Last week I finished doing a major revision on Jim and the Flims. I’d had my character Weena talking in the familiar Phil-Dickian California-speak that I’ve learned to do so smoothly. But if she’s really from 1907, it really makes more sense if she has an old-timey manner of speech. So I’m going through the book, searching for every occurrence of “Weena,” and rewriting all her lines.

I have a slight worry that I’m losing some nice Val-girl zingers, like “Don’t worry,” but those are, after all, rather facile. I think it’s going to be richer and funnier if Weena talks in an odder and more high-falutin way.

Changing the Weena dialog actually took three days, it was a lot more work than I’d expected. What made it more work especially was that I ended up noticing all kinds of loose threads and inconsistencies from the accumulation of reach-back changes I’ve made. But now I think it’s pretty solid. And it is sort of more fun to have Weena talking in this 1900s-style way—at least I hope that’s the era she sounds like. I might reread some of Hinton’s “scientific romances” to check the tone.

The drudge work of doing this long revision threw me off the roll I was on before that, a lovely writing binge, tearing through the Castle chapter and into the Quest Rose chapter, all excited about the higher-degree Mandelbrot sets. It was so nice being on a roll.

I had a couple of days when all I thought about from dawn to dusk was the novel, and I was belting out more than a thousand words a day, and that’s including two or three polish-revisions. I’d almost say those are my favorite kinds of days, when I’m almost in a trance, just thinking about the book all day long, problem-solving, rockin’ it, hitting the curl.

This week I didn’t get to write on the novel at all, I had to write this 6,000 word introduction for a collection of essays about infinity, to be published by the Templeton Foundation, a group interested in promoting scientific discussions that relate to theology.

They were going to have me to write an article last winter, but I wrote an SF story then, “Jack and the Aktuals, or, Physical Applications of Transfinite Set Theory,” and the intended publisher freaked out about having an *ack* science-fiction story in their scholarly tome. But the Templeton guys were nice about it, and this spring they told me I could write an intro instead, and they even said it would be okay if I put in a plug for my “Jack and the Aktuals” story online.

I liked this development fine, but then the papers that I’d be introducing showed up at my house, and instead of reading them right away, I kept putting it off, even though I’d said I’d do the intro by mid-September.

So a few days ago, the Templeton guys emailed me, like, “Where’s the intro?” So finally I tore into reading the papers. The good ones were quite strong—some great math ones, papers about physics and infinity, and a few of strong theology papers about God and infinity—written in philosophical jargon just this side of incomprehensibility, but sort of fun to read—like listening to the twittering of alien beetles.

For most people the math papers would be the alien beetle twitters, but for me those are more like hearing jazz that’s switched (over the years since I left grad school) to some new kinds of beats.

Anyway, I actually read all the papers and wrote a six thousand word introduction. I can’t quite understand how I did that so fast. I could never write six thousand words on a novel in just a few days. Of course for my intro, I was partly able to recycle stuff that I already knew from writing Infinity and the Mind, also I was able to drop in quotes from the papers in question. But I did write quite a bit of brand new stuff as well. And it was interesting to be writing about infinity again.

But at the same time, I was in a rush to finish because I wanted to get back to Jim and the Flims. I might be able to use some of that theology stuff in there, too, when Jim meets the god-like spirit of Flimsy herself, in the center of the Helaven sea—remember, I did a painting of that spot a few weeks ago. Anyway, I’ll still be working on the intro a little next week, as there’s still two more late-arriving papers coming in, also I want to improve it a little overall.

And I have something else coming over the horizon in the next few days as well.

I may get a little writing done around the edges in the coming days, I’ll try and keep the embers alive, but I won’t be doing any all-day rockin’ on a roll for maybe a week. But then, ah then, Muse willing, I’ll be carving Flimsy again…eventually getting to the Surf Zombie chapter!

Today’s blog offering is an excerpt from the current draft of my novel in progress, Jim and the Flims. What I’m posting today is based on the notion that my characters Jim and Weena are off in the afterworld called Flimsy, visiting with the mathematician Charles Howard Hinton. Hinton is carrying out an exceedingly extravagant computation along the lines that I outlined in my recent post, “Breaking the Bank of Computation.”

Hinton’s not using a computer. He’s using a giant geranium plant that’s fueled by vast amounts of the aethereal substance called kessence. And the shape he’s studying? He calls it the Quest Rose.

