by Various
“As the Sigma Structures see it.”
“A proof of what?”
“That is obscure, I must admit. Their symbols are hard to compare to ours. My preliminary finding is that the Bach cantata proves an elaborate theorem regarding confocal hypergeometric functions.”
“Ah.” Masoul allowed his mouth to take on a canny tilt. “Can we invert this process?”
“You mean, take a theorem of ours and somehow turn it into music?”
“Think of it as an experiment.”
Ruth had grown up in rough, blue-collar towns of the American South, and in that work-weary culture of callused hands found refuge in the abstract. Yet as she pursued mathematics and the data-dense world of modern library science (for a science it truly was, now, with alien texts to study), she became convinced that real knowledge came in the end from mastering the brute reality of material objects. She had loved motorbikes in high school and knew that loosening a stuck bolt without stripping its threads demanded craft and thought. Managing reality took knowledge galore, about the world as it was and about yourself, especially your limitations. That lay beyond merely following rules, as a computer does. Intuition brewed from experience came first, shaped by many meetings with tough problems and outright failure. In the moist bayous where fishing and farming ruled, nobody respected you if you couldn’t get the valve cover off a fouled engine.
In her high school senior year she rebuilt a Harley, the oldest internal combustion engine still allowed. Greasy, smelly, thick with tricky detail, still it seemed easier than dealing with the pressures of boys. While her mother taught piano lessons, the notes trickling out from open windows into the driveway like liquid commentary, she worked with grease and grime. From that Harley she learned a lot more than from her advanced calculus class, with its variational analysis and symbolic thickets. She ground down the gasket joining the cylinder heads to the intake ports, oily sweat beading on her forehead as she used files of increasing fineness. She traced the custom-fit gasket with an X-knife, shaved away metal fibers with a pneumatic die grinder, and felt a flush of pleasure as connections set perfectly in place with a quiet snick. She learned that small discoloring and blistered oil meant too much heat buildup, from skimpy lubrication. A valve stem that bulged slightly pointed to wear with its silent message; you had to know how to read the language of the seen.
The Library’s bureaucratic world was so very different. A manager’s decisions could get reversed by a higher-up, so it was crucial to your career that reversals did not register as defeats. That meant you didn’t just manage people and process; you managed what others thought of you—especially those higher in the food chain. It was hard to back down from an argument you made strongly, with real conviction, without seeming to lose integrity. Silent voices would say, If she gives up so easily, maybe she’s not that solid.
From that evolved the Library bureaucrat style: all thought and feeling was provisional, awaiting more information. Talking in doublespeak meant you could walk away from commitment to your own actions. Nothing was set, as it was when you were back home in Louisiana pouring concrete. So the visceral jolt of failure got edited out of careers.
But for a Librarian, there could be clear signs of success. Masoul’s instruction to attempt an inverse translation meant she had to create the algorithms opposite to what her training envisioned. If she succeeded, everyone would know. So, too, if she flopped.
Ruth worked for several days on the reverse conversion. Start with a theorem from differential geometry and use the context filters of the Sigma Structure to produce music. Play it and try to see how it could be music at all….
The work made her mind feel thick and sluggish. She made little headway. Finally she unloaded on Catkejen at dinner. Her friend nodded sympathetically and said, “You’re stuck?”
“What comes out doesn’t sound like tonal works at all. Listen, I got this from some complex algebra theorem.” She flicked on a recording she had made, translated from the Structure. Catkejen frowned. “Sounds a little like an Islamic chant.”
“Um.” Ruth sighed. “Could be. The term ‘algebra’ itself comes from al-jabr, an Arabic text. Hummmm…”
“Maybe some regression analysis…?” Catkejen ventured.
Ruth felt a rush of an emotion she could not name. “Maybe less analysis, more fun.”
3
Andante Moderato
The guy who snagged her attention wore clothes so loud they would have been revolting on a zebra. Plus he resembled a mountain more than a man. But he had eyes with solemn long lashes that shaded dark pools and drew her in.
