The Palgrave Handbook of Literature and Mathematics

Robert Tubbs, Alice Jenkins, Nina Engelhardt, Robert Tubbs, Alice Jenkins, Nina Engelhardt

• Publisher: Palgrave Macmillan
• Year: 2020
• Print ISBN: 9783030554774
• eBook ISBN: 9783030554781
• Topic: Literature
• Subtopic: Literary Criticism Theory
• Index: Literature

This handbook features essays written by both literary scholars and mathematicians that examine multiple facets of the connections between literature and mathematics. These connections range from mathematics and poetic meter to mathematics and modernism to mathematics as literature. Some chapters focus on a single author, such as mathematics and Ezra Pound, Gertrude Stein, or Charles Dickens, while others consider a mathematical topic common to two or more authors, such as squaring the circle, chaos theory, Newton's calculus, or stochastic processes. With appeal for scholars and students in literature, mathematics, cultural history, and history of mathematics, this important volume aims to introduce the range, fertility, and complexity of the connections between mathematics, literature, and literary theory.

Chapter 1 is available open access under a Creative Commons Attribution 4.0 International License via[link.springer.com|http://link.springer.com/].

© The Author(s) 2021

R. Tubbs et al. (eds.)The Palgrave Handbook of Literature and Mathematicshttps://doi.org/10.1007/978-3-030-55478-1_1

Begin Abstract

1. Introduction: Relationships and Connections Between Literature and Mathematics

Nina Engelhardt¹ and Robert Tubbs²

(1)

Department of English Literatures and Cultures, University of Stuttgart, Stuttgart, Germany

(2)

University of Colorado Boulder, Boulder, CO, USA

End Abstract

“A good preface must be at once the square root and the square of its book” (Schlegel [1797] 2003, p. 239). This statement by the German poet Friedrich Schlegel (1772–1829) is an example of a literary writer drawing on mathematics to communicate the ideal aim of a written text—calling up associations of mathematics with truth, clarity, and rigidity as well as implying the impossible: the “quadrature of the circle” of simultaneously getting to the root or core of a book as well as going far beyond its range by “multiplying it with itself.” Mathematically, Schlegel’s condition has the number 1 as its nonzero solution: the root of 1 is 1, and the square of 1 is 1. Figuratively, Schlegel’s “good preface” would thus be the book itself. We will follow this “mathematically deduced” conclusion and let the collection of essays speak for itself but also aim to use this introduction—knowing full well that we will inevitably fail to square this circle—to both address the fundamentals of relations between literature and mathematics and to give a broader context for the chapters to follow.

Literature and mathematics might seem to constitute entirely different domains of knowledge, practice, and meaning. Literature is often associated with subjective, individual experience, emotional depth, and the vagaries of human life, and as produced and read in particular historical, cultural, and social contexts. In contrast, mathematics is commonly seen as a system of eternal truths that are established by objective, rigorous methods employed in a steady accumulation of knowledge. Where literature is at least theoretically accessible to all literate readers and might develop its greatest power and appeal when giving rise to various interpretations, mathematics is celebrated for its certainty and precision and sometimes revered as the realm of geniuses. The chapters in this Handbook vividly demonstrate that these stereotypes and associations are at best half of the story. Neither literature nor mathematics lends itself to easy characterization, both fields experience remarkable changes, crises, and unresolved questions, and the relation between them is not one of clear-cut contrast but includes manifold connections, intricate parallels, and creative borrowings. This Handbook addresses interrelations of literature and mathematics in five categories, which work to organize and group together the chapters to follow. Like any categorization, the five groups can only delineate rough tendencies, cannot hope to cover all aspects in a broad field, and do not do justice to many of the chapters as these are wide-ranging and could be included in several or even all of the parts “Mathematics in Literature,” “Mathematics and Literary Form,” “Mathematics, Modernism, and Literature,” “Relations between Literature and Mathematics,” and “Mathematics as Literature.”

Mathematics in Literature

The first part presents chapters that examine literary texts’ employment of mathematics on the levels of plot and language, as topic, theme, and metaphor. This can include characters who practice mathematics as a profession, direct discussions of mathematical problems, and also the use of mathematical vocabulary and symbols. While some texts employ numbers to stand for the threat of inhuman rationalization, others introduce them in positive contexts as allowing for order or draw on the metaphorical potential of irrational numbers or imaginary numbers to suggest the “mathematically proven” existence of realms beyond reason and physical reality. Similarly, simple counting and quantification can have positive as well as negative implications: the successive reduction of King Lear’s knights in Shakespeare’s play suggests the unstoppable development of a mathematical series and the power that comes with commanding numbers (see Chapter 22 by Travis Williams). The protagonist in Samuel Beckett’s Molloy experiences the sense of order and control that counting and quantification can provide when he collects sixteen stones and attempts to rotate them between his four pockets in such a way as to take them out in a specific order. At the same time, the calculation of his rate of farting as being one fart every 3.62 minutes suggests the absurdity of quantifying life (see Chapter 18 by Chris Ackerley). The lures and dangers of quantifying and calculating probabilities have a presence in literature at least since the Middle Ages (see Chapter 2 by David Baker) and show their sometimes sterile, inhuman aspects in financial speculation and profit-making projects such as those of the character Merecraft in Ben Jonson’s The Devil Is an Ass (see Chapter 3 by Joe Jarrett).

