Way back when I first started my research I had read an article by Florian Cajori published in 1926. Rigorously researched and commendably thorough, Cajori’s consideration of the roots of the idea of the fourth dimension brought into play Henry More’s notion of ‘spissitude’. Cajori was responding to a German article written in 1881, at the height of Zollner’s pomp, by R. Zimmerman. Zimmerman argued that More’s spissitude was a mystical idea and shouldn’t be considered spatial. Cajori disagreed and I’m with him.

Let’s have a look at what More wrote:

That apart from those three dimensions which are appropriate to all extended things a fourth is to be admitted which is appropriate particularly to spirit. And, that I may not dissemble in any way, although all material substances considered in themselves are measured only in three dimensions, a fourth however is to be admitted in the universe, which can, I think, be sufficiently called essential spissitude. Which, although it refers most properly to those spirits which can contract their extension into a less Ubi, can however by an easy analogy be referred further to the mutual penetration of spirits, both of matter and of themselves, so that, wherever either many essences or more of essence is contained in some Ubi than that which is adequate to its amplitude, there is acknowledged this fourth dimension which I call essential spissitiude.

In this account spissitude was a quality of spirit, not an extension into higher Euclidean dimensions – indeed, contra Descartes, not an extension at all – and it was characterised by ‘self-penetration’. This was a deliberate move beyond the Cartesian grid. As Alexander Jacobs writes: ‘This feature of self-reduplication allows spiritual extension to be absolute, that is, at once infinite and eternal.’ The distinction between extended, Cartesian, mathematical space was underlined by More in an analogy shared with Descartes and surely borrowed for direct comparison; describing the malleability of wax, considered by Descartes in his second meditation, More argued:

For, unless one wishes to consider that a piece of wax extended, say, to an ell’s length, and afterwards gathered and rolled up into the form of a globe, would lose some of its original extension on account of this globulation, it would be necessary for one to acknowledge that a spirit has not lost anything of either its extension or essence in its contraction of itself into a less space, but, as in the case of the above-mentioned piece of wax, its diminution of longitude is compensated by the present increment of latitude and profundity, so, in the spirit contracting itself, the recent diminutions of its longitude, latitude, and depth are compensated by the essential spissitude which it acquires by this contraction of itself.

So the spirit is squashed in three dimensions and expands into spissitude. But I’d put the stress elsewhere. I think it’s the inter-penetrability of More’s spissitude that makes it an intriguing case in the pre-history of the spatial imagination. We find an indigenous theory of space that allows for spiritual inter-penetration, for co-location – More wrote in The Immortality of the Soul: ‘For I mean nothing else by Spissitude, but the redoubling or contracting of Substance into less space then (sic) it does sometimes occupy. And Analogous to this is the lying of two substances of several kinds in the same place at once.’

While Henry More was never an explicit source for late-nineteenth century theorists of higher space – although he was later an occasional addition to the Theosophical canon – we find a key feature of the fourth dimension mapped out in his work, a heritage for the conceptual nexus of the fourth dimension as it was at the fin de siècle.  Cassirer also notes the irony that More’s attempt to re-spiritualize the mechanistic space of Descartes informed Newton’s absolute space.  The gridded space of European thought was within Britain haunted by extra-extensive, inter-penetrating spirits.

Please get in touch if you’d like pdfs of that essay (copyright Palgrave Macmillan and the author, who exerts his moral rights, which probably don’t include posting a copy of his essay online, but who hopes the publisher might see this as wondrous advertisement). I can only recommend readers to the book itself. It came out of a conference at Oxford in Autumn of 2010. There were only five people in the room for my paper so it’s a pleasure to be able to share it more broadly in publication. I hesitated at first to submit because I wondered if it wouldn’t be better for journal publication but when the editors mentioned that Iain Sinclair, who had given a bravura closing session talk, would be contributing, I snapped at the possibility of being read by a Sinclair-following audience beyond the typical academic circles. I’m very glad I did: my essay sits between Matthew Beaumont, who gave the opening keynote, and David Trotter; between hard boards and with a colour cover; and nestled among Professors aplenty. Kudos to the editors Benjamin and Rosalind and the publishers at Palgrave Macmillan.

