There’s a cute one-panel comic review of my novel Mathematicians in Love online today.

A programmer named Wiliam Rood has been emailing me about three- and four-dimensional Mandelbrot-set-like fractals. He has a mind-blowing, interactive demo on his page—the controls do work, but it takes a while to figure them out. Like using an alien iPhone that dropped out of a flying saucer.

I’ve been bugging Rood that he should be working with the Cubic Connectedness Map as described by Douady, Hubbard, Milnor, which is a different take on higher-dimensional fractals than one usually sees. If the images look like taffy, they’re using the Peitgen quaternion approach, which is, I think misguided. What I want to see is spherical warts on warts, as if the regular 2D Mandelbrot set were only a cross-sectional slice.

The cubic connectedness map lets you compute a 2D family of 2D cubic Mandelbrot sets Mk, where k ranges over the complext numbers. If you combined all of the Mk you’d have a 4D object, but first the thing ot look at is a 3D stack of them, like just vary one of the parameters inside k. You can stack to get a 3D object or animate to see a movie. I’d like to see the guy above opening his “mouth” and roaring.

You can also run a diagonalization of the Mk to get a single 2D set I modestly call the Rudy set. I put all of these cubic connectedness map fractals into the old Autodesk Chaos program, still available for free download (runs in a DOS window). And I explain the algorithms and the theory on my own alien-scribed tablet, which also has a link to Chaos program download.

I’ve also been looking at some great demos by Daniel Piker, click on the image agove to se a 4D rotation of a horse. He’s using some software packages called Processing and Rhino, and getting some nice four-dimensional rotation videos, quite unlike any I’ve seen before.

[I might mention that if you embed a vimeo clip on your web page, the page goes into a continous-download mode with the vimeo site, thereby slaving your page to the corporate masters—which is why I’m not embedding the video.]

That’s all for today. Qeep on Quackin.

More from my memoir-in-progress, Nested Scrolls.

One of the last things I did in Lynchburg, Virginia, in 1986 was to join in a riverboat regatta. In 1775, two of my local ancestors, Anthony and Benjamin Rucker, had designed a flat-bottomed wooden boat that could be poled down the James River from Lynchburg to Richmond. They used it to ship hogsheads of tobacco from the local farms to Richmond. In numerous spots, the river becomes shallow rapids, so you have to slide your boat over the stretches of rocks—thus the sturdy, flat bottom. The Ruckers’ boats were called bateaus, and, with the help of their friend Thomas Jefferson, they patented the design.

In 1986, some people in Lynchburg had the idea of getting a bunch of crews to build their own bateaus, and to have a five day boat race down the river from Lynchburg to Richmond. (Since then, this has become an annual event.) My friend Henry Vaughan and I joined the rotating crew of the Spirit of Lynchburg for one day—camping out the night before in a pasture by the river.

It was nice out on the James. Henry and I wore kerchiefs against the sun, and I started calling him Otha, after a black guy named Otha Rucker whom I’d met in traffic school. The only hassle was that our so-called captain was a gung-ho jock who was seeing this event as a serious athletic competition, and kept exhorting us to pole like crazy, push through the wall of pain, put out a hundred and ten percent, bullsh*t like that.

Our home-made boat was so heavy and leaky that after the first hour, we were in last place, with the other boats out of sight far ahead. Maybe the preppy jock thought he was the captain—but, being a Rucker, I figured I was the Shadow Captain. I mocked and chaffed the tyrant, evoking merriment from the crew. At the end of the day, the jock wanted to slug me, but I slipped out of his reach amid my fellows.

Back in my Lynchburg office, three young artists from Richmond come to see me, as if sent by Eddie Poe to meet the Shadow Captain. They’d brought me some beautiful drawings of tesseracts unfolding, and of four-dimensional cubes. It was exhilarating to learn that, bit by bit, my ideas were getting out there.

[Drawing for the 2nd Edition of the Hollow Earth, see explanation.]

I began thinking about writing a historical SF novel involving one of my favorite notions from fringe science: the Hollow Earth. The idea is that our planet is in fact hollow like a tennis ball or like a fisherman’s float. A race of people live inside. But how do we get in there? Perhaps through holes in the ocean floor, or perhaps via an immense hole at the south pole.

