I’ve just cut the below from my Flatland chapter because it doesn’t fit with where it’s going any more. There is plenty more to be said on Flatland’s evolutionary concerns beyond this narrow focus on Galton, but I really enjoyed writing this and watching the liberal theologian give the eugenicist a proper kicking. This also fleshes out a remark in the previous post.

One focused target of Flatland’s satire can be drawn out from the first part of the text. As a theologian, Abbott was likely to have become aware of Francis Galton during the ‘prayer-gauge debate’ of 1872 which Galton joined in the pages of the Contemporary Review: this debate over attempts to scientifically measure the effectiveness of prayer was, after all, the ‘sensation of the season’.[1]  As an educator, Abbott could scarcely have failed to have followed the prolific Galton’s pronouncements on nature over nurture throughout the 1870s when the statistician’s research privileged the hereditary transmission of mental and moral characteristics.

Galton was then, as now, most associated with the theory he would neologise in Inquiries into the Human Faculties (1883) as eugenics, ‘the science of improving stock’.[2] Rosemary Jann has noted ‘the voice of the eugenicist’ in Flatland and others have described the context for Flatland’s particular version of geometric evolution.[3] Listening closely for this voice and recording its utterances not only beds Flatland into contemporary social and intellectual concerns but also points to a direct identification of Galton.

A Square describes a society that is an evolutionary hierarchy. As he explains: ‘It is a Law of Nature with us that a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility.’ (F, 7) At the lower echelons are female Flatlanders, straight lines, figures more one-dimensional than two-, with no interior angles to measure. The lower and middle classes are triangles: sharp isosceles are workmen and soldiers, the middle-class are equilaterals. The professional and gentlemanly classes are squares, such as the narrator, and pentagons. The nobility begin with hexagons and ascend through all polygons. At the very apex are the priestly class, circles, or at the very least figures with so many sides that they approximate circles.

A professional such as A Square feels pity and contempt for the ‘degraded condition’ (F, 8) of the Isosceles class who ‘can hardly be said to deserve the name of human figures, since they have not all their sides equal’ (F, 8). Fortunately for the Isosceles, a Lamarckian hereditary transmission of acquired characteristics means that focused self-improvement and careful selection of breeding partners combine to give a gradual increase in internal angles over the generations.

Lower even than Isosceles are Irregular figures who display no equality of sides. A Square informs us that ‘”Irregularity of Figure” means with us the same as, or more than, a combination of moral obliquity and criminality with you, and is treated accordingly’ (F, 24). This elision of moral and physical characteristics chimes directly with Galton’s study in Inquiries, in which he writes that ‘the innate moral and intellectual faculties are so closely bound up with the physical ones that these must be considered as well’ (IHF, 3). In Flatland, indeed, interior angle correlates directly with intellectual capacity: ‘the family brain was registered at only 58°.’ (F, 16)

Rosemary Jann has located the timbre of Galton’s arguments in A Square’s observation on ‘the extraordinary fecundity of the Criminal and Vagabond classes.’[4] In Inquiries Galton dealt with criminals and the insane in a brief chapter in which he gave his support to this popularly held Malthusian idea: ‘the criminal population […] is well-suited to flourish under half-savage conditions, being naturally both healthy and prolific’ (IHF, 43). It should be noted, though, that Galton diverged from Malthus’s conclusion that prudent men would check their fertility, arguing that the lower classes could not be relied upon to practice prudence.

Other eugenic motifs of Flatland appear remarkably prescient. The Sanitary and Social Board, responsible for certificating equilaterals, draws on the mid-century concern of social reformers with public hygiene and demographics to anticipate the concept of racial hygiene, coined by Alfred Ploetz in 1905, and taken up in eugenic discourse of the early twentieth century. The notion of eugenic certification itself anticipates with unerring accuracy the future trajectory of Galton’s thought: his unpublished utopian novel Kantsaywhere, discovered by Karl Pearson in his papers after his death, envisaged an even more advanced eugenic certification system in which those failing to achieve grading were segregated and prevented from reproducing.[5]

