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Posts Tagged ‘Charles Howard Hinton’

NEOT_cube

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.

tesseract

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

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

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!

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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.

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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 20th 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.


[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.

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A New Year’s Resolution: to post at least once a month. This is made all the more urgent by having pointed people to this blog in a three-line biog published in the essay collection Utopian Spaces of Modernism: British Literature and Culture, 1885-1945, and then sitting on my hands. Any visitors from that source may be underwhelmed by inactivity.

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!

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Literary historical discussions of Flatland have frequently toyed with the relationship between its author Edwin Abbott Abbott and Charles Howard Hinton. There are a handful of highly suggestive connections. 1) The pair were mutually aware. Hinton praised Abbott but stressed the difference between the two in the introduction to his third romance, A Plane World, first published in the summer of 1886:

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)

Cube illustration from 'Casting Out the Self'
Illustration of a block of cubes from ‘Casting Out the Self’, p.208 of Scientific Romances. Despite being lifted from the earlier published essay, it illustrates the same system described in ‘On the Education of the Imagination’

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.


[1] Edwin A. Abbott, The Kernel and the Husk: letters on spiritual Christianity (London: Macmillan, 1886) p. 259.

[2] See Ian Stewart, The Annotated Flatland (Cambridge, MA: Perseus, 2002), p. Xxiii, and Thomas Banchoff, ‘From Flatland to Hypergraphics: Interacting with Higher Dimensions’, Interdisciplinary Science Reviews,15: 4 (1990) 364-372.

[3] ‘On the Education of the Imagination’, Scientific Romances Vol. 2 (London: Swan Sonnenschein, 1895), pp. Xx (first published 1888). ‘On the Education’ details researches carried out with male pupils: Hinton started teaching at Uppingham in 1880, so it must have been written after this date. A piece entitled ‘The Next Step in Education’ was discussed with his publisher from mid-1885. All further references to this essay are given in the body of the text after the abbreviation OEI.

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I’m giving a talk at the ICA on Thursday night as part of the Strange Attractor curated series under the auspices of Nathaniel Mellors’s Ourhouse exhibition. Details and tickets here. This is in conjunction with an essay that appeared in the latest issue of the truly wonderful Strange Attractor Journal, where I’m in highly esteemed company, particularly that of Alan Moore who obviously has Hintonian pedigree himself:

Hinton in From Hell

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.

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Jumpstart time: this blog has been dormant for five long months, so I’ve decided to do something a bit more engaging (hopefully) to relaunch it.

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.

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