Squaring the Circle

This chapter highlights the practical and metaphysical issues which James Joyce associates with the application of Euclidean geometry as a geo-meter (a measure of the Earth) in “Ithaca.” It demonstrates how the “mathematical catechism” of “Ithaca” geometrizes the visible world, translating natural phenomena into their ideal Euclidean equivalents. In a topographical context, it illustrates how variably curved surfaces undergo a process of rectification as they are mediated by the catechetical narrative, and how this leads to a confusion between maps and their territories. In light of the narrative’s conceptualization of Molly Bloom as both a human and a heavenly body, this chapter also examines the mythical notions which originate from the mathematical catechism’s conflation of geometric objects and the visible world. By evoking an incongruity between visual objects and their meters, it argues, Joyce explores the possible limits of squaring the circle, both topographically (in terms of projecting a curved natural surface onto a two-dimensional map, as in Mercator’s projection) and figuratively (in the sense that the irregularly curved features of the natural world are rectified as they are represented textually on a rectilinear page).

Introduction

This chapter explores how James Joyce evokes an overarching concern with the linear in his works, both formally (in terms of the Euclidean ideal of rectilinearity) and conceptually (in terms of linear narratives, histories, arguments, modes of thought, etc.). In particular, it considers how the non-linearity of Joyce’s works reflects a wider questioning of the straight line in modernist literature which followed the development of non-Euclidean geometries in the nineteenth and twentieth centuries. This chapter also provides an overview of the geometric babble which entered into the context of Joyce’s writing following the popularization of non-Euclidean geometry in modernist art and literature, as well as the “fashionable nonsense” associated with the application of geometric concepts in contemporary literary criticism. By referring to the source texts which informed Joyce’s articulation of multiple geometric registers, it traces his engagement with non-Euclidean geometry to his early readings of Giordano Bruno’s mathematical and philosophical works, illustrating how notions associated with the curvature of the straight line inform the structural composition of Ulysses and Finnegans Wake.

Conclusion

The concluding chapter explores how James Joyce evokes the origins of geometry and language within the context of the Wakean Letter, which the Hen discovers in the dump. It argues that Joyce undermines the classical understanding of geometry as a transcendental system; rather, he presents geometry as a language which was “created by ourselves,” as Le Corbusier argues, and through the figure of the Wake’s progenitive Hen he illustrates how geometric ideal objectivities have their origin in the sensory world. This chapter also considers how the movement of Joyce’s work towards nonlinearity reaches its epitome in Finnegans Wake, which frustrates the topographical application of ideals which are founded on notions of geometric and conceptual rectitude. Rather than constituting a mere celebration of indeterminacy, it argues, the Wake’s Babelian disintegration of geometric univocity offers more varied contexts in which visible world can be understood. In light of Joyce’s polymedial representations of the human body, it further argues that Joyce’s geometric and topographical representations of Molly Bloom and ALP reflect a movement beyond “those symbols which represent to us perfection and the divine” and a return to the imperfect origins from which these symbols were created.

Textual Topography

This chapter examines how the branching narrative framework of “Wandering Rocks” reflects the structure of the manneristic maze and emulates the nonlinear visual structures which are traced by the characters of Ulysses as they wander through Dublin’s streets. In light of Henri Poincaré’s definition of geometry as “the summary of the laws by which images succeed each other,” it explores how James Joyce presents time presented as the fourth dimension of space in his construction of a textual “picture of Dublin” which follows the movement of wandering bodies. This chapter provides a schema of the narrative network in “Wandering Rocks,” illustrating how Joyce’s textual remapping of Dublin involves the structural emulation of fundamental geometric constructs and related topographical concepts which involve the coincident meeting of lines (as in triangulation, parallax, and the Cartesian coordinate system). In light of the parallactic perspectives which are facilitated by the episode’s branching structure, this chapter demonstrates how the labyrinthine “Wandering Rocks” narrative epitomizes Joyce’s Brunonian perversion of unidirectional rectilinearity on a structural level, disrupting “wider manifestations […] of ‘conceptual and behavioral rectilinearity’” in its nonlinear form.

Charting Wakean Territory

This chapter explores how geometry is presented as a language for describing both visual and nonvisual spaces in Finnegans Wake. It demonstrates how the Wake’s Protean visual landscape is shaped by its polyphonic narrative, and how the Wakean landscape’s boundaries expand and contract in accordance with the movement and breathing of human bodies. With reference to Bruno’s notion that “the infinite straight line […] becomes the infinite circle,” it illustrates how straight lines and rectilinear thought processes veer off course as they are projected onto the uneven bodily, textual, and terrestrial surfaces which record the Wake’s ouroboric narrative. This chapter also investigates how James Joyce incorporates the notion of a “4d universe” in Finnegans Wake, in which time constitutes the fourth dimension of space, and how the “fourdimmansions” of Wakean space-time are framed by the quadrilateral gaze of its four historians as they chart the Wake’s territories using crisscrossing lines of sight. By examining the four old men’s attempts to describe Mr. and Mrs. Porter’s “sleepingchambers” in cycles around the four bedposts in III.4, this chapter considers how the penultimate chapter of Finnegans Wake reflects Joyce’s own concerns with the quadrature of the circle in his writing of the Wake.

“Writings of Paraboles”

This chapter explores how James Joyce interrogates the traditional procedures through which geometric symbols of "perfection and the divine”—including the concept of the infinitely straight line—are first acquired. By referring to Joyce’s early readings of Euclid’s Elements and other geometric texts including the works of Giordano Bruno, it examines how geometry is presented as a traditional system of ideal objectivities in II.2. More specifically, it demonstrates how the schoolchildren’s senseless application of the Wakean classbook’s instructions, and their attempted measurements of the visible world, reflects Bruno’s and Edmund Husserl’s congruent concerns regarding the practice of geometry as a “tradition emptied of sense.” This chapter also sheds light on Joyce’s application of non-Euclidean concepts by referring to his manuscript drafts for II.2, illustrating how non-Euclidean concepts stemming from the works of Bruno and Henri Poincaré are developed within the context of ALP’s curved bodily and terrestrial forms. More generally, this chapter illustrates how Joyce disrupts the univocity of Euclidean symbols by referring to non-Euclidean alternatives, questioning the absolute rectitude (i.e., correctness) of Euclidean geometry. In doing so, it argues, Joyce responds to a history of uncertainty regarding Euclid’s parallel postulate which began over two thousand years ago.