White Light (Axoplasm Books) Read online

  “I’m going to be working with Nick DeLong. Come by his lab tomorrow afternoon and we might have something interesting to show you.”

  “I’ll be there.” He was off with a jaunty wave of his grade-book.

  * See The Selected Writings of C.H. Hinton, Dover Publications.

  No. 25

  The Banach-Tarshi Decomposition

  Nick’s office was the size of a broom-closet, but he had access to a well-equipped laboratory. The government had bought them all the best equipment in return for a contract assigning them the rights to any inventions. They thought the Bernco Physics department was developing anti-pollution devices. The Physics department thought Nick was doing publishable research. And Nick had all the toys he’d ever wanted.

  I found him at work on one of his experiments. The lights were dimmed, and he was studying the screen of a small oscilloscope, his arms elbow-deep in a tub of viscous liquid. I looked into his vat. There were wires in there, arrangements of glass tubing, and several evilly glowing little pyramids. What seemed to be a miniature steam engine was pumping away at the bottom.

  “Charles calls this my fondue chinoise,” Nick said without looking away from the oscilloscope. Suddenly the green squiggle locked into a stable saw-tooth curve. He gave a sigh of satisfaction. “That ought to hold for a half-hour.” He drew out his dripping bare forearms and went over to a sink to wash the stuff off.

  “Is that cooking oil, Nick?”

  “God, no. It’s liquid Teflon. Only stuff that has the right density and non-conductivity.” He dried off his arms and rolled his sleeves back down. “You said you had an idea?”

  Before I could answer, a red light began blinking at the other end of the table. “Hold on,” he said. “The laser’s warmed up.”

  He walked over and threw a switch. A pattern of glowing ruby lines sprang into life and hovered over the table. A system of mirrors and beam-splitters was arranged to weave a cat’s cradle out of his laser beam. The final knot rested on a thin quartz window in the side of his vat.

  Nick stepped with quick, sure steps to the wall, threw another switch, and something under the table began to hum. It sounded like a fan. A strange prickling feeling swept over me, and my hair tried to stand on end.

  “An air-ionizer,” Nick commented. “Can’t hurt to try it.” The green saw-tooth pattern held steady on the oscilloscope screen, and the tangle of light-beams glowed evenly on the table top. Nick threw one more switch and sat down heavily.

  “This run’ll take a half-hour. It’s on automatic.”

  “What exactly are you testing for?”

  “As you know from my paper, I’m working on a hypermatter theory.” I hadn’t read Nick’s paper very closely, but I nodded him on. “My idea is that there’s a different type of matter…gobs of invisible jelly floating around. That net of laser beams is supposed to herd the globs into the vat, and the little engine at the bottom is to condense them. The rest of the stuff is just to detect the condensed globs of hyper-matter.”

  “Bloogs,” I said.

  “What?”

  “Think of black water, think of white sky. Think of an island with bloogs blowing by,” I recited. “That’s from Dr. Seuss. You’re looking for bloogs!”

  “I guess you could say that,” Nick said. “Though I wouldn’t want to advertise the fact.” The connection struck him then. “Didn’t you claim you’d seen lots of bloogs when you were out of your body?”

  I nodded. “And I’ve learned how to control it.” I reached out to feel Nick’s consciousness, his learning and loneliness. I held the Manyness and made it One, then snapped back with a twist that left my astral body outside my physical body. I looked around the room. There was a little herd of bloogs clustered around a cabinet across the room.

  I flew over to them and tried to sweep them towards Nick’s fondue. The first time I tried, my hand went right through them. I made myself denser and smaller, tried again. This time there was a slight resistance as I slid through the bloogs. They had moved imperceptibly. I pushed through them over and over…combing them along.

  I went into a speed-up then, and after alef-null nudges I had forced six of the little gray bloogs through the window in Nick’s vat. It took me a couple of minutes. When I was done I merged bodies and told Nick.

  He bent over his equipment, his face lit by the dim dials. He turned a knob quickly, reexamined the meters, then broke into a grin. “You really did it, Felix! These are the best readings I’ve gotten yet!”

