Ezra Pound and the Materiality of the Fourth Dimension
I
Towards the end of The Fifth Decad of Cantos (1937), resting between the historical turbulence of Cantos 48 and 50, celebrating the tranquillity of ancient Chinese order and applauding the pleasure and relaxation of pre-industrial labour, Pound’s Canto 49 concludes on a note of particular quietude in its penultimate line: ‘The fourth; the dimension of stillness.’ A few years later, in a letter of June 1942 to Luigi Berti, we find a gloss on this quietude which remains one of only two open acknowledgements by Pound of the fourth dimension:
Stillness – the word is more concrete than IMMOTO [the motionless], for it also suggests silence. What is still is motionless and soundless. But the concept of motionlessness is more important in this line. In Dante, above the primum mobile there is the motionless, the sphere which does not turn. I conceive of a dimension of stillness which compenetrates the Euclidean dimensions. (Quoted in Bacigalupo, 1980, 78)
But such quietude and stillness are not achieved without a struggle – Canto 49 finishes ‘And the power over wild beasts.’ The syntax of this final couplet, compounded by the familiar disturbance of Pound’s fragmentary exposition, renders uneasy any connection between its two halves. It is helpful only up to a point to refer back to Canto 47, which ends with the same line and which, in its evocation of the Eleusinian Mysteries, enables us to read this ‘power’ as that of Dionysus and his ‘gift of healing’. We need, in a sense, a simpler reading, which sets the two halves of the couplet against each other – stillness is achieved against a world of ‘wild beasts’, is maintained against a world that, from various perspectives, is threatening. And this struggle in itself, as I shall suggest later, is a central aspect of fourth-dimensional thought: the oppositional nature of such thought characterises not only its own procedures (where it is most productively seen as a process of being, rather than an accomplished state) but also its role as a tactic within the modernist armoury (see also Tryphonopoulos, 1990).
For Pound to invoke the fourth dimension during the late 1930s and early 1940s is odd, not only for the singularity of its occasion but for its belatedness. While the term was ubiquitous around the turn of the century, it had, by this time, diminished considerably in currency. And while its resonance within non-Euclidean geometry and theosophical speculation became easily and widely translated into the modernist aesthetics of the visual arts, the literary arts seemed rarely to take explicit advantage of its possibilities (although see Clarke, 2001). Where modernist poetry is concerned, its nominative presence remains instructively tacit, and in the Poundian context, its most obvious site, Vorticism, appeared reluctant, as Linda Henderson (1983, xxi–xxii) has argued, to lay any claim to its creative force by name. Nevertheless, I want to suggest that modernist poetics did avail itself of trajectories within fourth-dimensional thought through a telling obliquity (obliquity will emerge as a further major characteristic of fourth-dimensional procedures), and that Vorticism and its allied activities (most notably Imagism) provide our most generative ground. Notions of stillness, silence and process will constitute the framework of the tapestry we need to weave.
In Four-Dimensional Vistas (1916), Claude Bragdon rehearsed a standard principle of such thought in the assumption that the known universe is but a portion of a greater universe and that:
This assumption readily lends itself to the conception of our universe as a three-dimensional meeting place of two portions of a universe of four dimensions – that is, its conception as a ‘higher’ surface. This is a fundamental postulate of higher space speculation. (1916, 50)
In other words, ‘our three-dimensional world is superficial – the surface, that is, of a four-dimensional universe’ (46). In Vorticist art, surface is a matter not only of form but of intimate expression which goes beyond conventional geometry. The defining statement is Gaudier-Brzeska’s in the second issue of Blast in 1915:
I SHALL DERIVE MY EMOTIONS SOLELY FROM THE ARRANGEMENT OF SURFACES, I shall present my emotions by the ARRANGEMENT OF MY SURFACES, THE PLANES AND LINES BY WHICH THEY ARE DEFINED. (1915, 34)
Pound’s ‘Vorticism’ essay in the Fortnightly Review of the previous year emphasises the extent to which the Vorticist surface belongs to advances on Euclidean geometry which move close to the surfaces we find in Bragdon:
Mr. Brzeska and Mr. Epstein are using ‘planes in relation,’ they are dealing with a relation of planes different from the sort of relation of planes dealt with in geometry, hence what is called ‘the need of organic forms in sculpture.’ (1970, 92)
We are not to understand ‘organic forms’ in any representational sense, or as having something to do with humanistic notions of growth and development. Rather, we are to read the phrase in the sense of the artist’s perception of sculptural material through ‘Will and consciousness’, the Nietzschean terms which provide the ending of Gaudier-Brzeska’s first ‘Vortex’ of 1914, the process whereby ‘we have crystalized the sphere into the cube, we have made a combination of all the possible massed shapes – concentrating them to express our abstract thoughts of conscious superiority’ (1914, 158). It is the association of ‘Will and consciousness’ with arrangements extending beyond conventional geometry that marks the trace of fourth-dimensional thinking at this juncture. Tellingly, Bragdon’s claim at this point in his text is prompted by speculations on the work of Charles Howard Hinton (arguably, along with Bragdon himself, the main articulator of the fourth dimension at the turn of the century) – specifically, Hinton’s views on the electric current. This is significant not only in the context of Pound’s widespread use of electromagnetic metaphors in his critical prose of the period (see Bell, 1981), but because it helps to locate one of the more puzzling images in Hugh Selwyn Mauberley, Pound’s history of early modernism: the image which finds Mauberley ‘For three years, diabolous in the scale’ (‘Mauberley’, II, l. 1).
