Counting Form: Gender and the Geometries of Address, in Frances Presley and Carol Watts

Abstract

This essay treats two innovative site-specific sequences produced by women in the first decade of the twenty first century. Both are explicitly interested in the relationship between geometry, writing (as material and political practice) and geo-cultural space, a relationship each finds inflected to some extent by gender emphases. Starting from the premise that any piece of writing is itself a place, the essay considers the self-conscious textualities of its primary texts—one concerned with Exmoor; the other with a sheep-farm in rural mid-Wales—in the light of their different, if similarly rural and relatively remote, contexts. Presley’s ‘Stone Settings’ explores the relationship between some of the quasi-geometrical Neolithic stone arrangements dotted across Exmoor, and the mediation of their apparently Euclidean sometimes barely visible forms in/as text. Watts’ work-in-progress Zeta Landscape mobilises in the ‘analytical’ or ‘projective’ (ie non-Euclidean) geometry of its title the complex weave of routine care-giving and accountancy charging the contemporary (Michel Foucault’s ‘distributive’) pastoral. Both sequences wryly suggest that poetic form can finally no more adequately figure place than the abstractions of mathematical discourse can utter the cultural ecology of any environment, however concrete-seeming. Aided by Jacques Derrida’s powerful essay ‘White Mythology’, the account comes to rest on the equally equivocal recognition of the in/effectuality of metaphor in any kind of address, critical or creative.

“[N]umber is always in the middle of things”

(Connor 2017, pp. 32–33).

However Stephen Connor’s “things” are conceived, his formula echoes Galileo’s ancient contention, ringing down the centuries, that the universe is written in mathematical language.1 Both constructions seem to accept that, like any language system, mathematics is at root communicative, thus dialogic:

Mathematics […] shows that numbers […] are tied together by hidden webs of relationship and entailment

(Connor 2013).

Perhaps partly thanks to the consonances between arithmetic and language which Connor notes, mathematical ideas and terms have long supplied writers with useful figurative resources. Arguably the first literary critic, Aristotle, was of course as much mathematician as philosopher. As William Goldbloom Bloch remarks, “Mathematics can be creative, whimsical and revelatory all at once. More to the point, as embodied in the different meanings of the word ‘analysis’, it is simultaneously a process and an intellectual structure” (Bloch 2008, p. xii). Arguably this doublehandedness explains why, from Hellenism to the European Renaissance; and in the English tradition from Chaucer via the Augustans and Romantics to the luminaries of the nineteenth century, literary writers have found in mathematical discourse, as Arielle Saiber says of Giordino Bruno, not so much inspiration per se as “a warehouse of metaphors and structures that could be called upon to help reinforce the scaffolding of [their] thought” (qtd Rowney 2016, p. 49).

If “numbers … are tied together” anywhere in literary expression, they are perhaps most obviously so in the poem, as George Puttenham famously argues in The Arte of English Poesie, (Puttenham 1589). Poetry might seem never more definitively itself than in the knowingly dialogic entanglement of word, number and counting within the limits of the self-determining space it occupies, paginary or otherwise. The influence of geometry, specifically, on poetic writing might not seem obvious. After all, as Jeffrey Ranta notes, proportionately few poems can be safely or strictly argued to observe the rigid mathematical rules of geometry in any exact way. And yet, as Ranta also points out human understanding of “vision … is thoroughly caught up with geometrical concepts, models and theories …” (Ranta 1978, p. 708).2 The very visual powers of poetic expression are precisely why and how, for Alexander R Galloway, poetry itself “comes to signify … the analogical branches of mathematics (like calculus or topology), what number theorists call the real number system, and hence geometry in the old Greek sense … By contrast, mathematics comes to signify … what number theorists call the rational number system—that is … arithmetic in the classical sense” (emphases added).3

Galloway’s observations confirm how far (to Ranta’s delight), “the visual surface of printed poetry in English, and indeed its non-visual depths of sound and imagery and meaning … open [onto different] kinds and degrees of geometrical shaping” (Ranta 1978, p. 707). As the texts featured in this account confirm, if the paginary poem is understood as itself to constitute a (textual) place, spatially arranged and culturally marked, its signifying life can only be compounded when it concerns or calls attention to location: topos. Not infrequently, the textualized spatialities of the poem—its material context, for example—serve to catalyse or heighten its resonances, aesthetic or otherwise. The following discussion considers how two English language sequences, produced by women working in the first decade of the twenty-first century, use the visual/formal materialities of the poetic sequence to examine the interrelation of counting and evaluation in both the spatially-oriented construct of the poem and the geo-cultural complex of its “address”. Both authors and their works can be situated in the wake of mid-century American ‘open field’ poetics promoted among others by the charismatic figure of Charles Olson, Rector of Black Mountain College and author of the enormously influential essay ‘PRO-Jective Verse’.4

Partly thanks to this shared genealogy, the texts on which I focus both negotiate with the legacy of Modernism in the field of mathematics—specifically Euclidean and non-Euclidean geometry—as well as literature: each takes a keen interest in the ways that what Galloway calls the “real number systems of geometry in the … Greek sense” operate and play out in the historical-cultural terrain and landscape(s) of the rural environment, in and beyond the space(s) of the page (Galloway 2011). Against this backdrop, their shared will to mark the insidious gendering of space and place—the political ramifications of which geographers like Doreen Massey and Gillian Rose have worked so assiduously to expose and unsettle—is hardly coincidental.5 Anchored in its several disciplinary contexts, framed by Harriet Tarlo’s assertion that “Language is a form in which landscape can come alive”, and animated in its later stages by Jacques Derrida’s brilliant probing of metaphor in ‘White Mythology’, this essay shows how Frances Presley and Carol Watts probe their different fields of address—as women, writers and culturally-situated subjects—through the geometrically inflected “field” of the text (Tarlo 2011, p. 10). Presley’s ‘Stone Settings’ takes as its subject the quasi-geometrical Neolithic stone arrangements dotted across Exmoor (Presley 2009). The sequence opens a collection actively interested in the creative effort to realize the “strange geometry” of the features in language on the page (Presley 2008b). Watts’s Zeta Landscape (2005–) meanwhile routes the abstract analytical geometry of its title through the cultural-economic landscape of rural mid-Wales: a terrain shaped in some ways (she demonstrates) more by human activity—that blend of commerce and ancient socio-cultural habits on which animal husbandry will always depend—than nature.6