That book arrived in the post a week before xmas; a week after I received from Holland a bundle I’d won in an auction. I’ve had a Google alert set up for a couple of years for all things Hinton and it hit pay-dirt late last year when it threw up a listing for a lot in an auction at Bubb Kuyper including a pamphlet edition of Hinton’s ‘What is the Fourth Dimension?’ This was published in 1884 as the first of his series of Scientific Romances with Swan Sonnenschein. It’s as rare as hen’s teeth. The British Library does not hold a pamphlet edition and I’ve yet to encounter one anywhere else. It is also very fragile and would probably benefit from some maintenance. It’s certainly an item to be filed away.

Also in the lot was this Dutch language book, Nothing ALL: Inzicht in de Vierde Dimensie, which appears not to assign authorship to any individual. Indeed, Nothing ALL may in fact be the authoring identity. My lack of Dutch is hampering any attempts to decipher exactly what is going on here and if there are, by freak chance, any Dutch readers of this blog, your help would be most warmly received. It does, however, contain some excellent original illustrations of 4d ideas, and I particularly enjoy the set below which attempt to depict visions of 4d objects in 3-space.

Fig. 1

Fig. 2

Figure 1 illustrates the passage of a tesseract through 3-space leading with a tetrahedral apex – the equivalent of a point becoming a triangle for the 3d-2d analogue. I’m unsure what’s happening in Figure 2, but it sure looks cool. And Figure 3 is an always doomed attempt to show the perspective of the rather sad-looking 3-space observer in relation to this passage, indicating a direction for the fourth dimension perpendicular to the other three (already projected down onto the plane). It’s a bit wonky, I’m sure you’ll agree, but winning nonetheless.

Fig. 3

And finally, on the 4d book front, my wife bought me a 1900 edition of Hinton’s A New Era of Thought for Xmas. This was a real treat – I’d been planning to buy a facsimile edition because it’s a core reference text for me: the only place in London with a copy is The British Library and photocopying costs there are prohibitive. There are digital versions but I’m never entirely confident with anyone else’s pagination and/or scanning, so it’s a boon to have this in excellent condition.

This is all a bit dusty tome/archivally concerned but I have a post on spissitude already partly written so I can promise some historical spatial theory soonest. May all your 2012s be para-extensive!

And I should have wished to be able to refer the reader altogether to that ingenious work, “Flatland.” But on turning over its pages again I find that the author has used his rare talent for a purpose foreign to the intent of our work. For evidently the physical conditions of life on the plane have not been his main object. He has used them as a setting wherein to place his satire and his lessons. (SR, 129)

Hinton was undercooking the debt slightly: ‘A Plane World’ may have had different intentions but its triangular characters and title didn’t really obscure the inspiration for his working in this way with this material. Abbott returned the acknowledgement in The Kernel and the Husk, a collection of theological essays published in 1887:

You know – or might know if you would read a little book recently published called Flatland, and still better, if you would study a very able and original work by Mr C. H. Hinton – that a being of Four Dimensions, if such there were, could come into our closed rooms without opening door or window, nay, could penetrate into, and inhabit, our bodies.[1]

A degree of social contact between the two writers has been noted. Specifically, Hinton’s colleague at Uppingham, Howard Candler, was a close friend of Abbott and, indeed, the dedicatee of Flatland. More tenuously, Hinton’s previous employer at Cheltenham Ladies College, the headmistress Dorothea Buss, had professional contact with Abbott.[2]

The Candler connection seems pretty suggestive to me. It’s not a reach to imagine old friends, both senior educators, gossiping about a new man at the school at which one of them teaches, especially if said new man is the son of a well-known and controversial man-of-letters and gave vent to his slightly unconventional views on space in the classroom.

