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A Ripple in the Cosmic Sea

October 2nd, 2015

Here’s my latest painting, Vlad and Monika. This was technically difficult for me—trying to make those circles look like translucent colored bubbles. This is meant to be a kind of spacy and intimidating alien world, a part of my novel in progress Million Mile Road Trip.

“Vlad and Monika” oil on canvas, Oct, 2015, 30” x 24”. Click for a larger version of the painting.

At first I was going to call the painting “Bubbleman,” and have the viewer imagine that the two eyes belonged to a single alien creature, but then I decided there were in fact two of them. But “Bubblepeople” didn’t seem interesting as a title, so I decided these characters speak in Polish accents, and their names are Vlad (short for Wladimir) and Monika. I usually give my alien characters oddball accents so that, in reading the novel, it’s easy to tell them apart.

Technically speaking, this was one of the more difficult paintings I’ve done. It was hard to give the bubbles the effect of being colored, translucent spheres—and I’m still not sure I got it entirely right. But I’ve done about eight layers on the painting now and I’m going to stop. Those volcano-like mountains took me about five or ten minutes each, by the way, as did the cliff, the sky, the patches of grass, and the two eyes. It was just the bubbles that were hard. More info on my work on my paintings page.

So what else is new? My son Rudy and his wife and kids were down here over Labor Day weekend. One of the girls took my photo with my good camera. Note how my expression is much kinder than usual.

This is a heavy-duty valve on a water pipe that runs from a hidden reservoir in the Santa Cruz mountains to Los Gatos. Freshly painted. Love the colors. The pipe runs along the public, and nearly dry, Lexington Reservoir next to Route 17. I like to go out walking or biking around Lex Reservoir,

I’ve been writing really a lot, like maybe a thousand words a day, pushing forward on Million Mile Road Trip, getting into that bloodlust frenzy that you get when you can sense that the end is in fact attainable. I mean, it’ll still take me till early next summer, but by now I’ve got a lot of the plot wrinkles worked out, and the characters’ personalities have settled down, and, on a good day, I can just sit there “dreaming while I’m awake” and write down the scenes I’m seeing, and transcribe the funny things that my characters say.

But I get worn out, and I get the need to escape the house and the coffee shop, so now and then I make an expedition into the Great Outdoors. The most interesting thing I’ve done lately was to go up near the west end of Lexington Reservoir near Los Gatos, like I was just talking about. I clambered down a slope to an exposed stream that runs through the somewhat green upper end of the reservoir, and hike up along the stream in my Keene’s shoes. And here’s a shot of some standing-wave type ripples where the stream goes under a log.

Patterns like this entrance me. To my way of thinking , that’s what my physical body is. That is, I am a moving, persistent pattern in the bustling cloud of matter in this world. Surfing Schrödinger’s wave equation, you might say—only I’m not on a surfboard, I’m a bump in the wave. Or, from a spacetime viewpoint, a macrame pattern in the weave.

I do like the image a feather floating on life’s stream. But, again, I don’t really see it that way. I’m a ripple, a part of the whole.

I saw a nice cattail. I’ve always thought cattails look like hot dogs on sticks, right? That you’d roast over a fire. The first time I saw a cattail was at a cookout on a family friend’s farm in Kentucky, we just drove out there across the pasture. And we had a fire, and we roasted things, like hot dogs and biscuit dough wrapped on a stick and of course marshmallows. I was five. I was sure that if I could manage to yank a cattail out of the pond, it would roast up just as good as a hot dog. I mention this in my recent, curiously neglected, novel The Big Aha.

Last week we went up to the Union Square area of San Francisco. Amazing how many stores have come and gone over the thirty years we’ve been living here. Saw a couple of guys tap dancing.

We hiked up the hill to the Grace cathedral. Saw a nice painting of Mary Magdalene. I like how she’s pointing at that egg. It gave me an idea for my novel: put a magic egg inside each of the big flying saucer, and if you kill a saucer and you can get hold of that egg—which is really a ball of smeel—well, then you’ve got something very valuable.

There’s a fountain in a tiny park in front of Grace cathedral. Got a kind of obvious shot here of the fountain, an sprite’s hand, and the Flag. Sort of a Robert Frank shot.

Here’s another standard kind of shot—the world-holding convex mirror by a parking lot entrance. I liked fitting in the dwindling grid perspective as well. And I think it’s good that I don’t show in the mirror. I’m the invisible man. A ripple in the cosmic sea.


