Hintonian Cubism (part 1)

Diagram of original catalogue cube from A New Era of Thought (1888)

Most visitors to this blog – and, indeed, to my academia.edu profile – come seeking Charles Howard Hinton and his system of cubes. No surprises there. Hinton’s biography is quite something and his work on visualising – or, perhaps more accurately, imagining – the fourth dimension of space was innovative, influential and almost completely out of its time.

The purpose of this post is to update a project I began almost four years ago and am only really now in a position to continue: the construction of a set of Hinton’s cubes, the material demonstration models that anchored his pedagogical enterprise.

Inside front fold-out plate of The Fourth Dimension (1904)

Hinton began working with cubes early in his career. The essay ‘On the Education of the Imagination’ (1888) may well have been written before ‘What is the Fourth Dimension?’ was first published in 1880. In this he describes working with a system of cubes with his school students, and he began teaching in 1876. The system is also based on what he termed ‘poiographs’ in a paper presented before the Physical Society in 1878, so it seems likely to have been a foundation stone for his project. Certainly, his proficiency with it was advanced by 1887, when he was able to claim that he’d memorised a cubic foot of his named cubes.

He refined the system of cubes over the course of his career. The system described in A New Era of Thought (1888), taking up the entire second-half of that remarkable, visionary text, described cubes with a different colour and name for each vertex, line and face. Relying on description and line drawings it is, unsurprisingly, fiendishly complicated. By 1904’s The Fourth Dimension he had developed a system of ‘catalogue’ cubes and plates to enable a more step-by-step working through of cubic training. There are also many more and far clearer illustrations in this text, so this is the version I’ve followed.

The first task is to paint the correct number of one inch cubes the correct colours, which are as follows:

Null	16
White	8
Yellow	8
Light yellow	4
Red	8
Pink	4
Orange	4
Ochre	2
Blue	8
Light blue	4
Green	4
Light green	2
Purple	4
Light purple	2
Brown	2
Light brown	1

I used model paints of the kind you use to paint Airfix aeroplanes. As a newbie to this game this process caused me more problems than you might imagine. For example, metallic paints sound exciting in the shop – wooh-hooh, electric pink! – but they are more liquid, don’t necessarily look all that great on wood, and can even look largely indistinguishable from lighter, non-metallic shades. Also, on which side do you rest a painted cube to dry? I never discovered the answer to this gnomic poser so my cubes are slightly messy. But hey! They’re my cubes – and they don’t need to be perfect.

Home-made wooden cubes

After the set of 81 coloured cubes there are the catalogue cubes. These are coloured to distinguish vertices, lines and faces and the fold-out colour-plate at the front of The Fourth Dimension shows how they should look.

As you can see, painting lines a fifth of an inch proved beyond me, either freehand or using tape to mask off. In the end I decided to print out coloured nets of the cubes onto card and cut these out and tape them together. Again, slightly imperfect, but I think they do the job nicely.

Printed onto nets and sellotaped together

There are also coloured slabs, to aid you in thinking like a plane being, as you will be asked to do in the first chapter of exercises, ‘Nomenclature and Analogies Preliminary to the Study of Fourdimensional Figures’ (pp.136-156). These I printed out on card aswell.

I’m going to break these posts up into a series in case anyone wants to join in so I’ll begin with the exercises in the next post sometime in the next week or so. In the meantime, an observation (owing entirely to Dr. Caroline Bassett who pointed it out to me at Weird Council, the China Mieville conference) that will be useful in understanding what’s to come. If, like me, you have about 50 pairs of 3d glasses sitting around the house because you have to buy a new pair every time you go to the cinema to watch Matt Damon Running Really Fast! 3D!, break a set out and take a squizz at the coloured plate above. Your colour-coded anaglyph glasses will be doing all kinds of funky things to the projection diagrams of cubes. Hinton intuitively recruited a colour-coding system to suggest the qualium of an extra dimension of space, which is kind of how we trick out puny brains into registering three dimensions when we drool at a FLAT screen for 90 minutes watching Matt Damon running really fast.

So, ponder that then get thee to a modelling shop (where the staff will be perfectly used to people using the archaic form of the vocative in that way and will possibly be dressed like hobbits).

