The Best of Gregory Benford

by David G. Hartwell

  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. It was immortality of a sort, 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 slim woman in a stern white robe, and the piece began.

  It began like liquid air. Stinging, swarming around the hall, cool and penetrating. She saw the underlying mathematics gleaming through the cadences. The swarming notes used precedents of tone and affect to find the optimal choice of orchestral roles, to bring the composition finally to bear on the human ear. She felt it move through her—the deep tones she could hear but whose texture lay below sound, flowing from the Structure. In the third passage through a fifteen-bar sequence, the woodwind balance had a shade more from the third and fourth bassoons, and a touch less from the first oboe. The harpsichord came in stronger at the very end of the eleventh bar.

  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.

  She lunged out through the same side entrance. Even though she wore formal shift and light sandals she set off walking swiftly. The storm behind her faded away as she looked up and out into the lunar lands and black sky towering above them. The Library buildings blended into the stark gray flanks of blasted rock and she began to run. Straight and true it was, to feel her legs pumping, lungs sucking in the cool dry air, as she sweated out her angry knot of feeling. She let it go, so only the music would finally remain in serene long memory.

  The world jolted by as she ran. Abruptly she was home, panting heavily, leaning against the door while wondering at the 4/4 time of her heartbeat.

  A shower, clothes cast aside. She blew a week of water ration, standing under cold rivulets.

  Something drew her out and into a robe standing before her bubble view of the steady bleak Lunar reaches. She drew in dry, cleansing air. Austerity appealed to her now, as if she sought the lean, intricate reaches of the alien music…

  The knock at her door brought her a man who filled the entrance. “I’d rather applaud in person,” Kane said. Blinking, she took a while to recognize him.

  Through the night she heard the music echoing in the hollow distance.

  She did not go to see Prefect Masoul the next day, did not seek to, and so got back to her routine office work. She did not go to the pod.

  Her e-comm inbox was a thousand times larger. It was full of hate.

  Many fundamentalist faiths opposed deciphering SETI messages. The idea of turning one into a creative composition sent them into frenzies.

  Orthodoxy never likes competition, especially backed with the authority of messages from the stars. The Sigma Structure Symphony—she still disliked the title, without knowing why—had gone viral, spreading to all the worlds. The musical world loved it but many others did not. The High Church style religions—such as the Church of England, known as Episcopalians in the Americas—could take the competition. So could Revised Islam. Adroitly, these translated what they culled from the buffet of SETI messages, into doctrines and terms they could live with.

  The fundies, as Ruth thought of them, could not stand the Library’s findings: the myriad creation narratives, saviors, moral lessons and commandments, the envisioned heavens and hells (or, interestingly, places that blended the two—the only truly alien idea that emerged from the Faith Messages). They disliked the Sigma Structure Symphony not only because it was alien, but because it was too much like human work.

  “They completely missed the point,” Catkejen said, peering over Ruth shoulder at some of the worse e-comms. “It’s like our baroque music because it comes from the same underlying math.”

  “Yes, but nobody ever made music directly from math, they think. So it’s unnatural, see.” She had never understood the fundamentalists of any religion, with their heavy bets on the next world. Why not max your enjoyments in this world, as a hedge?

  That thought made her pause. She was quite su
re the Ruth of a month ago would not have felt that way. Would have not had the idea.

  “Umm, look at those threats,” Catkejen said, scrolling through. “Not very original, though.”

  “You’re a threat connoisseur?”

  “Know your enemy. Here’s one who wants to toss you out an airlock for ‘rivaling the religious heights of J. S. Bach with alien music.’ I’d take that as a compliment, actually.”

  Some came in as simple, badly spelled e-comms. The explicit ones Ruth sent to the usual security people, while Catkejen watched with aghast fascination. Ruth shrugged them off. Years before, she had developed the art of tossing these on sight, forgetting them, not letting them gimp her game. Others were plainly generic: bellowed from pulpits, mosques, temples and churches. At least they were general, directed at the Library, not naming anyone but the Great Librarian, who was a figurehead anyway.