The incorporation of mathematical symbols in literary texts showcases, in an immediately visible way, the differences between these systems of notation. Charles Bernstein’s poem “Erosion Control Area 2” is creatively typeset and includes symbols from mathematics throughout:

Clothe ≤ ma

oμ β wolμ iε

WhicΦ t∩ ou ≥

(Bernstein 1996, p. 17).¹

The focus here is on the visual impression of these mathematical symbols rather than their sound or meaning, and their strangeness draws attention to the materiality of the text and the fact that words in alphabetical letters similarly do not give immediate access to meaning but are printed symbols on paper. The Russian avant-garde writer Velimir Khlebnikov (1885–1922) employs the symbol for an imaginary number, √−1, in his short prose piece “We Climbed Aboard” (1916): “We climbed aboard our √−1 and took our places at the control panel” (Khlebnikov 1989, p. 82). The mathematical symbol stands out from ordinary printed letters and visually expresses the imaginary position above everyday reality that allows the speaker and the poem to leave reality behind and observe how “centuries of warfare passed before me” (p. 82) (see Chapter 7 by Anke Niederbudde). While √−1 is a well-known mathematical symbol and it easily lends itself to associations with imaginary and fictional domains, Thomas Pynchon’s novel Gravity’s Rainbow (1972) displays a partial differential equation that readers cannot be expected to understand but that visually communicates that complex mathematics is involved in the development of the V-2 rocket during the Second World War (see Chapter 9 by Stuart Taylor).

The term “imaginary number,” which was introduced by René Descartes in La Géométrie, an appendix to Discourse on Method (1637), implies that this mathematical entity has no correspondence in reality while other numbers have a direct relation to the physical world. The idea of mathematics as the language of the book of nature (Galileo 1960, pp. 183–84) came under increasing pressure during the nineteenth century when mathematical concepts seemed to leave reality behind, for example, by formulating a four-dimensional space that goes beyond the three dimensions that can be physically experienced. Mathematically, the fourth, fifth, or sixth dimension does not differ from the first three, but literary texts, as well as occult and spiritual movements, interpreted further dimensions in mathematics as proof of a realm beyond material existence. In Joseph Conrad and Ford Madox Ford’s The Inheritors (1901) the fourth dimension harbors a superhuman race, and in The Time Machine (1895) by H. G. Wells, it is understood as time and can be manipulated to travel into the future and the past. While the mathematics of higher dimensions was taken to point to realms beyond physical existence, other developments showed long-established methods of calculation to lead to inadequate descriptions of the world: while Euclidean geometry works well to calculate triangles and spheres, “[c]louds are not spheres and mountains are not cones,” as Benoît Mandelbrot (1924–2010) put it ([1977] 1982, p. 1). Mandelbrot’s fractal geometry, which he developed in The Fractal Geometry of Nature (1977), can be used to describe more complex natural systems. As Chapter 8 by Alex Kasman demonstrates, fractal geometry and chaos theory appear in literary fiction, often, but not always, metaphorically or to take advantage of nonmathematical properties of these areas.

While Mandelbrot proposed a geometry better suited to describe the physical world than the geometry formulated by Euclid in the third century bce, the absolute truth of Euclidean geometry had already come under attack in the nineteenth century when Nikolai Lobachevsky (1792–1856) and János Bolyai (1802–1860) described an alternative geometry which does not rest on the so-called Parallel Postulate. Euclidean geometry was mainstay in mathematics education, particularly in the nineteenth century, and literary texts refer to it across the centuries (see Chapter 5 by Alice Jenkins). In the early fourteenth century, Dante appealed to the classical problem of squaring a circle with only using “Euclidean tools,” a straightedge and a compass, and its presumed impossibility, as a metaphor for humans’ inability to understand the Incarnation in Christianity, and this problem reappears in later literary texts (see Chapter 10 by Robert Tubbs). In the Romantic period, Euclid’s Elements inform William Wordsworth’s “Arab Dream,” (see Chapter 4 by Dan Brown), as well as Samuel Taylor Coleridge’s poem “A Mathematical Problem” (1840), which begins:

On a given finite Line

Which must no way incline;

To describe an equi--

--lateral Tri--

--A, N, G, L, E.

(Coleridge 1840, p. 24)

The poem goes on with the proof of Proposition 1 of Book I of the Elements, which describes how to construct an equilateral triangle on a given line segment, and, considering that many men encountered Euclid as a profound presence in their mathematics education, alludes to a commonly experienced type of mathematical problem in the nineteenth century. While Euclidean geometry thus works as a “language” that connects many Victorians, access to mathematical education for girls and c...

Table of contents

• Cover
• Front Matter
• 1. Introduction: Relationships and Connections Between Literature and Mathematics
• Part I. Mathematics in Literature
• Part II. Mathematics and Literary Forms
• Part III. Mathematics, Modernism, and Literature
• Part IV. Relations Between Literature and Mathematics
• Part V. Mathematics as Literature
• Back Matter