The Four-Dimensional Lord of Dance

I wrote two posts last year dealing with the fourth dimension:

• Views of a Tesseract
•  Arts and Crafts in Four Dimensions

The focus was mathematical, but along the way I looked at how the fourth (spacial) dimension appears in the works of authors like H. P. Lovecraft, Robert Heinlein, H. G. Wells, Jorge Luis Borges, and, most memorably, Madeleine L'Engle, whose A Wrinkle in Time is about to appear as an uninspired-looking Disney movie in March (sigh). I also talked about mathematical visionaries and mystics like Paul S. Donchian and Charles Howard Hinton, both of whom made real contributions to the field, if only in the sense that they developed and humanized what the academics were saying in their inaccessible research articles, and both of whom might be labeled as cranks or crackpots.

Since then I've done a little research on Hinton, Donchian, et al., and have found a number of other links between the idea of a fourth spacial dimension and various forms of spirituality or mysticism. For instance, the German astronomer Friedrich Zöllner (1834 – 1882) apparently tried to use the fourth dimension explain Spiritualist phenomena. In his eagerness, he was imposed upon by the medium Henry Slade in experiments that have since been debunked. Fantasy and horror authors in their turn used the claims of Spiritualism in their stories; some, like Arthur Machen and Algernon Blackwood, actually subscribed to its views. Hinton, who wrote a number of "scientific romances" himself, was a post-Christian altruist who speculated that spiritual agencies might work by means of the fourth dimension and believed in something like eternal return.

Some Christians of the late Victorian era, disconcerted by the advance of materialism, attempted to colonize the fourth dimension themselves. For other Christians, such as the liberal theologian Edwin Abbott Abbott (author of Flatland: A Romance of Many Dimensions, a book much admired by Hinton), higher spacial dimensions were merely a metaphor for gradual way in which the human mind must approach divine truths. 

[source]

Salvador Dalí appears to have used the fourth dimension in a similar way, in his famous 1954 painting Crucifixion (Corpus Hypercubus), which portrays Christ crucified on the net of a tesseract / hypercube / 8-cell (Schläfli symbol {4,3,3}) hovering over a square grid (Schläfli symbol {4,4}), illustrating the incomprehensibility of God to man.

I have in my hands a Dover edition of Speculations on the Fourth Dimension: Selected Writings of Charles H. Hinton, which includes several of Hinton's scientific romances. It's edited and has an excellent introduction by Rudolph v.B. Rucker, also known as Rudy Rucker, author of the Ware Tetralogy and a modern tribute to Flatland and all-around sci-fi author of note. So no doubt I'll soon be posting about all of this yet again.

*

My post on four-dimensional arts and crafts includes an account of my building the sections and net of a 120-cell. More recently, I've printed and built the sections and net of a 24-cell, which is a regular four-dimensional polytope built from twenty-four octahedra.

The sections proceed as follows, with colors given as the craft paints I bought at Wal-Mart: (I) the octahedral cell at the "south pole" (Parchment); (II) the truncated octahedral section cut by a hyperplane through the midpoints of the edges "above" the south pole (Parchment and Real Brown); (III) the cuboctahedral equatorial section cut by a hyperplane through the set of vertices to which these edges connect (Look At Me Blue and Real Brown); (IV) the truncated octahedral section analogous to Section II but in the "northern hemisphere" (Look At Me Blue and Real Brown); and (V) the octahedral cell at the "north pole" (Coffee Latte).

The net has the "south pole" at the center and the "north pole" at the base. For reasons fully known only to my subconscious, but partly inspired by Dalí's painting above, I decided to model it after traditional depictions of the Hindu god Shiva as Nataraja or Lord of Dance, with three-fold rotational symmetry.

Shiva is the destroyer, and his dance is the cosmic dance of creation / destruction. That puts me in mind of the line from the Bhagavad Gita, uttered by Krishna, quoted by Robert Oppenheimer, and used by me in the title of a short story: "Now I am become Death, destroyer of worlds."

Francisco Carvajal y Lopez: A (Self) Portrait

My story "White Rainbow and Brown Devil" is set to appear in Heroic Fantasy Quarterly Issue #35 in February. It's a direct sequel to my first Carvajal story, "Heart of Tashyas," coming between it and "I Am Become Death, Destroyer of Worlds," and takes place in the Southwest Texas border region, which is where I live, beginning at Sycamore Creek and traveling up the Rio Grande across Devil's River and Seminole Canyon to the Pecos crossing. (The geography is somewhat telescoped.)