“He’s big,” Catkejen said as they surveyed the room. “Huge. Maybe too huge. Remember, love’s from chemistry but sex is a matter of physics.”
Something odd stirred in her, maybe just impatience with the Sigma work. Or maybe she was just hungry. For what?
The SETI Library had plenty of men. After all, its pods and tech development labs had fine, shiny über-gadgets and many guys to tend them. But among men sheer weight of numbers did not ensure quality. There were plenty of the stareannosaurus breed who said nothing. Straight women did well among the Library throngs, though. Her odds were good, but the goods were odd.
The big man stood apart, not even trying to join a conversation. He was striking, resolutely alone like that. She knew that feeling well. And, big advantage, he was near the food.
He looked at her as she delicately picked up a handful of the fresh roasted crickets. “Take a whole lot,” his deep voice rolled over the table. “Crunchy, plenty spice. And they’ll be gone soon.”
She got through the introductions all right, mispronouncing his name, Kane, to comic effect. Go for banter, she thought. Another inner voice said tightly, What are you doing?
“You’re a…”
“Systems tech,” Kane said. “I keep the grow caverns perking along.”
“How long do you think this food shortage will go on?” Always wise to go to current and impersonal events.
“Seems like forever already,” he said. “Damn calorie companies.” Across the table the party chef was preparing a “land shrimp cocktail” from a basket of wax worms. She and Kane watched the chef discard the black ones, since that meant necrosis, and peel away the cocoons of those who had started to pupate. Kane smacked his lips comically. “Wax moth larvae, yum. Y’know, I get just standard rations, no boost at all.”
“That’s unfair,” Ruth said. “You must mass over a hundred.”
He nodded and swept some more of the brown roasted crickets into his mouth. “Twenty-five kilos above a hundred. An enemy of the ecology, I am.” They watched the chubby, firm larvae sway deliriously, testing the air.
“We can’t all be the same size,” she said, and thought, How dopey! Say something funny. And smile. She remembered his profile, standing alone and gazing out at the view through the bubble platform. She moved closer. “He who is alone is in bad company.”
“Sounds like a quotation,” Kane said, intently eyeing the chef as she dumped the larvae into a frying pan. They fell into the buttery goo there and squirmed and hissed and sizzled for a moment before all going suddenly still. Soon they were crusty and popping and a thick aroma like mushrooms rose from them. Catkejen edged up nearby and Ruth saw the whole rest of the party was grouped around the table, drawn by the tangy scent. “Food gets a crowd these days,” Kane said dryly.
The chef spread the roasted larvae out and the crowd descended on them. Ruth managed to get a scoopful and backed out of the press. “They’re soooo good,” Catkejen said, and Ruth had to introduce Kane. Amid the rush the three of them worked their way out onto a blister porch. Far below this pinnacle tower sprawled the Lunar Center under slanted sunlight, with the crescent Earth showing eastern Asia. Kane was nursing his plate of golden brown larvae, dipping them in a sauce. Honey!
“I didn’t see that,” Ruth began, and before she could say more Kane popped delicious fat larvae covered in tangy honey into her m
outh. “Um!” she managed.
Kane smiled and leaned on the railing, gazing at the brilliant view beyond the transparent bubble. The air was chilly but she could catch his scent, a warm bouquet that her nose liked. “As bee vomit goes,” he said, “not bad.”
“Oog!” Catkejen said, mouth wrenching aside—and caught Ruth’s look. “Think I’ll have more…” and she drifted off, on cue.
Kane looked down at Ruth appraisingly. “Neatly done.”
She summoned up her Southern accent. “Why, wea ah all alone.”
“And I, my deah, am an agent of Satan, though mah duties are largely ceremonial.”
“So can the Devil get me some actual meat?”
“You know the drill. Insect protein is much easier to raise in the caverns. Gloppy, sure, since it’s not muscle, as with cows or chickens.”