Hinton’s On the Education of the Imagination, issued as a pamphlet in 1888 dealt with Hinton’s system of cubes and their use in the classroom. Its endnote by editor Herman John Falk stated that it was written ‘some years ago’ and ‘contains the germ of the work, which is more fully illustrated in his more recent writings, and thus in some respects forms a good introduction to them’.[3] A pedagogical essay, addressed to a fellow educator and referring throughout to a putative pupil, it established its theoretical basis in the work of Johannes Kepler before outlining a practical course of education: ‘The first step, then, in the cultivation of the imagination, is to give a child 27 cubes, and make him name each of them according to its place, as he puts them up.’ (OEI, 12-13)

The author warned against constricting rules, and encouraged exercises and games based on newly acquired spatial skill:

If, for instance, he is told to put a chair in (1), another in (2), and himself in (11), he is highly amused at having to seat himself in the second chair; and if then he is told to put his hat in (20) he will, after a little consideration, put it on his head. (OEI, 13)

Hinton remarked that he had also developed a form of cubical chess (!) although he confessed that none of his pupils were able to play it. The author referred to the experimental nature of the work he had undertaken with his pupils, and suggested that he had further research in mind:

Owing to the co-operation of several of my pupils, who devoted a good deal of their spare time to testing different suggestions, I have been able to work out the application of this method in several directions; and, when certain experiments on colour and sound are finished, I hope to give a detailed account of the various ways in which the method may be found serviceable. (OEI, 17)

It’s easy to see how Hinton’s lessons might have been quite entertaining. What ‘On the Education’ makes clear is the genesis of Hinton’s system of cubes in his teaching. It is devised with, and for, children, and playful elements are stressed.

Compare this to the beginning of Section 15 of Flatland, in which A. Square describes giving a domestic geometry lesson to his grandson, a hexagon:

Taking nine Squares, each an inch every way, I had put them together so as to make one large Square, with a side of three inches, and I had hence proved to my little Grandson that – though it was impossible for us to see the inside of the Square – yet we might ascertain the number of square inches in a Square by simply squaring the number of inches in the side: “and thus,” said I, “we know that three-to-the-second, or nine, represents the number of square inches in a Square whose side is three inches long.”

The hexagon is a bright student and extrapolates by analogy from this planar system to inquire about three to the third, much as Hinton hoped students of his cubic system would start thinking about four-dimensional space: ‘It must be that a Square of three inches every way, moving somehow parallel to itself (but I don’t see how) must make Something else (but I don’t see what) of three inches every way – and this must be represented by three-to-the-third.’ The passage is brief, as A. Square behaves in an un-Hintonian fashion and dismisses his grandson’s speculations.

This is, to my mind, a pretty clear sketch of Charles Howard Hinton and his spatial exercises as developed in the classroom at Uppingham. What conclusions can we draw from this? The temptation to read the whole of Flatland as a parody of Hinton as a dreamer and crackpot is very great: it wouldn’t, after all, be so unfair. Also, A. Square does come across as more rigorous than the Sphere in his attempts to extrapolate by analogy, a comparison that seems to accurately represent the single-minded vision of the young Hinton in pursuing and developing his system.

Where this gets interesting is if we pick up on the suggestion made by Smith, Berkove and Baker, that Flatland is a criticism of the misapplication of reasoning by analogy. They argue that Abbott was keen to critique what he saw as the over-extension of analogical reasoning of which Cardinal Newman, for one, was guilty, and what he saw as the tendency to obscure the linguistic roots of this rhetorical construction. They conclude: ‘Flatland is a cautionary tale about the dangers of the imagination when wrongly applied.’

This really is compelling if we line Hinton up with A. Square because its reliance upon the dimensional analogy is surely the greatest flaw in Hinton’s spectacularly generative work.

The question is, is this a flaw also blackboxed in the theoretical physics that gives us contemporary string theory? Are we still obscuring that rhetorical construction in our reach for higher dimensions of space? Or is the extention of Cliffordian physics, developed algebraically, exempt from this charge? Clifford himself reached for the dimensional analogy. I’d be interested to hear from any physicists out there, if there are any.

Hintons in From Hell: James tells Gull about Charles

The talk will be a more informal fleshing out of the stories told there, an account that deals primarily with Charles Howard Hinton. It’s a real luxury to have a bit more time than the customary 20 minute slot to talk about this material and to a different audience too: an artistic setting is something of a homecoming for Hintonian higher space, after all.

In May I’m giving a paper at a 19th Century Maths and Literature colloquium in Glasgow. Again, I’m going to focus on Hinton, and this time specifically on the cubes. From the intial schedule it looks as though there are no fewer than four people presenting fourth dimension-related papers so this promises really lively discussion. Very exciting.

