Wednesday, May 17, 2017

Views of a Tesseract

…the breadth, and length, and depth, and height…
– Ephesians 3:18
And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal. And he measured the wall thereof, an hundred and forty and four cubits, according to the measure of a man, that is, of the angel. And the building of the wall of it was of jasper: and the city was pure gold, like unto clear glass.
– Revelation 21:16-18
Un homme qui y consacrerait son existence arriverait peut-être à se peindre la quatrième dimension. [A man who devoted his life to it could perhaps succeed in picturing to himself the fourth dimension.]
– Henri Poincaré
This spring I have scaled the awful, sanity-threatening Unknown Kadaths of the fourth dimension in a desperate, god-provoking quest to visualize the six regular polytopes.

What is a polytope, you ask? The word polytope is the general term in the sequence whose first terms are the line segment (dimension one), the polygon (dimension two), and the polyhedron (dimension three). A regular polytope is a polytope which is "completely symmetric."

Theatetus, a contemporary of Plato, proved that there are exactly five regular polyhedra: the tetrahedron, the octahedron, the icosahedron, the cube, and the dodecahedron. They are called the Platonic solids because Plato identified each of the first four with a material element (fire, air, water, earth), and the fifth with "the delineation of the universe" [Timaeus]. Their construction is the crowning achievement of Euclid's Elements, written in about 300 BC. But the world had to wait more than two thousand years for the "discovery" of their analogues in the fourth dimension.

Fourth-dimensional geometry, thought it might seem mysterious to the uninitiated, is defined axiomatically, just like Euclid's three-dimensional geometry, and has an intuitive basis. It was first described by Ludwig Schläfli, a Swiss mathematician, in the 1850s, but his work remained relatively inaccessible and unknown. Then, between 1880 and 1900, the geometry of higher dimensions was rediscovered in nine different publications written independently of each other. The time, it seems, was ripe. It was the dawn of a new era.

Not that era. [source]
This phenomenon of numerous researchers all suddenly reaching the same conclusion at the same time, though surprising when it happens, isn't all that uncommon in the history of math, science, and technology. What's striking is the way four-dimensional geometry fired the popular imagination, which seems in some cases to have outstripped academia.

Last year I blogged about Flatland: A Romance of Many Dimensions, a strange geometrical fantasy written by the English schoolmaster Edwin A. Abbott (1838-1926) and published in 1884. In it, Abbott gives what must be the first popular description of the tesseract, or four-dimensional hypercube, by way of analogy.
In One Dimension, did not a moving Point produce a Line with TWO terminal points?
In Two Dimensions, did not a moving Line produce a Square with FOUR terminal points?
In Three Dimensions, did not a moving Square produce – did not this eye of mine behold it – that blessed Being, a Cube, with EIGHT terminal points?
And in Four Dimensions shall not a moving Cube – alas, for Analogy, and alas for the Progress of Truth, if it be not so – shall not, I say, the motion of a divine Cube result in a still more divine Organization with SIXTEEN terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this – if I might quote my Lord's own words – "strictly according to Analogy"?
Again, was I not taught by my Lord that as in a Line there are TWO bounding Points, and in a Square there are FOUR bounding Lines, so in a Cube there must be SIX bounding Squares? Behold once more the confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have 8 bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to Analogy"?
How much exactly did Abbott know of contemporary research? One imagines he must have encountered something, but I can't seem to find anything definite. A matter for further research, I suppose.

Inspired by Abbott, a high school teacher and amateur mathematician by the name of Charles Howard Hinton (1853-1907) wrote a number of "scientific romances" exploring higher dimensions. It was Hinton who coined the term tesseract, and his book A New Era of Thought, published in 1888, provides a detailed account of the hypercube's structure. It also offers a mystical interpretation of the fourth dimension, following to some extent in Abbott's footsteps, but with considerably greater gravity and self-importance.
We have been subject to a limitation of the most absurd character. Let us open our eyes and see the facts.
Now, it requires some training to open the eyes. For many years I worked at the subject without the slightest success. All was mere formalism. But by adopting the simplest means, and by a more thorough knowledge of space, the whole flashed clear.
Space shapes can only be symbolical of four-dimensional shapes; and if we do not deal with space shapes directly, but only treat them by symbols on the plane – as in analytical geometry – we are trying to get a perception of higher space through symbols of symbols, and the task is hopeless. But a direct study of space leads us to the knowledge of higher space. And with the knowledge of higher space there come into our ken boundless possibilities. All those things may be real, whereof saints and philosophers have dreamed.
Hinton was read by Jorge Luis Borges, and his book is mentioned "Tlön, Uqbar, Orbis Tertius."