  I sat back with a smile. “I can get you all the bloogs you want, Nick.”

  Suddenly his smile faded. “But what good will it do? If anyone tries to reproduce my data it won’t work…unless you’re there. And if I tell them that, they’ll just write me off as a crazy psionics researcher.” Gloomily he ran his fingers through his thinning blond hair. “I’m crazy anyway to take your stories seriously. Maybe you can get away with it, Felix, but I can’t.”

  My mind was racing ahead, exploring the possibilities. What Nick needed was some physical proof of his theory. Physical proof which was accessible to everyone. And I, too, needed proof. Physical proof that infinity exists. Maybe…

  “Nick,” I said, leaning forward, “How good is that condenser you’ve got in there? I mean, if I shovelled in enough bloogs would you be able to get a chunk of aether…of hypermatter…big enough and solid enough for everyone to see?”

  Nick shrugged. “I don’t see why not. It would take an awful lot of…of bloogs, though. And I’m not sure if the hyper-matter would look that different from ordinary matter.”

  “Sure it would,” I said excitedly. “It would be made of alef-one particles so it would be possible to cut it into alef-null chunks which were big enough to see.” I jumped to my feet. “That’s it, Nick! We get a cube of the stuff and I’ll cut it into infinitely many slices. Let them try to write that off as experimenter bias!”

  We worked all afternoon. After I’d rounded up all the bloogs floating around the laboratory, Nick had the idea of my looking in the furnace downstairs. There were plenty of big ones there, and I brought them up through the floors one by one. When it was suppertime we called up our wives and arranged to meet at the local pizza parlor.

  Nick did most of the talking at dinner. He was fantasizing about a Nobel prize for the two of us. “They couldn’t fire me then” he gloated, ordering another pitcher of beer.

  April and Jessie were lively, happy to be out on a Friday night. They discounted Nick’s optimistic predictions, but were glad to see us working. Iris pounded happily on her slice of pizza, occasionally nibbling at the crust.

  I was kind of tired. Several times I thought I heard Kathy’s voice…somewhere inside me. It took a little effort to keep my bodies together. I kept forgetting which person at the table was me.

  We ate and drank for an hour, then all went over to our house to listen to records. There was more beer and some grass. The evening ended in a confused jumble. I fell asleep as soon as I lay down.

  I had the same dream again that night, or rather a new installment. This time the Devil stops laughing and sinks his teeth into the package he’s holding. The styrofoam makes a snapping noise, and the meat twitches. He jumps into that crack in the ground. I lean forward to see, and Jesus kicks me in after.

  I’m hurtling down past solid screams and hoarse light. Somehow it’s the Devil’s mouth, his throat. Kathy is there, falling too. Her smile is crazy and she locks her legs around my back, riding me like a nightmare.

  Ahead there’s something like the negative of a fire. All the heat and light are streaming into it…flowing out of everything and into that absolute black plexus in Satan’s belly.

  For the first time I remember what it was like to fall into the White Light at Nothing. But the memory slides away. Flames shoot out of my fingers, black flames, and we spiral around the heart of darkness.

  There are others there. They are turned inside out, with festoons of veins and organs decorating them li
ke grisly Christmas trees. Kathy is still clinging to my back, and I can’t turn my head enough to see her.

  I have the feeling that there is some trick of perspective, some four-dimensional reversal I can pull to put everything right…turn the people back, make the light flow out, turn black to white. I struggle, knowing that if I stop trying I’ll never start again.

  I woke up feeling like I hadn’t slept at all. It was Saturday. April and Jessie had decided to spend the day shopping, and I was supposed to take care of Iris.

  When the women had gone, Nick came over, and the three of us went back down to the lab. We had the building to ourselves. We laid some desks on their sides and pushed them together to make a sort of pen for Iris. She didn’t like it at first, but we kept giving her more things to play with until she quieted down. It was a box of brass weights that finally did the trick.

  When Nick had finished tuning up his equipment, we got back to work. There were fresh bloogs all over the laboratory…especially near the spot where the radioactive materials were stored. When these were gone, we opened all the windows and turned the thermostat up to eighty to keep the furnace going.

