White Light (Axoplasm Books) Page 7

  “I’ll miss you,” I said finally. I started to say more, but only made a sort of babbling sound which faded into silence.

  She rubbed her bill against my shoulder. “We’ll meet again,” she said gently. “Over the sea, beyond the mountain… we’ll meet again. Thank you, Felix. Don’t forget me.”

  I held her up in the air and she flew off, clumsily at first but then with growing grace. She circled back towards me once, dipped her wings, then wheeled and flew strongly towards the sea. I watched the dwindling speck until it merged with the distant blue haze. I was completely alone.

  PART 2

  “The actual infinite in its highest

  form has created and sustains us,

  and in its secondary transfinite

  forms occurs all around us and

  even inhabits our minds.”

  GEORG CANTOR

  No. 9

  Hilbert’s Hotel

  I tried to fly to the hotel, but discovered that here you needed wings to fly. I started walking across the fields sloping up towards it, circling around the larger boulders. I was naked.

  The grass in the fields was short and springy. It felt nice on my bare feet. I hadn’t heard a giggle since we’d landed, and I decided the ground wasn’t alive after all. It was something like an Alpine meadow on Earth, except that there was no sun. The light came from everywhere.

  I spotted a wiggly groove in the meadow and went over to it. It was a tiny brook, as I had hoped. I knelt to drink the water, clear and so cold that I could feel it all the way down. There had to be glaciers up there somewhere.

  I toiled up the gradually steepening slope for something like an hour, and the hotel was still not much nearer. The air was very clear. I looked back. We had landed several thousand feet above the level of the sea, but surely Kathy was already on it. She was lucky to have wings.

  Again I puzzled over the curious flatness of the landscape. I could feel that the slope was getting steeper, but it seemed to lie evenly with the rest of the land. I walked another half hour. The hotel didn’t look any nearer at all. I sat down to rest, sucking in rapid lungfuls of the tenuous air.

  Tiny yellow flowers were growing in the grass around me. I leaned close to examine one. At first it looked like a simple five-pointed star. But then I noticed that at each point of the star there was a smaller star. I looked closer. At each point of the secondary stars there were still smaller stars, tipped by tinier stars, which had… In a sudden flash I saw the whole infinitely regressing pattern at once.

  Trembling with excitement I held a blade of grass up to the sky. Halfway down its length it forked into two bladelets. In turn, each bladelet forked into two bladelets. Which branched and rebranched, again and again… With a snatch of my mind I comprehended the whole infinite structure at once. No wonder the grass was springy.

  I looked at the landscape around me with new eyes. Kathy and I had flown past alef-null. Out here infinity was as real as a pie in the face. And the body I had was equipped to deal with it.

  I thought back on the sort of mental twitch I had used to see the infinite complexity of the flower and leaf. Maybe…

  “La,” I said, “La, La, La,…” I did that thing with my mind and let my voice speed up into a high-pitched gabble. A few seconds later I had finished saying alef-null “La"s.

  Next I tried to count through all the natural numbers, but I got hung up trying to pronounce 217,876,234,110,899,720,123,650,123,124,687,857. I decided to use a simpler system and started over. “One. One plus one. One plus one plus one….” In a minute I was done. I had counted up to alef-null.

  I looked critically at the distance between me and the hotel. I sharpened my vision and began counting the boulders dotting the meadow. Sure enough there were alef-null of them to pass. No wonder I hadn’t felt like I was getting any closer. If I walked past ten more or a thousand more boulders there’d still be alef-null of them left.

  But my tongue had been able to do alef-null things when I’d counted out loud. Why shouldn’t my legs be able to do it too? I stood up and started running. Once again there was some sort of head trick I had to do to keep speeding up. The endless energy I needed to keep my body moving faster and faster flowed into me from the landscape around me. I had a feeling that the mountain was drawing me closer, that the air was parting to let me pass, that the ground was forming footholds for me.