Bon chance!

Charles Carleton Massey: corrections

Marc Demarest, who maintains the excellent Emma Hardinge Britten archive, a shining example of open-source web scholarship, has been in touch with a couple of corrections regarding the CCM post below. With apologies for sloppiness, here’s Marc’s message:

Thanks for the post. Too few people looking into CCM’s life.

Couple of things:

- William Stainton Moses was the co-editor of *LIght* (to which periodical CCM was perhaps the most regular contributor in the 1880s), not *The Medium and Daybreak* (as your post says). James Burns was the editor of the M&D, and the M&D stands, in relation to Light, like the New York Post to the New York Times

- WSM was not a founder of the TS. I’m not sure he was ever even a read-in member of the TS. He and Henry Steel Olcott were correspondents, and Blavatsky woo’d him for the TS, but (like Emma Hardinge Britten and CCM) he eventually turned against the TS in public.

- CCM didn’t just defend Slade; perhaps more importantly, in the broader sweep of things, he defended Penny, the astrologer, when he was brought up on the charge of violating English laws against fortune-telling. That case was the opening salvo in a battle that went on until Helen Duncan’s trial under the same act in the mid-1940s (if memory serves). CCM also acted for several other spiritualists and occultists in different matters.

I’m grateful for the pointers – they’re all spot-on. It’s never less than productive to make contact with other researchers in the field and a great advantage to have engaged readers. I can also heartily recommend Marc’s Chasing Down Emma blog, where he posts updates on his ongoing research. This recent post expands the picture of Massey’s legal activities defending spiritualists and occultists by reproducing a report on his defence of the astrologer Richard Henry Penny.

Keep an eye out for more updates on CCM.

An orphaned footnote on Thomas Reid and Flatland

Flatland’s critique of analogy is reminiscent of Thomas Reid, writing in 1767. Reid noted both the utility and frequency of analogical thinking, and the way in which it was particularly common in figuring thought itself as a material parallel to make clear the abstract: ‘The second, and the most common way in which men form their opinions concerning the mind and its operations we may call the way of analogy. There is nothing in the course of nature so singular, but we can find some resemblance, or at least some analogy, between it and other things with which we are acquainted. The mind naturally delights in hunting after such analogies, and attends to them with pleasure.’ Thomas Reid, An Inquiry into the Human Mind on the Principles of Common Sense, ed. by Derek R. Brookes (Edinburgh: Edinburgh University Press, 1997), p. 203.

Reid argued that philosophers were not immune from such a tendency and that until Descartes philosophy was liable to ‘materialize the mind and its faculties.’  (209) He doubted that many were capable of the rigorous reasoning required to reach concepts by other means: ‘If one attentively examines the systems of the ancient philosophers, either concerning the material world or concerning the mind, he will find them to be built solely upon the foundation of analogy.’ (204)

Intriguingly, in the same text from which these lines are taken Reid set out a thought experiment in which a race of two-dimensional beings he called Idomenians, confined to the surface of a sphere and having only the sense of sight, were unable to conceive of a three-dimensional geometry.

Hinton biographical erratum

Here’s one just for the Hinton spotters.

For some reason I was lying awake at 3 a.m. last night wondering if Charles Howard Hinton had met his bigamous bride Maude Florence while teaching at Cheltenham Ladies College. Perhaps she’d been a student: wouldn’t that be just scandalous! I thought to check it out this morning before dealing with REAL WORK and tried to find registers online. Searching for those came up null, but did reveal this: Charles Howard worked at Cheltenham College, not the Ladies College which of course makes total sense in retrospect. Seems worth correcting because every biographical account since Rudy Rucker (and possibly it was Marvin Ballard who was the source for this?) has him at Cheltenham Ladies. 

Another curiosity: he was on a list of examinees of the University of London in 1871, the year in which he matriculated as an non-collegiate student at Oxford. Any ideas on that would be interesting.

This heinous task-avoidance may be some use. I promise extensive higher-dimensional bibliographies imminently.

Happy Hallowmas!