“Ah, the engineer comes out at last.”
He chuckled, a deep bass like a log rolling over a tin roof. “The Devil has to know how things work.”
“I do wish we could get more to eat. I’m just a tad hungry all the time.”
“The chef has some really awful-looking gray longworms in a box. They’ll be out soon.”
“Ugh.”
“People will eat anything if it’s smothered in chocolate.”
“You said the magic word.”
He turned from the view and came closer, looming over her. His smile was broad and his eyes took on a skeptical depth. “What’s the difference between a southern zoo and a northern zoo?”
“Uh, I—”
“The southern zoo has a description of the animal along with a recipe.”
He studied her as she laughed. “They’re pretty stretched back there,” he threw a shoulder at the Earth, “but we have it better here.”
“I know.” She felt chastised. “I just—”
“Forget it. I lecture too much.” The smile got broader and a moment passed between them, something in the eyes.
“Say, think those worms will be out soon?”
She pulled the sheet up to below her breasts, which were white as soap where the sun had never known them, so they would still beckon to him.
His smile was as big as the room. She could see in it now his inner pleasure as he hardened and understood that for this man—and maybe for all of them, the just arrived center of them—it gave a sensation of there being now more of him. She had simply never sensed that before. She imagined what it was like to be a big, hairy animal, cock flopping as you walk, like a careless, unruly advertisement. From outside him, she thought of what it was like to be inside him.
Catkejen looked down at Ruth, eyes concerned. “It’s scary when you start making the same noises as your coffeemaker.”
“Uh, huh?” She blinked and the room lost its blur.
“You didn’t show up for your meeting with Prefect Masoul. Somebody called me.”
“Have I been—”
“Sleeping into the afternoon, yes.”
Ruth stretched. “I feel so…so…”
“Less horny, I’m guessing.”
She felt a blush spread over her cheeks. “Was I that obvious?”
“Well, you didn’t wear a sign.”
“I, I never do things like this.”
“C’mon up. Breakfast has a way of shrinking problems.”
As she showered in the skimpy water flow and got dressed in the usual Library smock the events of last night ran on her inner screen. By the time Catkejen got some protein into her she could talk and it all came bubbling out.
“I…Too many times I’ve woken up on the wrong side of the bed in the morning, only to realize that it was because I was waking up on the side of…no one.”
“Kane didn’t stay?”
“Oh, he did.” To her surprise, a giggle burst out of her. “I remember waking up for, for…”
“Seconds.”
“More like sevenths…. He must’ve let me sleep in.”
“Good man.”
“You…think so?”
“Good for you, that’s what counts.”
“He…he held me when I had the dreams.”
Catkejen raised an eyebrow, said nothing.
“They’re…colorful. Not much plot but lots of action. Strange images. Disturbing. I can’t remember them well but I recall the sounds, tastes, touches, smells, flashes of insight.”
“I’ve never had insights.” A wry shrug.
“Never?”
“Maybe that keeps my life interesting.”
“I could use some insight about Kane.”
“You seem to be doing pretty well on your own.”
“But—I never do something like that! Like last night. I don’t go out patrolling for a man, bring him home, spend most of the night—”
“What’s that phrase? ‘On the basis of current evidence, not proved.’”
“I really don’t. Really.”
“You sure have a knack for it.”
“What do I do now?”
She winked. “What comes naturally. And dream more.”
The very shape of the Institute encouraged collaboration and brainstorming. It had no dead-end corridors where introverted obsessives could hide out and every office faced the central, circular forum. All staff were expected to spend time in the open areas, not close their office doors, and show up for coffee and tea and stims. Writescreens and compu-pads were everywhere, even the bathrooms and elevators.
Normally Ruth was as social as needed, since that was the lubricating oil of bureaucracies. She was an ambitious loner and had to fight it. But she felt odd now, not talkative. For the moment at least, she didn’t want to see Kane. She did not know how she would react to him, or if she could control herself. She certainly hadn’t last night. The entire idea—control—struck her now as strange….
