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.
The Fairyland of Geometry 