Through his father, described by some as a religious crank, Hinton came to know the family of the late George Boole, the father of algebraic logic, whose untimely death had left his wife, Mary Everest* Boole, with their five daughters to raise. Mrs. Boole's interests ranged from mathematics to mysticism to politics; she wrote a number of pedagogical works, organized controversial discussion groups, and hobnobbed with the denizens of the fringes. Among these were the polygamy advocate James Hinton and his son Howard.

Howard married the eldest daughter, Mary Ellen Boole, in 1880, and they had four children together. A few later, he married a second woman under an assumed name, had two children with her, was convicted of bigamy, spent a few days in jail, lost his job, and moved to the United States with his (first) wife to become a university professor. He died unexpectedly in 1907, and Mary Ellen committed suicide the next year.

H. S. M. Coxeter's Regular Polytopes, published (in its second edition) in 1963, remains the main authority on its subject. I've entertained myself by constructing the various solids he describes in it.


More importantly for us, each chapter concludes with historical notes. There Coxeter discusses Alicia Boole Stott (1860-1940), another of George Boole's daughters, with whom he was personally acquainted in her later years. Curiously, though he mentions both Hinton and his book (in deprecatory terms), he says nothing about the family connection or about the fact that Stott assisted in finishing and publishing A New Era in Human Thought when Hinton left the country.
When Alice was about thirteen the five girls were reunited with their mother (whose books reveal her as one of the pioneers of modern pedagogy) in a poor, dark, dirty, and uncomfortable lodging in London. There was no possibility of education in the ordinary sense, but Mrs. Boole's friendship with James Hinton attracted to the house a continual stream of social crusaders and cranks. It was during those years that Hinton's son Howard brought a lot of small wooden cubes, and set the youngest three girls the task of memorizing the arbitrary list of Latin words by which he named them, and piling them into shapes. To Ethel, and possibly Lucy too, this was a meaningless bore; but it inspired Alice (at the age of about eighteen) to an extraordinarily intimate grasp of four-dimensional geometry. Howard Hinton wrote several books on higher space, including a considerable amount of mystical interpretation. His disciple did not care to follow him along these other lines of thought, but soon surpassed him in geometrical knowledge.
In 1890, she married an actuary and "led a life of drudgery" [Coxeter] as a wife and mother with a small income. But she continued to explore the fourth dimension as a kind of hobby, building cardboard models of three-dimensional "slices" of four-dimensional figures. Somehow her husband came across the work of the Dutch mathematician Pieter Hendrik Schoute, whose published diagrams mirrored her models. She contacted Schoute and the two began a long and fruitful collaboration. As Coxeter puts it,
Mrs. Stott's power of geometrical visualization supplemented Schoute's more orthodox methods, so they were an ideal team.
It was she who coined the term polytope.

Among other "enthusiasts" (as opposed to academicians) who contributed to four-dimensional geometry, Coxeter mentions Paul S. Donchian, an Armenian American.
His great-grandfather was a jeweller at the court of the Sultan of Turkey, and many of his other ancestors were oriental jewellers and handicraftsmen. He was born in Hartford, Connecticut, in 1895. His mathematical training ended with high school geometry and algebra, but he was always interested in scientific subjects. He inherited the rug business established by his father, and operated it for forty years. At about the age of thirty he suddenly began to experience a number of startling and challenging dreams of the previsionary type soon to be described by Dunne in 'An Experiment with Time'. In an attempt to solve the problems thus presented, he determined to make a thorough analysis of the geometry of hyper-space.
Donchian built delicate three-dimensional models of four-dimensional polytopes which were displayed at expositions in Chicago and Pittsburgh, several pictures of which appear in Coxeter's book.

I built a wire-solder model of the hypercube many years ago, using what I suppose are the same principles, though I didn't know it at the time. It remains in good shape, but it's in my parents' possession, and I don't have a picture of it handy.

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These days I'm working on a set of 3D printer files reproducing Stott's model of the 120-cell, a polytope composed of 120 dodecahedral cells. From her 1900 paper "On Certain Series of Sections  of the Regular Four-dimensional Hypersolids," I've created the virtual constructions from which I'll derive the vertex coordinates.