My special inspiration was Edgar Allen Poe’s novel, The Journey of Arthur Gordon Pym of Nantucket, which describes a sea voyage to the walls of ice around the Southern pole, with the implication that there is a huge opening to be found there, a great shaft leading into Mother Earth’s womb. Wanting this to be true, I reasoned that, even if Poe had erred about the hole being clearly visible, it might well be hidden beneath a sheet of accumulated snow and ice.

[See my paintings page for more info about my artwork.]

My old friend Gregory Gibson, in his capacity as antiquarian bookseller, sent me Wilkses’s The Narrative of the U. S. Exploring Expedition 1838-1842, Benjamin Morrell’s, A Narrative of Four Voyages to the South and North Seas, plus a fine twenty-volume edition of the collected works of Poe, who in fact used Morrell’s book himself.

I pored over these volumes, coming to identify with Eddie. He wrote of being possessed by an imp of the perverse, who impelled him to do deliberately alienating and antisocial things—which described my punk attitude to a tee.

While in Lynchburg, my expanding researches led me to the rare book room in the library of the University of Virginia, where I found writings about John Cleves Symmes, Jr., who began proselytizing his doctrine of the Hollow Earth in 1818.

Symmes lived in Newport, Kentucky, and he styled himself the Newton of the West. He was too busy lecturing—or too sly—to publish any books under his own name, but I found a nonfiction Symmes’ Theory of Concentric Spheres, and a novel, Symzonia: A Voyage of Discovery, which are purportedly written by Symmes’ followers. My feeling is that, as the books speak so very highly of Symmes, he either wrote them himself or collaborated heavily.

[A classic drawing of the Hollow Earth, see this post for further H.E. info.]

In California, I started work on my novel, The Hollow Earth: The Narrative of Mason Algiers Reynolds of Virginia. The book eventually appeared in hardback and in two paperback editions, and in ebook.  There’s even a free “Creative Commons” ebook version online.

The novel is about a country boy who leaves his farm, travels down the James as a stowaway in a bateau, accompanied by his dog Arf and his childhood companion Otha, who’s now an escaped slave. They meet Edgar Allan Poe in Richmond, and they travel onward to Antarctica and to the Hollow Earth.

I wasn’t sure how to light up the inside of the Hollow Earth, a land which I called Htrae. If you put an Inner Sun in the center, then it seems like everything would fall up into the sun. One day when I was walking around San Francisco with Marc Laidlaw, I found the solution.

It was a new science toy called a plasma sphere, on display in a New Age shop. By now nearly everyone’s seen these one of these things—it’s a hollow glass ball with an electrode in the center. Branching lines of electrical discharge reach out from the electrode to the outer surface, and if you move your fingertips around on the sphere, the glow lines trail after them. That’s the way to light up the Hollow Earth! Have great aurora-like streamers of light reaching from the Central Anomaly to the inhabited inner surface of Htrae.

The writing went slowly. I find it hard to keep my novelistic momentum if I only have a spare hour here and there in which to write. The only extended patches of free time that I had were during the school vacations—especially in the summer—but often we’d want to take family trips then, taking road trips around California or flying to visit Sylvia’s father and brother in Geneva.

When my first August in California came to an end and the fall semester loomed, I thought of the early sailing ships trying to reach the fabled southern continent of Antarctica. Sometimes they’d overstay the brief polar summer, become iced in, and spend the dark, howling winter hunkered in their vessels, hunting seals for food.

[Go to my “Hollow Earth” page to see the paperback and ebook editions available .]

Repeatedly iced in by my teaching duties as I was, it took about three years to finish writing The Hollow Earth. When I was done, I used the hoaxing Poe-like expedient of pretending that The Hollow Earth was a manuscript that I’d found in that rare books room at the University of Virginia.

To this day, I get occasional emails from readers taken in by this. They wonder why I haven’t done anything to help mount an expedition to retrace Mason’s steps. One guy even assumed that since The Hollow Earth was just an old public-domain manuscript that I’d edited, it was okay to post a page-scan of my book on the web!

[Kids with Arf, canine hero of The Hollow Earth.]

