Hinton’s hypercubes

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Illustration from The Fourth Dimension (1906) by Charles Howard Hinton.

A slight return to the worlds of Borges. I happened to be re-reading some of the stories in The Book of Sand (1975), one of the later collections which includes the story Borges dedicated to HP Lovecraft, There are more things. Borges’ writings are nothing if not filled with references to other works of literature, philosophies, religions, and ideas in general; following up the less-familiar references would preoccupy a reader to the detriment of the writing so there’s a tendency when reading a Borges piece to take for granted many of those nuggets of esoteric information. I’ve read There are more things many times—it’s a favourite in part for having the additional thrill of Borges going Lovecraftian—but only realised with this reading that I can now fully appreciate the following:

Years later, he was to lend me Hinton’s treatises which attempt to demonstrate the reality of four-dimensional space by means of complicated exercises with multicoloured cubes. I shall never forget the prisms and pyramids that we erected on the floor of his study.

Prior to reading this I did know that Hinton was Charles Howard Hinton (1853–1907), the British mathematician and dimensional theorist. Hinton’s name tends to turn up in discussions of the work of his mystical contemporaries, notably the Theosophists who were more taken with his theories than those in the scientific fields. (A conviction for bigamy didn’t help his reputation.) But those multicoloured cubes were a mystery until the publication of (fittingly) the fourth number of Strange Attractor Journal. Among the usual selection of fascinating articles the book contains a piece by Mark Blacklock about Hinton’s ideas including those mysterious cubes. Drawings of the cubes first appeared in A New Era of Thought (1888) where Hinton proposes using them as aids to a series of mental exercises with which the reader may visualise the higher dimensions of space. Hinton invented the word “tesseract” to describe the four-dimensional structure projected from the faces of his three-dimensional cubes.

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Crucifixion (Corpus Hypercubus, 1954) by Salvador Dalí.

Hinton may not have impressed his mathematical colleagues as much as he hoped but his ideas have an understandable attraction, as the Borges story demonstrates. The story concerns the refashioning of a Buenos Aires house for an unusual resident; thirty years earlier Robert Heinlein wrote “—And He Built a Crooked House—” in which an architect builds a house in the form of a four-dimensional hypercube: only the lowest cube attached to the ground is visible from the exterior. I read that story when I was a teenager, and was already acquainted with tesseracts thanks to school-friends who were maths whizzes; I was the arts whizz, and I think I was probably the first of us Dalí enthusiasts to discover the artist’s own take on the hypercube, Crucifixion (Corpus Hypercubus) from 1954. Borges and Heinlein in those stories were both writing their own forms of science fiction, and Dalí’s painting finds itself co-opted into another story with sf connections, The University of Death (1968) by JG Ballard, one of the chapters in The Atrocity Exhibition (1970):

He lit a gold-tipped cigarette, noticing that a photograph of Talbot had been cleverly montaged over a reproduction of Dalí’s ‘Hypercubic Christ’. Even the film festival had been devised as part of the scenario’s calculated psychodrama.

If we seem to have strayed a little then it’s worth noting that Borges was familiar with Ballard’s work: he included The Drowned Giant in the later editions of The Book of Fantasy, the anthology he edited with Adolfo Bioy Casares and Silvina Ocampo. The two writers also met on at least one occasion.

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JLB and JGB, circa 1970. Photo by Sophie Baker.

Charles Hinton’s coloured cubes and tesseracts are described in detail in The Fourth Dimension (1906), a reworking of the ideas from A New Era of Thought, and also the source of the colour illustration that everyone reproduces. Mark Blacklock has his own multi-dimensional website where you can read about his construction of a set of three-dimensional Hinton cubes. As for the mental exercises, Blacklock’s piece in Strange Attractor contains an anecdotal warning that the auto-hypnotic system required to fully visualise Hinton’s dimensions can result in a degree of obsession dangerous to the balance of mind. Proceed with caution.

Previously on { feuilleton }
Borges and the cats
Invasion, a film by Hugo Santiago
Spiderweb, a film by Paul Miller
Books Borges never wrote
Borges and I
Borges documentary
Borges in Performance

The Dreamlands: A Lovecraftian film

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A crowd-funding goal has been announced for The Dreamlands, a feature film set in the worlds of HP Lovecraft’s Dream Cycle which, if it goes ahead, will be director Huan Vu’s second Lovecraftian feature. His first, Die Farbe (2010), is an excellent adaptation of The Colour Out of Space which impressed me with its atmosphere and its serious attitude towards the material, qualities that you can’t always rely on where horror cinema is concerned.

The Dreamlands will of necessity be more fantastical and so warrants a larger budget, hence the funding bid. I was asked to contribute to the production side of this late last year but prior commitments intervened, not least all the work I was doing on Lovecraft’s Monsters. I did find time to design the star symbol that’s being used to promote the film, however, and there’s talk at the moment of my working on some of the gifts for the funders in the higher brackets. More about that later. Watch the teasers, they’re very good.

Elsewhere on { feuilleton }
The Lovecraft archive

Lovecraft’s Monsters unleashed

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I posted my illustrations for this anthology back in December, after which Tachyon also asked me to create a cover for the book, something that hadn’t been planned at the outset. Lovecraft’s Monsters, edited by Ellen Datlow, is in the shops this month so here’s the cover and a few of my page layouts from the interior. I’m very pleased with this one so it’s been good to hear it’s been selling well already, and picking up positive reviews. My illustrations may be seen at large size here while the book itself should be available via all the usual outlets. If you insist on shopping in a river filled with piranhas then here’s a link. (That fish head on the cover is based on a piranha as it happens.)