In these ways, each work finds the place-spaces of its address summoning and to some extent explained by the principles of geometry; a geometry which is for Presley’s Exmoor, Euclidean, and for Watts, in Powys, projective or analytical. And yet at the same time the mathematical tool which each site suggests somehow falls short of the mark; somehow fails the imaginative (metaphorical) demands which the poet seeks to make of it. In this way, both writers and their works replay and confirm the equivocation which animates and inscribes Derrida’s mesmerising dismantling of metaphor and its uses in ‘White Mythology’ (1974).

1. Geometry as (Modernist) Metaphor

“Numbers and signs translate and potentiate each other”

(Connor 2017, p. 45).

Navigating the seismic shifts in mathematics associated with the Victorian fin de siècle and early twentieth century, Jeremy Gray warns against over-determining the consonance of these developments with other kinds of modernism (Gray 2008, p. 14). Nevertheless, recent criticism flags the part played by mathematics in “the cultural vocabulary that modernist innovation drew on for its renewing power” (Goody 2011, p. 14). Baylee Brits confidently identifies

a genuine link between the mathematical and the literary that is developed in the late nineteenth century and across the twentieth century … facilitated by the advent of a modernist mathematics in [Europe]

(Brits 2018, p. h 2).

Some literary modernists took an active interest in contemporaneous developments in mathematical theory and practice. Jocelyn Rodal, examining Virginia Woolf’s works for their mobilising of number theory, points out for example how many of the central figures

in Woolf’s orbit were working on, and writing about, modernist mathematics, including Bertrand Russell, Frank Ramsey, G H Hardy and Alfred North Whitehead … December 1910 … saw not only Roger Fry’s post-impressionist exhibition but also the initial publication of Whitehead and Russell’s monumental Principia Mathematica. 1922 witnessed not only Jacob’s Room, Ulysses, and The Waste Land, but also David Hilbert’s “The New Grounding of Mathematics”

(Rodal 2018, pp. 75–76).

We could fill out the picture by noting that it was during the winter of 1920–1921 that Hilbert delivered the influential lectures he would publish a decade later as Anschauliche Geometrie and which subsequently appeared, in their English translation, as Geometry and the Imagination (1932). For Gray, however, it is the work Hilbert had produced some thirty years earlier which lies at the core of the scholarly disturbances he traces: “If there is a single exemplary work that ushered in modernism, it is perhaps Hilbert’s Grundlagen der Geometrie [Foundations of Geometry (1902)]” (Gray 2008, p. 5).

Like so many other developments in modern mathematics, Hilbert’s contributions were founded on the influence of fellow German Bernard Riemann (1826–1866), the diffident genius whose work on prime numbers proved the existence of non-Euclidean space: that is, space which is curved (‘hyperbolic’, ‘elliptical’ and/or ‘spherical’) rather than flat.7 It is partly for these reasons that a non-specialist might be tempted to conclude that the dramas of mathematical modernism are staged first and foremost in geometry. As far as Matthew Wickman is concerned,

one of modernism’s credos that new conceptions of non-Euclidean space, mathematically conceived during the nineteenth century, transformed cultural consciousness. Max Weber, Henri Lefebvre, Anthony Giddens, and other social theorists, reprising the credos of modernism, say that modernity involves a widespread “ability to critically estrange or reflexively engage the contemporary arrangement of the world”

(Wickman 2016, p. 6).

Certainly, literary critical readers have discerned geometrical principles and theorems supplying what Wickman calls “figures of thought” for a range of modernist authors and texts.8 The locution neatly depicts the way that the material (“figures”) and the conceptual (“thought”) converge and entwine in its geometrical resonance, much as geometry does itself. And as Wickman and others speculate, it seems precisely the figurative meshing of (concrete) form with (abstract) content that attracts literary authors to the language and ideas of geometry. Take Samuel Beckett, observing of James Joyce’s 1929 essay collection Our Exagmination …: “Here, form is content, content is form … His writing is not about something; it is that something itself” (‘Dante … Bruno … Vico … Joyce’ qtd Culik 1993, p. 135; emphases original). For Matthew Rowney, Jorge Luis Borges’s use of figures like the cell and the hexagon affords his writing a self-referentially “geometrical quality, as the words shape and are shaped by the spaces they inhabit” (Rowney 2016, p. 43; emphases added). With an apologetic eye on Connor (above), we might be inclined to rephrase Rowney’s point as “words and spaces translate and potentiate each other”. Or even, more boldly, as “numbers, words, signs and spaces are all (or can all be treated as) metaphors of and for each other”?