I’m reading Roger Luckhurst’s book The Mummy’s Curse and have reached a section on the Ghost Club, of which I was unaware until today. On this particular day, celebrated by the Ghost Club as the day in the calendar on which the skein between this world and the next was at its very thinnest, it seems particularly apt to recommend this reading matter. Luckhurst writes:

In 1882, the same year that the SPR was founded, a dining club was established by the spiritualist writer and medium the Reverend William Stainton Moses and the occultist Alfred Alaric Watts. It was called the Ghost Club (not to be confused with the better-known Cambridge Ghost Club that had been formed in 1862). It was started, as a brief history of the Club outlines, ‘expressly so that persons who might object to any general publication of their experiences might be encouraged to relate them at Ghost Club in the strictest confidence. [As Luckhurst later quips, 'The first rule of Ghost Club is that you don't talk about Ghost Club.' MB] It was also decidedly a club not a society: ‘We propose rigidly to confine ourselves to clubbable men.’ (The Mummy’s Curse, 46)

That last line was Moses writing to the gentleman below, Charles Carleton Massey.

Charles Carleton Massey by Eveleen Myers (née Tennant)
platinum print, 1890s
Reproduced under a creative commons license from The National Portrait Gallery
NPG Ax68485

Massey was something of a player in the scene of fin de siècle occultism, as William Barrett’s obituary in the Journal of the SPR explained [it's in this volume, if you're interested], participating in just about every group or society going.

He had been a signatory at the founding of the Theosophical Society [TS] in New York having met and befriended Colonel Henry Steel Olcott while both were visiting the Eddy ranch in Chittenden in 1875 in investigate the phenomena taking place there. In 1876, the qualified barrister Massey defended the medium Doctor Henry Slade in a highly entertaining trial for fraud  brought by Professor Edwin Ray Lankester. Massey went on to translate Zöllner’s Transcendental Physics [see posts passim], von Hartmann’s Der Spiritismus and Baron Carl du Prel’s The Philosophy of Mysticism: in the final analysis it was as a translator of occult works that he left a mark.

Massey’s translation of Transcendental Physics and subsequent defence of Zöllner’s reputation introduced English readers to this body of higher spatial theorisation. His professional status as a qualified barrister, and his family connections – his father was the liberal MP, Rt. Hon. William N. Massey – lent him a powerful legitimating role, both legally and socially, and he was a prized signatory to the foundation of the TS for this reason. He was the founder and later President of the London Lodge and his public departure in 1884, following the notorious Kiddle Incident, severely damaged the reputation of the Society.[1]His defection to the SPR, with whom he already had public connections, prefigured the SPR’s damning report into the TS.

Massey is exemplary of the permeability between the TS and other groups in this period. Many leading spiritualists were also, at one time or another, members of the TS, and vice versa. Alongside Massey at the foundation of the Society were Emma Hardinge Britten, who would go on to edit The Two Worlds and The Unseen Universe, and the aforementioned William Stainton Moses, editor of Medium and Daybreak and founding member of the Society for Psychic Research, the London Spiritualist Alliance and the College of Psychic Studies. Both Massey and Moses were present at the initiation of C. W. Leadbeater into the TS on February 21, 1884, as was Frederick Myers, and initiated on the same occasion were William Crookes and his wife: spiritualist aristocracy and leading lights in the SPR all present and correct. The English barrister played an important, and largely unrecorded, mediating role in the history of psychic research in the fin de siècle, Barrett’s obituary telling of ‘a profound student both of philosophy and psychology, and one of the most original and suggestive thinkers I have ever known’ and regretting the fact that ‘he has left behind him no work to make his name more widely known and admired’.[2]

Despite the fact that he remained lifelong friends with Olcott, Massey’s public defection probably explains Blavatsky’s less than enthusiastic embrace of higher space in The Secret Doctrine. She had, after all, given positive notice of Transcendental Physics in her review in The Theosophist, which trumpeted Massey’s achievements on behalf of the Society:

It is not too much to say that in this one case the agency of the Theosophical Society was productive of an effect upon the relations of exact science with psychological research the importance of which must be felt for long years to come. Not only was Slade originally chosen by Theosophists for the European experiment and sent abroad, but at his London trial he was defended by a Theosophist barrister, Mr. Massey; at St. Petersburg another Theosophist, Mr. Aksakoff, had him in charge; and now Mr. Massey has bequeathed to future generations of English readers the full story of his wondrous psychical gifts.[3]

By the time of the publication of The Secret Doctrine at the end of 1888, however, Blavatsky was considerably more critical of the ideas contained in the book and one senses a touch of sour grapes.