  I spent all morning stuffing bloogs into Nick’s condenser. My physical body climbed into the pen with Iris and fell asleep… much to the baby’s delight. Around noon Nick said he thought we had enough.

  For some reason I had a little trouble getting back into my body. There were some odd, unfamiliar thoughts in my brain which I had to push away to make room for me. When I had bonded in, I picked up Iris and went over to the vat of Teflon to see what we had. The liquid had been clear before, but now it was turbid with thousands of little specks. We hoped they were congealed aether.

  We stirred it up good and siphoned the stuff off into an empty plastic tub to settle. While we were waiting, we went up to Sammy’s for hamburgers. The same old fat waitress was there. She pretended to be feeding Iris, but kept eating her french fries. We all pretended we didn’t notice. Iris wasn’t very hungry, and she put her hamburger down for a nap in my lap.

  When we got back to the lab there was a nice film of sediment covering the bottom of the white plastic tub. We siphoned the liquid Teflon off from the top and poured the sediment into a little glass beaker. The stuff had an incredibly slippery feel to it. Nick got a water-powered porcelain suction filter from the chemistry lab, and we strained the rest of the Teflon out of the sediment.

  We dumped the sediment out onto a sheet of paper. It looked something like graphite…a gray slippery powder, fine beyond imagining.

  “I wonder what it is,” Nick said, rubbing some between thumb and forefinger.

  “Aether,” I said. “Hyper-matter. Concentrated bloog.”

  He sniffed a pinch of it doubtfully. “I don’t know. I’ve got a bad feeling this is just carbon or some crap like that.”

  “Let’s heat it up,” I suggested. “Maybe we can fuse it.”

  Nick found a little porcelain crucible. We filled it with the gray powder and let it reach white heat over the burner. After a few minutes of that I tonged the cover off the little crucible and carefully tipped it over.

  A perfect shiny sphere rolled across the table. Iris was watching from across the room. She stretched her hand out and shouted, “Mine!”

  It was too hot to touch, and we took turns poking at it with the tongs. In the process of melting, the powder had drawn itself into what looked like a geometrically perfect sphere. A big ball-bearing.

  There was an insistent hammering from the building’s front door. I went downstairs to investigate. It was Stuart. I had forgotten that I’d asked him to come over today. I let him in and led him upstairs.

  “The mad alchemists,” Stuart remarked as he looked around the dim lab.

  “Look at this,” Nick said, walking over with our shiny new sphere. His voice was loud with excitement. “We think this might be a new substance.”

  At the same moment Stuart and I reached to take it from Nick. Our three hands fumbled against each other, and the precious little ball escaped. But it didn’t fall.

  It just hung there in the air. It was immune to gravity. It had inertia…a heft to it…but the gravitational field didn’t affect it at all.

  Nick was ecstatic. “My God!” he exclaimed. “Just hanging there, that little ball wipes out Einstein’s General Theory of Relativity. And think of the applications!”

  Stuart rested his finger on the ball and it sank down. “It still won’t hold anyone up,” he complained.

  “But imagine an airplane with no gravitating mass,” Nick babbled. “Think of the fuel savings!”

  Iris was pointing at the ball and screaming, so I went and lifted her out of her pen. But before I could give her the little ball of hyper-matter, Nick grabbed it and ran across the laboratory.

  “I knew it!” Nick cried a moment later. “It’s a superconductor too!”

  Stuart raised his eyebrows at me questioningly. He had spent a lifetime avoiding physics. “He means that it doesn’t have any electrical resistance,” I explained. “So you could start a current in a loop of it, and it would flow forever. Makes a good magnet.”

  Iris was screaming so loud that it was hard to talk. “Come on, Nick,” I said. “Let Iris have the ball.”

  Grudgingly Nick unhooked his meter from the shiny little treasure and brought it over. Iris snatched it greedily and squeezed it in her fat little hand.

  “Ball!” she cried, waving her arm wildly. Suddenly her hand opened and the ball flew across the room. It smacked into the wall and seemed to shatter.