My mental model for the Quest Rose is a very cool three-dimensional fractal rendered by Daniel White, and recently posted on Fractal Forums. I show a detail below, and you can learn more about it by following some of the links in my post, “In Search of the Mandelbulb.”

Okay, so here we go with the excerpt from the draft version of Jim and the Flims. Do keep in mind that this passage is only an early draft, and I’ll be editing it a zillion more times. But I’ll leave this posted excerpt as it is, as a relic. A precursor of the finished product.

Oh, I should also mention that the Flims want to send Jim to earth with a jiva egg case designed to drain Earth’s vim in order to fuel the Quest Rose project, and that Jim is currently controlled by a parasitic jiva named Mijjy that lives inside his soul.

For most of today’s illustrations, I used my macro lens and went around the house and yard looking for interestingly gnarly things.

Not talking much, Weena and I cruised out through a door in her leaf and let the tendrils sweep us down the geranium’s stalk to the looming bulge that held the Quest Rose. A little hole near the gall’s top allowed us entrance.

A wondrously surreal marvelous landscape lay inside. We alit upon a ridge of woven furrows, with a deep view across gorges, undulating hills and ranges of mountains. The space within the gall seemed to be warped to an enormous size—I couldn’t really see to the opposite side.

The flow of the nearby terrain was Alpine—peaks alternated with saddles, and a deep valley meandered off to our right. Low, swooping walls wove back and forth along the ridges of the landscape, dancing in syncopated rhythms. The slopes of the valley were terraced as if by rice paddies, with puckered craters within the level spots. The lace-edged craters held their own little worlds of shapes, with dim tunnels leading who knew how far below.

The Quest Rose was an outgrowth of the geranium plant itself, a bit like a wildly growing cancer. The material making up this extravagant outgrowth was kessence of a very fine type—translucent and delicately shaded, like the substance of those geck lizards I’d seen. Yellows shaded to greens and mauves.

The level of detail went down to the smallest visible levels—the ridge around me was lush with plant-like shapes. Something like a prickly pear cactus stood slumped beside me, and its pads were nappy with a grid of tiny snouts.

And all the time, every bit of the Quest Rose was moving, but so slowly that I didn’t initially notice it. But now the prickly-pear nudged me, and when I glanced back into the valley, I saw that its walls had steepened, and that a row of cavernous tunnels had opened up. Everything was morphing, every part of the Quest Rose was ceaselessly probing for new configurations.

Call it art or call it science, it was very easy to believe that this supreme work was tearing through inconceivable amounts of kessence in its eternal progress towards greater levels of beauty and gnarl. So much kessence that the Duke was bent on draining my home planet dry.

Remembering this, I began to doubt the value of the Quest Rose. Yes, it was beautiful, but so was planet Earth. Was not a forest or a reef as lovely as this warped and unnatural form? How was the Quest Rose being generated, anyway? What was Hinton’s game?

Weena turned her face up, as if sniffing the air, then led me down the slope of a nearby gulch. We made our way to a trellised balcony three tiers down, a gently curved ledge with fresh doorways opening up and others closing off, everything shimmering with subtle layers of hue. Leaning on the porch’s wavy railing was Hinton himself.

“Jim Oster?” he said, looking at me. He was a solidly built man with a pleasant face and dreamy eyes. He reached out his hand towards me. He had a yuel-made body like Durkle’s, and his arm stretched a little farther than seemed quite natural. I took his hand.

“Hello, Charles,” I said. “This—this is exquisite.”

“The Quest Rose,” said Hinton. “Maybe I’ve gone too far, I don’t know. I feel bad about the debts. But I keep hoping to find—it’s hard to explain.”

“How is it designed?” I asked, sitting down on the soft floor. Weena stood to one side, watching us.

“Oh, you know,” said Hinton. “Math. You don’t want a lecture. The basic idea is that there’s a parameter space of possible higher-order fractals, and I’ve set this mass of kessence to continually looking for the best one. At this moment, the Quest Rose is quite lovely, but what if we grow a mountain over there, or perhaps another valley? Should the crater-mouths be shaped like eights? The kessence figures out the options and, knowing my taste by now, the Quest Rose morphs smoothly towards the next pattern that I might like. You might say I’m tracing a search through a dimensional parameter space. Climbing a heavenly hill.”