The following image represents a series of slices slices cut by hyperplanes parallel to a dodecahedral cell, starting with the cell itself (at the center of the image) and ending with the "equatorial" slice midway up the polytope (at the outside of the image). In my file the layers are numbered from VIII to XIV, in accord with the partial nets illustrated in her paper shown above.


And here is part of the "net" from which the 120-cell can be "folded." The "equatorial" layer of dodecahedra (not shown) fits in the interstices, with one for each edge of the dodecahedral cell forming the "base." A second set identical to the one shown then "caps" the 120-cell above the equator.


However, I find that I'm not the first to attempt reconstructing Stott's fascinating models. Well, I'll do the 600-cell as well, and that will be impressive. Here is my projection of the 600-cell to the plane.


I hope to recreate it in string art, the use of which in teaching children was pioneered by Mary Everest Boole.

Here are some of my printed polyhedra, which I built myself in Blender: we have a compound of five tetrahedra, a compound of five cubes, a compound of five tetrahedra (edges only), a great dodecahedron, and four rhombic dodecahedra, but no hypersolids yet. (Chessboard chosen advisedly: see below.)


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The geometry of the fourth dimension has made appearances in a number of imaginative works. Aside from Flatland, the earliest instance is probably The Time Machine by H. G. Wells, published in 1898. Unfortunately, he makes the rather common mistake of conflating temporal extension with a fourth spacial dimension.
"Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing.
"Scientific people," proceeded the Time Traveller, after the pause required for the proper assimilation of this, "know very well that Time is only a kind of Space. Here is a popular scientific diagram, a weather record. This line I trace with my finger shows the movement of the barometer. Yesterday it was so high, yesterday night it fell, then this morning it rose again, and so gently upward to here. Surely the mercury did not trace this line in any of the dimensions of Space generally recognized? But certainly it traced such a line, and that line, therefore, we must conclude was along the Time-Dimension."
H. P. Lovecraft gives a much better account of the fourth dimension in "The Dreams in the Witch House," published in 1933 and described by its Weird Tales tagline as "a story of mathematics, witchcraft and Walpurgis Night, in which the horror creeps and grows." Whatever you think of Lovecraft as a writer, one thing you can say is this: he knows when to be explicit and when to be vague and ominous. It serves him well here.
Toward the end of March he began to pick up in his mathematics, though the other studies bothered him increasingly. He was getting an intuitive knack for solving Riemannian equations, and astonished Professor Upham by his comprehension of fourth-dimensional and other problems which had floored all the rest of the class. One afternoon there was a discussion of possible freakish curvatures in space, and of theoretical points of approach or even contact between our part of the cosmos and various other regions as distant as the farthest stars or the transgalactic gulfs themselves – or even as fabulously remote as the tentatively conceivable cosmic units beyond the whole Einsteinian space-time continuum. Gilman's handling of this theme filled everyone with admiration, even though some of his hypothetical illustrations caused an increase in the always plentiful gossip about his nervous and solitary eccentricity. What made the students shake their heads was his sober theory that a man might – given mathematical knowledge admittedly beyond all likelihood of human acquirement – step deliberately from the earth to any other celestial body which might lie at one of an infinity of specific points in the cosmic pattern.
Reminds me of my own college days! Ha ha, actually, it doesn't. I spent an entire year of my life working a problem of 10- and 26-dimensional geometry, got stuck on a minus sign for most of its duration, and finally had to give up and start a new problem. My dissertation advisor may very well have wondered about my nervous and solitary eccentricity, and my fellow students may have shaken their heads at my theories, but not for the reasons Gilman found himself the source of such disturbance…

[source]
The net of a tesseract figures in Robert A. Heinlein's 1941 story "And He Built a Crooked House," in which an architect builds a house in the shape of the three-dimensional "net" of a tesseract (from which the polytope can be "folded" much as a cube is folded from a two-dimensional cruciform net); an earthquake causes it to collapse into an actual tesseract from which other worlds can be reached. The story was anthologized in Fantasia Mathematica in 1958.

