I put some more of my paintings up on Imagekind where you can buy prints of 34 of them and — tada! — you can now buy them as inexpensive greeting cards!

It’s a major hassle getting the pictures into digital form. I reshot some of the older ones too, by the way, to enhance the resolution. I photograph them on high-end slide film with my old “safari model” (i.e. green) Leica R3 single-lens reflex on a tripod, get the film devloped at Superior Color Lab in the Willow Glen neighborhood of San Jose, then send the slides to this nice place, My Special Photos, in Los Altos up the peninsula that scans them at 4,000 dpi to 16-bit deep color TIF files with effectively 24 megapixels per image, using a high-end Nikon scanner.

And then I PhotoShop the hell out of the images to make them pop. Speaking of PhotoShop, I just got CS3 and am playing a little with the HDR (High Dynamic Range) gimmick where you can fuse several images taken at different exposures so as to get better highlights and shadow areas; the image above is made of three exposures. The one below is a better picture, compositionally, using just one exposure, though it’s not all that sharp and maybe I over-PhotoShopped the color. Both shot at Castle Rock Park.

Every step of the way, in turning my paintings into digital files, I’m dogged by uncertainty and worry; the most maddening thing is that at the end of the road, I’ll often feel that the original photo I shot wasn’t as good as it could have been in terms of lighting. Glare is a problem, as is over or under exposure, even when I shoot bracket shots.

In any case, I’ve come to accept that the final colors are more or less arbitrary, with only a casual relation to the original. ‘s all PhotoShoppable. But bad glare or a blown-out negative is hard to compensate for.

My friend Mimi was kidding me about “learning to suffer for my art.” Uploading the 80 megabyte files to Imagekind is a hassle too, I might add, it takes about an hour per file, and doesn’t always work.

I’m feeling a little frazzled these days, as I’ve had a frikkin’ cold for three weeks, which gets depressing. Also I miss the “narcotic moment of creative bliss” that I get from writing. Now and then a photograph gives me a tiny hit. PhotoShop CS3 has this nice FilterDistort|Lens Correction filter that lets you get rid of barrel and keystone distortion in a shot of something rectangular like the frame above. I love neon martini signs.

It would be simpler to shoot my paintings with a heavy-duty SLR digital camera, of course, as then I could right away see what I’d shot, and I wouldn’t have to deal with two separate photo labs. But (a) I don’t have one, and (b) if I did, the current typical 12 megapixel size would be about half of the 24 megapixel I get via the hig-res scan, although it could be that the crispness would be just as good if I was doing it digitally, also I could be sure I got the framing and exposure right. It could well be that the slide to digital conversion puts in more noise than you’d have if you shot straight to digital and just did a resampling to raise the size.

I do love using that old Leica. Actually you can get an adapter to put Leica lenses onto Canon EOS bodies, although then you have to do manual focusing. The lower end bodies are plastic, which I hate the feel of, but you can get a magnesium body Canon 5D for under $2K, or a Canon 1D Mark III with a 20 megabyte sensor for maybe $5K, but that’s really a lot of money to spend on something I might not use that much.

In practice, I really like shooting with my pocket SONY Cybershot 8 Megapixel T100. If I have a camera in my pocket all the time, I get lots of shots, and if I have to put pounds-heavy camera around my neck, I hardly use it. And, after all, mostly I just use my photos for my blog at some really low pixel count, like 2 or 3 megapixels. Of course if I got into selling prints I could open up a whole new world of effort…

Anyway here’s descriptions of the five latest paintings of mine that you can buy prints of.

31. Mossy Trees

Acrylic on canvas, 18" x 24", November, 2007.

I got into an en plein air thing again in the sunny winter of 2007. I wore a paint stained overcoat and wedged my paints into a knapsack and strapped a canvas to that. It was great to be all covered in paint clothes with a knapsack. I looked like a bum. People looked askance.

On a ridge in the Castle Rock park above Los Gatos and Saratoga I found some trees that were completely covered with fronds of moss. The sun was going down in the west over the Pacific Ocean, edging the mossy trees with brilliant yellow-green. The tree’s a little like a woman’s legs, too, very fertile. To pep up the picture, I added an eye. I like to wrap my paintings around, painting on the edges so I don’t have to frame them. I put another eye on the left edge, though you can’t see it in this image.

It was beautiful here. I was thinking of a drawing by Hieronymus Bosch were he sketches an eye on the ground and an ear on a tree.

32. Giant’s Head

Acrylic on canvas, 18" x 24", December, 2007.