Most chilling are the stentorian tones of the eugenic principle in Flatland policy. Irregulars are frequently destroyed and ‘the diminution of the redundant Isosceles population [is] an object that every statesman in Flatland constantly keeps in view.’ (F, 17) For a reader familiar with Galton’s biography more personal attacks might have been discerned in Flatland’s text. Certainly, had Frances Galton been a Flatlander, his lot would have been unhappy. Galton had failed to gain a degree from Cambridge, having suffered a breakdown in the run-up to his exams. In Flatland

the condition of the unsuccessful minority is truly pitiable. Rejected from the higher class, they are also despised by the lower. They have neither the matured and systematically trained powers of the Polygonal Bachelors and Masters of Arts, nor yet the native precocity and mercurial versatility of the youthful Tradesman. The professions, the public services, are closed against them; and though in most States they are not actually debarred from marriage, yet they have the greatest difficulty in forming suitable alliances, as experience shews that the offspring of such unfortunate and ill-endowed parents is generally itself unfortunate, if not positively Irregular. It is from these specimens of the refuse of our Nobility that the great Tumults and Seditions of past ages have generally derived their leaders; and so great is the mischief thence arising that an increasing minority of our more progressive Statesmen are of opinion that true mercy would dictate their entire suppression, by enacting that all who fail to pass the Final Examination of the University should be either imprisoned for life, or extinguished by a painless death. (F, 22)

[1] The Prayer-Gauge Debate, ed. by John O’Means (Boston: Congregational Publishing Society, 1876), p. 3.

[2] Inquiries, 17

[3] Rosemary Jann, ‘Introduction’ in Flatland: A Romance of Many Dimensions (Oxford: Oxford University Press, 2006), p. xvii.

[4] Jann, ‘Introduction’, p. xvii.

[5] See Karl Pearson, Life, Letters and Labours of Francis Galton (1930), vol IIIA, pp. 414-424.


I’m going back into Flatland so I’m justifying procrastination by looking through Flatland adaptations. I’ve been trying to get my mitts on the below version for some time featuring, as it does, the inimitable Dudley Moore as A Square, an unsurpassable piece of casting. The animation was by John Hubley, who was blacklisted for refusing to name names to the House Committee on Un-American Activities and is noticeably influenced by the geometric Modernist stylings of Russian animation. It is available on DVD from Documentary Educational Resources, but they charge an absurd $65, which for an 11-minute film seems a bit steep. I guess the Greek youtuber below felt the same, and shared a copy in the interests of unhindered education.

I post this first because it is charming and seems closer to the spirit of the novel than the 2007 film, Flatland: The Movie, which had a significantly larger budget: significantly large enough to cast Martin Sheen as A Square and Michael York as the Sphere. It’s an interesting proposition. The animation is whizzy and while the kind of scriptwriting that has a character declaring “Dude, you’re freaking me out!” makes me instinctively uncomfortable – for a start, it’ll age pretty badly – I wonder if its good intentions and intended audience don’t actually mirror those of Abbott. When it came out in 2007 I thought they’d missed the opportunity to do it in 3D, which would have made so much sense and brought alive the Spaceland sections, so I’m glad they’re remastering it for 3D Imax, no less. Dude! You really are freaking me out!

Despite claims from the producer that selling it directly made more money than he had made on other projects, I guess they ran out of budget for the website. Thomas Banchoff was involved as a consultant, so the geometry and Abbott scholarship are rock solid.

This production must have been enormously bad news for the producers of Flatland: The Film, which also came out in 2007, without the big names. I’m afraid I’m not able to feel too much pity for them, though, because it looks as if they’ve played rather loose with plot and while the animation shows a debt to Abbott’s original illustrations, I’m not sure there’s a lot to be gained from making Flatland a war movie (and the soundtrack?)

Flatland has clearly found a contemporary niche as an educational resource, a way of instructing dimensionality. This is interesting, and certainly part of the story, but as a cultural historian I would hate to leave it to the maths classroom, as valuable as it may be there. Flatland’s complexity and responsive immersion in late-Victorian intellectual life seem reduced by these later versions. Given the prominence of ideas related to Malthus, Lamarck and Galton it might just as well be a resource for teaching evolutionary narratives. Biologists! To the DVD player!