  “You’ve got to be careful,” Catkejen said.

  “Not really. I’m going out with Kane tonight. I doubt anyone will take him on.”

  “You do, though in a different way. More music?”

  “Not a chance.” She needed a way to not see Masoul, mostly.

  4.

  Vivace

  Looked at abstractly, the human mind already did a lot of processing. It made sense of idiosyncratic arrangements, rendered in horizontal lines, of twenty-six phonetic symbols, ten Arabic numerals, and about eight punctuation marks—all without conscious effort. In the old days people had done that with sheets of bleached and flattened wood pulp!—and no real search functions or AI assists. The past had been a rough country.

  Ruth thought of this as she surveyed the interweaving sheets of mathematics the Sigma had yielded. They emerged only after weeks of concerted analysis, with a squad of math AIs to do the heavy lifting.

  Something made her think of P. T. Barnum. He had been a smart businessman at the beginning of the Age of Appetite who ran a circus—an old word for a commercial zoo, apparently. When crowds slowed the show he posted a sign saying to the egress. People short on vocabulary thought it was another animal and walked out the exit, which wouldn’t let them back in.

  Among Librarians to the egress was the classic example of a linguistic deception that is not a lie. No false statements, just words and a pointing arrow. SETI AIs could lie by avoiding the truth, by misleading descriptions and associations, or by accepting a falsehood. But the truly canny ones deceived by knowing human frailties.

  Something about the Sigma Structure smelled funny—to use an analog image. The music was a wonderful discovery, and she had already gotten many congratulations for the concert. Everybody knew Masoul had just made it happen, while she had discovered the pathways from math to music. But something else was itching at her, and she could not focus on the distracting, irritating tingle.

  Frustrated, she climbed out of her pod in mid afternoon and went for a walk. Alone, into the rec dome. It was the first time she had gone there since Ajima’s death.

  She chose the grasslands zone, which was in spring now. She’d thought of asking Catkejen along, but her idea of roughing it was eating at outdoor cafes. Dotting the tall grass plains beneath a sunny Earth-sky were deep blue lakes cloaked by Lunar-sized towering green canopy trees.

  Grass! Rippling oceans of it, gleams of amber, emerald and dashes of turquoise shivering on the crests of rustling waves, washing over the prairie. Somehow this all reminded her of her childhood. Her breath wreathed milky white around her in the chill, bright air, making her glad she wore the latest Lunar fashion—a centuries-old style heavy ruffled skirt of wool with a yoke at the top, down to the ankles. The equally heavy long-sleeved blouse had a high collar draped like double ply cotton—useful against the seeping Lunar cold. She was as covered as a woman can be short of chador, and somehow it gave the feeling of…safety. She needed that.

  She lay down in the tall sweet grass and let its sighing waves ripple around her. Despite the Dome rules she plucked a flower and set out about the grasslands zone, feeling as if she were immersed in centuries past, on great empty plains that stretched on forever and promised much.

  Something stirred in her mind…memories of the last few days she could not summon up as she walked the rippled grassland and beside the chilly lakes tossing with creamy froth. Veiled memories itched at her mind. The leafy lake trees vamp across a Bellini sky…and why am I thinking that? The itch.

  Then the sky began to crawl.

  She felt before she saw a flashing cometary trail scratch across the Dome’s dusky sky. The flaring yellow line marked her passage as she walked on soft clouds of grass. Stepping beneath the shining, crystalline gathering night felt like…falling into the sky. She paused, and slowly spun, giddy, glad at the owls hooting each other across the darkness, savoring the faint tang of wood smoke from hearth fires, transfixed by the soft clean beauty all around that came with each heartbeat, a wordless shout of praise—

  As flecked gray-rose tendrils coiled forth and shrouded out the night. They reached seeking across the now vibrant sky. She dropped her flower and looking down at it saw the pedals scatter in a rustling wind. The soft grass clouds under her heels now caught at her shoes. The snaky growths were closer now, hissing strangely in the now warm air. She began to run. Sweat beaded on her forehead in the now cloying heavy clothes and the entrance to the grasslands zone swam up toward her. Yet her steps were sluggish and the panic grew. Acid spittle rose in her mouth and sulfurous stench burned in nostrils.

