The Year's Best Science Fiction 10 - [Anthology]

by Edited By Judith Merril

  Ted Anderson was our metamathematician. He’s about half a nonosecond behind Ephraim Cohen (the co-inventor of BC-flight) and has about six nervous breakdowns a month trying to pass him. But he’s got the best practical knowledge of the BC-drive outside Princeton—if practical knowledge means anything with respect to a pure mathematical abstraction.

  And me—topologist. A topologist is a man who can’t tell a doughnut from a cup of coffee. (I’ll explain that some other time.) Seriously, I specialize in some of the more abstruse properties of geometric structures. “Did Galois discover that theorem before or after he died?” is a sample of my conversation.

  Sure, mathenauts are mathenuts. But as we found out, not quite mathenutty enough.

  The ship, the Albrecht Dold, was a twelve-googol scout that Ed Goldwasser and I’d picked up cheap from the N.Y.U. Courant Institute. She wasn’t the Princeton I.A.S. Von-Neumann, with googolplex coils and a chapter of the D.A.R., and she wasn’t one of those new toys you’ve been seeing for a rich man and his grandmother. Her coils were DNA molecules, and the psychosomatics were straight from the Brill Institute at Harvard. A sweet ship. For psychic ecology we’d gotten a bunch of kids from the Bronx College of the New York City University, commonsense types—business majors, engineers, pre-meds. But kids.

  I was looking over Ephraim Cohen’s latest paper, Nymphomaniac Nested Complexes with Rossian Irrevelancies (old Ice Cream Cohen loves sexy titles), when the trouble started. We’d abstracted, and Goldwasser and Pearl had signaled me from the lab that they were ready for the first tests. I made the Dold invariant, and shoved off through one of the passages that linked the isomorphomechanism and the lab. (We kept the ship in free fall for convenience.) I was about halfway along the tube when the immy failed and the walls began to close in.

  I spread my legs and braked against the walls of the tube, believing with all my might. On second thought I let the walls sink in and braked with my palms. It would’ve been no trick to hold the walls for awhile. Without the immy my own imagination would hold them, this far from the B.C.N.Y. kids. But that might’ve brought more trouble —I’d probably made some silly mistake, and the kids, who might not notice a simple contraction or shear, would crack up under some weirdomorphism. And if we lost the kids . . .

  So anyway I just dug my feet in against the mirage and tried to slow up, on a surface that no one’d bothered to think any friction into. Of course, if you’ve read some of the popular accounts of math-sailing, you’d think I’d just duck back through a hole in the fiftieth dimension to the immy. But it doesn’t work out that way. A ship in BC-flight is a very precarious structure in a philosophical sense. That’s why we carry a psychic ecology, and that’s why Brill conditioning takes six years, plus, with a PhD. in pure math, to absorb. Anyway, a mathenaut should never forget his postulates, or he’ll find himself floating in 27-space, with nary a notion to be named.

  Then the walls really did vanish—NO!—and I found myself at the junction of two passages. The other had a grabline. I caught it and rebounded, then swarmed back along the tube. After ten seconds I was climbing down into a funnel. I caught my breath, swallowed some Dramamine, and burst into the control room.

  The heart of the ship was pulsing and throbbing. For a moment I thought I was back in Hawaii with my aqualung, an invader in a shifting, shimmering world of sea fronds and barracuda. But it was no immy, no immy—a rubber room without the notion of distance that we take for granted (technically, a room with topological properties but no metric ones). Instrument racks and chairs and books shrank and ballooned and twisted, and floor and ceiling vibrated with my breath.

  It was horrible.

  Ted Anderson was hanging in front of the immy, the isomorphomechanism, but he was in no shape to do anything. In fact, he was in no shape at all. His body was pulsing and shaking, so his hands were too big or too small to manipulate the controls, or his eyes shrank or blossomed. Poor Ted’s nerves had gone again.

