White Light (Axoplasm Books) Read online

  “What did you say about white lights before?” I queried. “Red lights were dreamers, green lights were dead people, and white lights were what?”

  “People who have used inner discipline or trickery to dissolve their body and reform it somewhere else. It is relatively easy for humans to do – particularly if they inhale the smoke of fuzzweed. But I do not come from a race of drug-addicts. We are poets, mystics, philosopher-kings…”

  The frenzied tone was creeping back into his voice, and I cut him off. I was beginning to understand. “Stop me if I’m wrong, Franx, but I think I see what you’re so upset about. For all these hundreds of years here you never managed to go into the White Light.” He started to say something, but I talked louder, drowning him out. If I didn’t put it into words, he’d spend all day circling around the point. “Then on the Mountain it finally happened. You saw the light. You were the light. Your years of seeking finally paid off and you stepped into Heaven.” He nodded silently and I went on. “Maybe you liked it, and maybe you didn’t. But you came back. You materialized again, part-way up Mount On and as far from the Absolute as ever.”

  Franx’s legs were twitching, and he spoke in a choked whisper. “I wanted to stay there, Felix, I did. I’ve had enough. Time must have a stop. But now I’m scared, scared to go back. The Absolute is Everything, but it’s Nothing, too.”

  I ran my hand over the long curve of his back. “Does anyone ever go for good? To be with God?”

  The peak of Franx’s grief had passed and his legs were still again. His dry, expressionless eyes stared at me. I felt he was hiding something. “There’s no way to tell. People go white and disappear, but maybe they just rematerialize somewhere else in Cimön. After all, it’s infinite…”

  He was quiet for a minute, then with a visible effort began talking again in his usual convoluted way. “Anyway, the interesting thing about our two trips, the really marvelous thing is that you reached c and I reached alef-one. You conceived of all your possible lives, and grasped them as a unity. Fiat The Lives of Felix Rayman. Imprimatur and Nihil Obstat; Annie, get the TV Guide. No, don’t stop me, I have a point to make. The One and the Many, Felix. You saw the Many and I saw the One.” His voice cracked, but he pressed on. “I saw the One, I was the One, but then I clutched at it, tried to hold it. I – I killed it by looking, and ended up with alef-one.”

  “That’s called the Reflection Principle.”

  “Please elaborate. This is new to me.”

  “The Reflection Principle is an old theological notion which we use in Set Theory. Any specific description of the full universe of Set Theory also applies to some little set inside the universe. Any description of the Absolute also applies to some limited, relative thing.”

  Franx made a disappointed noise. “You’re just saying that the Absolute is unknowable. That’s the most elementary teaching of mysticism.”

  “Yes, but I still don’t think you see how it applies to Mount On. When you go white, and you are no longer really there, then there is no individual, and no conception of the Absolute. But the situation is unstable. The Absolute divides, tries to get outside itself, and wham, there’s a beetle looking at alef-one.”

  My mind felt very clear. For once Franx had nothing to add. We stared out of the arch at the deep blue sky, so clear and flawless.

  But there was something out there after all. A dark shape, rounded on top and with three smaller objects handing down from it. It was a Guide with three climbers.

  But he wasn’t flying up the mountain anymore. Instead he seemed to be moving away from the mountain, out and downward in a huge looping curve. Where were they going? I looked down past the stripes of cliff and meadow to the sea far, far below.

  The sea jutted out from the flat mountainside in a gentle curve, and I had the feeling that the Guide was taking these climbers there. But what was there? A sort of flickering orange light came from beyond the sea, but no matter how hard I squinted I could make out nothing more.

  Looking back at the sky near us I saw something else again…a bright spot which seemed to be moving straight towards us. Fast. Before I could duck there was a Whop and two arms were hanging from the bar across the arch. Two arms in the sleeves of a dark gray suit, with white cuffs peeping out. The arms swung gently to and fro.

  Franx hissed menacingly and backed slowly away from the arms, his mandibles spread and ready to snap. I followed his example, and we both backed down the tunnel.