Luckhurst records that Massey was also President of the Ghost Club and a post mortem visitor to seances held by the Brothers.

Happy Hallowmas!

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[1] For a detailed account of the Kiddle Incident see Massey’s own resignation letter, ‘Explanation of the “Kiddle Incident” in the Fourth Edition of “The Occult World”’, Light, 26 July, 1884, pp. 307-9.

[2] William Barrett, ‘Obituary: C.C. Massey’, Journal of Society for Psychical Research (June 1905), 95-99 (p. 95). Barrett went some way to correcting this by publishing an anthology of Massey’s essays and correspondence.

[3] H.P. Blavatsky, ‘Transcendental Physics’, The Theosophist, 2, 5, ( 1881), 95-97.

The Scientific Romance

I’m approaching completion of my thesis and am finding that some earlier material doesn’t fit anymore. The section below considers what exactly Charles Howard Hinton’s work is, and it doesn’t sit so well with the direction of an argument that now revolves around the mediations of space, matter and thought; so it naturally finds a home up here. It may be of interest to SF bods.

In the meantime, thanks to Fortean Dr Andrew May, who has drawn my attention to a really thorough piece of historical work on Zöllner, by Helge Kragh at Aarhus University. Andrew has previously blogged about Hinton and his site contains much that may be of interest to readers here. My second chapter deals with what I’ve come to think of as ‘the Zöllner event’, and this essay really usefully brings into play some of his German language work that was previously inaccessible to me. I’m delighted to be able to say at this very late stage that there is nothing game-changing for what I’m trying to argue!

Without any further preamble, here’s the Scientific Romance section:

The term Scientific Romance, coined by the publisher Swan Sonnenschein for Hinton’s essays, has surely contributed unhelpfully to subsequent attempts to locate his [CHH's] project. Adopted in the 1890s by H.G. Wells to describe his fiction in this period it has been considered as roughly equivalent to an early form of SF. Brian Stableford, whose 1985 book took the term for its title, used it to mark ‘the British tradition of speculative fiction’ as independent of American SF.[1] Writing about Hinton, Stableford argued

that there is a certain propriety in the juxtaposition of speculative fiction and speculative non-fiction in these collections. The term ‘scientific romance’ was generally used to refer to fiction, and it refers to fiction in the title of this book, but there has always been a close relationship between British scientific romance and a typically British species of speculative essays [...] Running parallel to the tradition of British scientific romance, therefore, is a tradition of essay-writing which is itself Romantic: always speculative, often futuristic, frequently blessed with an elegance of style and a delicate irony.[2]

Hinton, however, is considered by Stableford stylistically ‘inept’, a ‘hobbyist [...] who made little impact’ but was ‘possessed of remarkable powers of imagination’. Stableford argues that in this period the term scientific romance was most frequently used by critics rather than by writers or publishers. His exemplars of the kind of speculative essay writing he identifies as close to the romance are, curiously, J.B.S. Haldane and Julian Huxley, two writers most prolific in the 1920s, rather than any of writers of the 1880s with whom Hinton might bear closer comparison – either Clifford or Helmholtz in popularising mode, say.

Stableford here echoes the observations of Darko Suvin. Describing science fiction texts as circulating ‘outside the principal [...] fiction circuit’, Suvin assumed a different reader: ‘mostly upper-middle and middle class males with special interest in politics, religion and public affairs in general’. He went on to note the ‘the intertextual closeness to SF of such nonfiction genres as the social blueprint, the political tract, the predictive essay, even the semi-religious apocalypse’.[3]

Is Hinton’s work then some kind of early or hybrid SF? Bruce Clarke sees in Hinton’s The Persian King ‘science fiction in utero’.[4] Suvin includes both Flatland and the Scientific Romances in his survey, although his praise for the former is significant, while Hinton’s work is largely dismissed. Considering the conditions of emergence he describes in relation to his first case study, H.G. Wells, Roger Luckhurst makes brief mention of one of the pre-cursors of SF to which a direct connection back from Wells can be drawn: ‘The title ‘scientific romance’ was used for Charles Howard Hinton’s extremely odd mixture of stilted fiction and playful mathematical speculations about a fourth dimension in 1886.’[5]

