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.