Bragdon recapitulates an argument from Hinton’s The Fourth Dimension (1904) where Hinton conceives of the electric current as a ‘four-dimensional vortex’. Bragdon’s gloss is worth quoting in its entirety to give a more complete picture of his conclusion that ‘our three-dimensional world is superficial – the surface, that is, of a four-dimensional universe’, to note its parallel in a defining moment from Pound’s contemporary prose, and to pick up on the simile of the ‘spindle’ Bragdon uses to give it picture: it is this simile which informs the image in Mauberley. The first half of Bragdon’s gloss views electrical current through vortical action:
First, he examines the characteristics of a vortex in a three-dimensional fluid. Then he conceives of what such a vortex would be in a four-dimensional medium of analogous properties. The whirl would be about a plane, and the contour of this plane would correspond to the ends of the axis line in the former vortex; and as therein, the vortex would extend to the boundary of the medium. Every electric current forms a closed circuit: this is equivalent to the hyper-vortex having its ends in the boundary of the hyper-fluid. The vortex with a surface as its axis, therefore, affords a geometric image of a closed circuit. (1916, 45–46)
In 1912, Pound had already used the analogy of electricity to try to define the ‘energy’ of the ‘masterly use of words’, and in doing so he moved towards the kind of vortical ‘geometric image’ to which Bragdon alludes:
Let us imagine that words are like great hollow cones of steel of different dullness and acuteness[…]. Let us imagine them charged with a force like electricity, or, rather, radiating a force from their apexes – some radiating, some sucking in. We must have a greater variety of activity than with electricity – not merely positive and negative; but let us say +, −, ×,÷ +a, −a, ×a, ÷a, etc. Some of these kinds of force neutralise each other, some augment; but the only way any two cones can be got to act without waste is for them to be so placed that their apexes and a line of surface meet exactly. When this conjunction occurs let us say their force is not added one’s to the other’s, but multiplied the one’s by the other’s; thus three or four words in exact juxtaposition are capable of radiating this energy at a very high potentiality; mind you, the juxtaposition of their vertices must be exact and the angles or ‘signs’ of discharge must augment and not neutralise each other. (1973, 34)
Each relies upon on exact matching of vortices, surfaces and boundaries to suggest the discourse which, again, gestures beyond the immediately calculable.
The importance of ‘juxtaposition’ as orchestrating the entire process will shortly take on a further structural meaning as Pound embarks on his Imagistic precursors to Vorticism, as we shall see; but for the moment I want to continue with the second half of Bragdon’s gloss on Hinton, and draw attention to the strategic simile of the ‘spindle’, which lends proof to an argument for a four-dimensional universe:
Hinton supposes a conductor to be a body which has the property of serving as a terminal abutment to such a hyper-vortex as has been described. The conception that he forms of a closed current, therefore, is of a vortex sheet having its edge along the circuit of the conducting wire. The whole wire would then be like the centres on which a spindle turns in three-dimensional space, and any interruption of the continuity of the wire would produce a tension in place of a continuous revolution. The phenomena of electricity – polarity, induction, and the like – are of the nature of the stress and strain of a medium, but one possessing properties unlike those of ordinary matter. The phenomena lend themselves to explanation in terms of higher space. (1916, 46)
As Pound wants ‘a greater variety of activity than with electricity’ –than with, that is, the objectifiable activities of electricity – so Bragdon, thoroughly in tune with fourth-dimensional thought generally, is concerned with properties which are ‘unlike those of ordinary matter’. His simile of the spindle, however, signifies, for Mauberleyan purposes, more than merely a three-dimensional ghosting of four-dimensional action. Bragdon’s italicised words ‘edge’ and ‘tension’ bespeak the strain not only of action but of explanation, and it is in this sense that the simile enters the condition of being ‘diabolous in the scale’. Initially, Mauberley’s image refers to the ‘augmented fourth’ in music (see Espey, 1955, 76n), an additional note to the three notes which constitute a chord and generally functioning as a transitional moment, a preparation for shifting key. As a point of change, it belongs to the vocabularies of generation and transformation which structure this section of the Mauberley sequence (see Bell, 1978), but Mauberley’s situation of being caught, potentially paralysed, at these very moments is given a more complex register by its invocation of further devilment, the child’s game of ‘diabolo’, defined by the then current New English Dictionary as:
An ancient game, newly revived, played by one or more persons, each of whom holds two sticks connected by a cord, on which is whirled a reel-like top. The point of this is to keep the reel spinning on the cord, to throw it up into the air and catch it again on the cord, or to pass it to and fro over a net […] without allowing the reel to fall to the ground.
The mediary yet cacaphonic nature of the musical augmented fourth thus becomes visualised by the precarious balance of the reel, a balance that is possible only through the tenseness of the cord on which it spins. The diabolo has a function similar to Bragdon’s spindle, and it is worth suggesting also that Pound’s allusion to the augmented fourth may well carry a gesture towards the innovatory practices of his friend, the contemporary composer George Antheil, the self-advertised ‘Bad Boy of Music’ who, as Linda Henderson has shown (1983, 328–30), maintained a strong interest in ideas about the fourth dimension and was attracted particularly to its liberatory potential, its capacity for ‘almost endless forms’ beyond the three-dimensional illusions of customary dualisms (mind/matter, immaterial/material etc.). Here, an imaginative reader might feel encouraged to view ‘diabolous in the scale’ as containing a rather oblique literalism whereby the addition of a fourth note to the three of a chord suggests the move itself from a world of three dimensions to one of four. The suspension experienced by Mauberley during the poem is recognised by him with full consciousness: what is recognised here is the extent to which he is caught at a moment of metamorphosis between calculable and incalculable arenas, at the point where a three-dimensional surface holds the possibility of higher-dimensional space.