“Don’t start tutoring him, Charles,” said Weena. “Jim’s just a retired postman. We’re sending him to Earth with an egg case of jivas tomorrow. They’ll drain off enough kessence to get the Solsols and the Bulbers off our necks.”

“That might be nice,” said Hinton mildly.

“But Weena just told me the jivas might destroy our planet,” I put in, unsure of how much authority Hinton might have here. “You wouldn’t want that to happen, would you, Charles?”

“Destroy the Earth?” Hinton smiled. “In a certain mood, I might say it would serve them right for running their universities like factories and for laying me off.” He shook his head. “But I’m joking. There’s the children to think of, the young lovers, the men and women in the full vigor of life. Of course we shouldn’t harm Earth.”

“And we won’t, Charles,” said Weena easily. “You shouldn’t worry about it at all. Your great work is more important than mere bookkeeping.”

“Well—maybe yes,” said Hinton, fiddling with a row of puckers in the floor beside his hand. “And I’d really like to add a few more parameters pretty soon. If we can get enough kessence into the plant.”

I wanted to tell Hinton that Weena was a liar. But Mijjy was monitoring me, making it impossible to say or to teep the proper words.

“What’s the Quest Rose actually for?” was the best I could manage.

“I’m waiting for something. I’m not sure what. The image of a lost love. A shape so arcane as to provoke notice by the great mind of Flimsy itself. An invocation of the hidden God? Tarry with me, Jim, and we can talk it over.”

“I’d like that,” I said. “I don’t really have much to do here. I’m kind of a prisoner right now.”

Hinton glanced over at Weena. Was that a glint of cunning I saw in his gentle eyes? “You don’t have to stay, Weena. I know you have things to do. Leave Jim. His jiva and I will watch over on him.”

I have this idea that there are some mathematicians in my fictional afterworld Flimsy who are bent on doing some extremely demanding mathematical computations. The chief among these guys is the ghost of Charles Howard Hinton, a quirky character whom I’ve blogged about before, an early advocate of higher dimensional geometry.

My idea is that Hinton, who now lives in the Earth-based region of the afterworld, is computing such outré mathematical objects that he’s had to borrow energy from the neighboring realms of the afterworld, that is from the ghosts of Solsol and the ghosts of Bulber. And now the Solsol and Bulber ghosts are tired of waiting for their payback, and they plan to do a repo on Hinton. They’re going to siphon every living soul off Earth so as to pay off Hinton’s energy debt.

This is, in part, my satirical take on what the quantitative analysts of Wall Street did to the economy in 2008. But overcomputing is also something that interests me on its own.

Over the years, I’ve noticed that certain kinds of computations are inexhaustibly greedy, and that by dialing up certain of their parameters to values that seem not all that big, you can get a computation whose demands would overwhelm the physical world.

So what kind of computation is C. H. Hinton doing? Well, I’m going to have him computing a series of 3D fractal shapes that are based on a 27th-power polynomial equation, somewhat along the lines I described in my recent post “In Search of the Mandelbulb”

Let’s back up a step to see how gnarly his computation needs to be. What is the computational capacity of ordinary physical space? According to quantum mechanics, the smallest meaningful length is the Planck length, which, in meters, is 1 divided by 10-to-the-35th power. So the smallest meaningful volume is tiny block that is one Planck length long on each edge, and which holds a volume that’s the cube of the Planck length, that is, 1 divided by 10-to-the-105th power cubic meters.

[Note that I corrected this post on Oct 10, 2009 to accord with a comment by Fabiuz, that you can find below. Before Fabiuz I’d omitted the cubing stage.]

And the shortest meaningful time is the Planck time, which is how long it takes a light ray to travel a distance of on Planck length. Measured in seconds, the Planck time clocks in at 1 divided by 10-to-the-43rd power.

So if we assume that we might master a eldritch quantum computational technique that lets us carry out one computational operation per Planck length per Planck time, we’d be able to blaze along at 10-to-the-148th power operations per second per cubic meter.

It might actually be that our physical space is in fact doing this everywhere and everywhen…effortlessly. Just keeping itself going.

Planet Earth has a volume in cubic meters of about 10-to-the-21st power, so if we throw all of the planet at a problem, we can compute some 10-to-the-169th-power operations per second.