  A minute to the first boulder, half a minute to the next, a quarter minute to the third… Two minutes later I was standing in the grounds of the hotel, more than a little out of breath. It had been like the trip from Earth, but without the relativistic distortions. I was in a world beyond the physics of Earth.

  The hotel was built out of stone. The outside walls were covered with a rough cream-colored plaster, and the window frames were painted a dark red. Although the hotel was only two hundred feet high, it had infinitely many floors. The trick was that the upper floors got thinner and thinner. Each successive layer of rooms was flattened enough to use only one twentieth of the remaining hotel height…so there was always room for nineteen more floors.

  The building had no roof of course. None was needed, as each floor was protected from the elements by the floor above it. I stared up at one of the slit-like upper windows and wondered how anyone could use a room with an inch-high ceiling… let alone a room that an electron would have to stoop to enter.

  The fields beyond the hotel were open, and I spotted several groups of strollers. A raised restaurant terrace was attached to the side of the hotel, and a number of guests were lounging there. Not many of them were human.

  I made my way along a path towards the hotel entrance. A number of trees and bushes were planted on the grounds. They all branched endlessly into fantastic jumble of detail. I foolishly stuck a hand into one of the bushes, and it took me some minutes to disentangle myself. A huge jellyfish watched me blankly from a bench. I hurried on with a stiff nod.

  To my relief the staircase leading up to the hotel was finite. The lobby was dim and large, but not abnormally so. I walked over to the desk-man and blurted out the age-old question, “Where am I?”

  I spoke too loudly, and a number of the guests hanging around the lobby broke off their conversations to listen.

  The clerk seemed to be human, though a full black beard concealed most of his face. He was dressed in the 1900 style, and he peered at me through gold-rimmed spectacles with little oval lenses.

  “Where do you think you are?” He held a fountain pen poised over a little pad of paper, as if to record my answer.

  “Is…is this heaven?”

  The clerk made a quick notation. “Generally we call it Flipside. Flipside of Cimön.”

  The last name echoed in my ears. I’d really made it. If only I had read that pamphlet more carefully.

  “How did a fresher like you get here anyway?” the clerk broke in.

  “I flew.”

  He looked impressed. “Spontaneous? Not bad, not bad at all. I assume you want to climb Mount On?”

  “Not right away…” I began. For some reason this drew an amused smile. I let it pass. “What’s this hotel called?”

  “Hilbert’s Hotel.”

  The clerk’s clothes had already nudged my memory, and when I heard the hotel’s name my dream from the graveyard came back to me. David Hilbert. In his popular lectures he had often spoken of a hotel with alef-null rooms. Hilbert’s Hotel.

  I leaned towards the clerk in excitement. “Is he here?”

  “Professor Hilbert? You might see him at tea later…if you could find some clothes.”

  I realized that I was still naked and that everybody else was dressed. Suddenly I felt the pressure of many amused stares. I pinched my buttocks together defensively. “I don’t have any luggage…or anything…”

  I heard a gnashing and a twittering behind me and turned around, one hand over my genitals. A man-sized beetle was swinging itself quickly across the carpet towards me. Its two forelegs were raised and wa
ving, and streamers of fluid dripped from its mandibles. With a shriek I vaulted over the clerk’s counter.

  The beetle reached the counter and reared up against it. Two faceted eyes regarded me attentively, while a pool of viscous beetle-spit collected on the counter-top. “Do something,” I said to the clerk in a strained voice.

  He just chuckled and stepped aside so the beetle could see me better. Its forelimbs dipped in and out of the saliva repeatedly, forming tough silvery strands. Suddenly the beetle lost its footing and crashed back down to the lobby floor, pulling the wad of thickened spit along. I couldn’t see it then, but could hear its legs actively clicking.

  Cautiously I leaned across the counter to see what the creature was doing. All eight, or was it six, legs were darting around the silvery mass of spit-fibers. It looked as if it were spinning some sort of cocoon…perhaps to stuff me in while its larvae ate my flesh?

  “You ought to thank him, you know,” the clerk whispered to me. “His name is Franx.”

  “Thank him for what?”

  “For that suit he’s making you,” the clerk hissed.