Pound’s diabolo and Bragdon’s spindle are not merely figurative devices, chosen as advisedly partial means of explaining higher space: they carry an esoteric reference which promotes entry rather than description. In his recapitulatory volume of 1925, Old Lamps for New, where he moves from the foundations of fourth-dimensional thought to its transcendental goal, Bragdon devotes a chapter to ‘The Ritual of Play’, examining the toys of children’s play as allegories for higher experience. Two of these toys warrant our attention – the spinning top and the humming wheel. By the first, a child learns that ‘just as the top can stand only so long as it is in motion, activity and effort keep the soul fixed and firm amid the illusions and temptations of the world’, and by the second, that ‘if it would hear the song of life it must discover and observe the rhythm of life’ (1925, 177, 120). By this time, Bragdon is willing to dispense with the direct nomenclature of the fourth dimension – the new lamp which reworks and prepares for the recurrence of the old – in favour of a more familiar esoteric discourse (miming, perhaps, the diminution of the fourth dimension as effective intellectual furniture). Nevertheless, his allegories of these toys remind us again of the intimacy between fourth-dimensional thought and theosophy, an intimacy registered in a source that was particularly close to Pound – G. R. S. Mead, who, in his article on ‘Ceremonial Game – Playing and Dancing in Mediaeval Churches’ for The Quest in 1912, chose the whipping top and the humming top as two of the principal items in not only mediaeval but also Eleusinian ceremonies. Colin McDowell stresses the difference between the whipping top and the humming top for Mead:
The former Mead correlates with the cosmic ‘Spindle of Necessity’ and its eight whorls in Plato’s ‘Vision of Er,’ while the latter he compares with the heavenly pole or axis on which the spindle spins. ‘I venture to suggest,’ he concludes, ‘that the whipping-top of the mysteries was feigned to symbolise in its spinning the motion of the erratic spheres or seven planets, and the humming top that of the eighth sphere of the so-called fixed stars. (1983, 29)
The two toys, taken serially, thus graph distinct stages in the process towards higher knowledge and higher space, the process which itself is arguably (and certainly for both Hinton and Bragdon) the main thrust of fourth-dimensional thought. Mauberley’s diabolo locates both his condition of suspension and his glimpsed (but for him impossible, save as a series of fraught reveries), self-consciously agonised anticipation of higher regions.
If Hugh Selwyn Mauberley is about the crisis of art in the Vorticist period, what I have been suggesting so far prepares the ground for a claim that one of the most productive (and hitherto neglected) readings of that crisis emerges from the poem’s echoings of fourth-dimensional thinking. In short, the situation of Mauberley himself – paralysed by the limit and the extent of his knowledge and his aesthetic – is akin to a person who is conscious of a three-dimensional condition and imagining the difficulties in reaching that of the fourth dimension. Bragdon’s ‘higher space’ geometrical figure for such a person is the hyper-cube or tesseract, which he describes in A Primer of Higher Space in 1913 as ‘a four-dimensional figure related to the cube as the cube is related to the square’ – as a three-dimensional solid is related to a two-dimensional plane. The crisis here is that this figure ‘invisible to the eye, is known to the mind’. It is, following Hinton, mathematically but not experientially known – we have ‘no direct or sensory knowledge’ of it, and Bragdon asks ‘With the geometry of such a space mathematicians have long been familiar, but is there such a space – is there any body for this mathematical soul?’ (1939, 12–13). Mauberley’s instruments for exploration (biological and chemical rather than mathematical – see Bell, 1978) are designed to seek such a body.
The principal image for Mauberley’s crisis (see Bell, 1976) occurs in the stanza following his diabolo: ‘He had moved amid her phantasmagoria, / Amid her galaxies’ (ll. 5–6). While ‘galaxies’ recuperates the cosmic gestures of Mead, ‘phantasmagoria’ is given a more local function in Bragdon’s text where he addresses our partial knowledge of space:
What we think of as space is more probably only as much of it as is imaginable. It may be that our space bears a relation to infinite space analogous to that which the images cast by a magic lantern bear to the wall on which these images are made to appear – a wall with solidity, thickness, extension in other and more directions than those embraced within the wavering circle of light which would correspond to our sense of the cosmos. In other words, perhaps that which we think of as space is only so much of it as with our limited sensuous consciousness we are able to grasp. (1939, 14–15)
We might have expected Plato to be cited at this point (he is invoked later, as part of the ‘History of Higher Space Thought’, 26–27) and the omission is instructive. Bragdon uses the ‘images’ cast by the lantern as versions of the ‘shadows’ which serve as a representational shorthand for the relation between dimensions (in Plate 12 of the Primer, which provides a graphic illustration of his argument, he notes that ‘lower-dimensional representations may be conceived of as the shadows cast by higher-space forms on lower-space worlds’), but he wants also to demonstrate the modernity of his position. While he remains faithful (in a thoroughly Poundian manner) to the notion of ‘old lamps for new’, to the recasting of ancient wisdom within a contemporary idiom, he needs at the same time to negotiate the prime difficulty of all idealist thought – the difficulty of acknowledging the necessity of its distance from the material and calculable world while simultaneously arguing for the necessity of its place within that world. So he urges us to think ‘not of abstract space, but of material spaces, differentiated from one another by their dimensionality, and designated in terms of it (as a one-space, a two-space, a three-space, a four-space, and so on)’, and advises ‘Let us think of each space as generated from the next one below it, and as having the dimensionalities of all spaces lower than itself patent, and those higher than itself latent’ (17). This new materiality and its attendant problems succinctly point to a principal aspect of Mauberley’s crisis: he becomes trapped not by passive reverie but by the recognition that his suspended, fraught situation has the patency of its generation (the poem presents a wonderfully economical history of minor artistry from the 1880s onwards) while lacking the latency which can be seen and not grasped. The biological and chemical vocabularies he relies upon as articulative instruments simply fall short of the possibilities offered by the discourses of the fourth dimension and non-Euclidean geometry.