“Surf World”

September 22nd, 2015

This is a partial draft of a chapter named “Surf World,” from my novel in progress, Million Mile Road Trip, which will appear in late 2016 or in 2017. It’s in some ways inspired by the surfin’ SF stories I’ve written with Marc Laidlaw. See, for instance, our recent “Water Girl.”

Mount Shasta seen on a road trip in 2014…a moment that inspired this novel.

The cast of characters in “Surf World”: Villy and Zoe are on the point of graduating from high-school in Los Perros, Califorina. But they’ve left town for a road trip. A road trip across the worlds of a parallel universe. Their companions are a pair of “Szep” aliens named Pinchley and Yampa. Villy’s tenth-grade kid brother Scud has come along.

And now they’re entering a zone called Surf World.

“Endless Road Trip” oil on canvas, Sept, 2014, 30” x 24”. Includes images of my alien characters Pinchley and Yampa. Click for a larger version of the painting.

The Surf World light is a honeyed gold, like the light you get in Santa Cruz an hour before sunset. But as for the surf—maybe the waves are bigger than Villy realized before. Hard to judge, with their shapes so strange. And there’s no consistent flow. The waves go every which way, surging through each other, with no apparent regard for physical law. Staring at them does something unpleasant to Villy’s head and, in the weirdness of the moment, everything seems small and overly animated. Like he’s looking through binoculars the wrong way.

“Too gnarly?” asks Pinchley, waggling his lower jaw in an open-mouthed Szep grin. “You know what’s with them waves? They alive.”

“You mean ‘alive’ in the broad, stoner sense that everything is alive?” says Villy, trying to sound all ironic and calm.

“Alive in the sense that the Surf World ocean is ten percent smeel,” says Pinchley. “A brimming cocktail of consciousness, bro. Pure trippiness unmodified.”

It’s not remotely like anything he’s ever seen. The waves really are alive. Quirky, willful, and no two of them the same. Shape, shade, speed, size—everything’s up for alteration. The waves do what they want.

They’re driving a highly modified station wagon which they call the purple whale. They’ve equipped it with enormous paddle-wheel tires, and with a waterproof dark-energy engine. Pinchley issues his considered advice about how to launch the purple whale into massively chaotic wrong-way surf.

“Bomb on in there like you’re crazy and high.”

Four Mile Beach

Yeek!” says Zoe, getting into it. She revs the dark energy engine to the max and rockets into the sea. Almost immediately, a massive pup-tent wave blindsides the car. Like it’s a rival skater in a roller derby. Zoe stays cool. She keeps the wheels churning, turns the steering wheel, and maneuvers them through a stretch of puffballs and onto the backside of a monstrous comber that’s rolling away from the shore.

“When you get to the top, drop and ride,” counsels Villy.

And, yes, Zoe makes it up the back of the hundred-foot wave, teeters on the lip, and then drops onto the tube’s clean, smooth face. She idles the engine and the purple whale begins endlessly to skim along the self-renewing hill of water. It’s like riding a titan at Mavericks. Sweet.

It’s calm for awhile—the big wave is swallowing everything it hits, sweeping a path through the living sea. The greens and blues of the sea are beautiful in Surf World’s golden light. The whale rides the wave for nearly an hour. According to the car’s altered speedometer, they’re moving at four hundred miles an hour.

Blub, blub, bloo!” yells Scud. He’s got his window wide open, and he’s hanging out like a tongue-lolling dog on a car trip. “Here comes a pyramid covered with rice paddies?”

Yes, it’s an Incan ziggurat made of smeely seawater, a water-pyramid with stairstep escalators for its sides. Three times as high as the enormous comber and moving twice as fast. As it angles into their big wave, vicious eddies swirl towards the purple whale. The water’s surface is, like, pocked.

Skillful Zoe adjust their car’s rudder and uses the gas, speeding up and slowing down, and then—behold. She’s maneuvered them off their disintegrating pipeline and onto the rising terraces of the epic ziggurat.

“Ride the terraces to the peak,” Villy advises Zoe,. “Then gun it down the other side.”

Gravedigger monster truck, Kill Devil Hills, North Carolina.

“What a way to die, huh?” says Zoe, shooting him the briefest of glances over he shoulder. A pert smile. Okay, fine, Zoe’s not suicidal, but she does have a reckless side. Why else would she hang with Villy?