Like “Mossy Trees,” “Giant’s Head” is a painting I started outdoors in Castle Rock Park near Saratoga, California. This particular rock is called California Ridge. I circled around on a narrow ledge to get to this vantage point. I was somewhat worried about falling off, there was a hundred foot drop to the ground. I painted my hand in there, like clutching at the rock to show that I was scared.

The rock itself reminded me of the profile of Homer Simpson. There were a lot of little lichen patches on it, I just tried to suggest those with some spots of color. That white line in the sky is a jet contrail. The green of the trees was really lovely, it felt good being alone up here on the ledge. I didn’t have room to stay very clean and I got a lot of paint on myself.

33. The Muse

Acrylic on canvas, 24" x 18", January, 2008.

My wife was out of town for a week visiting our daughter in New York, and I took my knapsack of paints and a canvas out to a cliff overlooking Four Mile Beach north of Santa Cruz, California. This spire of rock was probably part of a natural bridge many years ago. I often walk along the beach to this spot, it’s usually deserted and very beautiful. You don’t see any sign of human activity in any direction.

This was the first time I’d gotten onto the cliff right above the rock. It was a very windy day, and I found a depression in the cliff, a little grassy dell, and I settle in there. I particularly wanted to get the shape of the long, breaking dark wave near the horizon. A pelican flew past and I got a digital photo of him. I wished my wife were there with me.

When I got home, I kind of had to laugh at the inadequacy of the few daubs of paint I’d made—compared to the joyful, living seascape that I’d been looking at. It’s insane. You’re daubing ground up bits of stone onto a cloth and hoping to capture the physical world. But I did two more layers on the painting and finally I was happy with it.

To liven it up, I printed out a large image of the pelican I’d scene, also an image of my wife, and I slid those images around on the canvas until the composition looked right. And then I outlined those spots and painted copies of the images. I wasn’t sure I could do a human face—and the woman doesn’t really look that much like my wife. I think of her as “The Muse.” When I go out alone in nature, that’s who I’m hoping to hear from: the muse.

34. Spacetime Donuts

Acrylic on paper, 17" x 13", April, 2008.

In April of 2008, I arranged for a small press to reprint two of my early science fiction novels, Spacetime Donuts and The Sex Sphere. As part of the deal, they agreed to let me design the covers.

Spacetime Donuts is about a somewhat punk-like young mathematician who finds a way to shrink down so small that he wraps around the scale axis and gets big. Scale turns out to be circular, and spacetime is in some sense like a donut. I wrote this novel in 1979, and it can be argued that this was one of the very first cyberpunk science-fiction novels. The characters in the book plug their brains into computers, which is why I have that wire coming out of his neck.

He’s wearing an earring that’s a variation on the W.A.S.T.E. symbol in Thomas Pynchon’s novel The Crying of Lot 49. As it turns out, the book’s plot resembles this symbol. I had fun making this image really pop with cadmium red and cadmium yellow.

35. The Sex Sphere

Acrylic on canvas, 14" x 18", April, 20087.

In April of 2008, I arranged for a small press to reprint two of my early science fiction novels, Spacetime Donuts and The Sex Sphere. As part of the deal, they agreed to let me design the covers.

The Sex Sphere is about a being from the fourth dimension named Babs. Her intersection with our 3D space looks like parts of a woman, squeezed together and rounded off. She manipulates some of the characters into setting off a terrorist A-bomb in Florence, Italy. You can see the mushroom cloud in the background. I liked painting this, as it’s so intense and cartoony and surreal. I think the sex sphere looks a little scary.

Originally this painting was going to be a landscape looking out over Silicon Valley. I went up on St. Joseph’s Hill with a canvas and paints and started the picture there with my painter friend Vernon Head. Vernon knows my working habits by now, and he knew something weird was going to show up in the foreground. For awhile I wasn’t sure what it should be, but when I realized I needed a cover image for The Sex Sphere, I was ready to go.

Click here to see an earlier blog description of my first thirty paintings.

This entry follows on my two previous ones:
“Is the Universe Infinite?”
“Dialog on ”˜Is the Universe Infinite?’”

I just finished reading a great book, The Endless Universe . It’s by these two highly respected physics guys Paul Steinhardt and Neil Turok .

The Endless Universe argues that the Big Bang / Inflationary cosmological scenario has too many kludges to be plausible anymore. Till reading the book, I hadn’t realized how arbitrary and patched-up the inflationary scenario is by now. Cosmology is really a mess.