It is also worth observing that narrative is precisely its strength today: the fact that the geometry is embedded in a story is what makes it so attractive to teachers. I think this, too, leads is into more interesting avenues of thought, particularly relating to how and where Flatland fits into literary history. An intriguing essay by Mark McGurl observes that the critically commonplace descriptions of characters as flat and round, coined by E.M. Forster in Aspects of the Novel (1927) , surely owes to Flatland. (I’m uncertain about other claims McGurl makes, regarding Flatland’s position on class, but this is a great point). Flatland , I think, actively participates in and is aware of its place in the literary theory of the 1880s.

As I have argued before on this blog, higher space is also play, so it is appropriate that Flatland has inspired a number of recent computer game projects, which I’ll round up in my next post.

For the past two days I’ve been at W.T. Stead: A Centenary Conference for a Newspaper Revolutionary. I find processing the intellectual grist of conferences takes more than 24 hours, so I’ll hold back on trying to put down any synthetic thoughts and will note, instead, what a joy it was to participate in and to thank the organisers, Laurel Brake, Jim Mussell (@jimmussell), Roger Luckhurst (@TheProfRog) and the British Library’s Ed King. Highlights included: being part of an occult-themed panel with Kate Cambell, Sarah Crofton and Will Tattersdill (@faceometer), in which the papers proved remarkably complementary (I guess we were all working in the shadowland sketched out by Roger Luckhurst’s account of Stead in The Invention of Telepathy) and after which I came away with avenues of research prompted by each of my co-panellists; meeting again Clare Gill and Beth Rodgers from Queens in Belfast,organisers of the first academic conference I ever attended and brilliant company; all the plenaries, but particularly John Durham Peters’s ‘Discourse Network 1912’, a Kittlerian take on Titanorackery; and also Gavin Weightman’s take-no-prisoners re-appraisal of ‘The Maiden Voyage’ and subsequent court case, a rare example of a paper critical of Stead that was all the more laudable for coming from a non-academic surrounded by tutting scholars. I blagged a copy of Gavin’s POD book and will respond to it in a  future post.

I post the text of my paper below and will add a link to the slides when I get those up somewhere.

“Throughth”: W.T. Stead’s Higher Spatial Holiday

I’d like to open by going straight to the source. Buckle up and allow William Stead, in full visionary mode, to take you on a voyage to another dimension. This is from the Review of Reviews, April 1893, an essay entitled Throughth: Or, On the Eve of the Fourth Dimension:

We are now living in space of three dimensions. But there is evidently more beyond. We are now in the stage in which our second dimension ancestors were to be found when the light began to stream in upon them from above and below the narrow plan of two dimensions in which they lived. As the two dimensional creatures had to open their minds and recognise that there was a space of three dimensions full of immense possibilities but hitherto invisible, so we now have to open our eyes and admit that beyond the space of three dimensions in which we live there exists a space of four dimensions of which we catch glimpses now and then in those phenomena which are entirely unaccountable for by any law of three dimensional space.

An admirable little book, entitled “I Awoke,” written automatically and published by Simpkin and Co. Last month, defines the fourth dimension as that of motion through, or interpenetration. Clairvoyance, by which a man can see in London what is passing in New York; telepathy, by which the mind of a man in Edinburgh can impress itself upon the mind of a percipient in Dublin; telepathic automatic handwriting, by which the mind of a person whose body is in Germany can use the hand of a writer who is in England; crystal vision, by which events past, present and to come are portrayed before the eye of the gazer; psychometry, whereby the character of an individual can be divined from a touch of a hair of his head,-

all these things are so many rifts in the limits of our three dimensional space through which the light of four dimensional space is pouring in upon us. It is becoming more and more evident to those who observe and note the signs of the times that we are in very deed and truth on the eve of the fourth dimension […]

In the new world which opens up before life becomes infinitely more divine and miraculous than it has ever been conceived by the wildest flights of imagination of the poet. Many attributes which have hitherto been regarded as the exclusive possession of the Deity will be shared with His creatures. The past mingles with the present, and the future unfolds its secrets. Death loses its sting, and parting its sadness. The limitations of time and space – three-dimensional space, that is – furl up and disappear. Spirit is manifested through matter, and we enter into a new heaven and a new earth. This and much more than this is involved in the statement, “We are on the eve of the fourth dimension.”