Madeleine L'Engle's A Wrinkle in Time, which contains the most well-known tesseract (and verbs the word as tesser), was published five years later, in 1963. I wonder if L'Engle got her idea (which is rather garbled) from the Heinlein story?
Meg sighed. "Just explain it to me."
"Okay," Charles said. "What is the first dimension?"
"Well, a line."
"Okay.  And the second dimension?"
"Well, you'd square the line. A flat square would be in the second dimension."
"And the third?"
"Well, you'd square the second dimension. Then the square wouldn't be flat any more. It would have a bottom, and sides, and a top."
"And the fourth?"
"Well, I guess if you want to put it into mathematical terms, you'd square the square. But you can't take a pencil and draw it the way you can the first three. I know it's got something to do with Einstein and time. I guess maybe you could call the fourth dimension Time."
"That's right," Charles said. "Good girl. Okay, then, for the fifth dimension you'd square the fourth, wouldn't you?"
"I guess so."
"Well the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through space without having to go the long way around. In other words, to put it into Euclid, or old-fashioned plane geometry, a straight line is not the shortest distance between two points."
Terrible! Just imagine an inhabitant of Flatland speaking like that: "The third dimension is Time. The fourth dimension's a cube. You add that to the three dimensions and you can travel through the plane without having to go the long way around. In other words, to put it into linear terms, a straight line is not the shortest distance between two points." Ugh! A novel is not a math textbook, it is true, but, for me, it's harder to overlook such nonsense than scientific speculation. There's nothing like 1 + 1 = 3 to break the suspension of disbelief. (Not that it's a bad book mind you.)

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[source]
Higher-dimensional geometry appears in art as well. Cubism is an oft-cited example, but geometry figures more directly in Salvador Dali's Crucifixion (Corpus Hypercubus), which depicts Christ crucified on the net of a tesseract. Just as the net permits us to approach what lies beyond our comprehension, in God, so does the Incarnation provides a "picture" of God comprehensible to humankind. That's how the picture usually seems to be interpreted.

Well, somehow this has turned into one of those posts of mine in which I draw connections between whatever unrelated topics I happen to be interested in. Here it's higher-dimensional geometry, science fiction and fantasy, the early twentieth century, and art. I do still want to describe the catalog of regular polytopes, but that will have to wait for a subsequent post.

* The mountain was named after her uncle. Quite a dynasty!

Friday, May 5, 2017

Ashes to Ashes

Today I'd like to talk about a man. We all know who he is. Some think of him as a great man; none more so than himself. He is, in many ways, the man for our times. True, he's not the most intelligent person. He's not the most emotionally mature. Most of his injuries are self-inflicted. He's apt to say whatever comes into his head, and his decisions reflect an extreme lack of forethought. His words and actions are frequently reprehensible, sometimes even disgusting. He's a bit of a racist, a bit of a xenophobe, a bit of a sexist. He thinks very highly of his attractiveness to women of all ages, and feels welcome to take what he wants when he sees it. Still, time and again, he's proven his detractors wrong. He's proven that he does have it in him to be a winner.

This is Donald Trump, the President of the United States.
He is not the subject of this post.

Thursday, May 4, 2017

The Bone King at HFQ

There's a Far Side cartoon with a crowd of art patrons admiring a painting in a gallery. In the back, one old lady is whispering to another, "My boy made the frame." In that spirit, I announce the appearance of my illustration to "The Enemy's True Name" by Mark Silcox at Heroic Fantasy Quarterly. That's right: I made the picture.


The Bone King: drawn in ink, digitally colored. Go check it out! And read the story, too!

As I've said, I've been toying with Photoshop workflow used by people in the comics industry. I've recently become interested in comics and in digital illustration in general. For me, it seems to work best when I begin with a hand-drawn picture with cross-hatched shading and build up a layer of flats, with highlights and shadows in separate layers. Not quite the same as painting, but it's exhilarating to actually be able to change things that need to be changed.

In other artsy news, I'm having an exhibition at a certain university out in Alpine, Texas, this August and September. More details to come. Stop by if you're in the area! I'm also still working on my Enoch and Carvajal stories – I've written several of the latter – but I've been too busy with school to blog regularly. Hopefully that will change once the semester is over.

Right now I'm wrapping up a graduate course on regular polytopes. My school recently purchased a large 3D printer which, for lack of a better place (and because of my shameless begging), is set up in my office, and I'm working on producing some of the interesting solids and compounds we explored this spring. I've also been composing a post on higher-dimensional geometry and genre fiction that I'll have to wrap up some time soon...

Tuesday, April 4, 2017

April is the Cruelest Month

Unreal City
Under the brown fog of a winter noon
– T. S. Eliot, "The Waste Land"
The more I read genre fiction, the more I realize that I'm not so much drawn in by any genre per se as by certain styles and artistic visions. One writer will click while another leaves me frustrated with myself for not enjoying what so many others esteem so highly.

