ICR Panel: Dark Mathematics. Reviewed by Catherine Engh and Jacob Henry Leveton
Panel: Dark Mathematics
- Joshua Wilner (City College and The Graduate Center, CUNY), “‘I Cannot Further Explain Myself on This Point’: Maimon’s Obscure Differentials”
- Amy Kahrmann Huseby (University of Wisconsin-Madison), “The Calculus, the Infinitesimal, and the Non-Narratable in Wordsworth’s Prelude”
- Rachel Feder (University of Denver), "Dark Horizons"
- Aaron Ottinger (University of Washington), "Between None and Don Juan"
by Catherine Engh (CUNY-The Graduate Center) and Jacob Henry Leveton (Northwestern U)
What does it mean to challenge oneself—and the others in one’s field—to be simultaneously out of our depth, but to nonetheless attempt to forge a new synthesis of knowledge? This is what the interdisciplinary turn in romantic studies calls for, a turn represented by those who took part in the “Dark Mathematics” panel at the 2016 International Conference in Romanticism, organized by Aaron Ottinger (@AaronOttinger).
Josh Wilner took on Salomon Maimon’s work on the “infinitesimal,” frankly admitting his own interest as well as confusion about Maimon’s attempts to prove that mathematics can succeed in transporting the physical beyond itself. Wilner offered Kant’s “mathematical sublime” as a frame, but noted that whereas Kant conceives of “magnitude” as that which increases exponentially, Maimon considers the obverse—an angle that diminishes exponentially. Maimon’s aim is to provide a “sense datum” or “quality”—a point in space—that can make intuitable the more abstracted geometrical rate at which the angle approaches zero. Comparison between Maimon and Kant is suggestive: whereas Kant strictly divides the spiritual from the natural, Maimon aspires to find a bridge that can connect these realms. Overall, Wilner made a clear case for the relevance of Maimon, a figure who we had never heard of, to the history of the Romantic sublime and was refreshingly candid about his skepticism concerning Maimon’s success.
Amy Huseby (@akhuseby) sought to draw connections between Wordsworth’s The Prelude, the infinitesimal in early calculus, and a politics of “moderation.” Working with The Prelude, Huseby drew attention to the passage in Book One where Wordsworth describes his writer’s block, a time when he was thwarted by “a timorous, from prudence, / From circumspection, infinite delay.” Citing Ann Lise Francois’s concept of “uncounted experience,” Huseby argued that this moment in The Prelude can be read as one where deferral is valued in itself, without a stress on outcomes. She then pointed to the form of The Prelude as a whole, suggesting that its resistance to closure exhibits “Romantic infinitesimals,” or limitless activity without bounds. While Huseby succeeded in doing something interesting with Wordsworth’s retrospective account of his early yearnings to “philosophic song,” her claims about the form of The Prelude are hardly new, and Catherine was left wondering how and why Kant, for whom reason must ultimately be practical, was being used as a touchstone for a politics of “moderation” where reason’s experiments are detached from results.
An additional question we had in response to Huseby’s paper—suggested by her brilliant use of a painting from the French Revolution to illustrate the sense of chaos against which the later Wordsworth reacted with recourse to a poetic mobilization of geometric thought—had to do with the possibilities one vector of interdisciplinarity opens for further engagement in another. Namely, if there are links between romantic-period poetry and geometry, and if there are further links between late eighteenth-century visual art and geometry, then what would it mean to place the “sister arts” of poetry and painting in conversation vis-à-vis mathematics as a link between modes of artistic practice? What new interdisciplinary formalisms might be made possible? What politics of the verbal and visual image might emerge?
Rachel Feder (@RachelFederDU) began by describing her work, which argues for the relevance of romantic era debates about infinity to “key enigmas in Romantic poetry” and to a politics of the anthropocene that emphasizes uncertain futurity. Feder’s critique of the “environmental humanities,” or of the notion that we will be able to globally reform our political and economic systems just in the nick of time to save the earth, was fresh and well taken. This talk felt impressively relevant, offering a spiritual, or poetic, solution to the challenges presented in the geologic “age of humans.” Now is a time when it makes sense, more than ever, to imagine a world of non-human forms that will continue without us. On this theme, Feder offered a virtuoso reading of “The Idiot Boy,” where the mother’s attachment to the boy as a source of her own continuity contrasts with the boy’s ability to imagine a world where he is taken out of the picture. The talk left Catherine applying this way of reading to another Wordsworth poem: in “Boy of Winander,” the entry of the “uncertain heaven” and the “bosom of the steady lake” into the boy’s mind anticipates a world without him. We only wish that Feder had spent a little more time describing where, ethically, this radically non-anthropocentric way of thinking leaves us. Is the solace we can take in the ontological persistence of matter a way of evading our responsibility for ecological depletion? If not, why?
Aaron Ottinger took on Byron’s Don Juan and argued that the mysterious relationship between the narrator and the character in the poem may be well understood in relation to attempts to liberate geometry from the determinate figure, specifically the Euclidean concept of infinity as two parallel lines which never intersect. Citing Byron’s essay on the sublime, Ottinger suggested that Byron himself might have conceived of the narrator postulating Don Juan as akin to a mathematician postulating infinity. Where we see a convergence between the narrator and his object Don Juan, the Euclidean concept of infinity is unsettled, replaced with an altogether more enigmatic infinity, one that cannot be represented as a simple 1:1 relationship. Ottinger reflected that “dark mathematics,” a term coined for the panel, might refer to math beyond the mainstream, beyond professionalized uses to which numbers and algorithms are put. If we can’t represent infinity determinately, we might refuse to assign power to algorithms used in software for financial speculation, for instance. Considered poetically, this indeterminacy might also help us imagine a mode of intersubjectivity that resists psychic mirroring, a mimesis and repetition of the same on to death.
Overall, the panel made the case that Romantic era debates about math may help us to think about some of the central themes and questions that concern us at present in romantic studies: What happens when we imagine agency as that which does not depend on a teleological futurity, on practical results, or on mimetic relations between people and things? What sort of ethics and politics might such a conception of agency make available? Which may it close off? In the Q&A, someone asked: Does it matter whether Wordsworth was good at geometry? The broader issue raised by this question recalls an old and new, and probably irresolvable, debate in the field of literature: What should we prioritize? Questions of aesthetic and intellectual complexity or material and biographical conditions of production and reception? Wilner and Ottinger clearly and helpfully explained historical developments in math, Ottinger making a case for math’s relevance to Byron’s poetics and Wilner for math’s relevance to the history of the romantic sublime. Huseby and Feder focused on formal and philosophical issues, arguing that Wordsworth’s poetry asks us to dwell with, rather than to attempt to overcome, our sense of a world without bounds.
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