The story will be accompanied by an original watercolor painting of its protagonist, the vagabond conquistador Francisco Carvajal y Lopez:

That is, essentially, a self portrait, except that I don't have long hair, I don't wear earrings, I don't encourage birds of the American subtropics to perch on my shoulder, and I don't go about armed to the teeth. Ultimately it's just a picture of the guy in my story, but to me it also asks the question To what extent do I identify with my protagonist? without really answering it. I looked to Frida Kahlo for inspiration.

Here's the slightly modified version that will accompany the story:

That's a green jay on his/my shoulder, incidentally. In the United States, green jays are found only in South Texas. The sewage treatment plant outside the town I live in is pretty much the northern limit of their range. I sometimes go there to bird-watch, and the jays are my favorite thing to see. A magnificent, lime green bird with a dark blue head. Much of the adjoining nature reserve occupies an old landfill covered with thickets of prickly pear; Carvajal's first adventure in "Heart of Tashyas" began at the foot of the small extinct volcano just across the highway, on a site now occupied by trailer homes and the ruins of a fort.

Here's the initial sketch:

The background is a prickly pear cactus wallpaper design of my own devising:

There are exactly seventeen types of wallpaper symmetry. My design is described by the group known as pg in the IUC (International Union of Crystallography) notation. I created it by drawing a single prickly pear image and copying it via translations and glide reflections.

I cast this wallpaper upon the Internet for noncommercial use, but I urge the reader to employ it in papering a room only with extreme caution.

Nightmare Alley

Question: What does William Lindsay Gresham, the American author of Nightmare Alley, a bitingly vitriolic, pessimistic, cynical novel about the rise and fall of a carnie conman, have in common with C. S. Lewis, the popular apologist and beloved writer of children's fantasy books?

Answer: They were both married to Joy Davidman.

I first learned of Nightmare Alley, which came out in 1946, when I watched the film noir of the same name starring Tyrone Power. After being rather difficult to find for a long time, it was available for streaming through Amazon for a brief period last fall, but has now mysteriously vanished again. It's an excellent film, a true gem among noirs. I must be getting worldly-wise, because I could tell exactly where the film was glossing over seedy details or pulling its punches. Most importantly, I could tell exactly how the story was supposed to end. I don't want to spoil it, but it's hard to think of a darker ending.

If the film is excellent, the novel is only that much better, a detached, merciless dissection of a man destroyed by his own small-mindedness and lack of self-understanding. Stanton Carlisle, the protagonist, uses what he learns at the carnival to start a big-time mentalist act, then reinvents himself as a spiritualist minister in a bid for money, lots of money. I don't think I'm giving anything away when I say that it all blows up in his face. He shows no mercy to marks and gets none when it's his turn to be the prey. The last line of the novel is so cold it burns.

And yet it's impossible not to pity Stan. There are several flashbacks to his childhood: you can't really look at a well-portrayed kid and say, yeah, he gets what's coming to him. As the pieces of his backstory fall into place, you see the picture of a child warped by selfish parents whose dysfunctional marriage pushes him into the adult world of fear, lies, compromise, manipulation, frustration, and abuse. The novel leans heavily (though not explicitly) on certain well-known Freudian theories, but its examination of Stan's psychology is no less incisive for all that.

Nightmare Alley is a grotesque but beautiful kaleidoscope of twisted humanity, in which the only freaks, inside the carnival or out, are those who aren't freaks. It's aptly named, because you can see the monstrous ending from far off in the very first pages, then proceed to step slowly toward it with the inevitability of a nightmare. Nightmare Alley is a masterpiece of noir.

A brief but detailed account of Gresham's life can be found here. He got to know the ins and outs of the carny world through a fellow volunteer in the Spanish Civil War. Shortly after the war his first marriage ended in divorce. He began drinking heavily and attempted suicide, after which he turned to writing and editing, marrying Davidman, his second wife, in 1942. They had two sons. His abiding interest in sideshows, spiritualism, magic acts, and debunking molded his literary career as a writer of both fiction and nonfiction.