Pound’s efforts to find expression for this new materiality are seen best in the scientific metaphors which inform the critical prose of his London years (see Bell, 1981; Kayman, 1986), efforts which are matched by Bragdon’s explorations of the fourth dimension during the same period. Biology and chemistry in general (and certainly for Mauberley’s temperament) remain too close, perhaps, to the phenomenal world for a negotiation of the higher dimensions – this latter belongs to the language of geometry, specifically non-Euclidean geometry. Pound registered the possibilities in his ‘Vorticism’ essay of 1914, where he explains the ‘intensive’ and ‘dynamic’ qualities of Vorticist art in mathematical terms. Dismissing arithmetic, algebra and Euclidean geometry as failures of form, he offers ‘Descartian’ or ‘analytic’ geometry as the creative idiom. It is here that he comes closest in his prose to acknowledging the aesthetic potential of the fourth dimension, where ‘one is able actually to create’. He exemplifies:
Thus, we learn that the equation (x–a)2 + (y–b)2 = r2 governs the circle. It is the circle. It is not a particular circle, it is any circle and all circles. It is nothing that is not a circle. It is the circle free of space and time limits. It is the universal, existing in perfection, in freedom from space and time […] in analytics we come upon a new way of dealing with form. It is in this way that art handles life. (1970, 90–91)
There is nothing particularly esoteric or eccentric about this claim (and that fact is important for the strategies whereby idealism is reconstructed by the new materiality). The previous year had seen a reprinting of Sir Oliver Lodge’s Pioneers of Science, a popular textbook first published in 1893 which consisted of a series of lectures surveying the major events in the history of science. Lecture VI was titled ‘Descartes and His Theory of Vortices’ and claimed Cartesian geometry not only as a more accurate system than that of Euclidean geometry but also as a means of overcoming the limitations of procedures dependent upon phenomenal models:
Thus geometry can not only be reasoned about in a more mechanical and therefore much easier manner, but it can be extended into regions of which we have and can have no direct conception, because we are deficient in sense organs for accumulating any kind of experience in connexion with such ideas. (Lodge, 1913, 151)
Lodge was not only a leading physicist and great populariser of scientific ideas, but also an active member of the Society for Psychical Research – in other words, thoroughly within that conjunction of science and theosophy which was such a generative ground for early modernism. Nevertheless, it is Bragdon who supplies the most sustained argument for the new materiality approached by Pound’s Vorticist ideas and by Mauberley’s strategically curtailed aesthetic.
At its most fundamental, the new materiality evades the idealist pitfall of eschewing the material world entirely by offering itself as apprehendable and non-apprehendable simultaneously. Herein lies its attractiveness for modernism’s cultivation of fresh space and fresh languages, for an art needing the contemporaneity of scientific and psychical research, and its opening up of the extra-sensory world, while remaining discontented with the transcendental hues of its idealism. Bragdon begins the substantial argument of Projective Ornament in 1915 by advising that the concept of a fourth dimension is understandable to anyone who ‘will not limit his thought of that which is possible by his opinion of that which is practicable. It is not reason, but experience, that balks at the idea of four mutually perpendicular directions’ (1972, 15). The concept is ‘in conformity with reason, however foreign to experience’ and the figures of hyperspace ‘though they are unknown to the senses, are known to the mind in great minuteness of detail’. The fourth dimension may lie beyond the physical, but the physical may indicate towards it – ‘We cannot point to it, we cannot picture it, though every point is the beginning of a pathway out of and into it’ – and, whatever else, its mathematical reality is certain: ‘However little the mathematician may be prepared to grant the physical reality of hyperspace – or, more properly, the hyper-dimensionality of matter – its mathematical reality he would never call in question’ (11–12, 15). Here we find the germ of Pound’s ambitions for the permanence of analytical geometry, a permanence which permits the kind of freedom suggested the following year when Bragdon offered Four-Dimensional Vistas as ‘giving the mind the freedom of new spaces’, where freedom is precisely the release from the illusions of physical experience: ‘the reader must be brought to see the fallacy of attempting to measure the limits of the possible by that faculty known as common sense – and by common sense is meant, not the appeal to abstract reason, but to concrete experience’ (1916, 17).
II
By the time Pound came to teach us how to read ‘In a Station of the Metro’ in his 1914 ‘Vorticism’ essay, he appeared to have forgotten, along with every other subsequent reprinting, that its first two printings, as part of the ‘Contemporania’ sequence in Poetry in April 1913 (on page 6) and in The New Freewoman in August 1914 (on page 87), insisted upon a particular typographical organisation:
The apparition of these faces in the crowd :
Petals on a wet, black bough .
Prior to the poem’s appearance in Poetry, Pound had insisted in a letter to the editor, Harriet Monroe, on the preservation of the ‘spaces between the rhythmic units’ (1951, 53). I shall turn to the implications of this Sypography shortly. Here, we should note that the initial effect of the spacing is to isolate particular words, to interrupt syntactical fluency and to draw attention to its various components. It is that first, key word, ‘apparition’, thus isolated and emphasised, that had currency in fourth-dimensional thought. In Four-Dimensional Vistas, Bragdon attempted to salvage some of the conclusions of Johann Friedrich Zöllner from the taint of their association with the discredited medium Henry Slade. Zöllner had wanted to prove that certain psychic phenomena could be explained ‘on the hypothesis of a four-dimensional space’. The first of these phenomena listed by Bragdon was ‘Apparitions’, which he defined as ‘The intrusion (as an apparition) of a person or thing into a completely enclosed portion of three-dimensional space; or contrariwise, the exit (as an evanishment) out of it’ and which he glossed:
Because we lack the sense of four-dimensional space, we must here have recourse to analogy, and assume three-dimensional space to be the unsensed higher region encompassing a world of two dimensions. To a hypothetical flat-man of a two-space, any portion of his plane surrounded by an unbroken line would constitute an enclosure. Were he confined within it, escape would be impossible by any means known to him. Had he the ability to move in the third dimension, however, he could rise, pass over the enclosing line without disturbing it, and descend on the other side. The moment he forsook the plane he would disappear from two-dimensional space. Such a disappearance would constitute an occult phenomenon in a world of two dimensions.
Correspondingly, an evanishment from any three-dimensional enclosure – such as a room with locked doors and windows – might be effected by means of a movement in the fourth dimension. Because a body would disappear from our perception the moment it forsook our space, such a disappearance would be a mystery; it would constitute an occult phenomenon. The thing would be no more mysterious, however, to a consciousness embracing four dimensions within its ken, than the transfer of an object from the inside to the outside of a plane figure without crossing its linear boundary is mysterious to us. (1916, 53–55)
This transfer would not have been mysterious to the Pound who wrote of ‘Metro’ that he was ‘trying to record the precise instant when a thing outward and objective transforms itself, or darts into a thing inward and subjective’ (1970, 89) and in the ‘Postscript’ to his memoir of Gaudier-Brzeska (in thoroughly four-dimensional mode) that ‘The real sculptor “sees” or is aware of, not only all the sides of his work, but of the “through,” that is the diameters that can be passed through it from any angle’ (1970, 145). To see ‘apparitions’ within the enclosure of a Parisian Metro station is to see through; is to glimpse, briefly, the higher dimension.