“Ready to surf?” Yampa asks Villy. “We’ll climb on the roof and mount our boards.”

“Not yet,” says Villy. “Too blown-out. Let’s wait for those giant walls we saw. Archetypal surf.”

The ziggurat is picking up speed, swallowing up a platoon of mammoth comber waves. Cathedral-sized pup-tent waves spawn off of these collisions and come pinballing up the pyramid’s terraced steps.

“Rock it, Zoe,” says Pinchley, “By the way, y’all, we’re flat-out unsinkable with these fatso tires. But a wave could wash a dumb-ass out one of these windows. If they was greenhorn enough to have it open and to be leanin out in a situation like this. Talkin to you, Scud.” Pinchley says the name like, “Scuuuuud.” He’s steadily amusing himself with his Southern accent routine.

Scud closes his window just in time. When they get to the top of the ziggurat, it turns out the very highest level—the square on the tippy-top—well, it’s a hole, an insane horror-movie elevator shaft running down into the dim, churning core the vast ziggurat’s metabolism.

Yeek!” yells Zoe once again. She floors the gas and the responsive dark-energy engine screams. Tires spinning like buzz saws, they rocket into the air and—arcing across the fearsome hole. And nosedive into one of the blocky pyramid’s square terraces, where they spend a full two minutes underwater, tumbling in the complex currents. When they bob back up, they’re on that same ziggurat terrace—or maybe it’s another one—bur for sure they’re descending towards sea level at a steady pace.

Various waves are moving into the smeel-rich waters around the drifting purple whale. Combers, pup-tents, puffballs, ziggurats and—

“A giant corkscrew?” says Zoe. “Like a big drill spinning through the water. Only the drill itself is made of water, too?”

“Catch it!” says Pinchley. “Those twisty suckers can carry you a thousand miles express. Get up to speed, Zoe, and edge onto it while its passing.”

“Yah, mon,” goes Zoe. “I have the whim-whams.”

The corkscrew wave is a helix of of curved, sloping faces, one behind the other, with each face rising out of the sea on the left, and arcing down on the right. A wave-train many miles long. The successive faces are linked by powerful underwater currents. A low bulge runs down the axis of the corkscrew, like the shaft of a ship’s propeller. Zoe has a little trouble getting the whale into a stable position on one of the blades. More than a little. At one point the car is totally submerged—tumbling ass over teakettle like a surfer in a wipe-out, and everyone screaming at once.

Villy and Scud are itching to take over, but Zoe persists. Eventually she finds a sweet spot where the car is endlessly sliding down a glassy face whose vortical motion is lifting then as fast as they descend. Like running on a treadmill. For the moment they don’t need the paddlewheels at all.

“Ready to surf?” says Yampa, leaning right into Villy’s face. She smells like curry and gasoline.


Buk buk squawk,” goes Yampa. Her notion of imitating a chicken.

“Look out there way ahead,” says Villy. “Those giant moving walls. They’re the waves we’ll ride. Zoe will tow us in.”

“Yaar,” says Yampa, parroting Villy. “Make tow ropes for us, Pinchley!”

Surf Pilgrim

Pinchley produces his green spider, and the indefatigable tool critter spins out a pair of lines that Pinchley rolls into two coils, each with a spider-woven tow-handle on one end.

“Need foot straps, too,” says Villy.

Pinchley’s tire-making marker bird pops his head out of the tool-belt and coughs out four fine, padded foot straps with sticky, fractalized ends. Easily on par with the finest tow-board straps that Da Kine makes.

“Tree of Life” oil on canvas, February, 2015, 40” x 30”. Click for a larger version of the painting.

They’re coming up on the big waves very fast. The first one seems to fill the entire horizon. It’s moving away from them. But the long line of the corkscrew wave is faster. Up ahead of them, the corkscrew wave has already drilled through the great sheet. Like a tunnel in a cliff. The surfers will jump into the water before the wall-wave, and the car will ride the corkscrew through it.

“That wall leans backwards a little,” observes Villy. “Towards us. And the top leans forward. Like a long S.”

“Or like an integral sign,” says Scud.

Oooo, math!” says Zoe in mock merriment that’s close to a scream.

“That integral wave is gonna to have a tube on the front,” says Villy. “Up at the top, where it curves over. We’ll shoot that tube, right Yampa? Mucho Goob-goob in there.”