In the account offered by 20^th century SF criticism Hinton’s essays and fictions are continuous and his stylistic shortcomings in the fictional mode make him a largely unsuccessful author of speculative work. Certainly, the utopian strain in his thought – and higher space may well be an exemplary ‘no-place’ – aligns him with this reading. Luckhurst’s description is surely accurate but would benefit from some qualification. The Scientific Romances are weighted heavily towards ‘playful mathematical speculations about a fourth dimension’ (and, indeed, physical speculations) and far less towards ‘stilted fiction’. It has been customary to consider the two collections of Hinton’s Scientific Romances together and this, I think, is the source of frequent distortion of Hinton’s work. The second collection, published in 1895, did include two extended pieces of speculative fiction – the novella ‘Stella’, an invisible woman narrative, clearly bearing the traces of Hinton’s oriental exile, and ‘An Unfinished Communication’, a metaphysical love story – and two pieces written earlier, before his departure from Britain. By 1895 H.G. Wells’s career was gathering significant momentum and the scientific romance had a practitioner perhaps more worthy of the title.

Hinton’s first collection of Romances, however, contains only one piece, The Persian King, that attempts any kind of narrative, and it is weighed down by extended sections of explicatory text dealing with thermodynamics. Intriguingly, Hinton had submitted to his publisher a set of ‘Unscientific Romances’, which were rejected shortly after his conviction for bigamy in November 1886, ‘owing to the crowded state of our list’.[6] It is useful to consider Hinton’s work chronologically, not least because the rupture between the two periods of his literary productivity is so marked, but perhaps even more useful to take an overview that reveals the eclectic nature of Hinton’s approach to his subject.

In toto, there are Luckhurst’s ‘stilted romances’, ‘Stella’ and ‘An Unfinished Communication’, narrative novellas offering intriguing ideas cloaked in metaphysical love stories; there are didactic, hybrid essays, the above-mentioned ‘What is the Fourth Dimension?’, ‘A Persian King’, ‘A Picture of our Universe’, ‘Casting out the Self’, ‘On the Education of the Imagination’ and ‘Many Dimensions’, using allegory and analogy to think through and explain higher spatial concepts and how they related to physics; there are the Flatland-inspired ‘A Plane World’ and An Episode of Flatland, responses to Abbott’s text that routed into mechanics; and there are the two book-length studies that instruct and contextualise his system of cubes, A New Era of Thought (1888) and The Fourth Dimension (1904), the first a quasi-visionary philosophical statement and manual and the second a more measured history of higher dimensional thought and refinement of his earlier system.

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[1] Brian Stableford, Scientific Romance in Britain 1890-1950 (New York: St Martin’s Press, 1985), p. 3.

[2] Stableford, 5.

[3] Darko Suvin, Victorian Science Fiction in the UK (Boston: GK Hall and Co, 1983), p. 403.

[4] Bruce Clarke, ‘A Scientific Romance: Thermodynamics and the Fourth Dimension in Charles Howard Hinton’s “The Persian King”’, Weber Studies, 14: 1 (Winter 1997).  <http://www.altx.com/ebr/w%28ebr%29/essays/clarke.html>, para. 1 [accessed 24th Feb 2010].

[5] Roger Luckhurst, (SF, 30)

[6] Archives of Swan Sonnenschein, Reading University. SS to CH, letter 336, 19 November 1886.

Weird Council: further konvolution

I’m going to spray wildly some thoughts about Weird Council in the hope that some of them cohere, or even more optimistically, attract comments…

We closed with China reading and fielding questions. The story he read condensed a number of the features of his work that make it so rich for research. Dialogue-heavy, it was perfect piece to read: sharp cracks whipped between its two protagonists. Dense and infolded like the chrysalis at its core, it welded commodity fetish to US neo-imperialism, presenting the idea of a deep black-market in numinous dark artefacts of a very contemporary nature: insects used in instruction 9) of the US torture manual for interrogating suspects at Guantanamo Bay.