In the course of putting together the talk at the ICA I’ve been looking at various animated gifs representing various projections, cross-sections and unfoldings of tesseracts. I’ll post links to a selection of these in short order.

That said, I’ve been making considerable progress with the thesis, elements of which have appeared here in the past. A draft of a third chapter on Theosophical engagements with higher dimensioned space is under the belt, and work well under way on chapter four, which is a welcome return to the happier hunting ground of fiction. In this chapter I’ll be looking at H.G. Wells’s continued engagements with the idea of the fourth dimension in his early scientific romances, Lilith (1895) by George MacDonald, The Inheritors (1901) by Conrad and Ford, The Mummy and Miss Nitocris (1906) – and the assorted stories that led up to it – by George Griffith, and a handful of British genre stories by folk like Algernon Blackwood. So lots of fun to be had in canonical SF and less-canonical pulp.

In the course of the Theosophical researches, some of which I’ll return to in future posts (really? does anyone believe that there will be future posts?), I turned up this intriguing clip from The Boy’s Own Paper of Saturday April 26, 1890.

Möbius Strip

The Boy’s Own Paper was pretty much what it said on the tin. Indeed, the phrase ‘real Boy’s Own stuff’ derives from the magazine’s title, so we can get an idea of its editorial content from its linguistic legacy: tales of adventure, instructions in edifying outdoor activities and advice on everything from keeping cats to fishing to putting down troublesome natives at the imperial margins. It was one of a great number of magazines for boys produced during the boom in print publishing from the late 1870s onwards, and the traditional account, that these catered for newly educated readers produced by the Education Reform Act of 1870, does tell part of the story. At the same time print was becoming cheaper and new publishers were entering the market by the week. (There’s a typically thorough and thought-provoking analysis of The BoP’s science content by Richard Nokes here, which also covers the  paper’s background in detail).

The Rev. Bartlett’s column was a regular piece, and the Rev becomes the latest in a long line of ordained men to have displayed an interest in the possibilities of higher space (Arthur Willink and C.W. Leadbeater were interested around the same time, as was the fictional vicar of Wells’s The Wonderful Visit (1895)). I remember reading somewhere of Möbius strips being used as parlour games around the turn of the century, so perhaps this is the source of that. It’s worth trying out, especially if you have kids, and I seem to remember doing this as a child myself.

Needless to say, despite the Rev’s 4-d addendum, the only connection this little trick has with the fourth dimension is through Möbius himself, who speculated in his paper on Barycentric Calculus (1827) that the assumption of a fourth dimension would enable the calculation of the gravitational centre of solid objects by the same means he’d outlined for plane figures. He added that there was, of course, no such thing as the fourth dimension, but he’d already let the cat out of the bag.

A Möbius strip is a topologically curious thing but it is resolutely 3-d – it has one boundary and one surface, but it still exists in 3-space without troubling 4. For me, this little piece illustrates the popular penetration of ideas of the fourth dimension around this time: no longer was it stuff for mathematicians or philosophers, it was precisely the sort of thing that would interest the adolescent readers of The Boy’s Own Paper. There’s subsequently a ludic element to this, which I’m encountering again and again in my research: 4-d is play. The whys and wherefores of this are less easy to unpick, but I have a theory I’m working on in my lab.

I’ll be giving a paper on the spaces of the late-19th-century novel alongside Prof Isobel Armstrong at the Nineteenth Century Studies Seminar on Saturday December 11th at Senate House. I’ll be offering readings of Flatland, The Wonderful Visit and The Inheritors and hoping that my middle-brow stuff doesn’t sound too feather-brained in the company of Isobel’s slightly intimidatingly cerebral work – I console myself that a balance is good and healthy. I think this is open to all so if anyone is interested…

Inside front colour plate, The Fourth Dimension

Huge thanks and respect go out to my comrade in research at Birkbeck, Iain Sinclair scholar, jazz drummer and second-hand bibliophile Henderson Downing (also involved in this great, though hopefully not Grand, project), who made the discovery in the Oxfam bookshop in Bloomsbury and tipped me off. It was £40, a very fair price, given how scarce Hinton first editions are (there are none on AbeBooks at the current time) and I can think of no other retailer to whom I’d rather give the money – in fact while there I dropped another fiver on Aldous Huxley paperbacks). Another friend, Mark Pilkington, says he has spotted a copy of the Scientific Romances in a second-hand bookshop on the South coast: at some point over the summer I plan on making the trip down to see if it’s still there.