“Tree of Life” oil on canvas, February, 2015, 40” x 30”. Click for a larger version of the painting.

“Yah, mon.” Yampa tosses the two loops of spider rope over her shoulder and grabs the four foot straps with one of her complex hands. She gives Pinchley a hug and opens her window. With surprising nimbleness, she crawls onto the roof of the car. Meanwhile Zoe’s holding a steady course on the slope of the corkscrew wave. Only minutes till they pass through the wall wave’s base.

“So, uh, goodbye for now,” Villy tells Zoe. “Right before you punch through the wave, be sure to veer. So you, like, slingshot us?”

“You’ll fall right back off that big wave. It tilts the wrong way. You just said so.”

“It’ll have a flow to it,” says Villy, hoping this is true. “And a stickiness to it. It’ll lift us up. We’ll be like water-striders.”

“Don’t go.”

“It’ll work, Zoe. The waves are alive, Like Scud said. They want to play.”

“How will we find each other afterwards?” says Zoe, flicking her eyes back and forth between Villy and the wall-wave.

“No sweat,” says Pinchley. “Yampa and Villy ride the gigundo wobbler as far as they can. Zoe and the rest of us ride the corkscrew to shore. And we meet at the Flatsies’ village. Beach party.”

“I’ll be able to locate everyone with my teep,” says Scud.

“And if there’s a prob, the gingerbread men surf out and round us up,” says Pinchley. “The Flatsies are really slick on these smeely waves.”

Villy begins levering himself out his window. He takes one last look at Zoe. And he sees stark sorrow on her face.

“Hey,” says Villy softly. “I’m gonna shred. And then we’ll camp together again.”

“If only,” says Zoe. Her hair flutters in the wind. She fastens her eyes on his. “My dear Villy.”

Before he can properly answer, Yampa grabs his hand and yanks him onto the roof. She’s stronger than she looks. And more organized. She’s already attached the straps to the boards and she’s tied the two tow lines to the whale’s roof rack. The big wall is coming up fast.

Scud leans out the window for a last look at his brother. “Good luck,” he says.

Villy snugs his feet into his foot straps, grabs one of the spider-woven tow handles and—yeek—he hops off the tilting roof of the car.

He’s going so fast that the water hisses when he lands. He hunches and sways, finding his balance. And then he’s tobogganing down the steep, helical pitch of the corkscrew wave. He hears a shrill, exultant cry behind him. Yampa’s with him.

Even in this tense moment, the Surf World light makes everything look mellow. Nostalgic almost. Like the scene is something he’s remembering. Glancing down at his feet, Villy notices that a sizable teep slug has affixed itself to his ankle. An orange little nudibranch with a cluster of lavender feelers at one end. Fine. It’ll heighten his awareness.

The plan is to angle out to the side and hope Zoe can sling them onto the big wall. The supernal wave is making a creepy sound— a deep, endless roar, like the soundtrack in a horror film just before a hideous ghoul appears. Villy is definitely sensing teep from the waves. The corkscrew is purposeful, gleeful, happy about drilling through the immense wall. As for the wall itself—it’s chanting a single cosmic Om—or something like that—a sacred syllable with no beginning and no end. And under that is—not exactly contempt, no, it’s more like the wall-wave is mildly amused. Like a woman noticing two tiny ants on her nail-polished toe. Ants with nearly invisible antennae.

Focus, Villy! Hold the handle tight!

And just as he thinks that, zonng, the slack plays out and the tow rope is like a steel cable, with drops of water flying off it. Villy clings to the tow-bar for all he’s worth. It feels like it’s pulling his arms from his sockets

He catches a glimpse of Zoe’s pale, determined face glancing back at them from the car up ahead. He can’t wave, but he nods. Zoe puts the hammer down, she accelerates down the corkscrew’s slope, veering away from the corkscrew’s axis. In her wake, Villy and Yampa sluice up great fountains of water.

And now he surfers are at the edge of the helical wave—a sharp cusp, woven from a thousand flow lines. Villy bends his knees and jumps. Sails through the air for maybe a hundred yards, then slaps down and goes skimming across the eerily calm patch before the sky-high water wall. It’s not quite level, no, it’s sloping a little. Meanwhile, Zoe arcs further out from the corkscrew, then speeds back. Villy’s going faster than he thought possible. When to release the tow bar? All his thinking is in his arms and legs.