  Suddenly more white light came flashing in on us. It stopped between the arms, grew irregular projections, darkened and solidified. Georg Cantor was standing there, his hands gripping the bar set into the archway. His piercing blue eyes took us in and he gave a small smile.

  “Felix Rayman and…perhaps I’ve seen you somewhere?”

  “My name is Franx,” the beetle said, then added proudly, “I climbed up here today, all the way to alef-one. And my sidekick here has a book with c pages right in his parka. Get it out, Felix, show him.” Sidekick, my ass. I began getting the book out while Franx rattled on. “Why don’t we just stand here and compare the book to the cliffs. We’ll straighten out your problem right now.”

  Cantor stiffened a little. “You’re referring to the Continuum Problem?”

  I held the book out towards him. I felt embarrassed. Franx’s suggestion seemed reasonable to me, but I was sure it had some stupid flaw which Cantor would cuttingly expose. “There’s c pages in here,” I said, smiling and nodding. “Franx was wondering why we couldn’t just try matching it up page by page with those cliffs out there…” I trailed off lamely.

  “Go ahead,” Cantor said finally. “Don’t let me stop you.”

  I went over to the edge and looked down. I was ready for it this time and felt no vertigo. I decided to move my eye up the cliff. I could fold down a page’s corner for every cliff I looked at. If every single corner was folded down by the time I finished, then I’d know that c is the same size as alef-null…that the Many can be reduced to the One.

  But it wasn’t so easy. My book had no first page and no last page. Wherever I opened it, I’d get another page, but there was never a next page. The sequence of cliffs, on the other hand, was perfectly well-ordered. Above every cliff or set of cliffs there was always a unique next cliff. The alef-one cliffs and the c pages were two different uncountable collections, each with its own natural ordering…and there was no obvious way to compare them. It was like dividing apples into oranges.

  Half-heartedly I went into a speed-up, but I gave up after awhile. To work through all alef-one cliffs I’d have to go white again. And I didn’t know how.

  “I can’t really handle uncountable sets,” I said handing the book to Cantor. “Can you…”

  He waved the book aside. “I’m through for the day. I’ll take you to Ellie’s instead. Come on.” He started walking down the tunnel.

  I had to trot to keep up with him. “Do you actually know the size of the continuum? Does the problem have a solution?”

  “For mathematicians it is very difficult,” he chuckled. “But mathematics is not everything, no? There is physics, there is metaphysics.” He was walking faster than ever, and I had to run to keep up. Franx was swinging along on the ceiling just behind us. Cantor went on, “If I were still on Earth I would carry out certain experiments, certain physical tests which could very well resolve the Continuum Problem.”

  I could hardly contain myself. “What tests? How would they work?”

  “The idea stems from my 1885 paper,” he said ofF-handedly. “If there were a third basic substance…in addition to mass and aether…then we would know that c has power at least alef-two. But this is Cimön, and here we stick.” He left it at that and redoubled his speed.

  I really couldn’t keep up with him anymore, and contented myself with running along behind him. I wondered what kind of experiment he meant. I made a special effort to fix the date 1885 in my mind. I’d have to look the paper up when I got back to Earth. If.

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nbsp; The walls of the tunnel flowed past as we ran along. It seemed farther than before. I always feel strange in tunnels. You’re walking or driving along as fast as you can and nothing seems to move. There’s always a circle around you, the light- strip, the curve ahead…a frozen pattern. You begin to feel that even if you spin the steering wheel nothing will happen. It’s only a game in a penny-arcade…

  No. 15

  High Tea

  When we were half-way through the thickness of Cimön, Cantor stopped by a round door set into the ceiling. The door was massive with a dial set into it. It looked like a safe.

  He gestured to the dial. “You are a mathematician, Dr. Rayman. Perhaps you can open the lock?”

  The dial had only ten markings, labelled zero through nine. I jumped to the conclusion that the combination would be a string of alef-null digits, the decimal expansion of some real number. But which real number?

  I reached up and spun the dial slowly clockwise, pressing one hand against the door. I felt a tumbler fall at 3. I reversed the direction and inched the dial counterclockwise. Another tumbler clicked at 1. There is only one familiar real number that starts with a three and a one. If my guess was right the rest would be easy.