One thing I find myself drawn to is the attempt on an author's part to make their invented world out of whole cloth. I don't mean that I like vivid descriptions and attention to detail, though these are fine when called for. What I mean is, I don't much like works that rely heavily on genre conventions, that bank on the reader's familiarity with common settings and tropes rather than building up an independent vision. My eyes just glide right over stuff like that. It's not that conventions are bad. All writing has abbreviations and shortcuts. But not much of truth or beauty, of strangeness or wonder or epiphany, is going to be found in an insubstantial tissue of borrowed elements.

I was recently introduced to the works of M. John Harrison through Fletcher Vredenburg's Black Gate reviews of the Viriconium books. What he had to say made me eager to read them, and an insightful older post by Matthew David Surridge at the same site piqued my curiosity even more. Thus far I've completed The Pastel City (1971) and A Storm of Wings (1980).

Here are stories that make their world out of whole cloth.

They're dying earth tales, it is true, and as such have something of a heroic fantasy or sword-and-sorcery "feel" while remaining what many people would call science fiction. That's what I like about the genre; that, and its peculiar blend of hopelessness, ennui, and hilarity, which the Viriconium books certainly embody. They paint their own picture, however, and it's a picture that's vivid to the point of painfulness but almost aggressively lacking in nuts-and-bolts world-building. About which more in a moment.

China Miéville has called it an injustice that Harrison hasn't received a Nobel Prize. I'm not competent to comment on that, as I rarely read the work of Nobel laureates. I do have to admit that I enjoyed the earlier and less ambitious Pastel City more than A Storm of Wings. I suppose I just gravitate toward the concrete, and A Storm of Wings is rather nebulous, with a weirdly drifting narrative and long passages describing the characters' perceptions and motivations.* I don't object to a book's being elliptical, mind you, and The Pastel City is certainly that. But it also kept me turning the pages to see what the resolution was going to be, and it's hard to think of a fantasy novel that's had that effect on me recently.

I think Mr. Vredenburgh puts the differences between the novels very well:
Despite sharing a similar structure with its predecessor, A Storm of Wings, is a more potent book, filled with headier feats of prose and narrative gameplaying. While The Pastel City remains an excellent heroic fantasy tale, I'm now able to perceive it best as the template for Harrison to build on and spin off from mad, wild, meta-fictional constructs. In an interview, Harrison said: "A good ground rule for writing in any genre is: start with a form, then undermine its confidence in itself," he says. "Ask what it's afraid of, what it's trying to hide – then write that." Too much heroic fantasy relies on a lazy adherence to simple tropes – the hero, the obvious enemy, etc. In this book, he is clearly taking it to task for that, and while you may agree with that, or not, it's hard not to hear and engage with his argument.
Both books are rather beautiful and rather melancholy. They revolve around ineffective protagonists who don't rightly know what they're doing or why. The tone isn't jocular like the Cugel stories, but there's some humor to go with the sadness and horror of slow decay. The style is broad, full-bodied, and poetic, with a painter's sensitivity to color. There are echoes of Jack Vance and The Dying Earth, but I think the books owe the greater debt to "The Waste Land," itself formed (like the world of Viriconium) of the incomprehensible detritus of ruined civilizations.**
THE river's tent is broken: the last fingers of leaf
Clutch and sink into the wet bank. The wind
Crosses the brown land, unheard. The nymphs are departed.
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In his first review, Mr. Vredenburgh links to two thought-provoking essays by Harrison: "What It Might Be Like to Live in Viriconium" and this essay on world-building.*** The latter begins with the following assertion, with which I wholeheartedly concur:
Every moment of a science fiction story must represent the triumph of writing over worldbuilding.
Amen to that! Harrison goes on to say a number of other things with which I sharply disagree, however, including this rather dumb statement:
The whole idea of worldbuilding is a bad idea about the world as much as it is a bad idea about fiction. It's a secularised, narcissised version of the fundamentalist Christian view that the world's a watch & God's the watchmaker.
Why is that dumb? (1) It employs the pejorative BS blanket term "fundamentalist Christian" and (2) it calls the watchmaker analogy a "fundamentalist Christian" view when it's actually more of an already-secularized Deist view. I mean, the history of the analogy is complicated, but I would hardly call people like Rene Descartes and Isaac Newton "fundamentalist Christians." Still, Harrison might have a point about watchmaking and world-building. Unfortunately, he goes on to this even dumber statement:
Worldbuilding is the province of people who, like Tolkien, actually resist the idea it's a game, and have installed their "secondary creation" concept as an aggressive defense of that position.
Tolkien resisted the idea that it's a game? In "On Fairy-Stories" he practically defines secondary creation as a game. Actually – and I suspect that this is the sticking point – it's defined as something of a divine game. Tolkien viewed fantasy much as his contemporary, the Catholic theologian Romano Guardini, viewed the liturgy of the mass, that is, as play. The self-deprecating yet gentle and hopeful tone of his essay's companion myth, "Leaf by Niggle," makes it pretty clear how he regarded his own world-building and its cosmic (in-)significance. His philosophy of fantasy bears little resemblance to the flattened caricature subjected to Harrison's procrustean bed.

