Back in 1976, when I was starting to be a writer, in Geneseo, New York, at night I’d write poems on my red IBM Selectric typewriter. Not that I bothered sending the poems out to magazines—submitting my math papers was heartbreak enough. A friend on the English faculty encouraged me to join in the periodic faculty poetry readings, where I’d hand out my works in mimeographed form.

Thirty years later, I’d run into Thom Metzger, who’d been a student of mine at Geneseo, and has since become a successful writer. He still has what may be the sole surviving copy of my mimeographed handout, and he shared a Xerox of it with me. Most of my old poems are in my Transreal collection, but the three below have never been reprinted.

[Today’s photos are from the Boardwalk in Santa Cruz, California.]

Dick Tracy With Crutches in a Bucket

Imagine
A national restaurant chain with
“crutches” of french-fries and
“chicken” of Tracy
a pot of honey with each meal
and French ticklers in the men’s room.

I remember exactly what I mean by that Dick Tracy poem. When I was a country kid in Louisville, my favorite restaurant was called Pryor’s. They had a big sign showing a tousled rooster playing golf. Their specialty was a dish called “Chicken in the Rough”— a huge mound of French fries, with pieces of fried chicken nestled into it. The meal came with soft dinner rolls and a tub of honey. And, as I think I mentioned earlier, my favorite comic strip as a boy was Chester Gould’s surreal Dick Tracy, with its peculiar insistence on grotesque criminals and the details of physical objects, often with lettered labels. So in my poem, I imagined a large bucket filled with dismembered and deep-fried limbs of Tracy, packed in among soft limp crutches of the kind you’d see in a painting by Salvador Dali. Of course!

Here are the other two poems. The first has to do with some mandatory vaccinations the government was promoting in the name of preventing that year’s flu du jour. And the last one is maybe, in part, a kind reminiscence of high-school.

Mr. Jones

One fall the
     people were vaccinated before the
          Election.

There are four plausible interpretations.
Or were.
     Now we are again singularities surfing
          on the wave of story.

Spore replication,
     Virus wars,
          it was there all
               the time.

Up All Night

I could fall
I realize as
The upturned faces begin
To shake
    Insanity is not a
    Habit but a “jackal’s
    Head” inside/outside the
    Lambency —
Imagine the hair-line cracks
Sudden black-dipt
Innards of a wind-faired
    Auto laid out in
    That basement with those H-2-0 trains
            Back there
After graduation the cars were empty
I was searching the glove compartments
For a pint
    Never mind
    We started kissing with thunder coming on, yeah
            thunder.

I recently acquired a copy of my old friend Clifford Pickover’s new tome, The Math Book , a really attractive and reasonably priced volume with 250 full page color illustrations, each illustration accompanied by a single-page description.

In Pickover’s words, “My goal in writing The Math Book is to provide a wide audience with a brief guide to important mathematical ideas and thinkers, with entries short enough to digest in a few minutes.”

[Breather Pseudosphere, Copyright (C) 2006 by Paul Nylander. See a larger image on Paul’s site.]

One of my favorite images in The Math Book is Paul Nylander’s rendition of the so-called Breather Pseudosphere. The idea behind this surface is that it has a constant curvature of -1, as opposed to a sphere, which might have a constant curvature of +1, and also as opposed to a plane, which has a constant curvature of 0. You’re supposed to ignore the ribs, and you need to accept that the surface intersects itself along a circle, which is clearer in the image below, by Xah Lee. You can rotate this image on Xah’s site.

[Segment of a Breather Pseudosphere, Copyright 2006 by Xah Lee.]

From the arcane math references that I’ve consulted—see for instance the Wikipedia “breather” page—I gather that the breather pseudosphere can in fact “breathe” in the sense that, by diddling a certain parameter, someone (not me anymore) could create a sequence of images of it and then assemble these into a video in which this negatively curved object will pulsate like some omnivorous space squid from Dimension Z. If any of you ultra-math-and-CS maniacs out there has access to such a video—or feels the urge to create one—share the link with us via a comment on this post!

[A traditional Beltrami pseudosphere, Copyright (C) 2006 by Richard Palais and the the 3DXM consortium.]