  “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.” I recited this slowly, moving the dial back and forth. The phrase is a well-known mnemonic for remembering the first fifteen digits of pi. You list the number of letters in each word to get 3.14159265358979. A tumbler clicked with each digit. It was pi for sure. I went into a speed-up.

  An easy way to get the full decimal expansion of pi is to sum up a special infinite series: 4/1 − 4/3 + 4/5 − 4/7 + 4/9 − 4/11 +… I started adding and dialing in the digits as they developed. It took me a couple of minutes and my neck got stiff from staring up at the dial.

  Finally I finished. There was a satisfying thok inside the heavy door. Another free game. I pushed and the door swung open. My arms were tired from reaching up, and I let them fall.

  “Very good,” Cantor said. “It’s a thousand meters up.” I peered into the dim shaft. I could make out metal rungs on the side of a body-sized tube. I wondered how we would be able to make the climb. A thousand meters straight up is no joke for a man Cantor’s age. I said something to this effect, but he assured me that as the gravity shifted the climb would get easier.

  If Franx was impressed by my feat he hid it pretty well. While Cantor and I talked, the beetle scrambled up my back and through the door – as if I were a turkey-bone leaning against a garbage can. Cantor took my arm.

  “Where did he latch onto you?”

  “Franx?” I said, stepping back with an upward glance. I could hear him scuttling away some fifty feet up. He was still my only friend here – even though he had been acting so strangely. “He’s from a place called Praha. We hooked up at Hilbert’s Hotel and climbed to epsilon-zero together. I breathed in some fuzzweed there, whited out through Dreamland and regained form at the Library. Meanwhile Franx kept flying up Mount On. He saw the One, merged in, and then used the Reflection Principle to get to alef-one. I think he’s upset that he couldn’t stay white.”

  “He could if he really wanted to,” Cantor observed. “It’s just across the Desert.” No more was forthcoming, so I went ahead. He closed the door behind us.

  The walls of the tube were metal, and the only light was what flickered through the occasional porthole cut out of the metal to expose the glowing ice of the Dreamland glacier. Our feet echoed against the rungs, and conversation was impossible. I wondered if the whole inside of the Cimön slab was made up of the crystalline dream-stuff.

  As Cantor had promised, the climb became steadily easier. Although the tube was perfectly straight, it soon felt like it was inclined towards the horizontal.

  I could see Franx far ahead when he would pass one of the light spots, and to keep up with him I had to climb without resting. The necessary movements were simple and repetitive. My body was running on automatic. Cantor followed some twenty feet behind me.

  When the rungs finally ended it took me a second to notice it. The tube had widened and turned into a carpeted staircase. I crawled up several steps before I realized that I could walk up the stairs. Franx was crouched before a door at the head of the stairs. “Felix,” he called, “Could you trouble yourself to ask your fellow mathematician what…”

  Cantor’s footsteps on the stairs behind me stopped. “Ring.”

  The staircase was carpeted with a red and blue runner held in place by brass rods. The walls and ceiling were panelled in dark wood, and the lighting was provided by candle sconces set into the wall.

  My head was clearing from the long drudgery of the climb. Franx was still turning himself laboriously around when I reached the top of the stairs. I reached over him to push the buzzer by the door.

  Rapid footsteps approached and the door swung open. It was a skeletal woman in a gray silk dress. Lots of jewelry: diamonds, platinum. I assumed that she was old, but it was hard to be sure. The sutures of her skull showed on her forehead and temples, and her gums had drawn far back from her teeth. The knobs of her knees looked like galls on weedstems.

  “Hello, Georg!” she said in a light, thin voice. “It’s good to see you’re safely back from Flipside. I’m sure you’re full of new ideas…and much more.” Her gaze fell on me. Her eyes had a strange sparkle to them.

  “This is Dr. Felix Rayman,” Cantor said, “and…”

  “My name is Franx,” the beetle interrupted, perhaps worrying that he would not be introduced.

