by Rudy Rucker
“A big old station-wagon muscle car,” I said proudly. “With squinty little windows on the sides in back. It’s a Bel Paese Squire, no less.”
“Don’t tell me you polish it all the time and take it to classic car shows where they play, like, The Crooners,” said Alma with a giggle.
“Well, no, my car’s a beater. Mostly white, but one fender has red primer, and the hood is yellow. It’s a piebald battle-scarred squinty-whale surf machine. Let’s go vote. My polling place is at the YWCA on Bancroft Way. We can walk by there on the way to get my board.”
“You live in Ratvale too?” She was smiling broadly. I noticed something a little needy about her smile; it made me want to care for her.
“Lend me some sugar, baby I am your neighbor!”
We drove across San Francisco to the end of Golden Gate Park where it meets the ocean. The sky was getting cloudier all the time, a spring shower coming on. We suited up and walked onto the damp, gritty beach, boards under our arms.
To the right were the wild, rocky Marin headlands. Out in front of us lay the vast Pacific, the horizon line scalloped by far outsider waves.
There were golden holes in the cloud cover, with shafts of sunlight like slanting pillars. The waves near the shore were sliding gray hills, breaking in sharp lips with crowns of spray blowing back off them towards the sea.
As always, the sound was wonderful: the crunch of the big waves, the hiss of the foam bubbles popping, the low tones of the wind—oceans make the best sonic chaos of all.
“Snowy plovers,” said Alma, pointing to some little white birds running past, their legs spinning like wheels and their bodies not even bobbing. She was wearing her pink and green wetsuit, the wind bouncing her blonde-streaked brown hair. "I’ve always wanted to hold one of them in my hand and feel his—his quickness. His racing heart, his little twitches.”
“Yes. And I like those birds over there with the long slightly up-curved bills, the way they’re rummaging in the deep sand. Like people eating noodles with chopsticks.”
“Marbled godwits,” said Alma, giving me a look that held a hint of a challenge.
“I’m impressed you know the birds,” I replied. “And what do I know? Hmm. The water surface between those two waves is a hyperbolic paraboloid. And the steep, rippled front of the one about to break? That’s the Cartesian product of an exponential curve and a sine function.”
“From China,” said Alma, pointing at a boxy container ship on its way to the straits under the Golden Gate Bridge. “Ha Jin line.”
I elaborated on this, keeping up my end of the courtship display. “Carrying cast iron tractor parts, flash memory chips, plastic action figures, jasmine tea, and dried sea cucumbers.”
“Look out for the rhetorician and the mathematician!” cried Alma, running into the surf.
We paddled past the breakers and started catching waves. At first I was lagging, but then the water got good to me. It was so nice to be surfing again. Alma was lovely on her board, like a flickering flame. Our final ride was a king kong magic slide right into the heart of a double-wide tube, the two of us together inside the curled wall of water for a shared heartbeat of forever. Boom.
We came out wet and laughing. In the spitting rain of the parking lot we changed out of our rubber suits and into our clothes; me getting a few glimpses of Alma’s shapely nude body—she wasn’t prudish. We scampered across the tropical plants in the street divider and hit a coffee shop at the corner of Judah and La Playa. It was cozy inside: checkered floor, black leather couches, a craggy old man wearing a red carnation, SF State students doing homework on laptops, the smell of coffee. We found a spot on a couch by the window.
“How did you end up majoring in math?” asked Alma. “I remember people would talk about it in the lineup. Like, ‘That stud’s a mathematician.’ ” Once again I noticed the tiny dimple below the corner of her mouth.
“They did not.”
“Oh, yeah,” said Alma, nodding. “And I was curious about you.”
“I was going to major in physics, but I took the wrong courses. I guess math is what I really wanted. I have this way of backing into my decisions. Math has always been easy for me. There’s nothing to memorize. It all follows from a few basic ideas. Like the trig formulas come from a single image of a circle. What about you and rhetoric?”