Perhaps yet more excitingly, and certainly more rewarding, Elizabeth Zvonar has very graciously been in touch with photographs of Object of Contemplation, the piece she made inspired by Hinton’s cubes - see posts passim. She responds clarifying her practice:

As for your comments about the veracity of my practice in relationship to an accurate history – agreed. I’m much less concerned with the details and intentionally draw from my research loosely and liberally juxtaposing all kinds of ideas that don’t necessarily have a connection when looked at outside the context of art. My influences are wide and varied. My proficiency is in making objects and my intention is to make aesthetic and dynamic works that anticipate a desire for deliberate thought or can facilitate a situation for a pause to contemplate. A device to abstract the tendency for the structure of the accelerated pace we live within, enabling a moment to reflect or open up space for new thinking.

Click to view slideshow.

From the photographs, Object looks like something I could contemplate for many hours: and on reflection glass, that peculiar not-quite-solid/not-quite-liquid compound, is the ideal medium in which to render them (or should that be ‘on refraction’? I wish I could experience the full chromatic effect of circumnavigating the piece). As a non-artist, I am admiring and not a little bit envious of the skill exhibited in making objects this perfectly realised. The intention of this work in encouraging thought, and resisting accelerated living, is also something I can really relate to: I get it as a researcher, and I powerfully believe in the importance of  contemplayion in an amnesiac culture that seems determined to annihilate times and spaces that enable it.

And of course, the Modernist artists with whose Elizabeth’s work engages, as she politely hinted to me in her response, were not so interested in historical or scientific accuracy as they were the aesthetic and abstracted possibilities of using and juxtaposing ideas from these sources.

Elizabeth is speaking at Glasgow CCA on May 1st, so any Scots interested in her practice would do well to attend.

Elizabeth also pointed me towards the work of Toril Johannessen, a Norwegian artist who shares our interest in higher dimensionality.  Her most recent piece, Trascendental Physics, is, as its title indiciates, Zöllner-derived. I’m a sucker for architectural work like this, and perhaps understandably, am big into optical illusions. My masters thesis was on geometry in J.G. Ballard’s work, and I wrote on his short story, ‘The Object of the Attack’, which features as a central plotting device an Ames Room. There is something inherently Ballardian about Transcendental Physics, and Ballard’s textual invocations and purturbations of geometry (see The Atrocity Exhibition for the most fully reaslised demonstration of these) cetainly participate in the cultural history of a space that is more malleable than absolute, but above anything else, it’s really exciting to see Zöllner’s optical work referenced in a piece of art: a large section of my thesis deals with Zöllner, and vision is central to his version of higher space. I’m also digging the Flatland reference in the ingenious Downward, but not Southward, and its confusion of compass navigation is a really clever way to disturb space, while its ‘rabbit hole’ location draws an arrow pointing directly to Carroll.

Given the clear object focus of this post, I think I’m going to have to pull up my sleeves and leap into some object-oriented philosophy. I know those guys are down with Bruno Latour, but that’s about it. Wish me luck!

Borges’s prologue is also included in Selected Non-Fiction, which is rather more accessible. It is eminently quotable, so I’d like to share a couple of choice nuggets here:

“Others seek and achieve notoriety; Hinton has achieved almost total obscurity. He is no less mysterious than his work.”

re: the introduction to A New Era of Thought: “This suggests a probable suicide or, more likely, that our fugitive friend had escaped to the fourth dimension which he had glimpsed, as he himself told us, thanks to a steadfast discipline.”

“Why not suppose Hinton’s book to be perhaps an artifice to evade an unfortunate fate? Why not suppose the same of all creators?”

Why not indeed.

‘In the long run, Einstein’s influence was to be far greater than that of Hinton, revolutionizing scientific theory and, after about 1919, the world view of laymen as well. However, in the first two decades of the twentieth century, the idea promulgated by Hinton and many others that space might possess a higher, unseen fourth dimension was the dominant intellectual influence [...] the impact of “the fourth dimension” was far more comprehensive than that of Black Holes or any other more recent scientific hypothesis except Relativity Theory after 1919.’ p. ix, my emphasis.