  Just then the beetle finished. After a few seconds of vigorous rocking he got off his back and onto his feet. With a burst of twittering he laid a silvery jumpsuit out on the floor.

  I climbed back over the counter and slipped into the silky garment. It fit perfectly and sealed up the front at the touch of a hand. It even had pockets.

  I bowed stiffly. “Thank you, Franx. If there’s ever anything I can do for…”

  The twittering came again and I strained to understand it. It was actually human speech, flowery English, only speeded- up. After comprehending only a minute’s worth I already felt like I had heard the story three times. Someone…"some benighted xenophobe"…had thrown an apple at him. It had stuck in his back and begun to rot. He lifted his armor-like wing-cover to show me the spot. Could I scoop out the decaying apple and flesh?

  “I guess,” I said hesitantly. “If I had a spoon…”

  Franx sped across the lobby to where a woman in a black and white tailored silk suit was drinking a demitasse of coffee. She recoiled from him, and he snatched her cup from the low table in front of her. With his other forelimb he snagged a newspaper and came scuttling back to me.

  There was nothing for it but to scoop the diseased region out of the huge insect’s back. I dumped the foul-smelling globs onto the newspaper Franx had spread out, trying not to retch. I felt I was making a poor impression on the other guests, and I was relieved when I finished.

  The giant cockroach had kept a stoic silence during the operation. Now he turned himself slowly around to examine the mess on the paper. Still without a sound, he lowered his head and began to feed.

  I turned away. The clerk was looking at me levelly, expressionless behind the beard and glasses. “You’re a kind man, Mr…?”

  “Rayman,” I said, “Felix Rayman. Can you give me a room? I’m very tired.”

  “The hotel is full.”

  “That’s impossible,” I protested. “You have infinitely many rooms.”

  “Yes,” the clerk said, his teeth flashing deep in his beard. “But we have infinitely many guests as well. One in each room. How could we fit you in?”

  The question was not rhetorical. Once again he uncapped his pen to record my answer. I thought back to an Ion the Quiet story by Stanislaw Lem, and the answer was clear.

  “Make the person in Room 1 move into Room 2. Make the guy in Room 2 move into Room 3. And so on. Each guest moves out of his room and into the room with the next higher number. Room 1 is left empty. You can put me there.”

  The clerk made a rapid notation on his pad. “That’s fine, Mr. Rayman. If you’ll just sign the register while I make the arrangements…” He handed me a slim leather-bound volume and turned to speak into a microphone.

  I riffled through the register, noticing a famous name here and there among the alien scrawls. I found a blank page and signed my name. Wondering how many pages were left, I began trying to flip through to the end of the book.

  It soon became clear that there were infinitely many pages. I went into a speed-up and flipped past alef-null of them. There were still more. I peeled off alef-null more, and alef-null more again. There were still plenty of pages left.

  I began picking up clumps of pages, flipping faster and faster… The clerk stopped me by reaching over and closing the book.

  “You’ll never reach the end at that rate. There’s alef-one pages.”

  Behind me, Franx the giant cockroach had finished his little snack. I looked at him with revulsion. He had been eating his own rotten flesh.

  “Come, come,” he said, reading my expression. “In my father’s house are many mansions, eh? When in Rome, act like the roaches! Cannibalism bespeaks, after all, nothing but the highest regard for the feastee, shall I say…be he even my humble servant I.” He gave a squeal of laughter at his eloquence, and lowered his head to suck up the last drop of goo.

  Before I could sidle away he was talking again. “Have you already qualified for a Guide? No? Good luck to you. Now it’s not impossible to get a Guide, not logically ruled out, you understand…but the probability…I do assume you understand the theory of probability?”

  I really wished I could get away from him. His loud and colorful speech had drawn the attention of the whole lobby. “I’m a mathematician,” I said shortly.

  “A mathematician! How perfectly delightful. May I ask your area of specialization?”