My kids liked hearing me talk about the Hollow Earth. Once when we were on a cross-country skiing vacation at Lake Tahoe, I pointed out to Isabel the blueness of the light that seemed to emerge from the holes our ski-poled made in the snow.

“Proof that the Earth is hollow!” I told her.

“As if more proof were needed,” she responded cheerfully. “When will they see?”

Oh, one more thing. There was an article about my novel in the paper in San Jose, and a bum came by my office to tell me this news:

“The sun is cold and hollow. That light you see overhead is just the interaction of some special rays from the sun with our upper atmosphere. I used to be a very famous surfer, you know. Look.”

He pulled out a page torn from an encyclopedia with a grainy picture of someone on a wave.

“That’s me. Inside the Hollow Sun.”

More from my memoir-in-progress, Nested Scrolls.

In March of 1983, I got the Philip K. Dick award for Software. Sylvia and I flew up to New York City for the awards ceremony. Earlier that evening we had dinner with my editor Susan Allison, the editor David Hartwell, a writer friend of Phil’s called Ray Faraday Nelson, and the well-known writer Tom Disch—who was the one who’d initially proposed starting the award. Disch was a good guy, immensely hip and cultured.

Our whole party walked over to Times Square, where we saw Bladerunner, the brand-new movie based on Phil’s novel, Do Androids Dream of Electric Sheep. On the way over, I talked to Ray Nelson—he was such an in-the-moment guy that later in the evening when he had to make a speech, he just went over the things we’d talked about.

[I finished a new painting this week, it’s called Caw! Crows don’t actually have yellow beaks, but I think they look right. Check out the worried, astounded expression in that poor little lizard’s eyes.]

I liked the Bladerunner movie a lot, particularly the first part, with the blimps bearing electronic billboards, and the cop smoking pot while he interviewed the android, and the dark futuristic city with the neon lights glinting off pavements slick with rain. The last part of the movie seemed too violent, and inappropriately so, given that Phil’s Androids novel had largely been about empathy and peace. But that’s Hollywood.

“Phil would have loved it,” Ray Nelson reassured me. Actually, I’ve always wondered if Phil’s worrying about the movie in progress was what drove him to his fatal stroke—remember that the old phrase for stroke was “apoplectic fit.” (In the past, I’ve blogged about how I imagine Phil as a person .)

[Note the squirrel on the clothesline!]

The award ceremony was in an artist’s loft, with the hallways covered in reflective silver paint. One of the first people I ran into was my artist friend Barry Feldman from college. Incredibly, he was wearing a suit, and he looked more like Chico Marx than ever. He seemed just a bit envious of me getting an award—although he was a great painter, working all day long in his studio, he wasn’t breaking into the gallery scene. On a sudden whim, I told Barry he could pose as me and enjoy the fame.

As I was such an outsider to the SF scene, nobody knew what I looked like, and the substitution worked for about half an hour. Barry stood by the store shaking hands and signing books, twinkling with delight. I stood across the room, drinking and hanging out with Sylvia, Eddie Marritz, his wife Hanna, and Gerard Vanderleun, who’d edited The Fourth Dimension at Houghton-Mifflin. In the end it all got sorted out, and I met the people I needed to meet—among them was Susan Protter, who’d end up being my literary agent for the years to come.

Finally I stood on the bar at one end of the room and delivered a short speech that I’d composed on the plane, thinking about the Garbage King, a guy whom I’d met at Lynchburg party and had imagined to be the ghost of Phil Dick.

“If I say that Phil Dick is not really dead, then this is what I mean: He was such a powerful writer that his works exercise a sort of hypnotic force. Many of us have been Phil Dick for brief flashes, and these flashes will continue as long as there are readers. … I’d like to think that, on some level, Phil and I are just different instances of the same Platonic form—call it the gonzo-philosopher-SF-writer form, if you like. … If it is at all possible for a spirit to return from the dead, I would imagine that Phil would be the one to do it. Let’s keep our eyes open tonight, he may show up.”

The next day we went to visit Barry and his wife at his studio. I’d lifted a bottle of liquor from the awards ceremony to give him. He looked a little embarrassed. It turned out he’d bagged three bottles himself. (I wrote some more about all this in an essay “Haunted by Phil Dick”, which appeared in my collection of essays, Seek!.)