Steinhardt and Turok propose a simpler scenario called the cyclic universe or the “ekpyrotic” (Greek for “make of fire”) scenario under which we have two parallel branes (3d hyperplanes, that is, spaces like the universe), and every trillion years the branes spring together and FLASH all of space is filled with energy, and then the branes move apart, but not very far, only about a Planck length apart. Then they stop moving apart and hang there for a trillion years.

While hanging there, the branes expand, producing the galactic recession. The branes are like infinite planes, so they can expand exponentially and always have more room. And then, after a trillion years, they spring back together. The space in between them is sometimes known as “the bulk.” Strictly speaking the branes are 9-dimensional, with 3D for space and the 6 extra dimensions for the curled up and verminous Calabi-Yau-manifold stringy subdimensions. And the bulk dimension in between the branes is the 10th dimension.

There have been, in principle, an infinite number of cycles, that way we don’t need to face explaining the FIRST one. Each tortoise stands on the back of a previous tortoise.

I’d thought the cyclic universe theory had been discredited, but it’s still going strong, and fighting for more air. The old guard of inflation is fighting hard against the cyclic model, not even taking it very seriously. The Endless Universe is somewhat tendentious, arguing hard for the cyclic model over and over. But it convinced me.

Looking on the web, I find there’s a newer Baum-Frampton cyclic model mentioned on Wikipedia . In this model they talk about a cosmic “Big Rip,” which was formulated by some other guys in a paper called “Phantom Energy and Cosmic Doomsday.” The Big Rip is a depressing notion: the idea is that maybe space’s expansion is accelerating so wildly that eventually the expansion overcomes gravity and the nuclear forces so that first Earth is torn to bits, and then our bodies and even our atoms and the elementary particles. No, no, I much prefer the Cyclic Univere. It’s kind of wild these days, how you can find all these far-out science papers online.

One touchy bit in the Steinhardt-Turok model is the odd moment when the branes collide. To my amateur eye, it seems like it might be nicer and more symmetric if the branes passed through each other instead of bouncing. By the way, the branes are, strictly speaking orbifolds, whatever that means…the concept uses some insane juicy buzzwords like “quiver diagrams”.

Some bits from The Endless Universe that impacted my SF sensors:

(1) In seeming violation of the law of conservation of energy, a universe is allowed to “borrow” more energy from the gravitational field with each cycle. Every trillion years, some gravity gets converted into yet more mass and energy—the former mass and energy having been squandered by expansion of the brane space.

(2) Gravity waves are the one thing that might survive from one cycle to the next. But, methinks there may be other vestiges of the previous cycles that are kicked up (down?) into subtler planes; it helps if, as I like to do, we suppose matter to be infinitely divisible. Suppose someone can hear these “voices in the white.”

(3) They mention that if you have a collapse of space that’s not controlled carefully, you get wild asymmetric oscillations where, like, you turn into a million-mile-long cigar or a sheet of paint the size of the solar system: the chaotic mixmaster scenario.

(4) They really dump on the anthropic principle, which one might present as something like this: “A huge number of possible universes exists, and there just happens to be one that has its constants tuned in just the right way to support fleshapoids on a planet orbiting a sun.” I hadn’t realize how desperate and bankrupt the Big Bang/Inflation model had become. Supposedly there are scads of inflating universe and we just happen to be in this pariticular just-right one. It’s much more intellectually satisfying to suppose there’s only one universe and that there are some deep reasons for its properties.

[Note the small profile on the right, my ripple in the Big Flash.]

(5) In either model (inflation or cyclic), it’s been about 14 billion years since the, uh, call it the “Big Flash,” when space was filled with something like white light (higher energy than light, actually). The image of that flash gets in the way of seeing more than 14 billion light years away. But in the cyclic model, the space is in fact endless, and there’s lots of galaxies out past the 14 billion light year haze. I’m supposing (SFictionally speaking) that we can see past the haze via (a) faint gravity waves or (b) subtle energies relating to the as yet unknown subtler levels of matter. Supposedly we have another trillion years to go before the collapse, before the Big Splat that produces the next Big Flash.

(6) During the initial phase right after the Big Flash, a ripple that’s only a few meters across can in fact serve as the seed for a galaxy. Hmm…

[Adult ripple becomes Joey Ramone / T. Rex]

I might write a story about all this: “Voices in the White.”

Today I’m presenting an email dialog I had with Jeff Weeks about the whether the space of our universe is infinite.