  “And this is Madam Elizabeth Luftballon,” Cantor concluded.

  She smiled and stepped back. “Just call me Ellie. And come on in. I adore meeting Georg’s students.” She flashed me a special smile. Despite her withered state there was something charming about her. Her smile’s perfect curves and ideal symmetries reminded me of a candied slice of lemon.

  Cantor led us past her and into a room off the hall. It was furnished something like Hilbert’s Hotel had been, with oriental carpets and handsome antiques. There were also a number of musical instruments. Piano, violin, harpsichord.

  A mullioned picture window gave onto a changing view like I had seen at the Library of Forms. Dreamland. I stared out for a minute, then turned back to the room.

  Cantor was exchanging a few low words with Ellie at the door, and Franx was sniffing around. Apparently they had expected company. There was a spindly-legged little table holding tea things and a beautiful Schwarzwaldtorte.

  “It’s starting again,” Franx twittered to me. A leg twitched in anxiety.

  “What is.” I drifted towards the cake. It was mostly whipped cream, and was decorated with curled shavings of chocolate.

  I was ready to eat some Cimön food.

  Franx dogged my steps, his voice shrill with anxiety. “Your prophecies are coming true again. I read all this. This room, this cake, these words, and again a horrible death draws near on whispering wings!”

  Didn’t he ever think about anything but himself? I was hoping to have some interesting conversation with Cantor here, and now Franx was ready to pull another freak-out. I turned and snapped. “Do something that’s not in the script. Something unexpected. And if you can’t it’s just too bad. Keep bugging me and I’ll pound your head in.”

  Before I had quite finished he screeched, “Free,” and sprang up at me. I flinched, lost my footing, and fell backwards with a strangled cry. On my way down I caught the tea-table with my elbow. It splintered and the tea and cake went flying.

  “That wasn’t in the script,” Franx piped happily. I ignored him and sat up. Ellie had disappeared, but Cantor was standing in the door, watching us with an alert, interested expression.

  I began gathering up the scattered tea-things. The rugs were soft and nothing but the table had broken, but hot tea and whipped cream were everywhere. Franx lost no time in burying his face in the smashed cake.

  “Sorry,” I said, rising.
“I hope…”

  Cantor cut me off with a wave of his hand. “It makes nothing. Ellie is happy to have guests.” He raised his voice suddenly and called out, “Ellie! We’ve had an accident! Please bring more tea and clean cups!”

  Franx was eating the last crumbs and smears off the floor. Cantor walked over and gave him a sharp nudge with his foot. “Hey! Do you want some tea?”

  At the unfriendly touch, Franx spun around with a warning hiss. But then he remembered his manners and chirped, “Yes, please. In a bowl with milk and perhaps a crust of bread. Preferably a blue china bowl.”

  Cantor relayed the request. I took off my shoes and parka and sat down cross-legged on a purple couch with large velvet cushions. Outside the window, a pattern of colored lines was arranging itself into the envelope of a helix. A spot of red light hovered nearby. The helix solidified and began hopping about like an animated bedspring. More helices appeared, and they began dancing with each other…

  “What is that out there?” I asked Cantor. He had seated himself in a massive easy chair, and Franx lay on the floor, one eye on the window and one eye on us. I hoped that he wouldn’t feel the need to do anything unexpected for awhile. The helices had turned into tentworms and were surrounding the spot of light with colored websheets.

  “Those are the dreams,” Cantor said in his deep voice. “The spots of red light are the dreamers.”

  “That’s what everyone keeps telling me. But does that mean that the spots of light are creating the whole…” I broke off, groping for a word. The colored tent had grown in size. There was a hole in the side, and you could see the spot of red light moving tenderly up and down the body of a huge, moist grubworm.

  “Felice!” Franx exclaimed, moving towards the window with a start. “My precious one!” The white grub’s body rippled, and a sort of mouth extruded from its near end. The spot of ruby light hovered there like a bee at a flower. Franx had reared up against the window now and was twittering incomprehensibly. A pair of erectile hairs protruded from his rear. A big drop of milky fluid slid along them, hung trembling, dripped onto the rug.