The big Lovecraft collection from Centipede Press, A Mountain Walked, was also supposed to be out this month but the release has been bumped (again) to May 2014. It’s a huge volume so I’m not surprised if it’s taking longer than expected.

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Elsewhere on { feuilleton }
The Lovecraft archive

Planète magazine covers

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Planète was a French magazine of “Fantastic realism” which ran throughout the 1960s. I’ve never seen a copy but sight of the immediately recognisable covers has always fascinated because this was the magazine established in the wake of the huge success of The Morning of the Magicians (1960), a unique “Introduction to Fantastic Realism” by Louis Pauwels and Jacques Bergier. Rather than enthuse at length about The Morning of the Magicians I’ll simply point you to this piece by the late RT Gault from his now-defunct website.

Pauwels and Bergier’s book was oft-imitated but never equalled during the 1970s. Where later authors such as Erich von Däniken tended to plough a single, narrow furrow, Pauwels and Bergier leapt breathlessly from one subject to another: alchemy in the 20th century, Forteana, a lengthy examination of the occult preoccupations of the Third Reich, speculations about nuclear physics, speculations about biological mutation, Hollow Earth theories, etc, etc, all the time dropping quotes from HP Lovecraft, Arthur Machen and Albert Einstein. It’s a very heady mix which is great fun to read even though there’s nothing like a solid argument that comes out of it all.

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Planète continued the blend of Futurology and fringe philosophy while using the magazine format to print translations of science fiction and fantasy stories; among other things it was notable for bringing the stories of Jorge Luis Borges to a wider audience in France. The magazine’s name may have been science fictional but the magazine as a whole is closer to the kind of borderline sf/art magazine that New Worlds became under Michael Moorcock’s editorship in the late 1960s. I’ve never seen Moorcock or anyone connected with New Worlds mention Planète but the covers at least pre-empt the style adopted by New Worlds during its large-format run: consistently bold typography and imagery that only obliquely relates to the contents.

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All these covers are from Noosfere where the story contents for each issue are also listed. No credits for the designer, unfortunately. If anyone knows who was responsible for the magazine design then please leave a comment.

Continue reading “Planète magazine covers”

Polypodes

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Sepia (no date) by Gao Jianfu.

Quelquefois, dans une nuit d’orage, pendant que des légions de poulpes ailés, ressemblant de loin à des corbeaux, planent au-dessus des nuages, en se dirigeant d’une rame raide vers les cités des humains, avec la mission de les avertir de changer de conduite, le caillou, à l’œil sombre, voit deux êtres passer à la lueur de l’éclair, l’un derrière l’autre; et, essuyant une furtive larme de compassion, qui coule de sa paupière glacée, il s’écrie: «Certes, il le mérite; et ce n’est que justice.» Après avoir dit cela, il se replace dans son attitude farouche, et continue de regarder, avec un tremblement nerveux, la chasse à l’homme, et les grandes lèvres du vagin d’ombre, d’où découlent, sans cesse, comme un fleuve, d’immenses spermatozoïdes ténébreux qui prennent leur essor dans l’éther lugubre, en cachant, avec le vaste déploiement de leurs ailes de chauve-souris, la nature entière, et les légions solitaires de poulpes, devenues mornes à l’aspect de ces fulgurations sourdes et inexprimables.

Les Chants de Maldoror (1869) by the Comte de Lautréamont

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Sometimes on a stormy night while legions of winged squids (at a distance resembling crows) float above the clouds and scud stiffly towards the cities of the humans, their mission to warn men to change their ways—the gloomy-eyed pebble perceives amid flashes of lightning two beings pass by, one behind the other, and, wiping away a furtive tear of compassion that trickles from its frozen eye, cries: “Certainly he deserves it; it’s only justice.” Having spoken thus it reverts to its timid pose and trembling nervously, continues to watch the manhunt and the vast lips of the vagina of darkness whence flow incessantly, like a river, immense shadowy spermatozoa that take flight into the dismal aether, the vast spread of their bat’s wings obscuring the whole of nature and the lonely legions of squids—grown downcast viewing these ineffable and muffled fulgurations.

Translation by Alexis Lykiard, 1970

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The Mask of Cthulhu, 1976 paperback reprint. Cover art by Bruce Pennington.

Above these apparent hieroglyphics was a figure of evidently pictorial intent, though its impressionistic execution forbade a very clear idea of its nature. It seemed to be a sort of monster, or symbol representing a monster, of a form which only a diseased fancy could conceive. If I say that my somewhat extravagant imagination yielded simultaneous pictures of an octopus, a dragon, and a human caricature, I shall not be unfaithful to the spirit of the thing. A pulpy, tentacled head surmounted a grotesque and scaly body with rudimentary wings; but it was the general outline of the whole which made it most shockingly frightful. Behind the figure was a vague suggestion of a Cyclopean architectural background.

The Call of Cthulhu (1928) by HP Lovecraft

Previously on { feuilleton }
Ulysses versus Maldoror
Maldoror
Vampyroteuthis Infernalis by Vilém Flusser
Books of blood
Magritte’s Maldoror
Frans De Geetere’s illustrated Maldoror
Maldoror illustrated