I looked away.
Goldwasser’s room was a duplicate of his old home—the metal desk, the electronics rigs, the immense bookshelves, half-filled with physics and half with religious works. I picked up a copy of Stace’s Time and Eternity and thumbed through it, then put it down, embarrassed.
“Good reading for a place like this.” Goldwasser smiled.
He sat down at the desk and began to check out his “instruments” from the locked drawer where he’d kept them. Once he reached across the desk and turned on a tape of Gene Gerard’s Excelsior! The flat midwestern voice murmured in the background.
“First, I need some hands,” said Ed.
Out in the nothingness two pairs of lines met at right angles. For an instant, all space was filled with them, jammed together every which way. Then it just settled down to two.
The lab was in darkness. Goldwasser’s big form crouched over the controls. He wore his engineer’s boots and his hair long, and a beard as well. He might have been some medieval monk, or primitive witchdoctor. He touched a knob and set a widget, and checked in his copy of Birkhoff and MacLane.
“Now,” he said, and played with his instruments. Two new vectors rose out of the intersections. “Cross-products. Now I’ve a right- and a left-handed system.”
All the while Gene Gerard was mumbling in the background: “ ‘Ah, now, my pretty,’ snarled the Count. ‘Come to my bedchamber, or I’ll leave you to Igor’s mercies.’ The misshapen dwarf cackled and rubbed his paws. ‘Decide, decide!’ cried the Count. His voice was a scream. ‘Decide, my dear. SEX—ELSE, IGOR!’”
“Augh,” said Goldwasser, and shut it off. “Now,” he said, “I’ve got some plasma in the next compartment.”
“Holy Halmos,” I whispered.
Ted Anderson stood beside the generator. He smiled, and went into topological convulsions. I looked away, and presently he came back in to shape. “Hard getting used to real space again,” he whispered. He looked thinner and paler than ever.
“I haven’t got long,” he said, “so here it is. You know I was working on Ephraim’s theories, looking for a flaw. There isn’t any flaw.”
“Ted, you’re rotating,” I cautioned.
He steadied, and continued. “There’s no flaw. But the theory is wrong. It’s backwards. This is the real universe,” he said, and gestured. Beyond the lab topological space remained as always, a blank, the color of the back of your head through your own eyes.
“Now listen to me, Goldy and Johnny and Kidder.” I saw that Pearl was standing in the iris of the tube. “What is the nature of intelligence? I guess it’s the power to abstract, to conceptualize. I don’t know what to say beyond that—I don’t know what it is. But I know where it came from! Here! In the math spaces—they’re alive with thought, flashing with mind!
“When the twiddles circuits failed, I cracked. I fell apart, lost faith in it all. For I had just found what I thought was a basic error in theory. I died, I vanished . . .
“But I didn’t. I’m a metamathematician. An operational philosopher, you might say. I may have gone mad—but I think I passed a threshold of knowledge. I understand . . .
“They’re out there. The things we thought we’d invented ourselves. The concepts and the notions and the pure structures—if you could see them . . .”
He looked around the room, desperately. Pearl was rigid against the iris of the tube. Goldy looked at Ted for a moment, then his head darted from side to side. His hands whitened on the controls.
“Jimmy,” Ted said.
I didn’t know. I moved toward him, across the lab to the edge of topological space, and beyond the psychic ecology. No time, no space, no matter. But how can I say it? How many people can stay awake over a book of modern algebra, and how many of those can understand?
—I saw a set bubbling and whirling, then take purpose and structure to itself and become a group, generate a second-unity element, mount itself and become a group, generate a second unity element, mount itself and become a field, ringed by rings. Near it, a mature field, shot through with ideals, threw off a splitting field in a passion of growth, and became complex.
—I saw the life of the matrices; the young ones sporting, adding and multiplying by a constant, the mature ones mating by composition: male and female make male, female and male make female—sex through anticom-mutivity! I saw them grow old, meeting false identities and loosing rows and columns into nullity.
—I saw a race of vectors, losing their universe to a newer race of tensors that conquered and humbled them.
—I watched the tyranny of the Well Ordering Principle, as a free set was lashed and whipped into structure. I saw a partially ordered set, free and happy broken before the Axiom of Zemelo.
—I saw the point sets, with their cliques and clubs, infinite numbers of sycophants clustering round a Bolzano-Weirstrauss aristocrat—the great compact medieval coverings of infinity with denumerable shires—the conflicts as closed sets created open ones, and the other way round.
—I saw the rigid castes of a society of transformations, orthogonal royalty, inner product gentry, degenerates— where intercomposition set the caste of the lower on the product.
—I saw the proud old cyclic groups, father and son and grandson, generating the generations, rebel and blacksheep and hero, following each other endlessly. Close by were the permutation groups, frolicking in a way that seemed like the way you sometimes repeat a sentence endlessly, stressing a different word each time.