The moment comes and goes. Villy’s on his own. It’s hard to see, with the spray in his eyes, but the teep is helping. Come to me, says the mighty wave. Villy crouches low, cutting his wind resistance. He feels a rapid chatter of pulses from his board skimming across the washboard surface, and he hears the sound echoed from Yampa’s board. And then—thank you—they’re on the all but vertical face of the horror-movie Om wave and, yes, it has a flow to it, and they’re sticking to it, and it’s raising Villy up and up and up. Like a woman lifting a child.

Far below, Zoe and the purple whale disappear through the rumbling cliff of water.


Saucerpeople and Smeely Waves

September 13th, 2015

I’m working a lot on my novel Million Mile Road Trip these days. It’s about half done, and I started last January, eight months ago, so I might finish it June, 2016.

I did revisions for most of August, making the plot much clearer and more focused. And now I have an elevator pitch.

Three teens on a million mile road trip across a landscape of alien civilizations. Goal? Stop the flying saucers from invading Earth. And learn about life and love.

“Saucerpeople” oil on canvas, Sept, 2015, 24” x 18”. Click for a larger version of the painting.

The saucers in my novel are living organisms, meaty flying things. And *eeeek* it is in principle for a female saucer to fertilize her seeds with human DNA. They can get the DNA just by kissing a boy—I’m holding back from full-on sex between men and saucers.

So a saucer gets pregnant from a man or boy, lays some fertilized eggs, hatches them…and you get saucerpeople, as shown above! The have saucer-like rims around their waists, and they can fly.

I’m looking forward to writing some scenes with these guys. My plan had been to postpone them till later in the book but—why hoard the treats? Maybe I can work a saucerperson into the chapter I’m working on right now, “Surf World.”

The Surf World basin is edged with high, crumbly cliffs and a wide beach. And from there on out, it’s nothing but ocean. With insane, unnatural surf. Huge glassy combers, lively little pup tents scooting off at angles, and—weirdly enough—giant staircases and glassy pyramids. All made of water. Way out to sea are some waves like mile-high walls, thin and wobbly, steaming along like express trains. Most of the waves are heading away from the shore, and out to sea—which is kind of scary and strange. Catch one of those suckers, and you’re not coming back.

I’ve written several SF stories about surfing with Marc Laidlaw. And recently I was inspired by a big wave on the so-called “Miller’s world” in the movie Interstellar. Generally I feel that you shouldn’t model your novel’s kicks on things you saw at the movies. But that Miller’s world wave made a big impression on me. Terrified me, sitting in the movie theater.

I looked online and found the movie’s consulting physicist Kip Thorne’s ideas about the wave, lifted from his interesting book, The Physics of Interstellar. His explanation is way more complicated than I expected. No surprise, as Thorne is a brilliant physicist—I first encountered his work in the 1973 nonfiction tome Gravitation, by Kip Thorne, John Wheeler, and Charles Misner, a book that was heavy in every sense of the world—and which had a big influence on my SF and science writing.

Thorne’s line is that Miller’s world is “tidally locked” to a supermassive black hole that it’s orbiting—locked means that it rotates in synch with the orbit so that the same side is always facing the central black hole. (Our moon is tidally locked to Earth, and thus we always see the same face of the moon.)

Using “tidal” in a different sense, note that the tides on a planet are in fact bulges that are taffy-pulled up by the gravity of the sun (or black hole) that they orbit. And there’s one tidal bulge on each side of the planet. And (handwaving a bit) given that the black hole’s gravity is so extreme, the tidal bulges might be a mile high and only a hundred meters thick. But if the planet is tidally locked (tidal in the other sense now), then that tidal bulge won’t be moving relative to the planet’s surface. It’s static.

So now Thorne adds the assumption that Miller’s world is nearly locked into position, but it does wobble a bit back and forth, like maybe an hour per wobble. And as it wobbles, the giant wave-wall sweeps back and forth like a windshield wiper. The ocean sloshes, you might say. And this would explain how one of those waves might rush in either direction…including away from the shore.

But…I don’t want to get into explanations like this. Too classroom. I always hated doing Physics homework in college and, truth be told, I wasn’t good at it. No, I don’t want my rubber science to be off-the-shelf physics-homework science. I want insane bullshit that nobody’s ever heard of. Also it’s my sense that biotech, hylozoism, and the philosophy of computation are more interesting these days than old school general relativity.