Zoltan Kovecses’s Metaphor lists common source and target domains for an exhaustive-seeming account of the part played by conceptual metaphor(s) in everyday language use. Interestingly, ideas of location, situation, even spatiality make no appearance in either list; neither do textuality or writing (Kovecses 2010, pp. 17–20). These omissions seem curious if only because, as his detailed explanations make clear, the discursive practices Kovecses describes depend for particular reasons on the self-evidently metaphorical term/practice of “mapping”. Even if the metaphor is being used for technical reasons by disciplinary specialists (Kovecses explains), as a figurative choice it certainly makes sense, thanks to the planar equivalence between—say—the written text, and terrestrial topography. Not only can any materially realised text be argued to constitute a form of topology, to be identified as place as well as utterance; conversely, as Georges Perec puts it, “the earth is a form of writing” (John [1974] 1999, p. 79). Texts and landscapes are more than coincidentally analogous with each other.

I am not alone in arguing that the poem’s spatio-material arrangement makes the closeness between text and topos more significant to poetry than other kinds of literary expression. Some commentators take for granted the analogies between the poem’s definitive spatialities and the specialised principles and discourses of geometry. Don Paterson, for example, speculates that the centuries-old popularity of the sonnet has to do with its geometric proportions, specifically “the visual appeal of an approximately square field on a sheet of white paper … Which is what a sonnet is, first and foremost: a small square poem. It presents both poet and the reader with a vivid symmetry that is the perfect emblem of the unity of meaning a sonnet seeks to employ” (Paterson 1999, p. xvi; qtd Chiasson and Rogers 2009, p. 49). Phillis Levin implicitly disagrees, in noting that “whatever its outward form, by virtue of its infrastructure the sonnet is assymmetrical. Opposition resides in its form the way load and support contend in a great building” (Levin 2001, p. xxv). Disingenuous as it might be, Paterson’s equation of the sonnet’s satisfying proportions—the visual harmony of its dimensions—with its intellectual intention (the “unity of meaning”) certainly presumes on the equivalence between form and content; as metaphors of each other, each domain offers the other creative validity. This feature is precisely what, for Paterson, makes the sonnet the “perfect emblem” of the ideal dialogue between poetic form and content which it stages (Paterson 1999, p. xvi; qtd Chiasson and Rogers 2009, p. 49).

Chiasson and Rogers help to justify Paterson’s claim. In the first place, the former point out, “the poetic innovators of the early thirteenth century that produced the sonnet, as well as other number-based forms like the sestina, the strambotto, and terza rima forms, were working within a mathematical renaissance of sorts”:

The sonnet was invented in the court of Emperor Frederick II [whose courtiers] included Leonardo ‘Fibonacci’ Pisano himself. Shortly before that time, Euclid’s Elements was translated from Arabic into Latin by Gherado of Cremona … It was this text that contained the first widely circulated formal statement and proof of the Pythagorean Theorem …

(Chiasson and Rogers 2009, p. 54).

Such historical convergences, these researchers suggest, are not coincidental; rather, they precisely explain why the numerical intricacies of the “single stanza” quadrangle of the Petrarchan sonnet—balancing the octave (two quatrains), sestet (two tercets) and pentametrical lineation—can be argued to “embod[y] two geometrical constructs exactly: the Pythagorean Theorem and the Primitive Pythagorean Triple” (Chiasson and Rogers 2009, pp. 50, 53; emphases added). They go on:

We can construct the Pythagorean Theorem out of the three primary numeric components of the sonnet; 8 (the octave), 6 (the sestet) and 10 (the number of syllables in each line): 8² + 6² = 10²; 64 + 36 = 100. In this respect, the sonnet form does not merely represent the Pythagorean Theorem … it also enacts the elegant mathematical form” …

The sestet (6) and the octave (8) are like the two perpendicular legs of the right-angled triangle, representing the distinct poetic split or fork … [T]he iambic pentameter (10), which persists through the entire poem [represents] the hypotenuse of a right-angled triangle; ultimately, the hypotenuse completes the triangle and makes a closed geometrical figure”

(Chiasson and Rogers 2009, p. 53, emphases original, p. 57).

The claim that the Petrarchan sonnet stages a geometrical proof self-evidently presumes on the analogies between the (cursive) text, and the triangle’s geometric shape. For all the satisfactions of the sonnet’s “inherently mathematical” formal character, however “exactly” any sonnet might seem to map onto the formal proportions of Pythagoras’s right-angled triangle, the transfer between the domains of language and form remains dependent on an intervening imagination. For one visually obvious thing, the sonnet’s conventional iambic pentameter ensures that block-like isomorphic appearance which Paterson identifies with its consolatory effects (Paterson 1999, pp. xxvi–xxvii).

There is nothing remotely triangular about the way that a traditional sonnet looks; the characteristics which Chiasson and Rogers tease out so assiduously may follow or model the arithmetical relationships which underpin the geometry of the triangle, but it seems worth reiterating that those same relationships are never realised or play out in any properly triangular form on the page. The exploration of poetic geometry might seem more safely anchored in some equivalence between the planar landscape of the (text-based) poem, and some kind of terrestrial landscape. In the wake of cultural modernism, any poem which deliberately links its own material spatialities with a particular locality, a geo-specific address—any poetic construct which proposes itself as the materialised analogue of a particular place—therefore begs questions not only about when but also why it might do so. Which observation returns us to Presley and Watts, both of whom use the geometrical inflections of both textual and geo-cultural landscapes to recuperate Modernism’s re-inscription of the poem’s numerate traditions.

2. Poetry in the Field: Site-Specificity and Form

“The word field may in fact be etymologically cognate with Greek πλατύς, broad and Latin planus, flat. A field is a closed-off openness; it is a space in which certain variations are drastically limited in order that other variations may be augmented. A field is already a computational machinery, perhaps even the kind of machine of white or maximally-multiplied possibility that a white page (Latin pagus, field) or a blank screen can be”

(Connor 2017, p. 28).

