paul! Alma! Please let us join you. Bela! Paul! Alma!”
I glanced up and recognized the people in the helicopter door: the supposed NSA agents Kenny Jones and Mary Smith, he of the curly hair and she of the pointy glasses. Kenny was holding his electric-net-gun.
I called a warning to the cone shell, but my voice was lost in the copter’s hideous clatter and roar. No matter; Rowena had more tricks up her snout. She darted out her red-tinged proboscis, sending it toward the black helicopter. The slender thread twined upward through the prop-wash, feeling its way. It found purchase upon the side of the helicopter and encircled it like a nightmarishly fast-growing vine.
The proboscis wove a field of dark light around the helicopter and some odd transformation began. The chopper dwindled as if moving further and further away, but yet it remained not very far overhead. It took a second to realize it was shrinking.
“That’s Cal Kweskin and Maria Reyes!” called Paul, staring up at the dwindling helicopter. Those were the names of the Stanford mathematicians whom we’d been racing for the Mor- phic Classification Theorem. Like I said, I’d never met them— but Paul knew them well. They had a research contract from the NSA—so they hadn’t been entirely lying when they’d claimed they were agents. And that black helicopter seemed like an NSA-type chopper for sure.
The tiny Cal Kweskin seemed elated by the bizarre change they were going through. Joyfully he tossed his tubular gun out the helicopter door—it dropped past my face; the size of a toothpick. Though it was hard to judge, the helicopter looked to be the size of a seagull now. Rowena withdrew her proboscis and, with an energetic roar, the tiny chopper sped out to sea, the minute figures on board waving in glee. Weirder and weirder.
Alma and I exchanged glances, mustering the courage to continue.
“Once again, Humelocke shows Stanford how it’s done,” said Paul, pleased by the encounter with his new colleagues. “Look out, guys, here comes a surge.”
We paddled further out through the surf.
In another few minutes we were inside the square stone passage. Rowena took up too much room to stay in there with us; she flew on through and waited on the ocean side. The surf was bigger than it had looked from the shore.
A wave broke outside, filling the square hole with rushing foam. I kicked against the currents, banging my knees and elbows against the jagged wall. Up near the top I saw a suitable ledge, flat and nearly a foot wide.
Alma was at the ocean end of the passageway, working the ebb and flow as gracefully as an otter. She had hold of the plastic leash cord that dangled from Paul’s board.
“Let’s start Haut’s Paradox,” I said to Paul, leaning in towards him. I opened the ziplock bag and squeezed the battery and teapot together. “I’ll hold it and you move the wires.”
“Okay,” said Paul, reaching forward.
Another surge of surf came through just then and it took a minute to reposition ourselves. As I kicked and paddled,
I happened to glance back at the beach. I saw a short man and a tall man, Henry Nunez and Tito Cruz, with Tito carrying his shotgun.
Alma saw them too. “Stay with it, boys,” she urged us. “We can’t turn back now.”
Paul and I hunched together like two desperate mountaineers trying to start a fire. Tito was yelling. Out in the sea, another wave was breaking. But now the wires met; a tiny spark flickered against the wiggly surface of the computational membrane. Yes. The off-center oval bands of red and blue began to pulse.
“Go!” I said, shoving Paul forward and letting the surge lift me up to the shelf. I laid the teapot on its side and paddled on through the stone arch, my motions lit by strobing red/blue light.
The sea was wilder by far than it had been fifteen minutes ago, the waves rough and badly formed. A hill of water rushed at us, as if bent upon hammering us into the rock. Alma and I ducked under the crest, holding Paul’s board from either side.
Paul caught a lungful of the icy water and emerged coughing. The sea tilted down and then up; a bigger wave was on its way. We turned our boards back towards the shore. Rowena steadied herself in the air above us, preparing to jet forward.
The square natural bridge housed a bulging egg of mauve light. The sea churned where the light touched it; bits of the rock walls were chipping away and swirling into the dimensional hypertunnel. I heard a boom—Tito’s shotgun or a wave hitting a rock?