  “Oh no!” Nick screamed, his voice cracking. He was a little over-excited.

  “Take it easy, Nick. We can always melt it again.”

  The ball had broken into two pieces, which had recoiled off the wall and were drifting back across the room.

  “Ouch,” Stuart said, snagging one. “It’s prickly.” He set it down on the table and I leaned over to examine it.

  The piece was a sphere like before, but with some parts missing. It looked something like a cockle burr or a sycamore ball. A collection of radii emanating from a central point. It was not completely even in texture. Here and there the radii were clustered more densely, and the surface had a shadowy sort of pattern like the globe map of some alien world.

  Nick caught the other piece and brought it over. It looked quite similar…an airy sphere of the same size with dense spots where the first piece had light spots. It was like a negative of the first piece.

  “Maybe we can just slide them together,” Stuart suggested. Something occurred to me and I stayed his hand. “How about a little Banach-Tarski action, Stuart? Two for the price of one!”

  Stuart knew what I was talking about and grinned appreciatively. “Piece A and piece B,” he said, touching the two in turn.

  I slipped my shoe off and smashed it down on the two little balls as hard as I could.

  Nick screamed a hoarse, “No!” and flung himself onto the table to catch the pieces that skittered out. Four of them.

  “Are you guys nuts?” he cried, lining up the four pieces and cupping his hand protectively over them.

  “Come on, Nick,” Stuart said. “Let’s have a look.”

  Nick moved his hand aside a little, and we leaned over the pieces. There were four little prickly spheres now, all the same size as before. Two looked exactly like piece A, and two looked exactly like piece B.

  “Bleaze broceed viz za demonztration, Brrofesszor Rrrayman,” Stuart said in his best Polish accent.

  Iris was tugging at my pants, so I set her on the table to watch. “Don’t worry, Nick,” I said, reaching for the four pieces. “I’ll put them together now.”

  “Do you think they’ll go back to the one ball?” he asked anxiously?”

  “Eefen batter,” Stuart intoned.

  “Ball, ball, ball, ball,” Iris chanted.

  I picked up one of the A’s and one of the B’s, turning them so that the denser areas on the one were in the same relativ
e position as the lighter areas on the other. Then I began pressing them against each other.

  The spines meshed, and for a minute the pieces would go no closer. I kept pushing and gently jiggling them. Suddenly it worked. The two pieces slid into each other and locked together to make a perfect solid shiny ball like before.

  I handed it to Iris, who chirped a bright, “Nanks!” Then I put the other two pieces together to make another perfect sphere. I gave it to Nick. We had broken the original sphere into four pieces and reassembled the four pieces to produce two spheres identical to the original one.

  “Why don’t you mathematicians let me in on the secret,” Nick said, wonderingly hanging his ball in the air.

  “It works because the hyper-matter sphere has uncountably many points,” I said. “Ordinary mass-objects only have alef-null points, but aether objects have alef-one. In 1924 Banach and Tarski proved that any such sphere can be broken into a finite number of pieces…which can then be reassembled to make two spheres identical to the original one. By Raphael Robinson’s 1947 refinement of their proof, we know that only four pieces are necessary.”

  “You guys are really serious aren’t you?” Stuart said, dropping his accent. “Why don’t you fill me in on the details?”

  “O.K.” I said. “How about adjourning to the Drop Inn?”

  “I’m ready,” Nick exclaimed. “Jesus! We may never have to work again.”

  No. 26

  Bloody Chiclets

  The Drop Inn is a square room…say forty feet on a side…with a bar along one side of it. The floor is dirty gray asphalt tile, except for a big strip of bare concrete the owner never got around to covering. There’s a plate-glass window next to the sidewalk. If you like, you can sit there, a spectacle for the Bernco shoppers.

  The bar-stools were mostly full, and the four of us took the window table. Nick went up to the bar to get a pitcher of beer and an orange-drink for Iris. I wasn’t sure if she was allowed to be there…in New York State you never know if you’re breaking a law. I felt pretty limp from my hangover, my bad sleep, and all the speed-ups I’d run to get enough bloogs into the condenser. Limp but happy.