We might round it up to call it ten to the two-hundredth power, which happens to be googol squared—googol is the mathematicians’ old friend, that is, 10 to the hundredth power. Googol-squared ops per second!

The diameter of our observable universe is currently estimated to be about 10-to-the-27th-power meters, so the whole universe has a volume on the order of 10-to-the-81st-power meters. And if you set all of that space to computing, you’ll rack up some 10-to-the-229th-power operations per second. Less than a googol cubed.

Using the whole universe as a computer doesn’t give you a very dramatic gain over just using Earth—the reason for this is that, relatively speaking, the jump from Planck length to Earth is in fact bigger than the jump from Earth to Universe.

Now let’s think of computations so greedy that they can swamp this level of computational capacity.

(1) Use a parallel computation which is spread out across a very large number of voxels, that is, small volume cells of idealized mathematical space. You can really increase the number of voxels by requiring that you can zoom down very deep into your views of the object.

(2) Have the basic step of your computation per voxel be somewhat demanding. Have it use a higher-order formula, and have it require the formula to be iterated a large number of times.

(3) Run a very large number of these computations at once because, we’ll suppose, you’re searching through a space of all possible formulae—hoping to find the best one.

(4) And, just to keep the demand flowing, suppose that you want to update the output reasonably fast, say at a hundred times per second, so as to create a nice smooth animation.

I’ve been thinking about three-dimensional fractals lately, so let’s suppose that’s the kind of computation we’ll use. I’ll want to look at a 3D fractal that’s twisting and changing in real time as some parameter is varied.

The familiar Mandelbrot set is based on a quadratic equation in a two-dimensional space. For our illustrations, suppose we’re interested in three-dimensional analogs of the Mandelbrot set. And, to make it funky, suppose that instead of just looking at quadratic equations, we’ll be looking at higher-degree equations as well, where the “degree” of an equation is the highest power used. A quadratic equation has degree 2, a cubic equation has degree 3 and so on.

If we pass to higher degrees, it’ll be convenient to write the degree in the form (N/2) for convenience. We’ll be using complex numbers as parameters, so that means that one of these equations has N parameters. And evaluating a polynomial of this form takes on the order of N-squared steps.

In order to really get greedy with the computations, once we specify the degree of the polynomial we’re using, we’ll want to be looking at all possible variations on the polynomial of this degree. It’s like we’d be searching for the gnarliest or the most beautiful fifth-degree three-dimensional analog of the Mandelbrot Set. And we’ll suppose that the search can be automated by doing a brute-force search and ranking the results according to some mathematical measure such as entropy.

So now let’s see how high the computational demand might run.

First of all, how many voxels per fractal? That is, how fine a mathematical grid do we want to look at? Well, let’s have a nice big cubical display, ten meters on a side, with a resolution down to the smallest visible level, say to a tenth of a millimeter. And let’s also require that I can zoom down into the fractal by a factor of a ten million (which is a series of seven ten-fold zoom steps). So that comes to a resolution of a trillion voxels per edge, and I cube that for 10-to-the-36th-power voxels in all.

And I’ll iterate my fractal formulae a thousand times per voxel, so that makes 10-to-the-39th-power steps.

Suppose I’m looking at all the possible fractals specified by let us say, a degree five polynomial that uses complex-number parameters. So, if we don’t to the trouble of eliminating terms from the polynomial and we don’t take into account the constant term, that makes a total of ten real-number parameters, and evaluating the polynomial might take on the order of ten-squared steps. So now we’re looking at 10-to-the-41st-power steps to generate one of our degree-six fractals.

And, as I said, we’ll look at a wide range of the possible fractals of this kind—again assuming that we have some background algorithm to select the most aesthetically pleasing one.

For our search through the range of all the possible fractals of this kind, suppose that we let each of our ten real-number parameters vary between -5.0 and +5.0, stepping them along rather coarsely by increments of a thousandth. So each parameter is stepped through 10,000 values. And there are ten parameters, so I get 10,000 to the 10th-power combinations of values, that is, a number of combinations that’s 10-to-the-40th-power.

Multiplying this number of fractals times the number computational steps per fractal, we get 10-to-the-79th-power computational steps in the case where we use a degree five equation. So it takes ten seconds for a cubic meter of space computing flat out to show the “best” of the degree five fractals.