So, okay, in Million Mile Road Trip, I have this stuff that I call smeel. It’s like an aethereal fluid that “is” consciousness. Smeel is the numeniferous aether, if you will—given that “numen” is Latin for “divine essence” or “magical power” or even “soul.”

As it happens, flying saucers like to vampirically leech smeel from us. They drink your smeel, and then you’re like a like a zombie. Note, by the way, that those sacuerpeople I talked about earlier are not necessarily down with the evil smeel-leeching of the mainstream saucers. Indeed some of the saucerpeople are going to serve as double agents to help my teen heroes avert the impending Invasion of the Saucers!

Anyway, it occurred to me that I can pep up the waves in my planet-sized Surf World sea by saying that the sea happens to be ten percent smeel. Not just water. And because of all this smeel, the waves are conscious and alive.

The smeel makes the waves playful. They race each other across the ocean. They pile way up on the far side, and then they race back. They take on shapes like staircases. It’s a totally surreal Mandelbrotian landscape. My character Villy gets lost and a friendly saucerperson shows up and guides him to his girlfriend Zoe and the rest of his gang.

In using smeel to animate the waves, I’m reprising an idea that Marc Laidlaw and I used in our latest surfing SF story, “Water Girl” — which appeared in Asimov’s in August, 2014, featuring, as usual, our characters Zep and Del.

Like why should I copy a Hollywood movie? Better to copy a story by Rucker and Laidlaw!

In “Water Girl,” it’s a substance called quantum aether that gives the waves consciousness. And the waves are alive, running their mental processes off quantum computations. The mad scientist in our story wrote a paper called “The Quantum-Aethereal Animation of Physical Fluids.” Here’s an extract from that story that I plan to draw on.

Stink Bay was teeming with small, erratic waves, three to five-footers … astir with frolicking shapes, powerful energetic forms that cut through the water like—well, like other water. Waves peaked from the flat surface, curled and gathered a bit of foam at their crests while cupping blue-green darkness at their long tubular hearts. The waves travelled without breaking, moving straight toward the shore then peeling away at clever angles, gouging divots out of the mud and sand. Small forms glided alongside the larger ones, and the “calves” word clicked for Del. The little waves reminded him of whale calves at play near a mother whale…The anomalous hump in the water began gliding towards the Pipeline, a shape like you’d see if something were swimming below the surface. The calf waves were herding…Zep and Del in the thing’s wake, pushing them out towards the unquiet open sea.

Squiddy detail of a painting by Robert “El Rey Magnifico” Williams.

Changing the subject again, shown below is a painful painting I did in August. I won’t go into great detail, but suffice it to say that I may need to get a “revision” operation on an artificial hip implant. It’s situationally depressing. In doing the painting below, I was doing kind of a Frida Kahlo routine—she used to do paintings of herself getting operations. If you do a painting like that it makes you feel better. And at least you’re getting some art out of your bad experience.

“X-Ray of Failed Hip Implant” oil on canvas, Aug, 2015, 18” x 24”. Click for a larger version of the painting.

Flickering flames of pain. I’m glad to be able to paint about it, and I’m glad I have a novel to work on. Writing takes my mind of any worries and cheers me up. It’s soothing to retreat into my own little worlds. Away from so-called reality. “No news is good news.”


John Conway and the Absolute Continuum

August 31st, 2015

I just read this wonderful biography of the mathematician and recreational-math maven par excellence, John Horton Conway, best known (to his mild annoyance) as the inventor of the cellular automaton rule known as the Game of Life. The book, Genius at Play , is by Siobhan Roberts.

Some great quotes. John Conway’s daughter: “There goes somebody looking strange. Ergo, it must be a friend of Dad’s!”

[This photo has no literal connection to what I’m talking about, although the musician is, in a way, like Conway. It was shot inside the San Jose California Theater during the Jazz Festival, it’s a group called Bombay Jazz.]

A lot of my favorite mathy people are in the book, many of whom I’ve managed to meet over the years: Kurt Gödel, Stephen Wolfram, Bill Gosper, Martin Gardner, and more. Bill Gosper (discoverer of the Life glider gun): “Conway is approximately the smartest man in the world.”