In an account I can't seem to locate right now, I read that he and his wife both became interested in Christianity and the works of C. S. Lewis; he ultimately moved on to other things (like Spiritualism and Scientology, strangely enough), but Davidman, who was a Jewish atheist, became a Christian and traveled to England to meet Lewis. Gresham had an affair with Davidman's cousin, Renee Rodriguez, while she was away. He had also become abusive toward her and their children, and their marriage ended in divorce, after which he married Rodriguez. Davidman's subsequent marriage to Lewis was made famous by his writings, most notably by A Grief Observed, written after her death in 1960. Gresham's sons remained with Lewis.

Gresham committed suicide at a Manhattan hotel in 1962 after being diagnosed with cancer of the tongue. In his pockets they found business cards that read: No Address. No Phone. No Business. No Money. Retired.

Metapost 2017

The year 2017 has come and gone. Time for a year-end retrospective metapost!

First, and most importantly to me, the list of books I read in 2017, in reverse chronological order:

• The Aztecs: People of the Sun by Alfonso Caso
• Flow My Tears, the Policeman Said by Philip K. Dick
• Story of a Soul by Therese of Lisieux *
• The Haunted Mesa by Louis L'Amour
• The Texas Stories of Nelson Algren by Nelson Algren
• The Haunting of Hill House by Shirley Jackson *
• Now Wait For Last Year by Philip K. Dick
• Alice's Adventures in Wonderland by Lewis Carroll *
• Kiss Me, Deadly by Mickey Spillane
• Mona Lisa Overdrive by William Gibson
• The Return of the King by J. R. R. Tolkien *
• The Big Kill by Mickey Spillane
• The Godwhale by T. J. Bass
• One Lonely Night by Mickey Spillane
• Half Past Human by T. J. Bass
• The Stars My Destination by Alfred Bester
• Count Zero by William Gibson
• King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts
• The Gulag Archipelago: Volume 3 by Aleksandr Solzhenitsyn
• The Two Towers by J. R. R. Tolkien *
• The Ministry of Fear by Graham Greene
• David Copperfield by Charles Dickens
• Necronomicon by H. P. Lovecraft
• Vulcan's Glory by D. C. Fontana
• The House on the Borderland by William Hope Hodgson
• Cugel's Saga by Jack Vance
• The Preparation of the Child for Science by Mary EverestBoole
• The Russia House by John le Carré
• The Fellowship of the Ring by J. R. R. Tolkien *
• Missions and Pueblos of the Old Southwest by Earle R. Forrest
• The Summer Stargazer by Robert Claiborne
• Life of William Blake by Alexander Gilchrist
• The Gulag Archipelago: Volume 2 by Aleksandr Solzhenitsyn
• Regular Polytopes by H. S. M. Coxeter
• A Storm of Wings by M. John Harrison
• The Pastel City by M. John Harrison
• The Pueblo Revolt by David Roberts
• Pueblo Gods and Myths by Hamilton A. Tyler
• The Conquering Sword of Conan by Robert E. Howard
• Life in the Pueblos by Ruth Underhill
• Hell House by Richard Matheson
• A Wizard of Earthsea by Ursula K. LeGuin *
• Vengeance is Mine! by Mickey Spillane

Isn't it sad how I only read old stuff? What's the matter with me? I do actually have a few newer things on my list of to-reads; my immanent venture into the world of e-books will hopefully help with that. (I'm not a complete luddite, just ten years behind the times. I do have a cell phone now. That is, my wife does.)

Asterixes denote works read aloud to my children. I read aloud to them for half an hour to an hour every night. Because they begged me to, I read them The Lord of the Rings this year. I'd been reluctant, thinking them a bit young (seven and nine) and reflecting that, after all, you can only read a book for the first time once. But they were starting to read it without me, so I figured I'd better take the opportunity while I still had it.

It was a long project: we went in something like real time, from Frodo's departure from Bag End to his awakening on the Field of Cormallen, and decided that we'd have to start it on September 22 next time around. This is my third time to read LOTR aloud, but...I still cry at certain parts. I'm not ashamed, dammit.

My literary high point for the year is probably my completion of The Gulag Archipelago. My low point would be those four Mickey Spillane novels, none of which I can clearly remember now, although I do seem to recall one whose resolution involved a baby blowing a woman's brains out with a handgun. I began Kiss Me, Deadly while standing in line at Wal-Mart, waiting to score a Super NES Classic when it became available at midnight of its release date, if that gives you any idea of the luridness of my daily life.