  I shoved against the wall and bulleted toward him, a fish in a weaving, shifting undersea landscape, concentrating desperately on my body and the old structure of the room. (This is why physical training is so important.) For an instant I was choking and screaming in a hairy blackness, a nightmare inside-out total inversion; then I was back in the control room, and had shoved Ted away from the instruments, cursing when nothing happened, then bracing against the wall panels and shoving again. He drifted away.

  The immy was all right. The twiddles circuits between the B.C.N.Y. kids and the rest of the Dold had been cut out. I set up an orthonormal system and punched the immy.

  Across the shuddering, shifting room Ted tried to speak, but found it too difficult. Great Gauss, he was lucky his aorta hadn’t contracted to a straw and given him a coronary! I clamped down on my own circulatory system viciously, while he struggled to speak. Finally he kicked off and came tumbling toward me, mouthing and flailing his notebook.

  I hit the circuit. The room shifted about and for an instant Ted Anderson hung, ghostly, amid the isomorphomechanism’s one-to-ones. Then he disappeared.

  The invention of BC-flight was the culmination of a century of work in algebraic topology and experimental psychology. For thousands of years men had speculated as to the nature of the world. For the past five hundred, physics and the physical sciences had held sway. Then Thomas Brill and Ephraim Cohen peeled away another layer of the reality Union, and the space-sciences came into being.

  If you insist on an analogy—well, a scientist touches and probes the real universe, and abstracts an idealization into his head. Mathenautics allows him to grab himself by the scruff of the neck and pull himself up into the idealization. See—I told you.

  Okay, we’ll try it slowly. Science assumes the universe to be ordered, and investigates the nature of the ordering. In the “hard” sciences, mathematics is the basis of the ordering the scientist puts on nature. By the twentieth century, a large portion of the physical processes and materials in the universe were found to submit to such an ordering (e.g.: analytic mechanics and the motions of the planets). Some scientists were even applying mathematical structures to aggregates of living things, and to living processes.

  Cohen and Brill asked (in ways far apart), “If order and organization seem to be a natural part of the universe, why can’t we remove these qualities from coarse matter and space, and study them separately?” The. answer was BC-flight.

  Through certain purely mathematical “mechanisms” and special psychological training, selected scientists (the term “mathenaut” came later, slang from the faddy “astronautics”) could be shifted into the abstract.

  The first mathenautical ships were crewed with young scientists and mathematicians who’d received Tom Brill’s treatments and Ephraim Cohen’s skullcracking sessions on the BC-field. The ships went into BC-flight and vanished.

  By the theory, the ships didn’t go anywhere. But the effect was somehow real. Just as a materialist might see organic machines instead of people, so the mathenauts saw the raw mathematical structure of space—Riemann space, Hausdorf space, vector space—without matter. A crowd of people existed as an immensely complicated something in vector space. The study of these somethings was yielding immense amounts of knowledge. Pataphysics, patasociology, patapsychology were wild, baffling new fields of knowledge.

  But the math universes were strange, alien. How could you learn to live in Flatland? The wildcat minds of the first crews were too creative. They became disoriented. Hence the immies and their power supplies—SayCows, Daught-AmRevs, the B.C.N.Y. kids—fatheads, stuffed shirts, personality types that clung to common sense where there was none, and preserved (locally) a ship’s psychic ecology. Inside the BC-field, normalcy. Outside, raw imagination.

  Johnny, Ted, Goldy and I had chosen vector spaces with certain topological properties to test Goldy’s commercial concept. Outside the BC-field there was dimension but no distance, structure but no shape. Inside—

  “By Riemann’s tensors!�
� Pearl cried.

  He was at the iris of one of the tubes. A moment later Ed Goldwasser joined him. “What happened to Ted?”

  “I—I don’t know. No—yes, I do!”

  I released the controls I had on my body, and stopped thinking about the room. The immy was working again. “He was doing something with the controls when the twiddles circuit failed. When I got them working again and the room snapped back into shape, he happened to be where the immy had been. The commonsense circuits rejected him.”