  She reached the perimeter. With dulled fingers she punched in codes that yawned open the lock. Glanced back. Snakes grasping down at her from a violent yellow sky now—

  And she was out, into cool air again. Panting, fevered, breath rasping, back in her world.

  You don’t know your own mind, gal…

  She could not deal with this any more. Now, Masoul.

  She composed herself outside Masoul’s office. A shower, some strong dark coffee and a change back into classic Library garb helped. But the shower couldn’t wash away her fears. You really must stop clenching your fists…

  This was more that what those cunning nucleic acids could do with the authority they wield over who you are, she thought—and wondered where the thought came from.

  Yet she knew where that crawling snaky image warping across the sky came from. Her old cultural imagistic studies told her. It was the tree of life appearing in Norse religion as Yggdrasil, the world tree, a massive spreading canopy that held all that life was or could be.

  But why that image? Drawn from her unconscious? By what?

  She recalled wearing a thick skirt of wool with a heavy long-sleeved blouse…watching the crawling sky…yet she did not own such clothes. When she had returned and stripped for the welcoming shower she had been wearing standard hiking gear…

  She knocked. The door translated it into a chime and ID announcement she could hear through the thin partitions. In Masoul’s voice the door said, “Welcome.”

  She had expected pristine indifference. Instead she got the Prefect’s troubled gaze, from eyes of deep brown.

  Wordlessly he handed her the program for the Symphony, which she had somehow not gotten at the performance. Oh yes, by sneaking in… She glanced at it, her arguments ready—and saw on the first page

  Sigma Structure Symphony

  Librarian Ruth Angle

  “I…did not know.”

  “Considering your behavior, I thought it best to simply go ahead and reveal your work,” he said.

  “Behavior?”

  “The Board has been quite concerned.” He knitted his hands and spoke softly, as if talking her back from the edge of an abyss. “We did not wish to disturb you in your work, for it is intensely valuable. So we kept our distance, let the actions of the Sigma Structure play out.”

  She smoothed her Librarian shift and tried to think. “Oh.”

  “You drew from the mathematics something strange, intriguing. I could not resist working upon it.”

&nbs
p; “I believe I understand.” And to her surprise she did, just now. “I found the emergent patterns in mathematics that you translated into what our minds best see as music.”

  He nodded. “It’s often said that Mozart wrote the music of joy. I cannot imagine what that might mean in mathematics.”

  Ruth thought a long moment. “To us, Bach wrote the music of glory. Somehow that emerges from something in the way we see mathematical structures.”

  “These is much rich ground here. Unfortunate that we cannot explore it further.”

  She sat upright. “What?”

  He peered at her, as if expecting her to make some logical jump. Masoul was well known for such pauses. After a while he quite obviously prompted, “The reason you came to me, and more.”

  “It’s personal, I don’t know how to say—”

  “No longer.” Again the pause.

  Was that a small sigh? “To elucidate—” he tapped his control pad and the screen wall leaped into a bright view over the Locutus Plain. It narrowed down to one of the spindly cryo towers that cooled the Library memory reserves. Again she thought of…cenotaphs. And felt a chill of recognition.

  A figure climbed the tower, the ornate one shaped like a classical minaret. No ropes or gear, hands and legs swinging from ledge to ledge. Ruth watched in silence. Against Lunar grav the slim figure in blue boots, pants and jacket scaled the heights, stopping only at the pinnacle. Those are mine…

  She saw herself stand and spread her arms upward, head back. The feet danced in a tricky way and this Ruth rotated, eyes sweeping the horizon.