What the initial typographical layout displays most immediately is the process of translation between the poem’s first and second series of terms: the ‘apparition’ is reconstructed as ‘petals’ and the ‘crowd’ as the ‘bough’, providing the co-ordinates whereby the axes of the instigatory emotion are to be plotted, or, within the lexicon of the ‘Vorticism’ essay, the planes whose relation constitutes the poem’s mood. Noun matches noun within this frame, but in the very centre of the picture, the ‘faces’, the occasion of the entire experience, are radically dissolved into a pair of misplaced adjectives, ‘wet, black’. The oddity of this dissolution is enhanced by Pound’s well known aversion to the adjectival mode, but, at the thematic level, it prescribes an apt mimesis (the dissolution is distortive and appropriate simultaneously). The poem’s theme is transience: beautiful faces are visible only temporarily in a rushing crowd, just as petals remain on the bough only until its drying, and it is the effect of the original typography to offer a visible register of such transience: the blank spaces anticipate literally the stillness and the silence at the end of Canto 49, but they also point, again literally, to the notion of the image as ‘beyond formulated language’, the image Pound finds in the explorative nature of Chinese and Japanese poetry which ‘understand the beauty of this sort of knowing’ and whose hokku form helped him out of the ‘impasse’ left by the Metro experience (1970, 88–89).
The blank spaces demand that we respond to the poem as a visual event, akin, perhaps, to looking at a Whistler painting, and as involving the process we use in reading Eastern forms. We can approach this process by turning to a later poetic moment, to Archibald MacLeish’s concern with images which make us ‘see’. He too takes his examples from China, from a poetry where the omission of all Western grammatical and syntactical aids to understanding oblige the reader to cultivate further faculties of apprehension, beyond those immediately available. The process involved here is very much the lesson of dramatising, to use Bragdon’s term, our sense of three-dimensional limitations so as to create the possibility of hyper-dimensional vision. MacLeish’s account of this process serves to exemplify such dramatisation in poetic form and to provide a good model for reading Pound’s ‘Metro’. He addresses a line from a poem by Tu Fu which concerns the lengthy civil war during the T’ang dynasty of the eighth century, ‘Blue … Smoke … Beacon Fires … White … Bones … Men’. MacLeish comments:
The grammatical connectives supply, themselves: ‘The blue is the smoke of beacon-fires: the white is bones.’ But something else supplies itself as you look at that blue smoke and those white bones. The blue smoke is now. Smoke is always now. It is only as the smoke blows now that we see it blue or white or grey or black on the air. But these bones of men are not now. They are long ago. They are white. So these two images are seen with time between them. Blue is the smoke of war – of this war – of this war now up here in the northwest where these bail fires, these watch fires, never go out, the acrid word smoke blowing blue on the thin cold air. White are the bones of men – of men killed long ago in this endless war that never ends. Time haunts these images set there side by side: time haunted by war and war haunted by time. And it is the two images that hold that tragedy of time and war between them. (1965, 54–55)
Certainly, here, we remain within a recognisable and measurable world, but the process enacted is thoroughly in tune with the explorations by ‘Will and consciousness’ that held true for both Gaudier-Brzeska’s ‘Vortex’ and fourth-dimensional thought.
Our progress towards the image of transience in ‘Metro’ requires the activity of the blank spaces in order to take it beyond the customary rhetoric of metaphor or simile; the process of fourth-dimensional thought requires that we do need such support, but only as stages in developing further. We are invited to see the poem as an ‘equation’, that of Cartesian geometry, an equation that has ‘something to do with mood’ – Pound goes so far as to suggest that the ‘hokku-like sentence’ that is ‘Metro’ is probably ‘meaningless unless one has drifted into a certain vein of thought’ (1970, 89, 92). The laconic tone here should not be distractive: the poem asks us to engage in a particular form of work in understanding its equation. The key term, ‘apparition’, focusses the predominant emotion of transience through its double reference both to the objects of perception and perception itself, creating thereby a tensile lexical arena where singular meaning is dissolved. This arena is then re-articulated through the recomposition of ‘apparition’ in the second line, where the spacing allows ‘Petals’ to function not simply as a noun but as a neologised verb. Pound’s word play here prepares us for the process whereby, in the visually central term of the ‘equation’, the noun ‘faces’ loses even its generalised specificity within the free-floating adjectives ‘wet, black’, a process that figuratively testifies to the tenuous position of words under the order of emotion to which the poem addresses itself. So the poem locates not only transience but transformation, and its equation refuses any fixity of composition in favour of an unfinished, provisory quality Pound admired in Gaudier-Brzeska and Whistler – models for the artist who, in Whistler’s phrase, would treat an object ‘as his key, not as his model’. Pound quotes this phrase in his memoir of the sculptor and sees the Whistlerian principle of the ‘key’ as the most important contributor to the new aesthetic of Vorticist ‘arrangements’, where he adds the ‘higher mathematician’ to this ‘common sanctuary’ of the arts (1970, 120–21). Hence, the ‘equation’ is to be understood not as a finite picture, an act of summary, but a form of exploration: the blank spaces in ‘Metro’ are literally the pictorial registers of the image understood as ‘beyond formulated language’ – the locations for the rapid moment of transience (Pound’s account insists upon the suddenness of the originating experience (1970, 86–87)) and the unspeakable moment of transformation, the invisible high point plotted by the curve of change.
In Pound the ‘image’ is ‘dynamic’ – a ‘VORTEX, from which, and through which, and into which, ideas are constantly rushing’ (1970, 92, my emphasis), as they would between the dimensions of hyperspace. Bragdon’s A Primer of Higher Space is instructive on such dynamism, on the ways in which the fourth dimension should be seen as a process of energy and alterability beyond the Euclidean system: ‘Think of the fourth dimension, not as a new region of space – a direction […] toward which we can never point – but as a principle of growth, of change, a measure of relations which cannot be expressed in terms of length, breadth and thickness’ (1939, 24–25). Pertinent to the thematics of ‘Metro’, this ‘principle’ and ‘measure’ have a temporal aspect:
If then, as thus appears, the third dimension could manifest itself to a consciousness limited to two dimensions as a sequence of changes in two-dimensional objects which required time for their unfoldment; then, by analogy, a fourth dimension, which implies spatial extension in some new direction at right angles to the three known to us, would manifest itself to our perception equally as a time change.