“I’m a woman of modest means,” said Alma. “My father’s a termite exterminator, and my mother’s a part-time realtor who sells about one house a year. Gary and Sarah. They smoke mu- cho pot. They’re comfortable bumping along the bottom. Sarah has a bunch of salt-water aquariums, and Gary’s biggest interest is his pumpkin patch in our backyard. We live in a little house in those flat blocks off Seabright Avenue near the harbor; every October, we sell pumpkins in our driveway, it’s the high point of the year. We make about twenty dollars and buy a couple of new fish. I’ve always wanted to have more stuff than my parents when I grow up, but I don’t want to give up being mellow. I studied pretty hard at Santa Cruz High, and I was on the debating team, but I’d cut school to surf. Hell yeah. I picked rhetoric as my major because I like to talk. I’m like you—I’m doing what’s easy for me. And I figure rhetoric could lead to a career in business, law, or politics.”
“A dreg yuppie larva,” I said, and put on the plummy tone of a nature show voice-over. “This voracious pink and green caterpillar is destined to pupate into an aristocratic highflier!” In the background I heard the whoosh of the espresso machine, the crackle of the milk steamer.
Alma cocked her head and appraised me. Her eyes were a nice shade of gray. "Are you upwardly mobile, Bela?”
“What is this, a job interview? My father’s dead and my mother runs a little Chinese restaurant in a strip mall in San Jose. It’s called East-Vest. My big sister is an accountant. No bucks. But I could have a huge future in universal dynamics. Even if I do get expelled. Not that money is very important to me. Day to day, it’s being interesting and funny that counts. And, maybe, in the long run, getting some fame.” I glanced around the crowded room, at the black and white tile floor, the chatting students, the man with the red carnation. How would it be if all these people knew who I was?
“I think about money so much,” said Alma. We’d turned to face each other on the couch. The rain outside was running down the windowpane. As she talked, Alma idly ran her finger along the path of a rain rivulet, following the motion of the water. “You’ve got no idea. Wanting the good clothes and the nice car. I'd like to get past it. One way or another. Talk about something interesting or funny, Bela.”
“Those trickles of rain. They’re just the kind of thing I dig thinking about. I like that you notice them too. Let’s understand them.”
“How do you mean?” She had a wonderfully intent gaze.
“What are their forms, what are their laws of behavior. Science project! The drops stuck to the glass, for instance, they’re not round or oval like people draw them in cartoons. Their edges are jagged. So their surfaces are concave as well as convex.”
“There’s drops of all sizes,” chimed in Alma. “Most of them aren’t moving. But then one of them gets fat enough to start rolling.”
“And this drop bumps into others and that helps her keep going for awhile,” I said. “But—whoops—sometimes she comes to a stop. Trickles of all sizes. According to universal dynamics, we can emulate these gnarly processes by snapping together a few standardized morphons in Minkowski sheaf hyperspace and—”
“Techie jargon is bad,” said Alma. “Alienating.”
“Follow the happy throng to Mathland!”
“Interesting?” said Alma, leaning back and shaking her head. “No. Funny? No.” But her mouth was spread in a long smile.
The rain rivulets had merged in my head with that tube we’d surfed. And yes, oh, yes, I was beginning to see a proof for the Morphic Classification Theorem. Five of the animated shapes, or morphons, that I’d been drawing—the fish, the dish, the teapot,
the birthday cake, the rake—surely I could connect them to make a universal emulator. And this would be the key to the big proof. A lovely series of diagrams was taking form in my mind with a sound track to match. Proofs without words. I wanted to start sketching on the folded-in-four sheet of paper that I always kept in my back pocket. But more than that I wanted to advance my relationship with Alma. The lively curves of her mouth were as interesting as any math I’d ever seen.
“Let’s drive back,” I suggested. “I could pick up some food and make us rabbit paprika for supper.” At some deep level I
felt myself wondering how it might be to live and eat with this woman for the rest of my life.
“Can I invite my roommate Leni?” asked Alma.
“I guess so. I’ve got a roommate too, did I mention that? Another math grad student. Paul Bridge. If we’re lucky, he might not be there.”
“Don’t you like him?”
“I do like him, in fact I’m eager to talk to him about that new demo I saw today. And about the raindrops, and my ideas on how to prove the big theorem. Lots to talk about. I meant ‘lucky if he’s not there’ in the sense of enhancing the probability of you and me fully hooking up tonight.”