Chilled, bruised, and terrified, Alma and I knelt upon our boards, holding the gasping Paul steady. The big wave rose behind us. I felt scared; and I kept wishing I’d phoned to say goodbye to my Ma. I hadn’t had the nerve. At least I’d transferred that money to her.
As I was thinking all this, we were sliding down the wave’s face as if sledding a hill of glass, steering ourselves towards the glowing oval that filled the square hole. The roar of the surf faded; the waves off to the sides became sluggish mounds; the flying droplets of spray behind me hung pulsing in the air.
I felt a rush of wind as Rowena sped past us, plunging headlong into the light. We followed in her wake, Alma first, me second, Paul trailing a bit behind.
The hypertunnel was constricted, wrapped round upon itself, a region of radically warped space. A gnarled cord ran along one side of the hypertunnel. I saw no signs of the natural bridge’s walls in here, only the sea, the air, the cable, our bodies and, in the distance, triangular Rowena and some spots of blue and green.
We three glided from beneath another natural bridge, this one high, lacy, and delicate, set in a calm aquamarine sea and surrounded by a faint blue glow. Where the waters of Big Sur had been icy and brutal, this sea was warm, nurturing, and fanned by a gentle breeze.
The mysterious gnarly cable through our hypertunnel had a bend in it here; it disappeared downwards into a small whirlpool. We kicked past it easily enough, our boards sliding across the glassy water, Alma still first, followed by me, and then Paul.
Ahead of us was Rowena the cone shell, flying towards a high-crowned green island nearby. Hearing a noise behind us, I looked back at the elegant natural bridge with its egg of hypertunnel light. A seagull-sized helicopter came powering through, passing overhead and shooting upwards, growing in size as it rose.
“The Stanford spies in their Pig machine,” I said. “I wish they'd crash.”
Quite abruptly, the chopper slammed into the sky. Some flaming pieces of wreckage dropped down to our ocean, while other bits melted into the sky itself.
"Whoah!” said Paul. “Take back that wish.”
“I didn’t mean I wanted them dead," I said hurriedly. “I hope they’re okay.” The sky was odd-looking. It was shiny and close, like a not-all-that-high ceiling. I could faintly see three human figures floating—behind it. “They’re alive!” I exclaimed, feeling relieved. “A woman and two men. And they’re swimming?” But now they grew hazy and faded away.
“It’s like there’s multiple levels to this world,” said Paul. “Is that another ocean up there? I think they swam through it.”
“I’m glad they’re not dead, but I don’t like them glomming onto our adventure,” I griped. “When Cal and Maria came to see me last night, Maria asked me to take them with us. It was like she knew we were hypertunneling over to La Hampa.”
“Well, yeah,” said Paul. “I gave them some hints. I was making a lot of phone calls last week when I was high on speed. I couldn’t shut up.”
“You were horrible,” put in Alma.
With the noise of the chopper gone, I could hear a slight hissing from the hypertunnel and the natural bridge, a sound like the electrical buzz around a high-tension transformer. I paddled away from it, keeping pace with Alma.
The scene before us resembled the island-sprinkled seas of Palau, save that floating in the sky were enormous balls of water like time-slowed drops of
spray. Nine of them. Each of these slowly drifting orbs was bespeckled with its own set of islands. And amidst the toy water planets hovered a small sun, not overly bright.
“Gorgeous,” breathed Alma.
“La Hampa,” I said. “The underworld.”
“Overworld,” said Paul. “Heaven. Nobody was able to stop us. And we can go back whenever we like. Unless—”
As if linked to a single axle, our heads turned to look back at the hypertunnel’s mouth. And just then—blip—the glowing oval shrank to a point and winked out. The blue nimbus faded from the natural bridge and all was still. It was so very quiet here.
“Oops,” I said. Surrounded by this calm, enchanted seascape, that was about as upset as I could get.
“Darn,” said Paul, equally mild. “I figured the mass of all that rock would hold the hypertunnel open. I just hope the La Hampans will help us go home.”
“Oh stop analyzing everything to death, you two,” said Alma. “It’s time for fun.” She slid off her surfboard, wormed her way out of her wetsuit, and kicked down into the water, looking around, her gold medallion and bright bikini flashing through the blue water. After a bit she emerged laughing. “Wow.”