One of the things Conway is most proud of is his expansion of the familiar real number line so as to become the so-called surreal numbers. The surreal numbers are very densely packed—technically speaking there’s so many of them that they comprise what set-theorists call a “proper class,” which is a collection so vast that it is in some sense impossible to think of it as a finished thing. The less daunting collections are called sets: an example is the collection of all subsets of the set of finite natural numbers {0,1,2,3,…}. This “power set of the natural numbers” is the same size as the set of all real numbers.

[Original Tenniel drawing of Carroll’s Alice holding a baby who turns into a pig.]

So how do the surreal numbers arise? There’s a good popular book about them: Donald Knuth’s Surreal Numbers, available in paperback and also for free online. The basic idea is fairly simple. Whenever you have a set L of numbers that are smaller than the numbers in a different set R, then there is going to be a surreal number in between the two sets…the number can be called {L | R}.

In the regular real number system we use a principle like this to say that there’s a number on the line just beyond 3, 3.1, 3.14, 3.141, 3.1415, 3.1459, etc. This number is our friend pi.

In Conway’s system, we go further, and squeeze more and more stuff in. Like there’s a number that’s bigger than 0, but smaller than 1/2, 1/3, 1/4, … , 1/n, … for all finite n. This infinitesimal number can be called 1/omega, where omega is a name often used for the simplest infinite number that lies beyond 1, 2, 3, …, n, …

In Conway’s rich system, however, omega isn’t the very first infinite number, you’ve got omega-1, omega / 2, and even the square root of omega.

Getting technical, the surreal numbers are what the early 20th C mathematician Felix Hausdorff would call an eta-On set, where On is the class of all finite and transfinite ordinal numbers—an ordinal being a generalized counting number. The class On is a subset of the surreal numbers…like the spine of integers inside the real number line. On goes on and on, including infinite numbers like alef-null, alef-one, and so on. When we fill in the surreal numbers, we can have cool things like (((alef-one divided by (square root of alef-one)) minus (pi divided by alef-seventeen) divided by two) minus 48.) It’s all there!

The surreal numbers make up what we can call an “Absolute Continuum” where there’s always yet another number lurking between any successive pairs of sets of numbers. Physics would make more sense, suggests Knuth, if it was based on surreal numbers instead of the so-called real numbers, and I think he’s right. Assume we have endlessly transfinite infinitesimals in the small, and space gets really smooth.

I’m fascinated by the notion that our physical space is in fact an absolute continuum. This is what we might call “infinities in the small” instead of “infinities in the large.” I’ve always felt that it’s a mistake to simply stare out at the stars and yearn for the vastness out there. In my opinion, we have huge infinities right here. Underfoot.

In a slightly different vein, the founder of transfinite number theory, Georg Cantor wrote a couple of great passages.

“The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.”

“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.”

I wrote about infinity in two of my pop math books, Infinity and the Mind and Mind Tools. But getting back to the idea of the absolute continuum, let’s just marinate a little more in the idea that physical space is not *feh* quantized, and it’s not just some mere real number line—it might have levels, sublevels, subsub………subsublevels. Inconceivably rich smoothness.

That quantum bump stuff is just a glitch, like a rumble strip by a toll booth, we trundle past that in our Shrink-O-Tron device, going ever downward in our hypertransfinite subdimensional bathyscaphe. In 2008, the ezine published my SF story along these lines called “Jack and the Aktuals, or, Physical Application of Transfinite Set Theory.”

If you have having absolute continua (plural of continuum) for your space and, indeed, the very substance of your body, then there’s no reason to suppose that you will ever be repeated, as a pattern, in the transfinite universe. Those pawky bean-counting quantum Lego-block arguments don’t work if we’re transfinitely smooth. I was talking about that issue in a series of 3 posts called “Against Recurrence” in May, 2015—disputing the common (and false) claim that, “in an infinite universe everything repeats.” No repetition if your gnarly down to the alef-seventh level and beyond, my friend.

I’ll work the details out for you with my occult analog continuum computer, which merely appears to be an electric-cord entangled with a semi-reflective mirror…

I’ll leave you with this image of Davina and the Vagabonds at the San Jose Jazz Festival. Davina was great, she never stopped mugging and making faces. Funny rootsy old songs. Davina looks like a WWII poster of a working woman here. She is, very clearly, embedded in an Absolute Continuum.

Having read to Siobhan Roberts’s charming bio, I get the impression J. H. Conway would enjoy meeting Davina and she, in turn, might well find him fascinating. A mathemagician among us.


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