  “So where did he go?” asked Pearl.

  “I don’t know.”

  I was sweating. I was thinking of all the things that could’ve happened when we lost the isomorphomechanism. Some subconscious twitch and you’re rotated half a dozen dimensions out of phase, so you’re floating in the raw stuff of thought, with maybe a hair-thin line around you to tell you where the ship has been. Or the ship takes the notion to shrink pea-size, so you’re squeezed through all the tubes and compartments and smashed to jelly when we orthonormalize. Galois! We’d been lucky.

  The last thought gave me a notion. “Could we have shrunk so we’re inside his body? Or he grown so we’re floating in his liver?”

  “No,” said Goldy. “Topology is preserved. But I don’t —or, hell—I really don’t know. If he grew so big he was outside the psychicecology, he might just have faded away.” The big pataphysicist wrinkled up his face inside his beard. “Alice should be required reading for mathenauts,” he muttered. “The real trouble is no one has ever been outside and been back to tell about it. The animal experiments and the Norbert Wiener and Wilbur on the Paul R. Halmos. They just disappeared.” “You know,” I said, “You can map the volume of a sphere into the whole universe using the ratio: Ir: R equals R:Or, where Ir and Or are the inside and outside distances for the points. Maybe that’s what happened to Ted. Maybe he’s just outside the ship, filling all space with his metamath and his acne?”

  “Down boy,” said Goldwasser. “I’ve got a simpler suggestion. Let’s check over the ship, compartment by compartment. Maybe he’s in it somewhere, unconscious.”

  But he wasn’t on the ship.

  We went over it twice, every tube, every compartment. (In reality, a mathenautic ship looks like a radio, ripped out of its case and flying through the air.) We ended up in the ecology section, a big Broadway-line subway car that roared and rattled in the middle of darkness in the middle of nothing. The B.C.N.Y. kids were all there—Freddi Urbont clucking happily away to her boy friend, chubby and smily and an education major; Byron and Burbitt, electronics engineers, ecstatic over the latest copy of C-Quantum; Stephen Seidmann, a number-theory major, quietly proving that since Harvard is the best school in the world, and B.C.N.Y. is better than Harvard, that B.C.N.Y. is the best school in the world; two citizens with nose jobs and names I’d forgotten, engaged in a filthy discussion of glands and organs and meat. The walls were firm, the straw seats scratchy and uncomfortable. The projectors showed we were just entering the 72nd Street stop. How real, how comforting! I slid the door open to rejoin Johnny and Ed. The subway riders saw me slip into freefall, and glimpsed the emptiness of vector space.

  Hell broke loose!

  The far side of the car bulged inward, the glass smashing and the metal groaning. The CUNYs had no compensation training!

  Freddi Urbont burst into tears. Byron and Burbitt yelled as a bubble in the floor swallowed them. The wall next to the nose jobs sprouted a dozen phallic symbols, while the seat bubbled with breasts. The walls began to melt. Seidmann began to yell about the special status of N. Y. City University Honors Program students.

  Pearl acted with a speed and a surety I’d never have imagined. He shoved me out of the way and launched himself furiously at the other end of the car, now in free fall. There he pivoted, smiled horribly and at the top of his lungs began singing “The Purple and the Black.”

  Goldy and I had enough presence of mind to join him. Concentrating desperately on the shape and form of the car, we blasted the air with our devotion to Sheppard Hall, our love of Convent Avenue and our eternal devotion to Lewisohn Stadium. Somehow it saved us. The room rumbled and twisted and reformed, and soon the eight of us were back in the tired old subway car that brought its daily catch of Beavers to 139th Street.

  The equilibrium was still precarious. I heard Goldwasser telling the nose jobs his terrible monologue about the “Volvo I want to buy. I can be the first to break the door membranes, and when I get my hands on that big, fat steering wheel, ohh!, it’ll be a week before I climb out of it!”