“I loathe that expression,” said Alma. “It sounds like two dragonflies fucking in midair. They do that, you know. They’re always going at it above our pumpkin patch. The sprinklers attract them. One year my father grew a pumpkin that was six hundred pounds. Even though it was stiff, its shape was soft and slumped. It was a grotesque, bloated parody of a healthful natural phenomenon, in some sense comparable to humans mating as fecklessly as insects.” Although she was looking down at her coffee, she shot me this stealthy half-smile from under her brow.
“Nice rhetoric,” I allowed. “Rabbit paprika, yes?”
“Yummo. I haven’t had slow food in weeks.”
Back in Humelocke, traffic was a mess, with a bunch of fire trucks on Bancroft Way. We didn’t mind, we were cozy in my motley high-horsepower wagon, holding hands in the dusk, with some of my E To The I Pi songs softly playing. Alma’s profile was as crisp as a face on a new-minted coin. And all the while, part of my attention was on the mathematical symphony taking shape in my head.
I dropped Alma off before going to the garage, she was planning to come over for dinner a bit later. With Leni, she said. They were going to bring something to drink. She gave me a nice, long wet good-bye kiss. Oh, Alma. It struck me that the onset of love was an aspect of universal dynamics as well.
After I got the squinty whale stashed, I took a gander at the fire trucks—they were parked by the YWCA building where I’d voted. Crap. Most of the windows were broken out, the walls were black with smoke, there was water everywhere. Somebody on the sidewalk said the fire had started at five o’clock, sparked by a short circuit in the electrical boxes. All the votes were lost. Haut had predicted a Barbara win by seventy-nine votes. If the election were really going to be that close, the unexpected fire might have tipped the balance the other way. Maybe the Her- itagists had set the fire.
Sadly I traced the karmic chain in my mind: my insulting Haut, him firing me as student, me breaking into his account and viewing his files, Alma uploading his images to the Web, the multiple downloads of same, the very real possibility that a Heritagist Van Veeter operative had drawn the conclusion that trashing a well-chosen polling-place would swing the election. I wondered if Haut had already set in motion the steps to get me expelled.
But that was all mundane bullshit. My big new ideas about universal dynamics were still in place. Mentally I pushed on them; they stood firm. I stopped under a streetlight to scratch a few marks on the piece of paper from my hip pocket, humming the sounds of the pattern as I drew. I’d meant to detour to a fancy organic market, but I wanted to get to my notebook before I lost any of this. I felt like the Cat in the Hat juggling a teapot, a rake, a birthday cake, a dish, a fish, and a sevendimensional hyperplane.
I grabbed some brown’n’serve rice balls and a tired-looking pack of rabbit quarters at a smelly little grocery on Telegraph and rushed back to the apartment. I’d have about an hour before Alma showed up. Paul was there, bent over his laptop at the kitchen table, tuned out of the workaday world, his laptop and his papers all neatly aligned parallel to the table’s edges. “I’m worried about that fire,” I remarked.
“What fire?” said Paul, not looking up. I had a paranoid flash that there was something sly and calculated about his response. But, no, he was just deep into Mathland. “I saw the frost and vote demo,” he said, still staring at his screen. “Good work liberating that, Bela. Haut was holding out on us. Cal Kweskin and Maria Reyes at Stanford saw the demo too. I got an e-mail from Maria.”
“How . .”
“My browser watches for posts about universal dynamics. I downloaded the movie thirty seconds before it went away. It’s terrific. All these doors are opening.” He made a deedle-deedle guitar sound, finally looking up at me, the gap between his teeth showing as he smiled. “The stairway to heaven.”
“I have an idea for a new diagram,” I said. “I want to show you. I feel close to some very big results.”
“Yes,” said Paul, right on my wavelength. “And it’ll take big results to make Haut forgive you. I say let’s team up. He already phoned here looking for you. Aging popinjay. He was steamed when I told him I’d seen the movie too. We’ll pull ahead of him, we’ll take him down, and we’ll beat Stanford, too. I was looking at your notebook again this afternoon. After the frost-vote demo, your drawings are making sense to me.”