As Pickover’s book explains, the notion of pseudospheres was invented in 1868 by the mathematician Eugenio Beltrami, who formulated the more familiar “double trumpet” model, as shown above, created by the 3DXM Consortium . (3DXM is a graphics program, now called 3D-XplorMath.)

You can find further images of various kinds of pseudospheres (these images by Xah Lee, Luc Bernard and other members of the 3DXM consortium) on the Gallery of Pseudospherical surfaces at the Virtual Math Museum. This page includes an essay “About Pseudospherical Surfaces,” which explains (amid much gnarly math) that, at least when depicted in our normal 3D space, any surface of constant curvature -1 will include “singularities” in the forms of self-intersections or cuspy lines where the surface has a crease in it—like those ribs in the breather pseudosphere or like the edge where Beltrami’s two trumpets meet. But you can smoothly embed pseudospheres into 4D space, I believe.

As I was discussing in an earlier post, another way to create a negatively curved space is to start with a disk of some ductile material, and the keep stretching the disk all over, but without overly stretching the outer edge. The inside of the disk acquires more area than one would find in a regular flat disk. The extra room is there because the interior is now a negatively curved surface. And I think this surface is something like a pseudosphere. (A different approach is to stretch the outer edge of the disk to infinite length, and this is a different model of negatively curved space called the Poincaré plane.)

[Copyright (C) 2009 by Vonda N. McIntyre . White hyperbolic anemone with red veins.]

Some knitters and beaders have crafted physical objects like the edge-stretched pseudosphere, some of which appear among a wild Crochet Reef show in 2009. Among the goodies on display was a bead construction of a pseudospherical sea anenome by no less a personage than the fantasy and SF writer Vonda N. McIntyre —see the MathCrafts section of her home page.

When I was snorkeling near Palau a few years ago, I noticed that many naturally occurring soft corals are indeed negatively curved surfaces.

It’s worth remembering, by the way, that if you’re living in a very small house, it might be nice to have negatively curved space inside…

It occurs to me that the yuels and the jivas in Jim and the Flims going to be better characters if they can talk—but that their speech should be strange.

[A jiva and a yuel.]

I think of the Unipuskers in Frek and the Elixir, who only talk in imperative sentences, that was rich, a great gimmick for expressing bossiness. And the devilish-looking Wackles in Spaceland, they talked in a kind of Beat poetry.

Here’s a simple and powerful idea: the yuels speak in strings of verbs, and the jivas speak in strings of nouns! The whole thing is to give the aliens’ speech a different texture.

It expresses a nice distinction between them. The yuels are more Zen-like, in action, flowing, shapeshifting. And the jivas are more capitalist, hoarding, acquiring.

[A yuel dinosaur and a jiva sun.]

Originally I had the jivas talking in a somewhat dull orotund society-lady Mrs. Earbore kind of way. Like a standard Hollywood SF-movie alien with a deep voice and *ugh* a British accent—and no use of contractions. It’s so stupid that superintelligent aliens in Hollywood can never master the trick of saying, like, “we’re” instead of “we are.”

It’s gonna be more fun, mysterious, poetic, and alien if my jivas speak in strings of nouns.

Nouns seem easier to string together than verbs, by the way.

I’m still getting the hang of it. These are alien modes of thought! So I need to practice.

Suppose that a jiva and a yuel are going to rent a cottage at the beach with their families. Maybe they’d say, respectively, something like this:

Jiva: “Ocean house family days.”
Yuel: “Surge soak sleep eat nurture.”

Feel free to send in (as comments) some further examples of noun and/or verb speak.

Yesterday I was out a favorite spot on Four Mile Beach, north of Santa Cruz. That forest fire they had inland has pretty much died down. I did a little routine that I’ve often done while working on a new novel in recent years—I draw a logarthmic spiral in the sand and I letter the slogan, “EADEM MUTATA RESURGO”, which is Latin for “The Same, Yet Changed, I Re-arise.”

The mathematician Jakob (also called James) Bernoulli (1655-1705) has this inscribed at the very bottom of his tombstone in Basel along with a picture of a spiral (the engraver mistakenly depicted a regular Archimediean spiral instead of a wildly growing logarithmic spiral, like the kind you see on seashells).