In Jonathan Bate’s influential words, “Every piece of land is itself a text, with its own syntax and signifying potential” (Bate 2000, p. 237). Conversely, and as Connor’s etymological ruminations (above) imply, a case can be made for approaching the textual ‘field’—specifically the page—much as we might any landscape. At the same time however, Denis Cosgrove’s oft-quoted insistence that “landscape is a way of seeing” (Cosgrove [1984] 1998) reminds us to pay some attention to who might be seeing—reading—any text-land/land-text, and how that might affect the emphases and nuances of its ‘scaping’; the gender-freighted emphases and nuances with which scholars like Massey and Rose among others take issue, for example. A relatively recent genre of creative expression, site-specific writing is invariably motivated by an awareness of the extent to which cultural-political contexts are staged in the materio-physical environment, and might therefore mark its representation. In the words of one influential practitioner, Michel De Certeau, “Space is a practiced place … In the same way, an act of reading is the space produced by the practice of a particular place: the written text i.e: a place constituted by a system of signs” (De Certeau 1984, p. 117; emphases original).

Harriet Tarlo groups Presley’s ‘Stone Settings’ and Watts’s Zeta Landscape in the (site-specific) genre she christens “radical landscape poetry” (Watts 2011, p. 7).9 Both sequences take close interest in a relatively remote landscape, distinctively (to retrieve Cosgrove) written on and through by human experience. Both works invest themselves in the reciprocity between the freighted physical, socio-cultural materialities of place and the differently freighted spatio-aesthetic materialities of the poetic construct: both explicitly ask to be addressed as a textual site addressing a textual site. In each case, the topoi which are the focus of the poetic address prove indelibly marked not only by geometry but also for one reason or another (the poets resolutely imply) by gender.

Nick Kaye grounds site-specific writing in the “exchange between [a poem] and the places in which its meanings are defined”. If “the meanings of utterances, actions and events are affected by their ‘local position’, by the situation of which they are a part, then a work of art too will be defined in relation to its place and position [which] might articulate and define itself through the properties, qualities or meanings produced in specific relationships between an ‘object’ or ‘event’ and a position it occupies” (Kaye 2000, p. 1). In Franco Moretti’s words, “What happens depends on where it happens” (Moretti 1998, p. 70). Which is why site-specific texts so often foreground, even find a kind of theatre in, their own compositional processes:

As well as the usual formal considerations of margins, lines, syntax and sound, the poem uses the page as a canvas for a painting, a painting made up of words used as material, and as a site for the verbal construction of the poem. The poem therefore combines the visual impact and effect of the arrangement of the material on the page with the signification of the words and their syntactical relationships. The arrangement of lines, shifting left-hand margin(s) and the use of white space all affect the rhythmic aspects of the language, the pace of reading, and the way attention is given to particular words

(Davidson 2004, p. 100).

The product of Presley’s collaboration with West Country poet-artist Tilla Brading, ‘Stone Settings’ takes its title from the Neolithic stone settings, or “arrangements of upright stones placed in roughly geometric patterns unique[ly found scattered across] Exmoor” (Lines of Sight 10). As Presley recounts, her efforts to explore these ancient monuments, many lying in remote and exposed situations, generated both “the sheer physical pleasure, or discomfort, of exploring the layout of the stones, [and] the sheer frustration of not finding them” (Hardy 2006, p. 3). For all the difficulties, Presley’s late modernist principles require that she remain “suspicious of all artistic evasions, including my own”:10

The push of modern writing has been for the individual to be more open to both the sensual, objective world and to the subjective inner world. So that’s the first thing—a being available to experience. And then, because of that, also, trying to make sure that the shaping, artistic process does not distort that experience

(Skelt 1991, pp. 129–30).

Presley replies to Exmoor’s challenges with the hybridism she honed in Somerset letters (Presley 2002), a blend of on-site improvisation (which “allows the site to ‘dictate’ the formation of the language, a deliberate permission of non-sense”) and “discontinuous prose” poetry, written off-site and “incorporat[ing] narratives of community and history” (Hardy 2006, p. 2). The most resonant of those narratives borrows the words of Hazel Eardley Wilmot, the amateur archaeologist on whose research knowledge of Exmoor’s mysterious antiquities is—even today—founded. Along with these practices, Presley found her subject matter demanding “New ways of treating the visual layout of the page and its relationship to forms in nature and human invention” (Hardy 2006, p. 2). The title poem of ‘Stone Settings’ begins:

per	pl	ex
				moor
	two					three			or		four
	paral					lel			rows
	rec					tangles
	double					square
	squat					shape

(‘Stone settings’, Lines of Sight 13)

This striking text dismembers itself across the open ‘canvas’ of the page, visually replaying the deliberate-seeming geometrical shapes etched on their surroundings by the actual stones. The same carefully-disposed materialities also mark the uninscribed spaces separating and sometimes fracturing the words themselves, playing out the interest Presley has long taken “in ‘gaps’ in the landscape, in our lives and in our language and the influence they have on our writing” (Presley 2008a). For Presley, the actual and metaphoric absences which Exmoor’s settings host and signpost only sharpen their allure:

the curiosity of these strange configurations is part of the pleasure of being puzzled … the framework which opens out a whole series of associated concerns, which form the layers of debris and complication, both on site and in the archaeological texts.