[I changed my earlier painting “Owl Creek” and gave it a new name, “A Fork in Time.” The picture represents more clearly than before the notion of someone going through a moment in time where the universe forks and in one branch they live and in the other they die.]

On Easter Day, 1989, I’d receive my second Philip K. Dick award—my third dick, you might say. It was for Wetware, my sequel to Software, and the ceremony was at a smallish regional SF con in Tacoma, Washington. It wasn’t like the artists’ loft in New York at all. It was in a windowless hotel ballroom with a dinner of rubber ham and mashed potatoes.

By then I was working a day job, and I didn’t have time to write as much as before, which had put me into a depressed state of mind. Winning the award, I felt like some ruined Fitzgerald character lolling on a luxury liner in the rain—his inheritance has finally come through, but it’s too late. He’s a broken man.

In my acceptance speech, I talked about why I’d dedicated Wetware to Phil Dick with a quote from Camus, “One must imagine Sisyphus happy.” I see Sisyphus as the god of writers or, for that matter, artists in general. You labor for months and years, rolling your thoughts and emotions into a great ball, inching it up to the mountain top. You let it go and—wheee! It’s gone. Nobody notices. And then Sisyphus walks down the mountain to start again.

In my speech, I read a little more from Camus’s “The Myth of Sisyphus”:

“Sisyphus, proletarian of the gods, powerless and rebellious, knows the whole extent of his wretched condition: it is what he thinks of during his descent. The lucidity that as to constitute his torture at the same time crowns his victory. There is no fate that cannot be surmounted by scorn.”

As so often happens, nobody got what I was talking about. One of the fans invited me to come to his room and shoot up with ketamine, an offer which I declined. Outside the weather was pearly gray, with uniformed high-school marching bands practicing for something in the empty streets.

But never mind all that ancient gloom! It’s a new world now. Happy Thanksgiving!

[Another excerpt from my memoir-in-progress, Nested Scrolls.]

Odd as it now seems, it was only in 1986, with Wetware—my thirteenth book—that I started writing on a computer. The previous dozen manuscripts were all typed, with much physical cutting and pasting. Sometimes, if I couldn’t face typing up a fair copy of the marked-up and glued-together final draft, I’d hire a typist.

[Our three cyberkids.]

But with Wetware I was ready to change. Sylvia, the kids and I went up to Charlottesville and visited the only computer store in the area. I ended up with what was known as a CP/M machine, made by Epson, with Peachtext word-processing software, and a daisy wheel printer. The system came with a Pac-Man-like computer game called Mouse Trap that the kids loved to play.

Although I knew a lot about the abstract computers discussed in mathematical logic, it would be several more years before I grasped how my kludgy, real-world computer worked—the whole schmear about copying software into system memory was a mystery to me. For the moment, all I knew was that I had to run two or three big floppy disks through the machine just to start it up.

While I was gearing up for Wetware, I’d started what I thought was going to be a short story called “People That Melt,” and I sent the story fragment to William Gibson, hoping that he’d help me finish it, and add some snazzy Gibsonian touches.

He said he was too busy to complete such a project, but he did write a couple of pages for me, and said I was free to fold them into my mix in any fashion I pleased. I think Whitey Mydol’s “ridgeback” Mohawk that extends all the way down his spine was Bill’s idea.

As I continued work on the story, it got good to me, and it ended up as the first chapter of Wetware. As a tip of the hat, I put in a character named Max Yukawa who resembled my notion of Bill Gibson—a reclusive mastermind with a thin, strangely flexible head.

Once I got rolling, I wrote Wetware at white heat. I think the actual keyboarding of the first draft took about six weeks. I made a special effort to give the boppers’ speech the bizarre beat rhythms of Kerouac’s writing—indeed, I’d sometimes look into his great Visions of Cody for inspiration. The book was insane, mind-boggling, a cyberpunk masterpiece. A couple of years later, it would win me a second Philip K. Dick award.

But no matter how fast and well I wrote, the money wasn’t coming in fast enough. I was going to have to leave freelancing and get another teaching job.