Rudy: I mentioned in my most recent blog post, “Is the Universe Infinite” , that there seem to be three notions of space’s size. (i) it’s finite (ii) it’s potentially infinite, in that it’s finite but will expand forever (iii) it’s actually infinite. As a one-time set theorist, I of course would prefer (iii). But I don’t read much about this option.

Jeff: The reason you don’t hear much about that is that cosmologists don’t like to talk about things that can’t be tested against observation. So, for example, they are willing to consider the hypothesis that the universe is smaller than our horizon sphere (in which case we could in principle see repeating images and confirm the finiteness of space). But if and when it’s established that the universe is sufficiently larger than our horizon sphere, then many (but not all) cosmologists lose interest in discussing whether its truly infinite or just very, very big.

Rudy: In a quick web search, I see some (non-academic) people arguing against infinite universes on more a priori reasons, but these seem simply to be rehashes of pre-Cantorian Scholastic arguments derived from the mistaken notion that an actual infinite is inherently contradictory.

Jeff: Most (but not all) cosmologists avoid stating an opinion one way or the other (re a finite or infinite universe). They take the view that if you can’t test a hypothesis against observations, then it’s not worth discussing. In my view that approach seems a little extreme, but on the other hand I can see where they are coming from. Many physicists feel burnt (or at least chastened) by quantum mechanics, leading them to seek refuge in the idea that the purpose of science is to predict the results of experiments, and that scientists shouldn’t waste their time speculating about what it all means. I don’t agree with that approach, but like I said I can see where they’re coming from. Anyhow, for that reason I think most cosmologists are agnostic on the question of a finite or infinite universe.

Rudy: I guess you’d need to be in 4D space to smoothly make the 3D torus or the Poincare dodecahedron.

Jeff: We humans like things to sit in Euclidean spaces, because we can imagine them more easily that way. But Mother Nature suffers no such limitations. Thus it makes perfect sense to imagine a 3-torus that doesn’t sit in 4D space (and in fact doesn’t sit in *any* space). It just is. It’s itself, and that’s that.

By the way, one of my motivations for writing the Torus and Klein Bottle Games was to let users develop some gut-level intuition for a finite multi-connected space that doesn’t sit in any higher-dimensional space. That is, when you play the games, you learn to understand the finite 2D surfaces “as themselves”, never having to wrap them around in 3- or 4-dimensional space.

Rudy: I’m not fully clear on how to express the difference between the hypersphere and the positively curved finite compact Poincaré dodecahedral space. I’m guessing it’s that the Poincare space is analogous to a multiple-genus surface with holes in it? Six holes?

Jeff: Yes, exactly, the Poincare dodecahedral space is analogous to a multiple-genus surface, in the sense that both are “multiply connected”.

The possible shapes for a 3D space are far richer than the possibilities for a 2D surface. So while a simple concept like the number of holes (or, equivalently, the number of handles) works great for classifying 2D surfaces, it breaks down in 3D. In other words, the set of (orientable) 2D surfaces is linear in the sense that you can line ”˜em up in a row and not miss anything, like:

sphere, doughnut surface, 2-holed doughnut surface, etc.

But the set of possible 3D shapes isn’t linear in that way. A more productive way to think about 3D spaces is to focus on which directions you could travel to return to your starting point, or, equivalently, in which directions you could look and see an image of yourself. For example, in a 3-torus you’d see your nearest self-images along a set of three mutually perpendicular axes (i.e. if you’re standing at the center of a cubical fundamental domain, and you direct your gaze towards the center of any of the cube’s six faces, you’ll see an image of yourself “one unit away”). In the dodecahedral space, by contrast, you can look towards any of the dodecahedron’s 12 faces to see a nearest self-image. You can enjoy these effects first hand in my Curved Spaces software: just open a space of interest and use the left- and right-arrow keys to give your a little window to see across each of the walls.

Rudy: I’m also groping for a good way to describe some in-space scenario that would make the “holes” evident.

Jeff: Maybe something related to where you see your self-images? Another interesting twist in the plot would be that when you see those images, you’re seeing into the past (because of the finite speed of light).

One last comment here: In the hypersphere you see exactly one image of yourself, and in fills the whole sky. I think that observation was in your first book, Geometry, Relativity and the Fourth Dimension ? That book had a big influence on my intellectual development. It was a real hit among my math/science friends!

Rudy: Your paper “The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations” suggests that, since we don’t see much in the way of a low mode gradient in the cosmic microwave background radiation (CMB) across the sky, our space is probably finite. But there are of course a number of ways out of this argument, right?