But here's an amusing Mickey Spillane story I heard at Thanksgiving. My godfather, who, like Spillane, lived in South Carolina, used to know a bar or some such place also frequented by Spillane. He went out one night with someone from out of town, and they saw Spillane. "Hey, want to meet Mickey Spillane?" my godfather asked. They went over and, like an old buddy, my godfather said, "Mickey, I'd like you to meet so-and-so." Spillane gave them both a hearty handshake and hello. It isn't known whether he realized he'd never met either of the two.

My 2017 reading completion rate is a bit of a falling-off from previous years, but in my defense I should list the works I'm in the middle of:

• History of the Conquest of Mexico by William H. Prescott
• The Habit of Being by Flannery O'Connor
• Summa Theologica by Thomas Aquinas

Not exactly light reading! There are also bits and pieces by writers like Plato, Aristotle, Pascal, Descartes, Nietzsche, and others. I've also read a bunch of comic books graphic novels and manga, including four superman comics, the first omnibus edition of Wonder Woman comics by George Perez, Nausicaä of the Valley of the Wind, and Akira. I meant to write a post about Wonder Woman comics, but seeing the movie (which everyone seemed to like so much but which I found depressingly stupid) sort of took the wind out of my sails. Sometime soon, perhaps.

As for stuff I produced this year, I had two Carvajal novelettes appear in the august e-pages of Heroic Fantasy Quarterly.

Heart of Tashyas, HFQ #31

I've got a couple more sitting in the trunk, to be produced in the future if there seems to be interest in more. One day I'd like to see a collection of Carvajal stories published in some way, shape, or form.

I Am Become Death, Destroyer of Worlds, HFQ #33

The third installment of my Carvajal narrative will appear in HFQ next month. Here's the sketch for the accompanying illustration:

That's based on a self-portrait, incidentally, though I don't have a pirate earring, and I don't let my hair grow that long these days. (I do like to go around with a sword in each hand, however.) The prickly pear wallpaper pattern, which is of type pg, is my own invention. I'll include the pattern itself in a future post.

All of which reminds me: one high point of 2017 was my attendance at the World Fantasy Convention in San Antonio, where I got to meet assorted heroes, villains, and rogues of the fantasy publication world in person, and had the heady experience of encountering some of my very own writing and illustration in the dealers' room.

I also showed my art in a one-man exhibition on the Sul Ross State University campus in Alpine, Texas. I sold a few pieces, gave a talk about art, math, and writing, ate some tasty snacks, and in general had a good time.

Unfortunately I didn't have the presence of mind to get any pictures during the closing reception. Some of the pictures will be familiar to readers of my books.

Speaking of Alpine, Nelson Algren, an author I discovered this year, has an interesting connection to Sul Ross. A college-educated would-be journalist from Chicago, he wound up in Alpine as a drifter / hobo during the Great Depression, where he began working on a novel on a typewriter at Sul Ross, which was then just a normal college. Upon leaving town by train, he decided to take the typewriter with him. The authorities caught up with him further down the line. He was arrested and thrown into the Brewster County jail, where he languished for months until a judge was in the area to hear his case. His lawyer compared him with Jean Valjean during the trial; although convicted, he was released and given twenty-four hours to leave the state. His imprisonment was a harrowing experience that colored his fiction for the rest of his life. He was a proletarian writer whose work petered out in the forties or fifties, though one of his best stories appeared in Playboy in the seventies. I encountered him in Flannery O'Connor's correspondence; O'Connor didn't have a high opinion of his work.

But back to me. I also showed some painting, drawings, and mathematical sculptures at a gallery in the town where I live. The 120-cell sections and net in the foreground are mine; the painting in the background is not.

My sections and net of the 24-cell were also on display, though not shown in this picture. I'll dedicate a post to them in the near future.

Lately I've mostly been working on Ark of the Hexaemeron, the third installment in my Enoch series. One of my 2018 resolutions is to get it finished and published this year. For various reasons my work speed has slowed down somewhat of late, which is why my blogging continues to be light. But I do plan to continue with reviewing noir films; the next one on my list is, I believe, The Killers.

The Coming of the White Worm

This year I'm also going to continue tinkering with techniques for digital illustration, as I'd really like to tell a story in pictures some day. I think of my various HFQ illustrations as playful exercises. I've played with doing colors solely on the computer, mainly because it's so difficult to ensure accurate color transitions from watercolor to digital files. In the end I suspect I'll try to compromise somehow.

Well, that about wraps it up. Let's send 2017 off on a high note!