Of course, it's arguable that Tolkien's "game," being in earnest rather than metafictional, isn't the kind of game Harrison likes to play. Still, I don't see how anyone could see Tolkien the author as some sort of demiurgic control freak. Is Middle Earth really such a closed system? If that's so, where do elements like Tom Bombadil fit in? Not even the characters of The Lord of the Rings are certain.
I don't think Tom needs philosophizing about, and is not improved by it. But many have found him an odd or indeed discordant ingredient. In historical fact I put him in because I had already "invented" him independently (he first appeared in the Oxford Magazine) and wanted an "adventure" on the way. But I kept him in, and as he was, because he represents certain things otherwise left out. [Tolkien, in a draft of a letter that wasn't sent ("it seemed to be taking myself too importantly"), The Letters of J. R. R. Tolkien, pp. 187-196]
The same letter contains a number of other interesting admissions. E.g.,
The tale is after all in the ultimate analysis a tale, a piece of literature, intended to have literary effect, and not real history. Thus the device adopted, that of giving its setting an historical air or feeling, and (an illusion of ?) three dimensions, is successful, seems shown by the fact that several correspondents have treated it in the same way – according to their different points of interest or knowledge: i.e., as if it were a report of "real" times and places, which my ignorance or carelessness had misrepresented in places or failed to describe properly to others. Its economics, science, artefacts, religion, and philosophy are defective, or at least sketchy. [ibid.]
Is that very different from the things Harrison has said about his Viriconium books? Actually, Tolkien's impatience with certain kinds of fans is familiar to anyone who's read his correspondence. In Tolkien's view, there is a broad difference between secondary creation and the kind of commercial world-building represented by this handy-dandy SFWA tips sheet, two approaches that Harrison appears to conflate.

Curiously, however, I believe that the other essay, "What It Might Be Like to Live in Viriconium," gets it exactly right from beginning to end.
The commercial fantasy that has replaced [the great modern fantasies] is often based on a mistaken attempt to literalise someone else's metaphor, or realise someone else's rhetorical imagery. For instance, the moment you begin to ask (or rather to answer) questions like, "Yes, but what did Sauron look like?"; or, "Just how might an Orc regiment organise itself?"; the moment you concern yourself with the economic geography of pseudo-feudal societies, with the real way to use swords, with the politics of courts, you have diluted the poetic power of Tolkien's images. You have brought them under control. You have tamed, colonised and put your own cultural mark on them.  Literalisation is important to both writers and readers of commercial fantasy. The apparent depth of the great fantasy inscapes – their appearance of being a whole world – is exhilarating: but that very depth creates anxiety. The revisionist wants to learn to operate in the inscape: this relieves anxiety and reasserts a sense of control over "Tolkien's World."
With far greater concision and profundity than my skills allow, this says something I've been trying to get at since I started this blog, and perfectly expresses my attitude toward commercial fantasy. The provenance of the two essays isn't altogether clear to me, and I find it puzzling that Harrison, who wrote "What It Might Be Like to Live in Viriconium" first, later transferred his judgment of the sandbox-building revisionists and their readers to Tolkien himself.

But here let us take our leave of M. John Harrison for the time being. I shall continue to read his Viriconium stories because I think they're good and well worth the effort, and his provoking essays have provided some grist for the old blog-mill, for which I thank him.