This extract contains much to analyse. Most obviously, we have Stead’s interest in occult and psychical phenomena such as telepathy and automatic writing. By the time he wrote this Stead had been interested in psychical research for over a decade; he attended his first séance in 1881 and in 1884 he had hosted the thought-reader Stuart Cumberland at the offices of the Pall Mall Gazette. By 1893 he had been editing and publishing the Review of Reviews for three years and his absorption in spiritualism was increasingly evident to his readers, who encountered frequent articles and editorials on thought-reading, ghosts and the after-life. He had published Real Ghost Stories in November 1892, in which he aimed, in Roger Luckhurst’s phrase, to ‘democratise psychical research by appropriating the sober SPR ‘Census of Hallucinations’ Project’. He had become increasingly interested in automatic writing following the death of American journalist Julia Ames, and had in 1892 suggested that the readers of the Review of Reviews investigate the phenomenon, by which stage he was already collecting the automatic scripts which would later be published as Letters from Julia (1897). The following pages of Throughth gave an account of some of these experiments.

It also gives a sense of various aspects of Stead’s journalistic style. The synoptic function of Review of Reviews is indicated by that reference to ‘an admirable little book’, to which I’ll return. The visionary tone is a wee bit febrile in sections of this but it extends from the affective sensationalism Stead practiced in his journalism. We also have an indication of his internationalism – all those people in New York, Edinburgh, Germany, Dublin. And, of course, his focus on communication and mediation.

What has drawn me to this essay, though, is Stead’s engagement with the idea of the fourth dimension, which is the focus of my research. As far as I can discover this was Stead’s only sortie into higher space – if there are any Stead scholars in the audience who can direct me to other fourth dimensional references I’d be thrilled to hear from you. The section I’ve just read comes from the second page of the essay. In the first, he outlines some of the arguments current in 1893 for the existence of a fourth dimension.

What I would like to do with this paper is to describe the shape of Stead’s engagement with higher space. We won’t be staying in the lowly fourth dimension for long, but will be ascending to the fifth, sixth, seventh and beyond. In describing this background we’ll probe the aspects of Stead’s method I’ve just outlined before tarrying a while with automatism, and communication more broadly, in its spatial aspect.

Stead’s higher spatial holiday began, as far as I can tell, only a month earlier. In the Review of Reviews for March 1893, he recommended a cluster of books of interest to psychic researchers. These books were ‘the signs of the times’ to which he would refer.


Frederick Myers’s essay on the Subliminal Consciousness in the Proceedings of the Society for Psychical Research, was commended for explaining ‘so clearly and exhaustively the method by which the psychologist is learning to evolve a new science of the hitherto invisible and unknown world’. Myers’s essay will be known to scholars of both psychology and psychic research. It was a source for Freud, who was just about to begin publishing. We should note Stead’s description of the subliminal consciousness as the ‘invisible and unknown world’. Under this banner the workings of mind fall into the same category as electromagnetism and assorted physical phenomena.


A brief paragraph went on to suggest as complementary Arthur Willink’s The World of the Unseen: ‘Mr. Willink holds that the unseen world is of four dimensions, and into this space of four dimensions or Higher Space, as he calls it, the dead pass, and from which they can communicate with us.’

Willink’s book was the latest contribution to a canon that had dragged the ideas of n-dimensional geometry into occultist discourse. These texts used analogical arguments first rehearsed in a mathematical context to claim that there was by necessity a fourth dimension of space, that it too was in the invisible and unknown world by dint of the fact that it could not be accessed by sense perception, but claimed that evidence of it could be discerned in séance phenomena. These arguments hinged around the fact that projective geometry had suggested a key feature of a four dimensional space. That intelligences of a higher dimensionality would be able to access the interior of closed objects in a lower dimensionality – just as we three dimensional intelligences can access the inside of a two-dimensional square or circle.


Stead went on to review Do the Dead Return? A Record of Experience of Spiritualism by a Clergyman of the Church of England; Mr Carlyle Petersilea’s Discovered Country, ‘which is said to have been written automatically, describing life on the other side’; and Dreams of the Dead by Edward Stanton, of which he wrote:

‘It is very curious and more theosophical than Christian. The writer holds that we are on the advent of the sixth race. A new physical sense is developing in the nerve constitution of man. The time is at hand when a new civilisation will be founded by a select amalgam.’