“Yes,” I said. We were feeding each other’s excitement. “I’ve been thinking about your equations. I’m finally seeing what they mean. I want to crank some math.”
“I’m ready.”
I noticed I was holding a sack of groceries. “Two girls are coming over in an hour,” I told him.
“No,” said Paul, pushing his glasses up on his nose.
“I said I’d make supper.”
“No.”
“I went surfing with one of them this afternoon. The girl who reported that Buzz story. Alma.”
“I saw the movie of her kissing you in the elevator,” said Paul with a slight snicker.
“She’s bringing her roommate Leni. That’s who you talk to. Don’t be flirting with Alma.”
“I don’t want to flirt,” said Paul righteously. “I want to do math.”
“Women, Paul,” I said, pouring some oil into a frying pan and adding the rabbit. “The fair sex. The civilizing influence. All relevant influences must be factored in. Observe. I dredge the meat.” The pan clanked happily, I sprinkled on flour and paprika. “I show you my partial sketch of the universal emulator, a morphon construct capable of simulating any process at all.” I skimmed my pocket-scrap of paper over to him. “I complete the meal preparations.” I poured a can of bouillon into the pan and put on a clattering lid. “And we have a brief and cogent predinner discussion about our revolutionary plans for universal dynamics.” Everything was math: the sounds of our voices, the flow of expressions on Paul’s friendly face. “We share a healthful repast with our lovely guests, and come the morrow, you and I will make mathematical history.” I made mystic passes in the air.
“Come sit down and tell me about this new picture,” said Paul coaxingly.
I pulled a chair over beside him and smoothed out my scrap of paper. “I think that all we need is those five basic morphons. Fish, dish, rake, birthday cake, teapot. They’re like the cross-cap and the torus in algebraic topology, Paul. All-purpose building blocks. Each of them is a sound, too.” I sang the sounds to him.
The fact that I was using Cat-in-the-Hat-style names for the morphons made perfect sense to Paul. As I talked and sang, he began turning my images into rows of symbols on a lined pad of paper. Our conversation was like telepathy, with one plus one becoming more than two.
Seeing Haut’s second demo had hipped us to a fundamentally new technique for fin
ding patterns. Haut had matched plant growth to water splashes and election results to frost crystals, well and good, but now we were pairing ocean waves with trickling raindrops, mood swings with candle flames, food fads with fluttering leaves, city neighborhood distributions with the acoustics of church organ music, and the spread of rumors with milk swirls in coffee cups.
Each of these resonances could be explained by modeling the processes as combinations of my five morphons. Each morphon had a characteristic activity—the fish swam; the dish shattered; the teapot poured; the rake dragged; the cake blazed with candles. And implicit in these behaviors were five fundamental processes: rhythm, fracture, flow, aggregation, transformation. I hadn’t been quite sure that these basic modes were sufficient to model everything, but now, in just a few lines of symbols, Paul confirmed my intuition.
“Draw your picture again,” said Paul. “It wasn’t correct before, but, you know, I think if we use the rake handle, we really can get a universal emulator.”
“Yes,” I said, my pen springing to the page. “The dish mor- phon goes under the birthday cake, with the teapot sitting on the cake inside the circle of candles. The fish is in the teapot peeking out. All just like in my first version. But this time the rake has its teeth embedded in the side of the cake and the handle is all rubbery. The rubbery handle swoops under the plate and coils to make a helical spring holding up the plate, and then the tip-ass end of the handle grows out to the side and up over the top and—and then what, Paul?”
“The handle gets thin and it threads in through the teapot’s spout!” exclaimed Paul. “It dips into the tea, squeezes past the fish, pokes out the top of the teapot and wraps around the—” “Around the handle!” I cried. “Yes! The rake is holding the dish and lifting the teapot! And it goes like this.” I sang the picture as if it were a musical score.
“Math loves us,” said Paul. “We’ve sketched a proof for the Morphic Classification Theorem!”
“Using a five-morphon universal emulator,” I gloated. “Hmm. Do you think we can prove that we have to use all five? Or can we get it down to four?” Math is never over.