(Hardy 2006, p. 2)

The same destabilising ironies haunt the gappy symmetries of ‘White ladder’, the poem which addresses its eponymous subject, “the double row of small standing stones, originally a quarter of a mile long” discovered inadvertently in 1975 (Presley 2009, p. 16).11 At first only 71 stones could be seen, although in all its orderly spacing the setting—mostly of quartz—was plainly intended to be visible: the remaining stones were subsequently found “either submerged though still upright, or fallen and overgrown” (Eardley-Wilmot 1983, p. 24).12 And yet, however verifiable the details of the site’s dimensions and features, complicated by its antiquity, any signifying life it might once have codified remains a matter of speculation. Hence the symbolic vacancies and elisions which haunt the site, not least its name, as Eardley-Wilmot confides:

Known in [ancient] times as a landmark, named in the final perambulation record and shown on the 1819 Inclosure Map when the Crown land was sold, White Ladder was then forgotten except as a name. (Hunting people still sometimes speak of ‘Whiteladders Combe’ at the foot of the hill)

(Eardley-Wilmot 1983, p. 24).

Intervening on the dialogues and cross-currents (between material and imaginary; contemporary and ancient; signified—written/voiced—and implied or thought; space and time) which the site hosts, Presley honours the debt we owe to Eardley-Wilmot for our knowledge of White Ladder’s very existence. Every word of her own 23-line treatment of a site that, she records amusedly, she was herself “wholly unable to find”, has been drawn from the text of Ancient Exmoor. The resulting poem appears here in full (Hardy 2006, p. 3):

entirely							chance
cold							spring
short							grass
double							row
quartz							stones
sandstone							slabs
one					‘		stride
two
between
ladder							like
slow							search
not							wall
not							bank
not							boundary
shining							stone
ploughed							out
road							metalling
one				by			one
deceptively							swallowed
boggy							source
				Kinsford
				Cunet			(io)
Girl		=		Kunti	=		Spring13

In ‘White ladder’, the self-conscious textualities which tilt ‘Stone settings’ towards unpredictability by contrast help to stiffen the spine-like space holding the textual ladder’s two columns apart; the poem’s centre is constituted of and by absence. These starkly geometrical formalities both reduce and simultaneously point up the “polyphony” which the settings, mute as they are, might voice (‘notes and’). In interview, Presley points out “the multiplicity of voices that exist in any landscape, in any discourse, and our responsibility to listen to those voices as well as the recognition of our own very limited lines of sight” (Hardy 2006, p. 3). Such multiplicity helps, as she explains elsewhere, to undo the symbolically burdened and delimited field of vision associated with the “individual lyric ‘eye’ [in favour of] the plurality and the commonality of experience [of seeing]” (Presley 2008a).

To the same end, the sequence unapologetically and repeatedly appropriates Eardley-Wilmot’s own writing. Its use of the late archaeologist’s words implicitly constructs her as a post hoc—indeed posthumous—collaborator/co-producer of the sequence. In borrowing her words, Presley not only respectfully defers to the scholarly expertise which enabled Eardley-Wilmot’s re-writing of Exmoor. More subtly and suggestively, this decisively gendered gesture of inclusion also subverts not only the historic gendering of archaeological and geographical discourses but also the conventional hierarchies of Presley’s own address to the same inscrutable landscape: “in setting aside the illusions of closure, completion, stasis, perfection—the ideals of a patriarchal society—[collaboration permits] the possibility of the open text, the so-called ‘fragment’, … activated in the process of reading/making/collaborating” (Presley and James 2001, p. 16).

In conjunction with these perhaps inexplicit self-problematising habits, ‘Stone settings’ never falls entirely prey to the (quasi-)geometries of Exmoor’s pre-historical settings. As Moretti dryly notes: “A geometrical pattern is too orderly a shape to be the product of chance. It is a sign that something is at work here” (Moretti 1998, p. 56). For all the impossibility of decoding its original purposes, Presley’s decision to bring the site of White Ladder and its immediate locale to the domain of the poetic page, to shape the setting in the fabric of the printed text, seems motivated in part by mischievous anticipation of the failure of the enterprise. After all, Barry Stocker remarks, “Geometry as ideal object must be contaminated by the empirical event of its expression, which must be explained by words at some point; however self-evident its truths, the symbolism cannot be ostensive in such an absolute way as to exclude language” (Stocker 2000, p. 129).14

Presley’s own treatment of White Ladder suggests some scepticism about how far the lines which the stones etch on their environs might be claimed to testify to pre-historic geometrical knowledge. As she confides to Edmund Hardy, the “most geometric page layouts” of her own poems, constructed out of their own context of frustration, interruption and (in the case of the ladder, of course) failure in some senses have no choice but to “express both perfection and an underlying irony about perfect form” (Hardy 2006, p. 2). Certainly, whether or not Exmoor’s stone settings can be understood as the product of ancient geometry, an impossible prefiguring of Euclidean exactness, the sequence contrives that they rescue from their long-occluded history something much more richly provisional and ambiguous.

In the final analysis, Presley’s knowingly imperfect re-presentation of her antique subjects seemingly affirms that, whatever their originary motivation, now (as then) the settings depend for their existence chiefly on being read; poem-like, in that unavoidable process and practice they fall mute subject to whatever interpretative code (geometric, geological, archaeological, geo-historical) is produced in or by their reading or reader. In this fundamental recognition, the sequence does more than rehearse the “incompleteness, approximation and the limitations of language … congruent with broad cultural anxieties about explanatory systems” which Culik discovers in the mathematical inflections of Samuel Beckett’s modernist aesthetics (Culik 1993, p. 147). Arguably, in fact, the verbal geometries in and out of which Presley conjures some of the most suggestive poetic text/topoi of her ‘Stone Settings’ seem intended less to summon the places “where words cannot go” than to figure a terrain where (unlike numbers) words have hardly, if ever, been at all (Culik 1993, p. 137). Such an aspiration, successful or not, seems indebted partly to the (literally) inscrutable geometry in which the occluded White Ladder silently accounts for itself, and partly of course to the woman whose self-deprecating voice brought its features to light.