She sat herself down in her office and considered the layers of results from her pod. Focus!
Music as mathematical proof? Bizarre. And the big question Librarians pursued: What did that tell her about the aliens behind the Sigma?
There was nothing more to gain from staring at data, so she climbed back into her pod. Its welcoming graces calmed her uneasiness.
She trolled the background database and found human work on musical applications of set theory, abstract algebra, and number analysis. That made sense. Without the boundaries of rhythmic structure—a clean, fundamental, equal, and regular arrangement of pulse repetition, accents, phrase, and duration—music would be impossible. Earth languages reflected that. In Old English the word “rhyme” derived from “rhythm” and became associated and confused with “rim”—an ancient word meaning “number.”
Millennia before, Pythagoras developed tuning based solely on the perfect consonances, the resonant octave, perfect fifth, and perfect fourth—all based on the consonant ratio 3:2. Ruth followed his lead.
By applying simple operations such as transposition and inversion, she uncovered deep structures in the alien mathematics. Then she wrote codes that then elevated these structures into music. With considerable effort she chose instruments and progression for the interweaving coherent lines, and the mathematics did the rest: tempo, cadence, details she did not fathom. After more hours of work she relaxed in her pod, letting the effects play over her. The equations led to cascading effects while still preserving the intervals between tones in a set. Her pod had descriptions of this.
Notes in an equal temperament octave form an Abelian group with 12 elements. Glissando moving upwards, starting tones so each is the golden ratio between an equal-tempered minor and major sixth. Two opposing systems: those of the golden ratio and the acoustic scale below the previous tone. The proof for confocal hypergeometric functions imposes order on these antagonisms. 3rd movement occurs at the intervals 1:2:3:5:8:5:3:2:1…
All good enough, she thought, but the proof is in the song.
Scientific proof was fickle. The next experiment could disprove a scientific idea, but a mathematical proof stood on logic and
so once found, could never be wrong. Unless logic somehow changed, but she could not imagine how that could occur even among alien minds. Pythagoras died knowing that his theorem about the relation between the sides of a right triangle would hold up for eternity. Everywhere in the universe, given a Euclidean geometry.
But how to communicate proof into a living, singing pattern-with-a-purpose—the sense of movement in the intricate strands of music? She felt herself getting closer.
Her work gnawed away through more days and then weeks.
When she stopped in at her office between long sessions in the pod she largely ignored the routine work. So she missed the etalk around the Library, ignored the voice sheets, and when she met with Catkejen for a drink and some crunchy mixed insects with veggies, news of the concert came as a shock.
“Prefect Masoul put it on the weekly program,” Catkejen said. “I thought you knew.”
“Know?” Ruth blinked. “What’s the program?”
“The Sigma Structure Symphony, I think it’s called. Tomorrow.”
She allowed herself a small thin smile.
She knew the labyrinths of the Library well by now and so had avoided the entrance. She did not want to see Masoul or anyone on his staff. Through a side door she eased into a seat near the front and stared at the assembled orchestra as it readied. There was no announcement; the conductor appeared, a woman in white, and the piece began.
It began like liquid air. Stinging, swarming around the hall, cool and penetrating. She felt it move through her—the deep tones she could hear but whose texture lay below sound, flowing from the Structure. It felt strangely like Bach yet she knew it was something else, a frothing cascade of thought and emotion that human words and concepts could barely capture. She cried through the last half and did not know why. When Catkejen asked why later she could not say.
The crowd roared its approval. Ruth sat through the storm of sound, thinking, realizing. The soaring themes were better with the deeper amplifications Prefect Masoul had added. The man knew more about this than she did and he brought to the composition a range she, who had never even played an actual analog instrument, could not possibly summon. She had seen that as the music enveloped her, seeming to swarm up her nostrils and wrap around her in a warm grasp. The stormy audience was noise she could not stand because the deep slow bass tones were still resonating in her.