It’s clear from this brief selection that Stead had synthesized the arguments of these books for his essay: Myers’s theorisation and early mapping of a psychological basis for psychic phenomena, Willink’s accessible description of the spiritualist hypothesis of the fourth dimension, the automatism of Petersilea’s book, the millennial sentiments of Stanton’s.


As far as I’m concerned these are all but mere morcels compared to I Awoke! Conditions of Life on the Other Side Communicated by Automatic Writing (1893), the final piece of the occult jigsaw Stead assembled in his essay.

I Awoke! sold at one shilling net and was popular enough to be reprinted and extended two years later. It offered a first-hand account of the conditions of the kind of higher dimensional afterlife argued for by Willink. It referred throughout to ‘the Master’, a Christ, of ‘a form which is in four dimensions, and which cannot be seen by ordinary earthly vision.’ An appendix described the conditions of the various dimensions in which the dead lived, and is notable for its embrace of a full range of higher dimensionalities.


The Appendix, ‘received’ in 1891, claimed that ‘there is a fourth dimension […] which represents what you might call the inter-penetrative sphere’. It continued: ‘This fourth dimension, only guessed at by you, is our first, the other three fall from us as crude and imperfect.’ The inhabitants of this dimension were capable of improbable feats of transportation:

This power, when perfected, would give man absolute power of progression in every direction and in every part of the universe. He could pass through the heart of mountains, or could rise into the atmosphere to any height by altering, as it were, his own density, and the density of his path; nothing would prove a hindrance.

Perhaps unnecessarily, the fifth dimension extended these capabilities to cosmic space:


‘Let us call the fourth dimension inter-progression, then the fifth might be called trans-progression. From sphere to sphere, from star to star, and from star to sun shall the children of men wander at free will.’ The less than complete understanding of astronomy demonstrated by the dictating intelligence did not deter further revelations. ‘As men rise from dimension to dimension their powers are changed and increased in many ways.’ The sixth dimension was the first ‘time-dimension’ in which linear time was infinitely malleable. In the seventh ‘time may be said to have no existence’: the past was as accessible as the present; only the future remained hidden. The powers of those who had access to dimensions beyond the seventh were vague: ‘After the time-dimensions come those that belong more directly to the human will, its powers and its limitations.’

Heady stuff, and tremendous fun. Okay. But what to make of it? And how to treat it? Any text that purports to be transmitted through automatic writing occupies a curious cultural position. To proponents of the practice the text’s very existence offers evidence of the phenomenon of automatism and legitimates content offering mediated access to the mysterious unseen. A more distanced analysis might observe merely that such texts reflect the conditions of their composition; regardless of their origin, the ‘medium’ through which they are channelled is inevitably embedded in an occult network. Such texts tend to synoptically appropriate (or confirm) current occultist or scientistic thought – certainly, this was true in the case of HP Blavatsky, whose Secret Doctrine and Isis Unveiled were both written automatically.

In terms of content, in I Awoke! we re-encounter the conceptual hinge of Stead’s essay, that horrible neologism – throughth. We should forgive Stead this, however. Higher dimensioned space is prepositionally confusing – in the period it was called variously hyper-space, meta-space and pro-space. In fact, it causes problems for language at a basic level by disturbing standard spatiality. We realise, as soon as directions such as up, down, above, below are taken away from us, how much of our romantic language is spatially grounded.


What I think is interesting is that Stead’s synthesis focused on inter-penetration – Stead wrote of the fourth dimension:

We however get glimpses of it in clairvoyance, in the phenomena of hypnotism, and in all the experiments which are known as telepathy, crystal-gazing, thought-reading, and all things in which we see, hear or communicate through things, which according to the known laws of third dimensional space, would render communication impossible.

Here was also recalling a section quoted from Myers the previous month: ‘The possible law of which I speak is that of the Interpenetration of Worlds.’ Stead was binding together different forms of interpenetration and his original contribution, appropriately enough for a radical journalist, was to focus on the communicative nature of the medium, the subjectivity through whom. Employing the speculated interpenetrative qualities of higher space Stead’s throughth was unhindered communication.