3. Field as Fold: Enumerating the Pastoral Landscape

“Place fluctuates, gives way to other spatial topologies: site, field, milieu, terrain. Grid, fold, mesh”

(Watts 2012, p. 282).

Like ‘Stone Settings’, Watts’s open-ended Zeta Landscape reaches out of the topological and material entanglement of human and natural towards the organising abstractions of geometry.15 Like Presley, Watts discovers in geometrical forms and theorems instruments with and in which to conjure and address a remote location she finds suggestively rich in gender-implications. However, where the familiar classical forms confronting Presley point the former to Euclid, in an ongoing project to explore “the boundaries of [her own] loco-descriptive writing”, Watts turns instead to the ‘projective’ or ‘analytical’ geometry which emerged in the nineteenth century, thanks to Bernard Riemann among others (Watts 2012, p. 294).

In place of Presley’s arguably uninhabitable sites, Watts studies the environs of Rhosybreidden, a small hill-farm situated in rural Powys, and a place she has visited often enough to know well. To this familiar and familial setting, trailing centuries of inhabitation and contoured by the cultural-economic “shapes that things and events make in time and space”, as its title signals, Watts’s Zeta Landscape summons the eponymous mathematics of non-Euclidean geometry, a constellation of propositions and theories addressing the puzzle of the prime numbers which find focus in the so-called ‘zeta’ function (Ranta 1978, p. 715).

For Marcus Du Sautoy, the prime numbers are “the very atoms of mathematics”: “the jewels studded throughout the vast expanse of the infinite universe of numbers … the mathematician’s own periodic table”. Paradoxically, however, for all their instrumental value, as Du Sautoy goes on to warn, “prime numbers remain the most mysterious objects studied by mathematicians. In a subject dedicated to finding patterns and order, the primes offer the ultimate challenge. Look through a list of prime numbers and you’ll find it’s almost impossible to predict when the next prime will appear … The list of primes is the heartbeat of mathematics, but it is a pulse wired by a powerful caffeine cocktail” (Du Sautoy 2004, p. 5). Quite apart from their habit of emerging in unexpected places (they turn out to govern the relationship between pitch and frequency in the production of harmonic sound, for example), the apparently infinite resistance of the primes to predictable sequencing lies at the root of their magnetism for mathematicians; unless and until a satisfactory mathematical proof is discovered for Riemann’s legendary ‘Hypothesis’, of course. Put simply, Riemann’s work feeds the mathematics of the infinitesimal, also known as ‘calculus’, which underpins non-Euclidean (that is, projective or analytical) geometry. Broadly speaking, the Prime Number Theorem and Riemann’s Hypothesis work in concert to refine aspects of the calculus which mathematicians use to try to explain the behaviour, distribution and frequency of the prime numbers: the so-called ‘zeta’ [ζ] function.

John Derbyshire explains the significance of the zeta function, at root, as helping to bridge the epistemological space “between counting and measuring” in a theoretical domain which reaches to infinity in any and every direction (Derbyshire 2003, p. 310). Combining exactness (which we could call “enumeration”) with approximation (or “evaluation”), the zeta function constitutes an algorithmic multi-tool which can be used to calculate (thus pinpoint the position or frequency of) primes of exponentially increasing size. At the same time, however, the function can never escape the horizon of infinity which renders its calculations—many of them unimaginably complex—hypothetical; at some point, the empirical precision of enumeration is always forced to give way to the more imprecise but still usable results produced by approximation.

Watts’s sequence is less interested in the Hypothesis per se than the sinuous three-dimensional landform-like features produced when the co-ordinates which the function yields are plotted or mapped on the horizontal x-y or (‘east-west’) and vertical (‘north-south’) axes of a graph; that is, when the function is spatialized. [See supplementary file for a three-dimensional and dynamic representation of the function when the mathematical calculations are graphed in this way.] (originated from https://sketchfab.com/3d-models/riemann-zeta-function-b6ed0fac6170446f941d6f02e64ac067). The two series of poems comprising Watts’s Zeta Landscape—each of its nineteen-line lyrics identified with a different prime number—crisscross the farm “whose name carries the eighteenth-century trace of its enclosure, once a ‘hill-common’”16

The farm is off the beaten track, part of a complex history of land ownership in the region shaped by everyday Welsh and English exchange. … The poems walk this particular place with its contours, the three fields … rising up from the banks of the river, picking up on the rhythms and sounds of the birthing and accounting of sheep, the daily ordering of work

(Watts 2012, p. 283).

For Watts, an attachment both emotional and commercial binds the farm’s human and animal inhabitants together in the equivocal traditions and practices of husbandry, “a form of conducting—and at the same time provision of subsistence, care, a daily watching over” (Watts 2012, p. 285). Conjuring and conjured from the steep pastures which shelter and sustain the farm’s income source, the poems are saturated in the enumerative/evaluative habits directing and directed by “the seasonal and daily flow of animals. I went out at night … counting eyes in the torchlight. Looking out for crows, foxes. At times I went out in the moonless dark and could only hear them close by, the deep rumination the ewes make, moving on at the sound of some intruder” (Watts 2009, p. 26):

• 1
• the feeding of one into the landscape results
• in a climbing to infinity    this opens the labour of a day
• the task is   to find a distribution   of fields
• and from these the truth of this place:     hill common
• in its own pitch   said   rhos y breidden
• and from this one point   sines of all hills and valleys
• as if pastoral could predict them   by counterintuitive
• measure in the dark meadow   its starless   spectrum
• at night   where the ram is sleeping   its breath
• barely rising   the mound is a shadow   the reservoir
• pumped down the hill   leading to a thought
• of depth   or scarcity   and thinness (…)