In Appendix B she details how non-euclidean geometry and the fourth dimension weren’t integrated into earlier versions of Relativity, notes that there was no reference to Einstein in cubist literature, and uses the Scientific American essay contest to provide an accessible definition of Relativity to date the popularisation of Einstein’s theory to 1920. So Ms Zvonar has indeed misread, quite spectacularly. Next week: I police some message board comments and wag my finger at the perpetrators. Be sure to come back!

It’s exciting that a practising and exhibiting artist is disinterring Hinton’s cubes at the same time as an obsessional dusty-book-head is making some rather shoddy approximations in his part-time post-graduate student’s garrett. It would be fantastic if there were a resurgence of interest in this work, as there was in the late seventies and early eighties when Rucker produced all his 4d stuff, Sinclair wrote White Chappell and Iain McEwan published ‘Solid Geometry’.

That said, I’m not sure Zvonar covers herself in glory in the interview. I think there’s some confusion about Henderson’s book, one of the most important functions of which was to re-establish the pre-Einsteinian spatiality of the fourth dimension.  Henderson’s point is precisely that Relativity wasn’t popularly known until the twenties, and that the Parisian Modernists were reading Poincare and Ouspensky and not Einstein. Priveledging time in this equation recapitualates the mid-century misreadings of the fourth dimension that Henderson’s work so usefully corrected.

But maybe I’ve misremembered. I’ll check. And besides, this is an interview, and not an essay, so ideas are communicated in a much chattier way, and these sound like they could be rather fetching baubles, ironing out some of that distasteful period ‘clunk’ (raises a quizzical eyebrow). Also, Zvonar’s previous shows demonstrate a continued engagement with Modernist art history, and I would like to see more.

For what it’s worth, if I were an artist working into this wonderfully rich field, I’d construct Hinton’s cubes at 24x scale (we’re imperial here, obviously) and from some kind of  highly tactile substance – perhaps memory-foam, a material whose function is only realised when it’s touched – and then forbid audiences from touching them. Or perhaps there’s a material that would be more period appropriate: wax? This would reference other of Hinton’s work. I think the key is to attempt to communicate the ambivalence of these objects, their position on the threshold of the empirical and the ideal, and the promise of transportation they make, not easily accessed.

I’d also like to see a pile of such blocks as high as person, just because. Maybe higher? Maybe I should be thinking 120x scale. Anyone got access to any funding?

I’ve been busy on the newly retooled and refangled 19: Journal of Interdisciplinary Studies in the Long Nineteenth Century, which is now live in an OJS template, with essays available in html and integrated with Nines. We’re all rather proud of it.

Since finishing my contract there at the end of October, I’ve been catching up with my own research, long overdue (I’m sure my supervisor would agree). I’m still working on a second draft chapter, and should be doing so right now. BUT…

The catalogue cube Nala as detailed in A New Era of Thought

A section of this chapter is going to be devoted to Charles Howard Hinton’s system of cubes. The cubes are the foundation blocks – pretty much literally – of Hinton’s approach to thinking higher space and I am keen to meet them head on, because I’m convinced that they’re highly significant with regard to the writers who follow him. But they’re a wee bit daunting. The second half of A New Era of Thought is devoted to describing the construction of the cubes, a system for naming them, and various exercises for conducting with them.

It was written by Alicia Boole Stott, Hinton’s sister-in-law, who is the best advert for the effectiveness of the system, as demonstrated by her intuitive work with higher dimensional mathematics, published in a series of three papers 1900, 1908 and 1910, and discussed by HSM Coxeter, among others. But what mght have come readily to Alicia is not necessarily straightforward. The lists of names for the cubes alone deflect casual attention.

