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Archive for December, 2009

I’ve been back to Linda Dalrymple Henderson’s The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983) to check that I wasn’t misremembering her arguments. It’s all in the intro:

‘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!

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Cubic addendum

No sooner have I posted the previous, than I’ve come across this interview with the artist Elizabeth Zvonar, who has also constructed some of Hinton’s cubes – from rainbow-coloured glass, no less. I’d realy like to see these, but there aren’t any images of them on the site of the gallery hosting her show, sadly. What images there are look worth investigating further, featuring manipulated photographs and rainbow colour-fields. They seem to recall surrealist photography, so carry through some of the art-historical promise.

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?

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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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