  Pearl was cooing to Urbont how wonderful she was as the valedictorian at her junior high, how great the teaching profession was, and how useful, and how interesting.

  As for me; “Well, I guess you’re right, Steve. I should have gone to B.C.N.Y. instead of Berkeley.”

  “That’s right, Jimmy. After all, B.C.N.Y. has some of the best number-theory people in the world. And some of the greatest educators, too. Like Dean Cashew who started the Privileged Student Program. It sure is wonderful.”

  “I guess you’re right, Steve.”

  “I’m right, all right. At schools like Berkeley, you’re just another student, but at B.C.N.Y. you can be a P.S., and get all the good professors and small classes and high grades.”

  “You’re right, Steve.”

  “I’m right, all right. Listen, we have people that’ve quit Cornell and Harvard and M.I.T. Of course, they don’t do much but run home after school and sit in their houses, but their parents all say how much happier they are—like back in high school . . .”

  When the scrap paper and the gum wrappers were up to our knees and there were four false panhandlers in the car, Johnny called a halt. The little psychist smiled and nodded as he walked the three of us carefully out the door.

  “Standard technique,” he murmured to no one in particular. “Doing something immediately rather than the best thing a while later. Their morale was shot, so I—” He trailed off.

  “Are they really that sensitive?” Goldwasser asked. “I thought their training was better than that.”

  “You act like they were components in an electronics rig,” said Pearl jerkily. “You know that Premedial Sensory Perception, the ability to perceive the dull routine that normal people ignore, is a very delicate talent!”

  Pearl was well launched. “In the dark ages such people were called dullards and subnormals. Only now, in our enlightened age, do we realize their true ability to know things outside the ordinary senses—a talent vital for BC-flight.”

  The tedium and meaninglessness of life which we rationalize away—

  “A ship is more mind than matter, and if you upset that mind—”

  He paled suddenly. “I, I think I’d better stay with them,” he said. He flung open the door and went back into the coach. Goldwasser and I looked at each other. Pearl was a trained mathenaut, but his specialty was people, not paramath.

  “Let’s check the lab,” I muttered.

  Neither of us spoke as we moved toward the lab—slap a wall, pull yourself forward, twist round some instrumentation—the “reaction swim” of a man in free fall. The walls began to quiver again, and I could see Goldy clamp down on his body and memories of this part of the ship. We were nearing the limits of the BC-field. The lab itself, and the experimental apparatus, stuck out into vector space.

  “Let’s make our tests and go home,” I told Goldy.

  Neither of us mentioned Ted as we entered the lab.

  Remember this was a commercial project. We weren’t patasociologists studying abstract groups, or super-purists looking for the first point. We wanted money.

  Goldy thought he had a moneymaking scheme for us, but Goldy hasn’t been normal since he took Polykarp Kusch’s “Kusch of Death” at Columbia, “Electrodimensions and Magnespace.” He was going to build four-dimensional molecules.

  Go back to Flatland. Imagine a hollow paper pyramid on the surface of that two-dimensional world. To a Flat-lande
r, it is a triangle. Flop down the sides—four triangles. Now put a molecule in each face—one molecule, four molecules. And recall that you have infinite dimensions available. Think of the storage possibilities alone. All the books of the world in a viewer, all the food in the world in your pack. A television the size of a piece of paper; circuits looped through dim-19. Loop an entire industrial plant through hyperspace, and get one the size and shape of a billboard. Shove raw materials in one side—pull finished products out the other!

  But how do you make 4-dim molecules? Goldy thought he had a way, and Ted Anderson had checked over the math and pronounced it workable. The notion rested in the middle of the lab: a queer, half-understood machine of mind and matter called a Grahm-Schmidt generator.

  “Jeez, Ed! This lab looks like your old room back in Diego Borough.”

  “Yeah,” said Goldwasser. “Johnny said it would be a good idea. Orientation against that.”

  That was the outside of the lab, raw topological space, without energy or matter or time. It was the shape and color of what you see in the back of your head.