A table of Latin names for identifying the different sides of cubes in a 36-cube system

A few lines printed in A New Era urged readers to contact the publisher to buy readymade sets of the cubes, but this didn’t quite work out as smoothly as planned. Correspondence from Swan Sonnenschein to Howard’s friend and editor John Falk shows the rocky ride. On 21st September 1888, some months after publication, SS received an inquiry about the cubes. Sonnenschein wrote: “It would perhaps be as well, should this gentleman give an order for a set, to have two sets made, as it looks rather bad to have to admit that inquiries for them are unusual.” Another inquiry was received in January of 1889, but it wasn’t until February that Falk provided the first sets to the publisher, who returned them, writing: “The workmanship of the cubes is so rough it would affect sales very badly.” It took Falk until November to source improved sets, with the price set at 17/6 for trade plus 20% for public sales.

The models seem to have been more trouble than they were worth as a commercial venture, particularly when Charles resumed correspondence with his publishers upon his arrival in the USA in 1892: a alrge proportion of the correspondence mentions them. They sold very slowly but continued to pique interest. In 1903, SS wrote: “Can you send me one set of your models which a lady resident in Nice is very anxious to purchase?” In 1904 a Mr Dyson returned his set. Mr Dyson had possibly bought a copy of The Fourth Dimension, published in that year, in which a refined version of the system was presented, and clearer instructions provided for DIY cubesters. The naming system had been done away with as unworkable, and colour-coding was now the way forward. The colour plates presented in this book can be seen by clicking through the banubula and Greylodge links below.

'Kindergarten cubes': suggested activities do not include mind-destruction

It’s been helpful for me to review Hinton’s work and to reconstruct his bibliography. The sixth of the Romances, ‘On the Education of the Imagination’, issued as a pamphlet in 1888 with a brief endnote by Falk, also deals with the cubes, and was probably composed sometime in the early 1880s, despite its later publication. The endnote states that it was written ‘some years ago’ and ‘contains the germ of the work, which is more fully illustrated in his more recent writings, and thus in some respects forms a good introduction to them’. It describes the development of the cube system and its use in the classroom. It underlines Hinton’s role as a professional educator, and his approach to the aquisition of knowledge that comes from this job. And of course the cubes are in some way a game: an educational game, certainly, but a game none the less. I want to disinter the ‘ludic’ aspect of the cubes so I’ve decided to make a set for myself. I’ll blog about my progress (doubtlessly slow), here.

First step was to buy a set of ‘kindergarten cubes’, as recommended by the authors. They’re a natural wood colour so I can colour-code them myself.

Not quite Farrow and Ball

I had initially thought I’d go with Farrow and Ball colours, because being a good middle-class, South-West London homeowner, I have a stack of Farrow and Ball sample pots, so I figured I could reproduce some faux-authentic period colours, like Bourgeois Blue, Nostalgia Rouge and Opium Ochre. Sadly, this collection of samples has been loaned to a neighbour’s sister, so I’ve gone with what I had in the house – children’s paints.

If these end up being washed out, I’ll retrieve the F&B house paints and use those (decorators assure me that Dulux are better quality paints and that anyway, you can reproduce any colour with Dulux colour match, but I’m sure the inferior F&B should suffice for this).

There has been some interest in Hinton’s cubes online in recent years. There were a couple of posts on the now defunct blog banubula, showing scans of the coloured plates from The Fourth Dimension. Greylodge onlined a tidied-up  [pdf] instruction sheet, which is very useful – I would have used this, but getting my colours to match would be too tricky.

This took me back to airfix days, when the parts would become glued to the paper

I think a contemporary legacy for the cubes has been assured by a letter received by Martin Gardner, a popular science writer of the mid-century who wrote about higher space puzzles in the Scientific American. The letter from Hiram Barton, “a consulting engineer of Etchingham, Sussex, England” responded to an account of Hinton’s cubes, and was published by Gardner on p.52 his book Mathematical Carnival (and reposted by Banubula, and cited also by Rucker).