I would like to note here the parallel between automatism and creative writing. After Surrealism’s appropriation of automatic technique for artistic production, it’s perhaps an obvious link for us to make to compare automatic writing with any kind of creative artistic production, but while this is a parallel that 19th century practitioners would have rejected, it surely holds. We can’t quite read these texts directly as fiction but we can certainly apply the same critical armature we do with fiction. I’d like to say there now follows an analysis of the use of indirect free discourse in automatic texts, but I’m going to spare you that in favour of the rather more diffuse observation that this urge towards communicating through, a spatial elision of first and third person, is mirrored in Henry James’s fiction and theoretical writing of the same period. James spilt much ink over his concern with achieving the optimal perspective. He even used the idea of possession.


This is from the preface to the New York edition of The American:

For the interest of everything is all that it is his vision, his conception, his interpretation: at the window of his wide, quite sufficiently wide consciousness we are seated, from that admirable position we “assist”. He therefore supremely matters; all the rest matters only as he feels it, treats it, meets it. A beautiful infatuation this, always, I think, the intensity of the creative effort to get into the skin of the creature; the act of personal possession of one being by another at its completest – and with the high enhancement, ever, that it is, by the same stroke, the effort of the artist to preserve for his subject that unity, and for his use of it (in other words for the interest he desires to excite) that effect of a centre, which most economise its value.

What I hope to suggest by highlighting this parallel is that the spatial imaginary of the late nineteenth century had been altered by the ideas of higher space, that co-presence, the co-habitation of the same space by two different consciousnesses was very much in the air, and that this altered imaginary can be discerned in both the theorisation of fiction-writing technique and Stead’s utopian vision of technologised communication: ‘the human telephone’, as he called it elsewhere in his essay. The aim of affecting the reader is also continuous between James and Stead. Where Stead departs from that old snob James is in his democracy. Roger Luckhurst probes Stead’s ‘affective journalism’ in the context of his urge to democratise knowledge, his obsession with electrical technologies and the way these came together in his internationalism and vision of a technologically connected empire. We read all these in Throughth. Stead disagreed with Stanton that it would only be a select amalgam of spiritual artistocrats who would be able to communicate in this way. In Stead’s account, the new world was available to all.

Stead’s democratised fourth dimension did not last long, however. In the May issue of Review of Reviews he noted a paper by Professor Hermann Schubert published in The Monist, ‘The Fourth Dimension: Mathematical and Spiritualistic’. Prof Schubert was ‘very hostile to spiritualism’ and stressed the need for ‘slow, unceasing research’ rather than ‘the thoughtless employment of fanciful ideas’. Stead retreated from his previous enthusiasm in the fourth dimension with an unconvincing objection to an ‘unscientific’ line of argument. And poof! That was it.

This is something I encounter again and again in researching higher space: no sooner does a supernaturalist account of the dimensionality of ‘the other side’ appear to offer a millenarian vision of the future, than a hard-headed philosopher cuts down speculations. Little wonder that the general public frequently expressed confusion at the idea. Yet as is evidenced by Stead’s reading list, millennial visions were enjoying some currency in 1893,


and although many drew directly from Revelations, they managed to maintain optimism about the changes in store in the new century. Stead’s engagement with the fourth dimension constitutes a fascinating case study of the oscillatory cultural operation of higher space, bouncing between high and low culture, and its vagaries even within the field of psychical research. It gives some indication of the seemingly limitless properties of such a fugitive space and the difficulties and risks inherent in trying to contain it, particularly in a form accessible to a mass readership. Stead introduced the idea in a sensational mode typical of his journalistic practice, and accented its potential with the same obsessions and interests he brought to thought transference: technology, affective reach, empire.

Thank you for your time.


I’ve been redrafting my first chapter on the conditions for emergence of cultural higher space. In so doing I’ve been thinking about the spatial imaginary before Kant. The question of how far back to go has been a troubling, but necessary one, and answered by going back all the way: to Pythagoras, Plato and Aristotle, albeit briefly. I’ve stopped for a pause in the middle ages.

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.

4d bibliophilia

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!

Flat Charles

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.

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.