There was much I saw that I did not understand, for mathematics is a deep, and even a mathenaut must choose his wedge of specialty. But that world of abstractions flamed with a beauty and meaning that chilled the works and worlds of men, so I wept in futility.
Presently we found ourselves back in the lab. I sat beside Ted Anderson and leaned on him, and I did not speak for fear my voice would break.
Anderson talked to Johnny and Ed.
“There was a—a race, here, that grew prideful. It knew the Riemann space, and the vector space, the algebras and the topologies, and yet it was unfulfilled. In some way— oddly like this craft,” he murmured, gesturing—”they wove the worlds together, creating the real universe you knew in your youth.
“Yet still it was unsatisfied. Somehow the race yearned so for newness that it surpassed itself, conceiving matter and energy and entropy and creating them.
“And there were laws and properties for these: inertia, speed, potential, quantumization. Perhaps life was an accident. It was not noticed for a long time, and proceeded apace. For the proud race had come to know itself, and saw that the new concepts were . . . flawed.” Anderson smiled faintly, and turned to Ed.
“Goldy, remember when we had Berkowitz for algebra,” he asked. “Remember what he said the first day?”
Goldwasser smiled. “Any math majors?
“Hmm, that’s good.
“Any physics majors?
“Physics majors! You guys are just super engineers!
“Any chemistry majors?
“Chemistry major! You’d be better off as a cook!”
Ted finished, “And so on, down to the, ahem, baloney majors.”
“He was number happy,” said Ed, smiling.
“No. He was right, in a way.” Ted continued. “The race had found its new notions were crudities, simple copies of algebras and geometries past. What it thought was vigor was really sloth and decay.
“It knew how to add and multiply, but it had forgotten what a field was, and what commutivity was. If entropy and time wreaked harm on matter, they did worse by this race. It wasn’t interested in expeditions though the fiber bundles; rather it wanted to count apples.
“There was conflict and argument, but it was too late to turn back. The race had already degenerated too far to turn back. Then life was discovered.
“The majority of the race took matter for a bride. Its esthetic and creative powers ruined, it wallowed in passion and pain. Only remnants of reason remaine
d.
“For the rest, return to abstraction was impossible. Time, entropy, had robbed them of their knowledge, their heritage. Yet they still hoped and expended themselves to leave, well, call it a ‘seed’ of sorts.”
“Mathematics?” cried Pearl.
“It explains some things,” mused Goldwasser softly. “Why abstract mathematics, developed in the mind, turns out fifty years or a century later to accurately describe the physical universe. Tensor calculus and relativity, for example. If you look at it this way, the math was there first.”
“Yes, yes, yes. Mathematicians talked about their subject as an art form. One system is more ‘elegant’ than another if its logical structure is more austere. But Occam’s Razor, the law of simplest hypothesis, isn’t logical.
“Many of the great mathematicians did their greatest work as children and youths before they were dissipated by the sensual world. In a trivial sense, scientists and mathematicians most of all are described as ‘unworldly’ . . .”
Anderson bobbled his head in the old familiar way. “You. have almost returned,” he said quietly. “This ship is really a heuristic device, an aid to perception. You are on the threshold. You have come all the way back.”
The metamathematician took his notebook, and seemed to set all his will upon it. “See Ephraim gets this,” he murmured. “He, you, I ... the oneness—”
Abruptly he disappeared. The notebook fell to the floor.
I took it up. Neither Ed nor Johnny Pearl met my eyes. We may have sat and stood there for several hours, numbed, silent. Presently the two began setting up the isomorphomechanism for realization. I joined them.
The National Mathenautics and Hyperspace Administration had jurisdiction over civilian flights then, even as it does today. Ted was pretty important, it seemed. Our preliminary debriefing won us a maximum-security session with their research chief.
Perhaps, as I’d thought passionately for an instant, I’d have done better to smash the immy, rupture the psychic ecology, let the eggshell be shattered at last. But that’s not the way of it. For all of our progress, some rules of scientific investigation don’t change. Our first duty was to report back. Better heads than ours would decide what to do next.
They did. Ephraim Cohen didn’t say anything after he heard us out and looked at Ted’s notebook. Old Ice Cream sat there, a big teddy-bear-shaped genius with thick black hair and a dumb smile, and grinned at us. It was in Institute code.
The B.C.N.Y. kids hadn’t seen anything, of course. So nobody talked.
Johnny Pearl married a girl named Judy Shatz and they had fifteen kids. I guess that showed Johnny’s views on the matter of matter.
Ed Goldwasser got religion. Zen-Judaism is pretty orthodox these days, yet somehow he found it suited him. But he didn’t forget what had happened back out in space. His book, The Cosmic Mind, came out last month, and it’s a good summation of Ted’s ideas, with a minimum of spiritual overtones.
Myself. Well, a mathematician, especially a topologist, is useless after thirty, the way progress is going along these days. But Dim-Dustries is a commercial enterprise, and I guess I’m good for twenty years more as a businessman.