Discontinuous, disjointed, the lyrics seem straightforwardly to present themselves, much like the figurative (but apparently solid) terrain produced by graphing the zeta function, as “land that might be walked, north to south, east and west, with peaks and valleys”. The white spaces which are scattered through and punctuate each line fracture the words into cryptic paratactic clusters, brief phrase-like fragments which sometimes seem connected, sometimes not. Each momentary break is also a rupture, a pause offering the chance to replay and reflect on whatever precedes and follows. In one discussion of the sequence, Watts explains, illuminatingly, that for her site-specific poetry is definitively concerned with “the practice and nature of its taking place”. The ambulatory self-inspecting way in which each line of Zeta Landscape unfolds itself seems to replay this stringently “sustained and exploratory mode of attention to”, which practices itself and in turn echoes the business and function of any farm, a form of labour whose productivity is predicated on care-giving:

The word “pastoral” comes from shepherd, or pastor, and combines the notion of “to lead to pasture, graze” with “to tend, keep, pasture, feed, guard”. So pastoral names a kind of movement—direction, understood as a form of conducting—and at the same time, provision of subsistence, care, a daily watching-over and enumeration

(Watts 2012, p. 285).

In this powerfully three-dimensional environment, compassion and care displace topos. The poem draws (folds) the topos of the farm—delineated by the intersecting vectors of the routine practices which sustain and safeguard its future—into the textual-sonic space it occupies. In these ways, Zeta Landscape intently folds and re-folds its defining and cognate terms (“field”, “fold” and “manifold”) into the “distributive” contemporary pastoral which, as Watts reminds us, Michel Foucault himself dubs “the matter of the sheep-fold” (Watts 2012, p. 281). The fields themselves are addressed more as backdrop or afterthought than front-and-centre subject, in a belated or deferred (to quote the poet again) “folding back on what has occurred, a form of afterwardsness” (2012, p. 281). As the topographical enclosure (or ‘fold’) of the farm is unfolded, it reveals in Rhosybreidden a dynamic and compound construct closely resembling a Foucauldian “milieu”: a “space in which a series of uncertain elements unfold” (Foucault 2009; qtd Watts 2012, p. 287). It seems partly thanks to Foucault, then, that the terms in which Watts’s ‘loco-descriptive’ poem addresses the farm in its Powys setting are neither straightforwardly material nor straightforwardly temporal: “To think the fold of Rhosybreidden in terms of a pastoral imaginary is to think not simply of a spatial set of relations sliding one of another, but a complexity of relational foldings in space-time” (Watts 2012, p. 302). Those terms of address are also, at least partly as a consequence, relentlessly dialogic:

The matter of pastoral mov[es] between the two types of multiplicity or “manifold”, one discrete and enumerated, the other in continual affective modification: intensities of care … The first a vision of a flock, contained; the second, on the move, continuously flowing across the bounds of enclosures …

(Watts 2012, p. 300).

The sequence presses the precarious economics of the farm through the mesh of these lexical figures, their metaphoric resonances overlapping in a complex weave of rural husbandry, calculus and literary convention

describing the world of the farm as well as a spatialized zeta world, a means of conceptual “slurring”, as if the tropes of the poems, and the sheep themselves in their generation, are “sieves” for the discovery of the primes [which in turn] become sieves for something irreducibly … given in nature

(Watts 2012, p. 299).

To appropriate a trope of classical mathematics, the sequence “sieves out” the many dialectics which inscribe and animate sheep farming, among them the familiar archetype at its heart. The poet’s immersive night-time experiences in the lambing field and on the darkened mountainside teach her to re-see the apparently humdrum work of sheep-counting as less stupefying or comforting so much as provisional and equivocal: “Flocks are aggregates, subject to wandering and itinerancy, gathering and rounding up” (p. 299). The sequence uncovers other equally powerful dialectics—certainty and uncertainty, care and calculus—likewise interlocking in “the deeper accountancies” which quite literally resound in this ancient-modern site and its ancient-modern routines:17

The counting of animals on the other hand gave way to encounter with the nature and movement of a flock. The waywardness of particular ewes. The mysterious timing of oestrus. The sound of rumination in the dark. The limit of the anthropomorphic. Irreducible biology”

(Watts 2012, p. 286).

Mathematicians have known since Pythagoras that “the very physics of music has at its root the basics of mathematics”, captured in the relationship between ‘pitch’ (how high or low a note sounds) and ‘frequency’ (how loud or soft it sounds), the numerical prime-led patterns of which are called “the harmonic series” (Du Sautoy 2004, p. 78). To Watts’s cultural-politically tuned ear, the gendered geographies of the farm’s poem-like landscape, and the fragile economic “milieu” it sustains, resonate as suggestively as they can be numbered or read, and especially in the seasonal female-centred dramas of lambing time, the moment in the year when perhaps above all the habits of care-giving and accountancy intersect in the focus on maternal biology and instincts. These twin seasonal exigencies converge and are troped in one sheep in particular: “Number 37, the twelfth prime … named for her auction lot number, who lived until her thirteenth year; a ‘lucky’ prime, she moves in singular ways through the sequence of the first two seasons” (Watts 2012, p. 299). The first appearance of this unlikely seeming heroine (in the third lyric of the text’s first series) is framed by sound production, expression which is both spatial and—being without concrete three-dimensional form—not, which, as such, simultaneously invites and implacably resists interpretation:

the further east the louder the note   waking early

to orchestras  of demand  not quite synchronous

as a swarm is    knowing the constancy of waiting

has its consequences   the muscle of congregating

number 37  sings  what is a well  (…)