Such change is, for Bragdon, ‘the universal flux of things – life, growth, organic being, the transition from simplicity to complexity, the shrinkage or expansion of solids’ (25–26). If this account appears to rely over-much on physical properties, then Plate 14, illustrating how ‘The phenomena of life-growth are significantly suggestive of 4th dimensional entrances upon 3-space experience’, counters such discourse by expressing itself in wholly geometrical terms to sustain its argument that ‘The fourth dimension may be manifested to us through certain motions in our space of three dimensions by translating itself for our experience into time’.
These forms of manifestation depend upon penetration, upon moving through and beyond the surfaces and boundaries of dimensions. The most useful way of adapting such penetration for aesthetic purposes – and as an extension of the principle that fourth-dimensional thought is very much a matter of imaginative will and the development of consciousness – is to see it as a function of projection (the thrust, of course, in Bragdon’s sense of ‘projective’ ornament). Here, a recent commentator, Luc Ferry, is helpful. Ferry claims that the principal effect of the fourth dimension and non-Euclidean geometries on artists belonged to the effort to ‘put an end to perspective’ in order to return, in practice, to an art of two dimensions:
The plastic effect of four-dimensional geometry was the reduction of the canvas to bidimensionality, within which alone the fourth dimension could be represented through projection. Perspective, an art of illusion, is in fact of no use in representing hyperbodies, so that a plastic representation of the fourth dimension can only be effected by considering only the purely mathematical properties of figures that are definitely limited to two dimensions. (1993, 217–18)
He goes on to claim that because bidimensionality is ‘the plastic consequence of the fourth dimension’ it thereby ‘becomes the real, that is to say the intelligible’ (225). It is always potentially dangerous to transpose the terms of one art form onto another, but Pound’s apprehension of his Metro experience not in words but in ‘little splotches of colour’ which would constitute a ‘new’ school of ‘non-representative painting’, coupled with his invocations of Whistler and Kandinsky and his insistence on the original spacing of the poem itself, guides us clearly in that direction. When Pound claims that the ‘one-image poem’ is a form of ‘super-position’, where we have ‘one idea set on top of another’, he gives us a literary version of visual bidimensionality (1970, 89). In ‘Metro’ we have two syntactical images, the ‘apparition’ and the ‘Petals’, which produce the third or ‘one-image’ of transience and transformation, the ‘one-image’ that is not in the poem but is the poem. These are, as it were, the poem’s three-dimensional stages, the work towards an apprehension of what may be in the fourth dimension, marked by the generative blank of the spaces themselves – the risk, simultaneously, of nothingness in three-dimensional terms and of its thereby limited putative promise of the hyperspace that is otherwise unintelligible. It is into these spaces that the existing images project or ‘dramatise’ themselves to suggest what may lie beyond their Euclidean boundaries.
Both the Bradgonian ornament and the Poundian image are, then, projective; they are dramatisations of the effort of consciousness to secure non-Euclidean liberations from which to adventure into the dimensions of hyperspace. And if Pound’s Vorticist literariness in ‘Metro’ takes us to the pictorial aspect of this adventure, then the visual shape of projection itself warrants attention. A starting point would be ‘Before Sleep’, one of the poems Pound published in the first issue of Blast. The title suggests that interstitial site which is not available to the conventional language of the states of waking or sleeping that surround it, and the two sections of the poem prescribe two different worlds within the interstitial condition. The first is the ‘drugged’, ‘undulant’ underworld of Annubis (sic), the world of contemporary physicality, ‘pathetic’ and ‘financial’, and its movement is ‘lateral’. The second is the world of ‘Light’, of Athene, where the movement is vigorously and insistently ‘up’, to follow the goddess. These two movements provide the grid of activity, which is displayed as illusory by fourth-dimensional thought. As Linda Henderson has argued, taking her cue from one of its main proponents, P. D. Ouspensky, ‘In the fourth dimension, the self-oriented sense of up–down and left–right fades away, and objects can be viewed from all sides at once’ (1986, 221). Against and out of this grid is the movement of Athene herself:
You were gone up as a rocket,
Bending your passages from right to left and from left to right
In the flat projection of a spiral.
(II, ll. 4–6)
Here, as Bruce Clarke has observed (private correspondence), the poem’s tracing of the spiral trajectory is ‘redolent of a typical Hintonian demonstration of the incursion of higher into lower dimensions’. In short, the movement of the spiral is taken to be the sign of four-dimensional possibilities. It marks also an escape from the caressability Pound associates with the art of the physical world and seen here to belong to lateral movement: the poem begins ‘The lateral vibrations caress me, / They leap and caress me’ and sees the realm of the underworld as one of ‘lateral courses’ inhabited by ‘gods of drugged sleep’, from whom the speaker wishes to be ‘Up and out of their caresses’. Pound, in his 1915 essay on Epstein, regards the caressable as seductive, certainly, but always illusory and ultimately a substitute for something else, and he contrasts it with the creative power of the Vorticist artist, who is not distracted by the caressability of subject matter in pursuit of the ‘arrangement of forms’ (1970, 97–98).
This joining of the lateral with the caressable is a joining of geometry with gender – the ‘Undulant’ movements of the caresses in the first section of the poem are undeniably feminine, and pejoratively so, despite the masculinised energy of Athene, whose movement is powerfully and reiteratively ‘up’ in the second section. While in one sense this privileging of the latter over the former may be seen as a version of Pound’s familiar phallocentrism (most stridently displayed towards the end of his Vorticist years in his introduction to Remy de Gourmont’s The Natural Philosophy of Love), this gendering of geometry also formed a less aggressive part of Bragdon’s preoccupations in The Beautiful Necessity of 1910. Working out from the principle that time and spirit are masculine while space and matter are feminine, vertical lines are housed with the former and horizontal lines with the latter (Bragdon, 1978, 31–32). There is, however, in architecture, the need for a third term: the arch, a curved line which is capable of reconciling the other two and which contributes to the ‘double spiral’ that expresses the masculine and feminine together (35, 44–45). Above all, the reconciliation achieved by the spiral is viewed as actively creative: duality (of masculine and feminine) is ‘not static but dynamic’, with ‘the two parts acting and reacting upon one another to produce a third’ (60). It is in this sense that Athene’s spiral is projected by a masculinised female.