Jeff: Yes. The weak broad-scale CMB fluctuations could be a result of a multiconnected topology, or they could be the result of some other effect, or they could be just a statistical fluke.

Rudy: Funny, it seems so IMPORTANT to me whether there are alef-null stars, and to many this is a meaningless question. I gather that at least it’s not viewed as impossible, which is reassuring.

Jeff: It’s a natural human drive to want to understand the world we live in. What aspects of the world we find interesting are shaped by our previous experience. This is a healthy thing, I think, because it means that different people end up obsessed by different things (you with infinite sets, me with topology/geometry, and so on) and thus we avoid having everybody thinking alike. Thank goodness!

Rudy: I have a dream that eventually the transfinite will emerge into testable quotidien physics

Jeff: That’s the beautiful part — lots of people with lots of dreams.

These days there are a wide range of competing notions about the size and shape of the space that we live in. The cosmologists are kind of lost. So I might as well put in my two cents worth!

I’ll group my comments in three sections, relating to how big space is. 1: Finite, 2: Potentially Infinite, and 3: Actually Infinite.

This initial post is somewhat hasty, and I may refine it a bit more in the days to come.

[1: Finite Space] Space is finite, but without edges. Although the total volume of space is expanding, it won’t expand forever.

There are different ways in which space can be finite without edges. You can have a so-called flat 3D torus, in which you essentially take a cubical room and glue the opposite walls together in pairs, and glue the ceiling to the floor. I don’t mean that you crush the walls in. I mean that you pull them around and stretch—think of taking a square of paper and gluing two opposite edges to make a cylinder, and then gluing the cylinder’s two ends together to make a torus. By the way you’d need to be in 4D space to smoothly make the 3D torus.

Another very well known finite 3D space is the hypersurface of a hypersphere, a 3D space analogous to the surface of a sphere. Or space might be lumpy as in the picture below, with regions of various curvature.

[Illustration by David Povilaitis from my book, The Fourth Dimension]

This picture shows our two-dimensional Flatland friend A Square on the surface of a finite space. A standard move in trying to visualize curved 3D space is to think of a flat guy living on a curved 2D space.

But people often think our space ought to be smooth. If you want a smooth space that’s not sphere-like you can look at an odd-ball finite space known as Poincare dodecahedral space, which can be produced by gluing together opposite faces of a dodecahedron with the smallest amount of clockwise twist needed to make the pentagons match.

I copied this picture from a wonderful and easily-read book by Jeffrey R. Weeks, The Shape of Space, now out in a new edition. In the early 1980s, I used to correspond with Weeks about the fourth dimension, and I’m proud to say that I suggested the title for his book. More recently, Weeks published an interesting paper discussing the notion that our universe’s space might actually be Poincare dodecahedral space. Weeks also has some nice geometry visualization software on line.

Although this is far from being obvious, you can also produce the Poincare dodecahedral space by taking two pretzels, that is two two-holed donuts, and gluing their surfaces together—analogously to how you might produce a hypersphere by gluing the surfaces of two spheres together. Of course for these weird gluings to work and for everything to look smooth, you’d have to warp the hell out of the pieces in a higher-dimensional space, but mathematicians don’t mind that kind of thing.

[Another Povilaitis illo from my book, The Fourth Dimension.]

How would you decide what the shape of our space is, anyway? It has to do with cosmic background radiation (CBR), the faint hiss of microwave static in the sky, and the possibility that we might be able to see “around” our space in certain directions. Disappointingly, the very latest measurements on the CBR suggest that, if space is finite, it’s just as likely to be a mere hypersphere as being a Poincare dodecahedral space. Although it might not be finite at all, as I’ll discuss below.

The reason I’m into this topic these days is because I just read a very good book by Donal O’Shea, The Poincare Conjecture, involving an eccentric (are there any other kind?) mathematician, Grigory Perelman, who proved old-time mathematician Henri Poincare’s conjecture that, um, well, that something that acts enough like a hypersphere really is a hypersphere.

By the way, the Poincare dodecahedral space is different enough (what with those hyper pretzel holes) that it doesn’t “act like a hypersphere” in the sesne that we’re talking about. But—until Perelman proved the Poincare conjecture (around 2002)—there was a lingering chance that there might be something that does act very much like a hypersphere that isn’t a hypersphere.

Perelman might get $1,000,000 from the Clay Mathematics Institute for his proof. But he’s not saying yet if he would accept the prize. He has some issues with the mathematics community.