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* It has occurred to me that, whatever its artistic value, the use of postmodernist deconstruction in genre fiction is potentially a very clever commercial ploy. People nowadays have little patience for the less-than-consistent, fly-by-the-seat-of-your-pants serials of yesteryear. Well, if carefully cultivated, a postmodernist pose lets the genre writer get away with pretty much anything in the way of self-contradiction, and critics (genre critics) will laud his or her work to the skies and gush about how close it is to real literature. That reflects what I'm always saying, which is that fantasy, when it tries to stop being itself and hobnob with high society, just ends up appropriating a bunch of outdated fashions. There's something absurd about genre writing that festoons itself with the trappings of what the cool kids were doing decades ago and calls itself "literary." Not that I think The Pastel City or A Storm of Wings fall into that, exactly...

A little deconstruction is a fine thing in a genre story. It adds bite. But you see what I mean? It's as much a material element as any of the little tricks Lin Carter recommends in Imaginary Worlds. Readers tolerate it, or even enjoy it, so long as it's subordinated to the end of the story. Deconstruction as an end in itself is a pursuit for the literati. In genre fiction, it's just a narcissistic (!) betrayal of readers. It's also as pointless, derivative, and time-bound as Lin Carter's clumsiest pastiche.

** T. S. Eliot was famously inspired by Jessie Weston's From Ritual to Romance. His poems are referenced repeatedly by Apocalypse Now, and From Ritual to Romance – the very same edition I have on my bookshelf, as a matter of fact – is visible in Kurtz's dwelling at the end of the film. What I'm saying is, I could have worked all this into my last post, which also touched on The Valley of Gwangi, hollow earth theories, Pellucidar, Kong: Skull Island, "Heart of Darkness," colonialism, weird German conquistador movies, and various other things, but I didn't.

*** "What It Might Be Like to Live in Viriconium" was (so far as I can discover) written in 1996 and subsequently published in a fanzine. The other essay appears to have been copied from an archived version of a blog post. It's possible that they were both typed by dogs with keyboards. That's the Internet for you.

Thursday, March 23, 2017

Heart of the Hollow Earth

I recently watched Apocalypse Now for the first time. It is undoubtedly the best and most beautiful film I've seen in some time. People generally regard it as the best Vietnam film. Though gritty and realistic in its details, and, to some extent, inspired by real events, it represents an almost mythical vision, floating from The Ride of the Valkyries to Dante's Inferno and man's primordial roots in the jungle.

What made me want to see it was a comparison someone made between it and my Tashyas story. Actually, as I've said, I was thinking about Herzog's Aguirre, the Wrath of God and Conrad's Heart of Darkness. As is well known, though, Francis Ford Coppola cited both of these as major influences on Apocalypse Now. As a matter of fact, it's fair to say that Apocalypse Now is nothing more than a film treatment of Heart of Darkness, translating the Company's involvement in equatorial Africa into that of the United States in Vietnam, each presented just as imbecilic, futile, and destructive as human endeavors tend to be.

I've started to regard Heart of Darkness as a kind of modern myth. It has two basic motifs: the dark journey inward, and the great man who goes native and betrays humanity. The moral is that civilization is a veneer over something very dark indeed. Like the plot of Red Harvest (which I regard as another modern myth), it seems to have become part of the dream-logic of our culture. Aguirre and Apocalypse Now have been mentioned; I'm reminded also of Ridley Scott's Alien (whose ship and shuttle are named from Conrad stories) and James Cameron's popcorn-selling sequel. And, as a very recent and not-quite-legitimate descendant, we have Kong: Skull Island, which I went to see at the $4.00 matinee last week.

It's pretty plain that the makers of Skull Island were wanting to evoke and/or perfectly willing to plunder the visuals and general atmosphere of Apocalypse Now. It opens at the close of the Vietnam war, and the first scenes are chock-full of in-your-face historical details that let you know exactly what era you're looking at, while the jungle scenes are overlaid with the predictable rock songs so that you don't forget that this is the Vietnam era despite the overwhelming chronological ambiguity. (Me, to my eight-year-old son: "They played a Creedence song in that movie I just saw. Can you guess which one?" Him, without a moment's thought: "'Run Through the Jungle'!")  It's one of those movies where the older, uglier, and/or more annoying actors tend to meet grisly fates, and the young, pretty, highly paid actors do not. There's one guy I knew was destined to get picked apart by pterodactyls or something from the first moment I saw him.

Well, so, kind of a stupid movie.* But, as you may know, I'm a sucker for movies about little people running from giant monsters, and this one is pretty awesome in that department.