Nevertheless, there is a significant difference between the gendered privileging of ‘Before Sleep’ and the less hierarchical exposition we find in Bragdon. The difference can be identified by comparing ‘Before Sleep’ with the poem Pound chose to conclude his ‘Vortex’, again in the first issue of Blast, as the example of Vorticist poetry: H.D.’s ‘Oread’. It is wholly an ‘image’ in Pound’s Vorticist sense: eschewing the narrative quality of ‘Before Sleep’, it exhibits only what Pound calls here the necessity of the ‘primary’ – of ‘media’, ‘pigment’ and ‘expression’ (1914, 154). While Pound’s poem relies upon the masculinised goddess herself, H.D.’s poem needs a less bold gesture – not to the, again masculinised, figure of Diana the huntress, but to the Oreads, the nymphs who attended her. The movement here is vertical (the sea is instructed to ‘Whirl up’) and the three principal verbs are highly energetic – ‘whirl’, ‘splash’ and ‘hurl’. Equivalent to Pound’s ‘spiral’ is H.D.’s ‘whirl’ (a word that, as we shall see, has an important place in the Vorticist lexicon) as the prime instrument for creativity, and its action seems remarkably close to Bragdon’s deployment of gender in Projective Ornament where he discusses a further form of reconciliation – that of fate and free will. The former is seen in masculine and geometrical terms as a ‘frame’ and the latter in feminine and vegetative terms as an ‘arabesque’:
There is the fixed frame or barrier, and there is the free-growing arabesque where vigour faints against the crystalline rigidity of the frame – the diminishing energy returning upon itself in exquisite curves and spirals, like a wave from the face of a cliff. (1972, 68)
Bragdon finds here ‘an expression of the highest spiritual truth – fate and free-will in perfect reconcilement’ (63), having already determined the cliff as masculine and the waves as feminine in The Beautiful Necessity (1978, 34). H.D.’s ‘whirl’ dramatises such reconciliation as a projective force rather than merely a layering of ideas, which is what happens in ‘Before Sleep’.
Richard Aldington was right, surely, to define the chief quality of H.D.’s poetry as ‘a kind of accurate mystery’ (1915, 23). This phrase is an acute summary of the ambition for modernist theosophy, the newly material, and it registers, again, the difference between Pound’s ‘spiral’ and H.D.’s ‘whirl’. Both belong to a similar programme, but the latter is more successful as dramatic and poetic action. The ‘mystery’ of ‘Oread’ becomes ultimately unmeasurable when we try to translate it beyond its own image, but the closest we can come is to think of it in terms that are elaborated in one of the most immediate sources for Pound’s Vorticist activity – Allen Upward’s The New Word of 1908 (see Pound, 1973, 373–82; Davie, 1975, 62–74; Bush, 1976, 91–102). Upward is interested in energy: the idea of it and the words and shapes for it. He finds it most convenient to conceive of energy as strength, and I want to suggest that the shapes and movements he relies upon for its action are precisely those which constitute the pure image produced by ‘Oread’. They are the shapes and movements to be associated not only with both Vortical apprehension and four-dimensional projection, but with a wider discourse of growth and development during the modernist period – all of which make strategic use of the ‘whirl’ and the ‘spiral’.
Upward is dissatisfied with the idea of strength as ‘two rigid and definite and indestructible strengths’, and anticipates the movement in H.D.’s poem to argue that ‘strength is like a wave with two forces which are neither rigid nor definite nor indestructible, but are forever changing into one another, as the wave’s crest becomes the trough, and the trough, the crest; and Force and Energy are not two Powers, but two names for one Power, working To and Fro’ (1908, 133). It is on this basis that he decides on ‘strength’ as ‘the atom of thought’ and that he figures it as a ‘ball’ which is ‘the most real of all words’. This new reality is recognised as a ‘very old’ idea (discernible not only in Cartesian vortices but also in the ‘spiral form’ of the world’s initial formation), and Upward extrapolates: ‘since living strength does not shrink and swell along straight lines, I caught a glimpse of mysterious spirals leading inwards and outwards’ (181–83). On the basis of this movement, the figure of the ball required some refinement: ‘As fast as it whirls inward it must swirl outward, and the whirl and the swirl must compensate each other. So that the strength-ball ought rightly to be called a Whirl-Swirl’. Here, Upward is not only deploying one of the principal figures for fourth-dimensional consciousness, but in his subsequent dissociation of ‘material’ and ‘ideal’ perceptions he draws upon the developmental process of that consciousness:
Now the materialist is busy measuring the whirl, and as it seems to me his eyes are sometimes so far dazed by watching it as to be no longer able to mark the swirl. Again his speech bewrays (sic) him, when he uses words like whirl and universe, as though he had nothing but a whirlpool before him. One materialist has likened the life of a man to a whirlpool. Whereas what we have before us is more like a water-spout, and the spiral of life points upward instead of downward. Now the business of the Idealist is measuring the swirl.
Here is not only a difference in perception but a difference in an understanding of higher reality, and it has specific consequences for aesthetics: ‘when the Materialist does enter the field of literature, his work is apt to be unbearably informal, and his words unbearably bad; and his highest achievement is History; whereas when the Idealist enters the same field, his work is apt to take on the severe and crystal form of poetry’ (184–85). Pound’s understanding of history as ‘luminous detail’ (1973, 21–25) coexists comfortably with his ambitions for a ‘crystal’ form of poetry, a form which recalls also Bragdon’s ‘crystalline’ frame in ‘reconcilement’ with the ‘arabesque’ as a figure for ‘an expression of the highest spiritual truth’ (1972, 63) – the ‘reconcilement’ which, as I suggested above, informs the procedure of ‘Oread’. And both Pound and Bragdon associated crystal with their vision of an ideal dimension: the Cantos’ four-walled city of Ecbatan is a close neighbour to the ‘crystal heaven’, the ‘one great crystal cube, the Heavenly city’ of Bragdon’s Man the Square (1939, 79) and its claim that ‘Heaven is all about you: a city lying four-square, clear as glass and filled with light’ (76).