And now, as I mentioned, we’ll require that the display be updated in real time while some additional parameter is being smoothly varied. I want, as I said, a hundred updates per second. But each update takes ten seconds. Fine, I’ll throw a thousand cubic meters of space at my problem. That’s just a cube that’s ten meters on a side, so my display field is just large enough to compute my image in real time.

But now Hinton wants to crank up the degree! He’s not happy with degree five.

Suppose we specify some arbitrary degree that I’ll write in the form (N/2). This is an order N/2 polynomial with complex numbers as parameters and, therefore N real-number parameters to worry about. Evaluating the polynomial takes on the order of N-squared steps, and doing this a thousand times for our preferred voxel sizes makes for (10-to-the-36th times N-squared) steps.

And we step our parameters along at that same small increment we talked about above, the number of possible fractals of this kind are (10-to-the-4N-power).

So, all in all, if we go to a degree of the form (N/2), it takes (10-to-the-36th times N-squared times 10-to-the-4N-power) steps to generate all variations of the 3D fractals of this degree.

So if Hinton wants to look at fractals of degree 35, that means an N value of 70 parameters. So then our number of computations needed to show the best of these fractals is 10-to-the-36th-power times 70-squared times 10-to-the-280th-power. That means our product is going to be a number between 10-to-the-319th-power and 10-to-the-320th-power. Well over a googol-cubed.

ZZZT! System overload.

For, remember, Earth can only compute about a googol-squared operations per second, and the whole visible universe can only handle 10-to-the-229th-power!

Time to have a talk with those Solsols and Bulbers about borrowing googol-squared computations per second…

I think I already mentioned that I recently finished a rewrite of my memoir, Nested Scrolls: The Memoir of a Cyberpunk Philsopher. Here’s a bit from the very end of the book, and some photos I took recently around the SF Bay Area.

[A back entrance to Three Mile Beach north of Santa Cruz.]

When my father was on his last legs, he said, “What was I so worried about all those years? What difference did any of it make?”

Like many writers, I spend an inordinate amount of time fretting about the relative success of my works. But I also work at being grateful for what I have. After all, the vast majority of people don’t get published at all. My books are printed and find a substantial audience; I get money and respect in return. I’m lucky to have the ability to write.

[Guy riding on a cart pulled by a kite, Ocean Beach, San Francisco]

And, thanks to the chapter I wrote about society as a kind of computation in The Lifebox, the Seashell and the Soul, I’ve finally came to accept that writers’ sales obey a scaling law that’s technically known as an inverse power law distribution. You’re not getting lackluster book advances because someone is actively screwing you. It’s the scaling law.

The scaling law applies across the board—to the populations of cities, the number of hits on websites, the heights of mountains, the number of friends that people have, the areas of lakes, and the sales of books. There’s no getting around it. Thus, if you’re the hundredth-most popular writer, you earn a hundredth as much as the most popular one. Instead of a million dollars, you get ten thousand bucks. That’s how nature is. It’s not anyone’s fault.

[Pumpkin crop on Wilder Ranch farmland, north of Cruz.]

Even if the financial rewards are modest, I revel in the craft of writing. I like being able to control these little realities where things work out the way I want. It’s no accident that so many of my heroes leave the ordinary world for adventures in fabulous other lands. In just the same way, I move my mind from the day-to-day world into the fantastic worlds of my books. I make art because it feels good to do so.

Writing is hard, and after each book is finished, I wonder if I’ll be able to write another. But I keep coming back And I’ve got painting as well—another path to creative bliss.

It’s been deep and intense, here inside this cosmic novel.

[With Jon Pearce by a yonic rock formation, near Strawberry Beach, north of Cruz at this Google Earth location.]

When I started writing my memoir, Nested Scrolls, I was wondering what my life has meant. But now I see that’s not a question I’m in a position to analyze. I’m inside my story, not outside of it. What does a flower mean? A waterfall?

This said, as a writer, I can think about my life’s structure, about the story arc. I see a few obvious themes.

I searched for ultimate reality, and I found contentment in creativity. I tried to scale the heights of science, and I found my calling in philosophy and in science fiction. I was a loner, I found love, I became a family man. I was a rebel and I became a helpful professor. And I never stopped seeing the world in my own special way.

It’s been a wonderful trip.