Dear Mr. Gardner:

A shudder ran down my spine when I read your reference to Hinton’s cubes. I nearly got hooked on them myself in the nineteen-twenties. Please believe me when I say that they are completely mind-destroying. The only person I ever met who had worked with them seriously was Francis Sedlak, a Czech neo-Hegelian Philosopher (he wrote a book called The Creation of Heaven and Earth) who lived in an Oneida-like community near Stroud, in Gloucestershire.
As you must know, the technique consists essentially in the sequential visualizing of the adjoint internal faces of the poly-colored unit cubes making up the larger cube. It is not difficult to acquire considerable facility in this, but the process is one of autohypnosis and, after a while, the sequences begin to parade themselves through one’s mind of their own accord. This is pleasurable, in a way, and it was not until I went to see Sedlak in 1929 that I realized the dangers of setting up an autonomous process in one’s own brain. For the record, the way out is to establish consciously a countersystem differing from the first in that the core cube shows different colored faces, but withdrawal is slow and I wouldn’t recommend anyone to play around with the cubes at all.

Frances Sedlak probably used old copies of The Theosophist instead of The Guardian

The sensational tone of this letter falls in line with a current of response to higher dimensional thinking that is seeded with the anti-Zollner propaganda in the early 1880s and emerges more consistently at the fin-de-siecle: the idea that  thinking higher space results inevitably in madness. What Barton doesn’t mention is that Sedlak was also, unsurprisingly, a Theosophist, contributing frequent articles to The Theosophical Review from 1906-1908 and to The Theosophist in 1911-1912. He later also contributed an article to Orage’s The New Age disputing Einstein’s Theory of Relativity on the grounds that Einstein was insensible to the dictates of “Pure Reason”. His partner in a “free union”, Nellie Shaw, wrote an account of their life together in the Whiteway Colony in A Czech philosopher on the Cotswolds; being an account of the life and work of Francis Sedlak. Shaw’s account of Sedlak’s interest in the cubes gives it an altogether more positive spin, and beds into the utopian Theosophical verison of higher spatial thinking:

Some readers may be acquainted with a book by C. Howard Hinton, entitled The Fourth Dimension, which contains a coloured diagram representing twenty-seven cubes of various colours. This idea was [108] seized upon by Francis, who adapted it to his own ideas.

A box of children’s playing blocks was obtained and each one painted a different ad nameable shade. So far as I am able to understand, the idea was to build up from the whole twenty-seven cubes one cube, each separate colour being in a particular relation to the next one, and then to gaze fixedly at it until the whole was mentally visualised. This accomplished, the cube was unbuilt and then rebuilt with a different combination of colour, and visualised mentally as before.

This amazing performance required hours of time at first, but gradually the speed quickened, until eventually it became focused upon the mind, and Francis was able to review the blocks in all their twenty-seven positions so swiftly, that it became almost like seeing the cube from all sides at once.

It will be realised that the changes of position were almost innumerable. At first a very hard laborious task, it became an absorbing occupation, to which was given every spare moment. Many persons, not understanding, looked on it as a most unproductive way of spending time. Others admired the wonderful patience, but could see no useful result.

Just as the would-be athlete twists and turns on the parallel bars, using time and energy to develop his muscles and gain strength which can be used later in any direction which he may desire, so Francis assumed that this power gained by practice in visualisation, seeing mentally the block of cubes on all sides simultaneously, could also be used in any sphere and on any subject; in fact, it was ability to see through anything, and must eventually lead to clairvoyance.

This study of the cubes was followed intermittently, [109] since it was not a mental exercise calling for philosophic reasoning or mental effort whatever. So, after devoting many months to the cubes and having an urge in another direction, Francis would drop them again for several years.

The extraordinary thing was that afterwards he could resume the practice without difficulty. He did not lose the power; indeed, he seemed to have a positive affection for these bits of wood, which he would tenderly dust and preserve.

Towards the end of his long and trying illness, when terrible coughing prevented him from sleeping at night, the long silent hours seemed interminable. On my enquiring one morning as to what sort of a night he had had, he said almost joyfully, “Oh, being awake does not trouble me now. I do the cubes, and the time flies.” So I thanked God and blessed the cubes, for which had been found a utilitarian use at a most desperate psychological juncture. Power won cannot be lost, and will some day be utilised.

So I’m hoping, really, to achieve a new mental power before I get bored. But not to go mad. That wouldn’t further the research, I don’t think. My next post will probably look more closely at the theory presented in A New Era, which makes clear an interesting nexus in Hinton’s thought that is also significant. I’m hoping in future posts to develop the varied and playful cultural legacy of Hinton’s cubes, and pledge to make sure there are no more five month lapses.