Upward argues that his ‘whirl-swirl’ should be considered not as a ‘mere word’ but as a ‘magic crystal’ (1908, 197). The shift involves more than nomenclature. As a ‘word’, the ‘whirl-swirl’ is only ‘like Euclid’s triangle’, it is only ‘Pure Verihood’. But to be more than a word, to earn the title of ‘crystal’, it ‘must take shape’, and the outline of that shape, to become ‘pure Shape’, must be gained ‘in battle’ (188). Upward’s ‘battle’ matches the dramatisation advanced by Bragdon as the means of developing a perception of the higher dimensions; it is what provides the ‘outline’ for the image in ‘Oread’ and the programme for ‘Before Sleep’. Upward’s ‘pure Shape’, whereby the ‘whirl-swirl’ moves beyond the mere word of a Euclidean triangle, is ‘reached by the same road by which the mathematician reaches his flats and lines’ (194–95). So the Athene of Pound’s poem moves ‘In the flat projection of a spiral’, but what is disconcerting is another kind of flatness – the flatness (and this is particularly striking within all the highly forceful performances of Blast) of a work which seems content to offer itself as a statement rather than engaging in a battle: as a poetic act, the energy and difficulty of fourth-dimensional projection seem distinctly muted.
This other flatness seems to become a deliberate tactic in what is Pound’s most avowedly Vorticist poem, from the second issue of Blast, ‘The Game of Chess’, subtitled ‘Dogmatic Statement Concerning the Game of Chess: Theme for a Series of Pictures’. ‘Dogmatic’ is rather a crude self-irony, but it underlines the programmatic ambitions of the poem to offer a thesis on the kind of painting being produced by Lewis, Wadsworth or Etchells. Energy is present, certainly – in the main, through the proliferation of present participles – but it is assertive rather than demonstrative. The poem claims ‘contest’ as its final word, prepared for by the ‘Whirl’ and the ‘vortex’ a couple of lines earlier, and it graphs rather neatly a testament to the fourth-dimensional freedom of the oblique as opposed to the vertical and horizontal line (see Henderson, 1983, 329) in its movement from the ‘“L’s” of colour’ to the ‘“X’s” of queens’ and the ‘“Y” pawns’ – but, again, we are told rather than shown these things. Here, however, and unlike ‘Before Sleep’, the tactic of the subtitle is to release our interest in poetic action and to address the tactics of poetic programme. Charles Altieri has written well of the defensiveness of the poem as evidencing a different sort of ‘contest’, that of the self-consciousness of Pound’s aesthetic intelligence (1989, 292), and ‘The Game of Chess’ is clearly viewed best as a critical essay. Chess provides an apposite metaphor in general for the kinds of abstraction sought after by Vorticist art, but we can be more specific by turning back to fourth-dimensional thought.
Bragdon uses the ‘Knight’s Tour’ in chess to illustrate the potential shapes of ‘Magic Lines in Magic Squares’ (1972, 51–52). He summarises his argument:
The numerical harmony in magic squares finds graphic expression in the magic lines which may be traced in them. These lines, translated into ornament, yield patterns often of amazing richness and variety, beyond the power of the unaided aesthetic sense to compass. Magic lines have relations to spaces higher than a plane – they, too, are Projective Ornament. (47)
The ‘aesthetic sense’ to appreciate these lines requires the aid of fourth-dimensional vision. Magic lines are projective ornament understood in a ‘very strict’ manner: ‘These lines, though figures on a plane, represent an extension at right angles to the plane, and they have relations to the third and higher dimensions’ (55–56). It is because the lines are capable of extension beyond existing dimensions that they constitute a projective capacity, a capacity which marks, dogmatically, the ‘contest’ offered by Pound’s poem, the contest of its ‘Whirl’ and ‘vortex’. The pattern produced from the ‘Knight’s Tour’ is of a ‘knot’ (54), a figure to which Bragdon attaches considerable ‘mystic’ significance. Thinking of the knots which fascinated Dürer and da Vinci, he asks ‘were these knots of theirs not only ornaments, but symbols – password and counter-sign pointing to knowledge not possessed by the generality of men?’ (55). Knots belong to the mathematical history of the vortex (see Bell, 1981, 165–66), and they join with the whirl-swirl and the spiral as the principal figurative expressions, the projective shapes, belonging to both Vorticism and the fourth dimension.
III
Why does the fourth dimension remain nominatively tacit within Vorticist discourses despite maintaining a clear ideational practice? Linda Henderson has commented upon this taciturnity, noting that the fourth dimension ‘had become almost a household word by 1910’ (1983, 43), and its very ubiquity and familiarity may provide a simple answer, in that the suppression of the name registers a tactic to mark the newness of Vorticism, its strident declarations of its own modernity, its aggressive distancing of itself from all the other newnesses that were fighting the modernist battle. While taking advantage of the permissions granted by several fourth-dimensional procedures, Vorticism needed to advertise itself in different ways (and we should not forget that Vorticism was very much a matter of publicity). Pictographically, Blast chose for its logo an image of a cone penetrated by a straight line rather than the spiral celebrated by Hinton and Bragdon, the spiral that was obviously more suited to vortical action. Visually, the cone operates as a flattened version of the spiral, emphasises the two-dimensionality that is not only the inevitable feature of a figure on a plane surface, but is also the plastic effect of fourth-dimensional thought. This was a strategy which enabled the new materiality of such thought to match that of the Vorticist enterprise, allowing us to see the shared projective element of the material spaces in Bragdon’s ornament, Antheil’s ‘solid’ music and Gaudier-Brzeska’s ‘arrangements’ through Pound’s Vorticist vocabulary and its fourth-dimensional assumptions.