I started this particular routine while writing Frek and the Elixir, and in fact the slogan is mentioned in that novel. If you feel like it, you can search my blog for “resurgo” to see the other spots where I’ve mentioned it.

I did some good work on my novel-in-progress Jim and the Flims today. Here’s a fun passage I wrote today, about a sinister alien plant. [Note that what I’m printing here is only the first draft, and I will in fact be revising it repeatedly on my way to finishing the novel.]

In the morning, Durkle woke me with a nudge of his foot. I heard a babble of voices nearby. Sitting up and looking around, I saw something like an umbrella projecting from the ground a short way off.

“It’s an offer fan,” said Durkle. “Did I tell you about them? A mobile plant—see those writhing roots at its base? They can walk, a little bit. It must have teeped us here. Mostly they live in the swamp, a few miles off. Isn’t it cool? I’ve heard you can get anything you want from an offer fan—if you’re quick enough. Watch me.”

All sorts of desirable objects were dancing beneath the offer fan’s greenish umbrella. It seemed that the offer fan could read my mind, for as I stared, it produced some items that I myself might want right about now: a cup of tea, fried eggs on rye, a map of Flimsy, a bag of pot with rolling papers, and a cantaloupe—all marching in giddy circles with the others across the roots beneath the thick umbrella, everything seemingly quite real. Perhaps the odd, alien plant had perfected a kind of direct matter control?

It was of course obvious to me that I shouldn’t try grabbing for the goodies, but Durkle was a willing fish for the bait. Having grown up in a land without computers or television, the boy was naive. Manfully he approached the offer fan, skipping to the left and the right as if he hoped to outmaneuver it.

The fan’s umbrella made continual slight adjustments in its position—the broad cap sat alertly atop a flexible stalk the thickness of a leg. I noticed that the underside of the umbrella was spongy and damp, as on certain unwholesome mushrooms. The thing’s roots were twitching and obviously eager to act. I was guessing that the fan’s kill technique would involve poison spray as well as strangling.

Durkle seemed oblivious of the risk—his eyes were fixed upon a scuffed-up board identical to Flam’s, a tasseled orange racing cap, a little chessboard, a shiny sword, and a fleshy glob that was forming itself into the body of—a naked woman, but with rounded off arms and legs and a smooth bulb for a head.

“Stop right there, Durkle!” cried Ginnie, sitting up beside me.

“I know I can beat this thing,” said Durkle, glancing back at her. “You want me to get you something too, Ginnie? Make her something, fan! I dare you.”

Sensitive to our group’s dynamics, the fan extended its offers to include a steaming mug of coffee and a very fashionable pair of sunglasses in wide tortoise-shell frames. Durkle crouched, preparing for his final dash.

I couldn’t let this continue. I ran forward and grabbed him around the waist.

“Senile loser!” he hollered. “You’re just jealous that I’m young and fast! Ginnie wants me, not you!”

Maybe I was old, but I had a jiva inside me. Durkle wasn’t going to break free of my grip. But he did manage to knock me off balance. The two of us fell to the practically into the shadow of the offer fan’s umbrella—a very bad place to be.

Fast as a whip, the thing had its roots around our wrists and ankles. And now, sure enough, an evil-smelling mist began wafting down from the cap. Most of the offers had disappeared now that the fan was getting down its real business. It’s central stalk tilted over, maneuvering the umbrella so that it could flop down right on top of us. I felt drowsy, and the spray was stinging my skin. As well as being a soporific, the spray was a digestive fluid.

Suddenly the umbrella tumbled off to one side. Ginnie’s jiva had cut the stalk! The offer fan let out a telepathic scream that filled my mind with red and yellow jaggies. Ginnie was circling around us, lashing at the carnivorous plant with her jiva tendrils and now—slow as always to defend me—my own jiva, Mijjy, began attacking the offer plant as well.

Durkle had managed to free one of his wrists and he’d gotten hold of that little sword the plant had made as bait—this desirable item had remained on offer to the end. It was indeed a real and solid blade. The boy slashed away at the roots, freeing our hands and ankles. He crawled a few feet away and tugged me after him. Slowly the fan’s frenzied alarm waves within my head died down—and the mist drifted away. I could think again. In a belated coup de grace, Mijjy set the remains of the offer fan on fire.

“Got any more good deals for us?” I asked Durkle.