At the end of the Q&A China remarked that he was surprised not to have been asked any questions about Speculative Realism (heretoforward SR), noting that as an audience we were either too cool or not cool enough. I’d kind of wafted at some of these ideas in my talk so felt as if I’d bottled it a bit: in truth, it hadn’t occurred to ask anything at all; by that stage in proceedings my thinking gubbins had gummed up. With twenty-four hours’ distance it is once again slithering.

On the SR front, then, his story was highly intriguing. Imagined non-human objects had interior lives, biographies, even, and affected the humans between whom they passed with much more than their exchange value: they had agency. This agency had originally been conferred onto them by what humans did (or had done to them by other humans in their presence) but ultimately the insect inserted into a box as a torture weapon reverted to chrysalis form and did not re-emerge: became unknowable, unusable, except, perhaps, as a commodity; yet pregnant with futurity.

I’m wary of any kind of direct reading: this story seems freighted with object ambiguity. One is tempted to correlate numinosity with the noumenal, and I guess this is where my understanding of SR falls short (I suggest that this means I am on-point cool). Because if these objects are perceived as having noumenal lives, inaccessible to human thought, we’re recapitulating Kant and we aren’t doing the work of SR, letting the objects be objects and removing human thought from the centre of the process. Yet granting objects the kind of pregnant form of becoming that is the nature of the chrysalis – not to mention a chrysalis in which the insect pupating is powerfully, darkly magical – is to give them a kind of quasi-knowability perhaps appropriate for what might be quasi-objects. Their agency remains, indeed, their potential agency is metaphorically increased.

Glancing back to Graham Harman’s essay on Lovecraft in Collapse, which is available on his site here (while ‘fessing that I haven’t read his Zer0 book on Lovecraft) he argues that Lovecraft’s unrepresentables and unknowables are exemplars of a ‘weird realism’ that undermines Kant’s noumenal. There’s a lot more to say here. China’s remark that he was interested in totalities and in particular in competing totalities indicates that there would be fruitful research to be done in After Finitude, Badiou etc. There is certainly much for me to ponder about how n-dimensional geometry fits into a philosophy that argues for mathematics as providing us with the tools for escaping correlationism. At the moment my thoughts around this are folding in on themselves like the hypercube animation doing its perpetual rounds below so I’ll not push any further at this right now.

Instead, there’s something I want to add to the discussions on genre theory revolving around Suvin’s definition of sf as a literature of ‘cognitive estrangement’, a discussion very fruitfully engaged by Jon Rieder, Rhy Williams, Sheryl Vint and commented on by Roger Luckhurst and China. I want to push a bit at the idea of cognition and – surprise surprise! – I’d like to use n-dimensional geometry as the lever with which to do it. (Suvin, by the way, is highly approving of Flatland, whose ‘novum’ he deems a lot more radical than it actually was – the ‘novum’ aspect of Suvin’s definition was pretty neatly challenged by Jon Rieder’s more fluid account of genre as something socially and culturally imposed on a text, rather than internally expressed).

The cognitive logic that leads us to n-dimensional space is solid enough in logical terms – we reason it by analogy, as from two dimensions to three, so from three dimensions to four. Just because it is produced through the privileged discipline of geometry, or by analogy, a process of reasoning sanctioned since Aristotle, that doesn’t mean that we find ourselves in a situation any different from a fairyland. Geometry is a model of space governed by a set of axiomatic rules, but we can tweak those rules and produce new geometries. We can then read back from the tweaked model and speculate spaces that conform to the tweaked versions. The process has been led by reason, but a form of reason no different to metaphor, because geometry is a metaphor for space and can be abreal. We’ve just been quite merrily translating backwards and forwards between metaphors and the thing they express.

This insistence on cognition does not seem to distinguish between the types of reasoning employed by supposedly materialist science, even when those forms of reasoning are metaphorical. I’ve had a look at Engels’ Anti-Duhring and Lenin’s Empirio-criticism and in their focus on tracking down idealism, these foundational materialist theories of science go all the way in the other direction. This definitely wants some nuancing and I’m sure Rhys could clarify or correct this and it’s something I’ll try to develop in greater detail, but wanted to post while the conference was still pretty fresh.