Archive for January, 2012


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.

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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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