(‘3′, Zeta Landscape Tarlo 2011, p. 113)

Explicitly intermingling the “hallucinatory and material” in this way (that is, doing no more than any more conventional lyric), the ambulatory, self-attentive mode of Zeta Landscape constructs in each new stanza a fresh “site for superimposition”, readied for the “series of translative acts” that the mode demands of itself as well as its readers (Watts 2012, p. 285). In its blockish sonnet-like stanzas, shot through by the gender emphases etched everywhere, Zeta Landscape might seem to reprise and refresh for its twenty-first century moment something of “the experimental energy” which issued in the seventeenth-century European sonnet (Chiasson and Rogers 2009, p. 55). In the eponymous ‘37’, the final poem of Season Two (the second of the series comprising the sequence), the ewe conjures both the shade of Robert Recorde, the mathematician from Pembrokeshire who invented the equals sign, and his The Whetstone of Witte (1557)18 in which it is used, alongside plus and minus signs, for the first time:

37   bred from a whetstone  wit  equals

as long as  each  recording is mistaken

stone for thing   (…)

Folding such a figure into the elements which it counts, or takes into account, Zeta Landscape returns us again to the layers of dialogue which resonate—across a variety of dimensions—in a landscape which both is and is not entirely abstract; is and is not entirely material. Individually and sequentially, the texts tirelessly “interrogat[e] physical space … where it connects most directly with mathematics”, iteratively confirming Connor’s view that if “number is the direction in which nature moves … that movement is not all in the same direction. It is not a steadily rolling river, but tidal, vortical, polyvectorial” (Connor 2017, p. 44). At the same time, in the central trope of its title if nothing else, Zeta Landscape affirms in mathematics itself—like language and unlike nature—a signifying system; insists that its representational function is dialogic in nature, function and effect. To make sense of the relationships between the abstract elements (conjecture, proposition, theorem or proof) which their symbols notate, mathematicians depend as much on hermeneutic engagement, on interlocution (virtual, imaginary and/or abstract), as any form of expression, linguistic or otherwise. The very assumption of equivalence which the equals sign inscribes is, of course, dialogic.

Watts links the “combination of chance and dependency” which she discovers in Rhosybreidden to the cultural-economic ecology of pastoral, the socio-economic as well as literary traditions anchoring both farm and sequence which are marked by “often violent accumulation and removal, and yet intimations of a translative surplus, gift” (Watts 2012, pp. 295, 297, 300). It is in this way that the dialogues which anchor and animate Watts’s Zeta Landscape do more than simply recall or equate with the ambivalent and discreetly gendered geometries of Presley’s site-specific poetic addresses. Coincidentally or not, those dialogues also recollect the argument of ‘White Mythology’, Derrida’s powerful theoretical deconstruction of metaphor as a bi-directional figure of thought, as illustrated by the synonym he finds, with characteristic dexterity, in the French usure. As the translator’s note explains, this term “means both usury, the acquisition of too much interest, and using up, deterioration through usage” (Derrida [1972] 1984, p. 209 fn2). Like the double-faced coin which Derrida’s agile re-metaphorizing of metaphor rescues in the essay’s exergue, the activity of metaphor is ghosted by the “double import of usure: erasure by rubbing, exhaustion… [and] the exchange which far from losing the original investment would fructify its initial wealth, would increase its return in the form of revenue … the two histories of the word remaining indistinguishable” (Derrida [1972] 1984, p. 210). The result of this construction is the recognition that as a figure of explication or illumination, metaphor must be understood to adopt or mimic the equivocal stance of the supplement. Simultaneously enacting both generation and loss, the movement of metaphor is consequently always and only interrogative; it marks neither equivalence nor difference, neither commensurability nor incommensurability but rather the ineradicable condition of difference. Pertinently, indeed, we might argue that in the bewitching deconstructive manoeuvres laid out in the essay, Derrida calls the dialogic operation of the equals sign into question.

Kevin Mills has argued that, “In the drawing of boundaries that can never belong to the place itself, every place is made up of other places; it is the product of difference and articulation; not an identity, but a mobile economy of discursive relations” (Mills 2017). If the written page can be acknowledged as a place, Mills’ assertion holds as true of text as of any site, domain or location. The site-specific poem utters the complexities of the topos in which it has been produced by re-framing it as the spatio-aesthetic textual construct: in this reciprocal process, text and landscape adopt and become mutual and (in Derridean terms) mutually insufficient referents of and for each other. It might therefore seem inevitable that the “incommensurable and uncertain relations” sought out in Watts’s Zeta Landscape echo Presley’s textual unpicking of the dialogues between topographical and arithmetical in and on Exmoor (Watts 2012, p. 297). In their different ways both women mobilise a recognisably Modernist literary sensibility to argue that the metaphorical consonance between number and terrain can be gestured at, if never exactly represented, in the textual landscape—the material formalities—of the poem.

It seems worth returning, at this juncture, to Tarlo’s description of poetic form as “a landscape in which language can come alive” (Tarlo 2011, p. 10). My own reading of Presley and Watts causes me to wonder whether those defining terms might not be more usefully swapped over; whether, and not unlike the different kinds of geometry which both poets mobilise, poetic form is not in fact better conceived as “a language in which landscape can come alive”. Certainly it does not seem unreasonable to conclude from my examples that it is perhaps above all through the unobtrusive geometries framing their very different fields of address that these absorbing texts perhaps most suggestively express their shared and knowing in/capacity to represent an equivalence which is not, quite.