“Fish?” I asked.
“Yeah."
I slid in and peeled off my wetsuit. I tasted the water; it wasn’t salty. Without really thinking it over, I swallowed a bit of it. It felt tingly in my gullet. And now I took a deep breath and dove down, eyes open. The water felt good on my eyes. Somewhat magically, I could see nearly as well as if I were wearing a face mask. The obliging, unearthly water was acting like a lens.
I was surrounded by a shoal of perhaps five thousand tiny tropical fish, similar to the zebras or tetras you’d see in someone’s home aquarium. Their bodies moved like iron filings in a magnetic field, with ropes and scarves of density emerging from the parallel computations of the school. I swam below the school and looked up towards the surface. The quivering fishies were green or gray or blue, depending on the precise angle of light, each watery, gleaming shade lovelier than the next.
I surfaced, grabbed a breath, and swam down deeper. Some of the little fish followed me, changing their shapes as they swam. They morphed into yellow and white oval butterfly fish with Turing-style leopard spots and tiger stripes, and as I went still deeper, they became parrot fish the size of salmon, with their scales shaded in rust and acid green, their mouths beaky, and tiny chartreuse fins on their sides. It was very odd and even a little creepy to see the fish morphing as they whirled around me; it was as if they were taking on the shapes I wanted to see.
I was almost at the bottom now; it looked interestingly shiny and smooth. I kicked for it, arms outstretched.
To my surprise I shot through the shiny film and into the air of a twilight sky. I’d entered an enormous, dimly lit bubble of air that lay beneath the sea I’d been swimming in. The bubble contained its own little sun and its own floating water planets, ten of them. The sun was nearby, faint and blotchy, the size of a sports stadium. Fluttering along with me were some of the parrot fish, who’d now become parrot birds with chartreuse wings. I happened to think of a long-tailed white tropic bird just then, and one of the parrots took on that form as well.
All very magical and mysterious. But how was I to rejoin Paul and Alma? I had no way of moving back upwards; indeed I was dropping at an ever-faster rate through the dimly lit air towards a particular water ball that held a green-black island with a murky lake. Even so I was calm—I had the sense that I might be able to dive painlessly into the approaching water planet. On its island stood a little square cottage. Light flickered at me from beside the house, as if someone were aiming a mirror at my eyes to blind me. Faintly I glimpsed a figure in white. Roland Haut!
Over the beating sound of the air, I heard a whistling noise. A flying cone shell was swooping towards me from above, avid and intent, quite menacing in the gloom. The birds around me squawked and fluttered.
“Don’t1.” I screamed. “Don’t eat me!”
The shell's dark red proboscis shot out, wrapped around my waist, and pulled me towards a snout with a familiar mouth. Rowena.
“He crazy,” she said, suctioning her slimy foot to my bare back. She began powering upwards towards the underside of the sea I’d come through. She seemed to be in a hurry.
I heard a faint crackling from the island far below; a bolt of energy sizzled past us, heating my skin and incinerating a couple of the parrots. A ray gun? I got no explanation from Rowena. She pushed through the thin skin of the high sea and reunited me with Alma and Paul.
"Luau now,” said Rowena. “Talk math.” She flew some distance towards the nearest island, pausing this time to make sure we followed.
“What the fuck happened to you?” asked Paul as we pad- died. “We thought you’d drowned.”
“There’s—another sky down there,” I said. “A giant air bubble with its own floating seas. Someone else lives down there. I think it’s Haut. He was shooting at me, the asshole.” I craned up at the sky above our sea. It glistened; it was concave. “And we’re inside an even bigger air bubble right now. Look—” I pointed at the local sun. "That’s a ball of fire only a few hundred yards across. It’s not all that far. See how it reflects off the dome of our sky? The sky’s a film of water, I tell you, and there’s another ocean surface above that and—”
“Do you have to turn everything into a mind-breaking math trip, Bela?” interrupted Alma. “I want to go to the luau.” She paddled out ahead of us, Paul and I following in her wake. Alma was graceful and alluring in her yellow bikini. She was my girlfriend and we were on our way to a luau with alien mathematicians. I relaxed. I drank some more of the delicious water. It was all good.
