Mathematical Monsters and the Continuum

Elizabeth de Freitas

conference: DARE 2015: the dark precursor
date: ongoing
venue: Orpheus Institute, Auditorium
format: in absence
practice: philosophy
keywords: Georg Cantor, Imre Lakatos, mathematics

abstract about the author(s)

abstract

As Erin Manning (2015, 48) says of artfulness, there is always “a rigorous process that consists in pushing technique to its limit, revealing its technicity.” This technicity becomes more than a confining habit when it is attuned to the force of its own potential, when it evolves into a technicity that unleashes “a becoming that could not have been mapped in advance” (ibid., 60). Technicity is thus at the heart of becoming monstrous, rather than in opposition to it. This presentation uses Deleuze’s work on problematics to discuss performance art that explores mathematical technicity and mathematical monsters. Examples of monsters are everywhere in mathematics, as though the discipline itself were a breeding ground for them. Lakatos (1976) argued that mathematics is the process of creating opportunities for monsters to be born, and then redesigning the rules in order to banish them. Deleuze (1994) opposes two kinds of mathematics—problematics and axiomatics—to describe this process of birthing and bearing monsters. For problematics, mathematics is propelled by an inventive automatism and by the event-nature of concepts, while for axiomatics (or theorematics), mathematics entails the derivation of a set of theorems from a set of axioms. The latter serves state-sanctioned major mathematics, “whereas problems concern only events and affections” (Deleuze 1994, 160).

This presentation focuses on the mathematical continuum, an enduring source for mathematical invention and paradox over many centuries. The mathematical continuum refers to both the geometric number line and the real number system that occupies it. Concerns that Euclid’s axioms could not, in principle, construct the continuity of the number line lead to various attempts to do so in the nineteenth century. Dedekind (1831–1916), intent on banishing all geometric “intuition” from mathematics, used sets and “cuts” to compose the infinite granularity needed for the continuum. Cantor (1845–1918) would offer a similar approach, proposing necessary and sufficient conditions for continuity that relied on set theoretic constraints. These attempts to erase the materiality of the number line reveal an awkward haunting. How can a line be composed of points? The mathematical continuum seems to vibrate with traumatic desire, a desire to be both discrete and continuous, counted and uncountable, separate but connected.

Deleuze and Guattari (1987) tap into the mathematical concept of the infinitesimal as the calculating engine of their ontology—a means of differentiating the continuum and tapping singularities, the generative and immanent dark precursors of the bendable line. In this presentation, I discuss artists who explore the mathematical continuum as an attractor both for problematics and for axiomatics, a site of artful technicity and spiritual automatism. I discuss the work of performance artist Idris Onez who performs the affective material dimensions of mathematics, the traumatic investment in cutting up the continuum, showing how mathematics taps an animal desire, a desire that sustains the vibrancy and potentiality of the continuum. In a five-minute video, Onez performs the monstrous desire of mathematics, a desire to reassemble the discrete with the continuous, the finite with the infinite, the point with the line. I argue that this work links to Deleuze’s notion of a “spiritual automatism” in following a will to art that breaks with a phenomenology of the human body as the administrator of all its participation. The mathematical continuum serves a non-human will to art, “aspiring to deploy itself through involuntary movements,” but always risking new methods that may destroy that same will (Deleuze 1989, 266). In pushing technique to its limit, the scratching and cutting of the mathematical continuum is an artful automatism that recalls surrealist automatic writing in which the hand becomes a conduit for non-human forces. But rather than see automatism as a conduit or form of communication between the human and the nonhuman, this is an automatism that plugs into pure immanence, an iterative but creative automatism that escapes the logic of resemblance, correspondence, exchange, and remainder.

References

Deleuze, Gilles. 1994. Difference and Repetition. Translated by Paul Patton. New York: Columbia University Press.

—. 1989. Cinema 2: The Time Image. Translated by Hugh Tomlinson and Robert Galeta. London: Athlone Press.

Deleuze, Gilles, and Félix Guattari. 1987. A Thousand Plateaus: Capitalism and Schizophrenia. Translated by Brian Massumi. Minneapolis: University of Minnesota Press.

Lakatos, Imre. 1976. Proofs and Refutations: The Logic of Mathematical Discovery. Edited by John Worrall and Elie Zahar. Cambridge: Cambridge University Press.

Manning, Erin. 2015. “Artfulness.” In The Nonhuman Turn, edited by Richard A. Grusin, 45-80, Minneapolis: University of Minnesota Press.

about the author(s)

Elizabeth de Freitas

Elizabeth de Freitas’s research focuses on the philosophical and cultural studies of education, with particular emphasis on research methodologies and mathematics education. She is an associate editor of the journal Educational Studies in Mathematics. She is the author of the novel Keel Kissing Bottom (Random House), co-editor of the book Opening the Research Text: Critical Insights and In(ter)ventions into Mathematics Education (Springer), and co-author of the book Mathematics and the Body: Material Entanglements in the Classroom (Cambridge University Press).

info & contact

affiliation

Manchester Metropolitan University, UK