  “I’m very tired.” I took a step away from him. “Perhaps later…”

  “Perhaps later it will be too late,” the beetle cried, interposing himself between me and the elevator. “There is zero probability of getting a guide. As a mathematician you understand. Not impossible, but zero probability. Nevertheless you wish to climb Mount On. I also have such ambitions. What a team we will make. Franx and Felix!” He shouted out our names so that the whole lobby could hear. I groaned, but he babbled on. “Felix and Franx. I am a poet, Felix, a visionary, a philosopher-king. And you…you are a good Samaritan, a mathematician, and more. Much, much more, but at the very least a mathematician with a specialization in…in…”

  He wasn’t going to stop until I told him. “Set Theory,” I said wearily. “Transfinite numbers.” I wished I had never accepted the jumpsuit.

  The beetle raised its forelimbs high and made a mock salaam. “My prayers have been answered,” he said. “Go in peace, my son. Render to no man evil for evil. Hold fast to that which…”

  With a lop-sided smile frozen on my face I strode over to the elevators.

  No. 10

  What is Milk?

  The elevator was run by a shrimp in a blue coat with brass buttons. At least it looked like a shrimp. It had its segmented tail curled under it and sat in a contoured bucket of what might have been consommé. Instead of elevator buttons there was simply a horizontal lever which the shrimp could ease back and forth with its feelers.

  I was still curious about how people could fit into those low rooms at the top of the hotel, and meant to ask about it. “I’m in Room 1…” I began.

  The shrimp’s squeaky voice interrupted. “Don’t tell the bellboys that! Thanks to you they had to move everyone!” He turned his head to stare at me with a black bead of an eye. “That suit you’re wearing looks like roach-spit,” he remarked after a time. The elevator had still not moved.

  I was rather hurt. I had thought I looked jet-setty. “How about running me up to the top,” I suggested.

  “Sure thing, sport.” The elevator had a glass door, and I watched the numberless hallways flicker past.

  “Why aren’t the ceilings getting lower?” I asked after a time.

  “You tell me,” the shrimp squeaked. We were speeding up and I had to keep regearing my thought processes to keep track of the floors strobing past. In many of them I saw people and creatures moving…creatures of every possible type. You can’t be exclusive if you have alef-null rooms to fill
. But the ceilings seemed to stay steady at 10 feet above the floor.

  “I guess there’s some sort of space distorter,” I said to the shrimp questioningly. “Something that makes everything keep shrinking its height as it moves up.”

  “And what’s going to happen on the top?” the shrimp shrilled knowingly. “Are we going to turn into Blondie and Dagwood?”

  I shook my head slowly. It didn’t seem like we could ever reach the top. The hotel had no roof, no last floor. If someone parachuted down on the hotel from above what would he see? I remembered the way my hand had stuck to that infinitely branching bush outside…

  Suddenly everything went black. I could hear the shrimp snickering somewhere nearby. “This is the top, Professor. Care to get out?”

  I groped around, unable to find the walls of the elevator. Was it the walls or my body which had disappeared? “Where are we?” At least my voice still worked.

  “Where do you think we are?”

  “No…nowhere.”

  “Right again,” the shrimp squeaked gaily. There was a huge lurch, the lights came back on and we were zipping back down past the alef-null floors of the Hilbert Hotel.

  I was shaken, and annoyed at the shrimp’s rudeness. The last straw was when he tickled my ear with a sharp feeler.

  “I’d like you a lot more on a skewer with mushrooms and onions,” I snapped. We rode the rest of the way down in silence.

  I got off at the floor above the lobby and quickly found my room. There was a bed with muslin-covered down quilt, a comfortable looking easy chair, an elegant walnut desk and a wash- stand. There was a red and blue oriental carpet on the floor and a few pictures on the walls.

  I shut the door behind me and walked over to the window, which gave onto the mountain. As far as I could see the steep meadows stretched up, interrupted regularly by bands of rock. Counting the stripes of rock I could make out many infinite stretches. Infinitely many infinite stretches, and infinitely many infinite stretches of infinite stretches. Climbing up there wasn’t going to be as easy as getting to the hotel.