[2: Potentially Infinite Space] Space is finite without edges, and it will expand forever, eventually passing through each finite size.

It’s well known that space is expanding, that is, all the galaxies are rushing apart from each other. Twenty years ago, people thought that space had no intrinsic reason to expand forever and that even though it was now expanding, the gravitational attraction of the galaxies would eventually pull it back. In this context, the Flatland image to use is that of an expanding balloon.

But now we’ve got this “dark energy” factor that may make our universe expand forever. Nobody really knows what dark energy is .

Some careless speakers say this means that an endless expansion means that our space is infinite, but that’s not the kind of infinity that I’m after. I want infinity here right now.

[3: Actually Infinite Space] Space is infinite right now, like an endless Euclidean 3D space.

How does infinite space jibe with the “Big Bang,” which is often thought of in terms of space expanding from a point?

[Figure from my first book, Geometry, Relativity and the Fourth Dimension. The left image represents a hyperspherical space that expands from a point-like Big Bang; the right image extends this to a scenario where space collapses back to a point.]

The way out is the so-called “ekpyrotic scenario” or “cyclic universe” which seems compatible with space being infinite and still having a “big bang” sort of event. The idea, as I understand it, is that we think of two endless parallel universes, two infinite hypersheets or “branes” of space. They’re quite close, perhaps only a few million Planck lengths apart.

The the branes are oscillating back and forth and that every few billion years they bounce off one another, and in these wonderful bounce instants — ZOW! — every crevice of space is flooded with a burst of energy. And the energy turns into matter, and it’s all rushing apart. See Princeton physicist Paul Steinhardt’s site for some short papers about it, an animation, and a link to his The Endless Universe , a book about the cyclic universe, written with Neil Turok. Rather than talking about the Big Bang, they talk about the Big Splat! Here’s a five minute talk by Steinhardt with some graphic animations:

[YouTube talk by Steinhardt]

By the way, you might think that an infinite space wouldn’t have room to be expanding, but simply think of a space in which every minute you map the point (x,y, z) into (2x, 2y, 2z). Contrary to one’s initial intuition, the expansion in such a space is homogeneous and the origin won’t look special. Wherever you are, you’re pulling away of stuff behind you and the stuff ahead is pulling ahead of you.

Really, you don’t have to think of the space itself expanding in the cyclic universe scenario, you can just think of the matter rushing apart. And eventually it’s all so far apart that the universes are quite cool and empty. And then they drift back together for another Great Spacef*ck and — ZOW again.

The notion of a cosmos in which we have two parallel branes of reality is something I adapted from the physicist Lisa Randall, for my last novel, Postsingular, where I call the two parallel worlds the Lobrane and the Hibrane. This carries over into the sequel Hylozoic, too.

In a quick web search, I do see some ill-informed people arguing against infinite universes on a priori reasons. These are rehashes of pre-Cantorian Scholastic arguments that are derived from the mistaken notion that an actual infinite is inherently contradictory.

I’ve always meant to write an SF story about an infinite Flat Earth. Where you could walk or drive and if you went far enough you’d get somewhere that nobody in your home civilization had ever been. Like an Age of Exploration that never has to stop.

One of my favorite papers about infinite universes is by Max Tegmark. In his paper, “Parallel Universes,” he argues that instead of worrying about having alternate worlds, we can just suppose that our universe goes on forever in space right now.

Eventually, I’m going to be talking about 4: Transfinite Space, but this blog post is too small, and my energy too low, to present all that today. Quite briefly, the third of my psipunk Postsingular books will (probably) be called Transfinite, and will involve some adventures in a world where actual infinities exist—as in my early novel White Light. But this time I’ll do it a little differently, I want the infinities to leak back into our actual lives.

In an earlier blog post I mentioned that I was warming up for writing Transfinite by writing a story about infinity that ended up with the title “Jack and the Aktuals.” If all goes well, this story will appear in the new online fiction site, Tor.com this summer.

Maybe if I could get out to transfinite space, I’d find my missing mathematician friend Jim Carrig there, safe in heaven dead.

By the way, I found an online reference to a painter, Alfred Russell, who started out as an abstract expressionist, and later turned to classical style.

He did a painting called “Transfinite Space” around 1950.

And another called “Transfinite Structure” around 1951. I’m thinking maybe there’s lots of much smaller quadrilaterals that we don’t see!

I also see that there’s an anthology of SF stories by A. E. van Vogt called Transfinite.