Goldwasser’s Grahm-Schmidt generator worked, but that was just the beginning. Dimensional extension’s made Earth a paradise, with housing hidden in the probabilities and automated industries tucked away in the dimensions.
The biggest boon was something no one anticipated. A space of infinite dimensions solves all the basic problems of modern computer-circuit design. Now all components can be linked with short electron paths, no matter how big and complex the device.
There have been any number of other benefits. The space hospitals, for example, where topological surgery can cure the most terrible wounds—and topological psychiatry the most baffling syndromes. (Four years of math is required for pre-meds these days.) Patapsychology and patasociology finally made some progress, so that political and economic woes have declined—thanks, too, to the spaces, which have drained off a good deal of poor Earth’s overpopulation. There are even spaces resorts, or so I’m told —I don’t get away much.
I’ve struck it lucky. Fantastically so. The Private Enterprise Acts had just been passed, you’ll recall, and I had decided I didn’t want to go spacing again. With the training required for the subject, I guess I was the only qualified man who had a peddler’s pack, too. Jaffee, one of my friends down at Securities and Exchange, went so far as to say that Dim-Dustries was a hyper-spherical trust (math is required for pre-laws too). But I placated him and I got some of my mathemateers to realign the Street on a moebius strip, so he had to side with me.
Me, I’ll stick to the Earth. The “real” planet is a garden spot now, and the girls are very lovely.
Ted Anderson was recorded lost in topological space. He wasn’t the first, and he was far from the last. Twiddles circuits have burned out, DaughtAmsRevs have gone mad, and no doubt there have been some believers who have sought out the Great Race.
<
* * * *
If you have not yet heard of Alfred Jarry, you were just about to.
I came across the name first in a small, brilliant-red, extremely outspoken Moroccan magazine, Gnaoua, in which one item was not only printable (by U.S. standards) but eminently reprintable—Jarry’s “The Other Alcestis.”
Turned out it was not only -able, but very much -ed. Jarry lived in France at the turn of the century—and wrote in a vein startlingly similar to the newest surreal-science-fantasy. He is currently having a revival among the avant-garde, with an off-Broadway production of his play, Uhu Roi, and new editions of his work from New Directions. He is also the founder (prophet? inventor? perpetrator? saint?) of the Science of ‘Pataphysics.
Actually the Jarry renaissance began in 1961 with a special issue of Evergreen Review, edited by Roger Shattuck (Provediteur-General Propagator for the Islands and the Americas, in the College of ‘Pataphysics).
Space limitations prevent me from attempting here what Shattuck (pessimistically) set out to perform in 192 pages complete with magnificent maps, charts, photographs and footnotes, describing the history, scope, and organization of the illustrious
College: i.e., “the self-contradictory task of defining ‘Pataphysics in nonpataphysical terms.” I can offer only some gleanings. ‘Pataphysics (according to Shattuck) is—
—the science of the realm beyond metaphysics (as far beyond metaphysics as metaphysics is beyond physics—in one direction or another).
—the science of imaginary solutions,
—the science of the particular, of laws governing exceptions (a “pure science, lawless, and therefore impossible to outlaw”).
—imperturbable in aspect. (“The pataphysician does not burst out laughing or curse when asked to fill in quadruplicate a questionaire on his political affiliations or sexual habits: on the contrary, he details a different and equally valid activity on each of the four sheets.”)
‘Pataphysics “can be seen as a method, a discipline, a faith, a cult, a point of view, a hoax. It is all of these and none of them.” And conclusively, “All things are pataphysical, yet few men practice ‘Pataphysics consciously.”
I trust this brief introduction will serve as additional explication of Mr. Kagan’s story—and perhaps bring some readers to a further study of this remarkable science. (It should also be readily observable that “Family Portrait,” the first published story of a young California electronics technician, is as fine an example of unconscious pataphysical writing as one might readily find: it appears to satisfy virtually every one of the precepts set forth above.)
* * * *
FAMILY PORTRAIT
Morgan Kent
She put down her sewing. “You haven’t listened to a word I’ve said all evening,” she said.
“The last thing you said,” he replied from behind his newspaper, “Was, ‘so . . . that Morrison woman said to me . . .’”
“She’s putting on wei
ght, too.”
“Oh? I hadn’t noticed.”
He read a few more paragraphs, but his attention was diverted. .
“Well? Come on, what did Mattie Morrison say? I’m all agog,” he said patiently.
“You look all agog.”
“Oh, for heaven’s sake. Look at me. Agog, agog, agog.”
She picked up her sewing, and peered at it.
“I don’t think I’ll ever be able to make a hem-line as well as she can. I’ll say that for her, anyway.” She made a face and began picking out the stitches. “In any case, that woman had the nerve to tell me don’t write on the wall!”
The Year's Best Science Fiction 10 - [Anthology] Page 35