“Investigations of Curved Surfaces," said Paul, staring fixedly at Alma. This was the title of Carl Friedrich Gauss’s classic treatise about how to assign a numerical curvature value to each point of a surface. Hills and valleys are regions of positive curvature, with the size of the curvature measuring how sharply the local landscape differs from a plane. Saddle-shaped mountain passes are regions of negative curvature whose numerical size is, again, proportional to non-planarity.
“I’d say Alma’s butt cheeks have a curvature of four at their local summits,” continued my mathematician pal. “With the value dropping to negative two at the arch of her back. The numbers being based on a one-meter unit, you understand.”
“Don’t slobber over her,” I said. “Alma is a person. Think of her as a friend. Like a sister-in-law.”
“I want her back,” said Paul.
“I’m not having this conversation. Let’s talk about the big picture, dog. Did you even hear what I said about the bubbles before?”
“La Hampa is a fractal,” said Paul simply. “Seas inside bubbles inside seas inside bubbles forever up and down. With islands on each sea and a sun in every bubble. And no doubt the space inside the bubbles has a negative Gaussian curvature proportional to the radius of the bubble, so that, in effect, you shrink to fit as you explore downward, and you grow to take up more room if you fly up through the sky to the next level.”
“Yes!” I exclaimed. “That’s it!” Good old Paul.
“I wonder why Roland shot at you,” said Paul.
“Maybe it was Rowena he was aiming at,” I said. “You know how paranoid he is about cone shells.”
“He’d not gonna be a happy camper here,” said Paul, shaking his head with a little laugh.
Rowena’s verdant island domed up from the water, the very image of a tropical hideaway. Thickets of red-blooming shinyleaved bushes lined the shores amid stands of succulent broadleaved stalks dangling purple flowers and clusters of bananas; higher up the island’s slope were gnarly lop-leaved trees bearing heavy oval breadfruits and ivory blossoms; the island’s summit was crowned by tall, swaying palms. Springs trickled from the dark soil; ferns and fat-leaved epiphytes nestled in the tree crotches; vines twisted about the mossy trunks; bright b
irds fluttered from branch to branch.
The sea was so clear that it was as if our surfboards were gliding through empty space. Orange-pink, mauve, and pale- green corals encrusted the island’s submerged rocky base with flat spiral dishes, brain-shaped lumps, and staghorn antlers bearing exquisite lavender tips.
Innumerable fish finned amidst the living stones. I saw, for instance, a school of twenty tiny black-and-white arrowheadshaped damselfish just below the surface, each of them a slightly different size; they hovered over a chartreuse flat-topped tree of coral, nipping in and out of the nooks, disappearing like magicians hopping into each other’s pockets.
We followed Rowena straight through an inlet into a calm lagoon with sand on the bottom and a smooth rock ledge at the shady far end. I saw a fire in a pit back there. Waiting on some comfortably curved rocks by the fire were six aliens: Rowena’s cone shell sister, the two big cockroaches I'd seen in my mirror, a pair of man-sized lizards, and a flat white mollusk with a crest of branching tendrils. This last creature resembled a six-foot- long sea slug of the type called a nudibranch.
Let me interject that these alien creatures weren’t exactly like over-sized cone shell snails, cockroaches, lizards, or nudi- branchs. I speak of them that way only as a convenience. The so-called roaches had humanoid hands; the lizardlike aliens had pinkish skin, little blue bat wings, and colorful triangles ridging their long tails; the by-now-familiar cone shell snail aliens had unearthly jets in their rears; and the nudibranchlike creature’s tree of soft palps was, as I’d soon learn, a specialized electromagnetic sense organ rather than a mere gill.
“Happy greeting,” said Rowena, flying out to meet us. “Introduce Jewelle.”
“Hello Alma hello Bela hello Paul,” said the second cone shell in a breathy singsong. She rose into the air and extended her red proboscis-tendril to help Alma step on shore.
The smooth stone edge of the lagoon had regularly curved steps rising out of the sea. Glancing down into the water, I noticed a fancifully arched door with colorful borders set into the submerged wall.