One really cool aspect is the hint that all these weird creatures are coming out of gigantic caverns beneath the earth's surface, where MUTOs have apparently been thriving for millions of years. Skull Island is set in the same universe as that Godzilla movie that came out in 2014 (also stupid, but also quite enjoyable), and it seems likely that we're looking at appearances by Mothra, Rodan, and Ghidora in the near future. Bring on the MUTOs! All monsters attack! I'm giddy with excitement!

But back to the hollow earth thing. Since my earliest childhood, I've known deep down in my heart that the whole earth-is-just-melted-rock-until-you-get-to-China theory is false. I mean, no one has actually been down there, have they? It's much more likely that there are massive caverns inhabited by gigantic prehistoric creatures and forested with huge mushrooms. Otherwise, the planet would be mostly wasted space, and, if there's one thing we know about Nature, it's that she hates for things to go to waste.

So I was very interested to read some of the amazing hollow earth theories recounted by Ryan Harvey over at Black Gate in some of his Pellucidar posts. Clearly, I'm not alone in my deep-seated convictions. But the most interesting, I think, is the theory of Cyrus Teed, an amateur scientist who founded a religious sect (Koreshanity) in the belief that we are already living on the inside of the world. From his Cellular Cosmogony:
The sun is an invisible electromagnetic battery revolving in the universe's center on a 24-year cycle. Our visible sun is only a reflection, as is the moon, with the stars reflecting off seven mercurial discs that float in the sphere's center. Inside the earth there are three separate atmospheres: the first composed of oxygen and nitrogen and closest to the earth; the second, a hydrogen atmosphere above it; the third, an aboron atmosphere at the center. The earth's shell is one hundred miles thick and has seventeen layers. The outer seven are metallic with a gold rind on the outermost layer, the middle five are mineral and the five inward are geologic strata. Inside the shell there is life, outside a void.**
Teed established a commune in Florida in 1894, which finally fizzled out in the 1960s. The place is now a state historical site. Strangely enough, soon after reading Mr. Harvey's post, I met a professor who lives near the site and takes his students there on occasion. So when he started talking about this theory that we live on the inside of the earth, I actually knew what he was talking about and could respond intelligently. It's called social networking, people. "You see?" I told my wife. "Reading weird stuff on the Internet isn't just wasting time after all!"

But it's strange, isn't it, how many "alternative" scientific theories (hollow earth, Atlantis, spiritualism, etc.) of the turn of the century gave birth to subgenres of fantastic literature? One wonders what theories Burroughs was familiar with in creating Pellucidar. At any rate, he was apparently unfamiliar with the shell theorem, first proved by Isaac Newton, which states that, at any given point in a spherically symmetric distribution of mass, only the mass closer to the center than the point contributes to the gravitational force at that point; all other mass can be ignored because its gravity cancels itself out, so to speak. The upshot is that, inside a perfectly hollow spherical shell, there would be no gravity at all; if, as in Pellucidar, there were a massive sun-like body at the center of the hollow, everything would fall into that body and burn. Of course, there would be nothing to keep such a body in its place at the center.

Speaking of Pellucidar and stupid movies, I recently watched At the Earth's Core, an Amicus production starring Peter Cushing and Doug McClure, with my kids. ("Hi! I'm Doug McClure! You may remember me from such films as At the Earth's Core!") Not so great, but the kids loved it. We also recently watched The Valley of the Gwangi, a Ray Harryhausen film about cowboys trying to capture dinosaurs for their wild west show in Mexico. It has same basic plot as King Kong (another modern-myth candidate) and ends with an allosaurus stalking a cowboy, his girlfriend, and a boy named Lope through an empty cathedral, which is pretty awesome.

Kong-derived stories seem always to feature some kind of dark journey upriver to primordial beginnings, which we saw as a key element in the Heart of Darkness myth. And so we're brought back to the primordial beginnings of this post, that is, Apocalypse Now.

* At one point, a search party happens upon a letter that a guy who got eaten was writing to his family. They make a big deal about how they're going to see that his widow gets his things. It's a solemn moment, but I couldn't help but imagine how that would go: "Ma'am, I'm very sorry to inform you that your husband was killed in action. Well, no, actually it wasn't in Vietnam. No, he survived that. What happened was, we were sent on this special mission to a secret unexplored island inhabited by prehistoric monsters, where he was eaten by a giant lizard creature. I'm so sorry for your loss."

** Actually, I imagine that there's probably prehistoric creatures on the outside.