Alice sits at a table in Wonderland with three strange characters: the Hatter, March Hare and Dormouse. Time, who has fallen out with the Hatter, is absent, and out of pique won¡¯t move the clocks past six. Without Time, we are told, the characters are stuck at the tea-table, constantly moving round to find clean cups and saucers. Their movement is reminiscent of William Rowan Hamilton¡¯s early attempts to calculate motion.?

Hamilton¡¯s discovery of in 1843 was hailed as a mathematical milestone, allowing rotations to be calculated algebraically. He spent years working on quaternions with three terms ¨C one for each dimension of space ¨C but could only make them rotate on a plane. When he added a fourth term, he got the three-dimensional rotation he was looking for but had trouble conceptualising what this extra term meant. In the preface to?Lectures on Quaternions?(1853), he added a footnote: ¡°It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception of time.¡± Algebra, he believed, allowed the investigation of ¡°pure time¡±, an esoteric concept he derived from Kant that was meant to be a kind of Platonic ideal of time, distinct from the real time we experience. Thus, the Hatter¡¯s tea party becomes Carroll¡¯s joke on contemporary mathematics, which contradicted the basic laws of arithmetic to open up strange new worlds.

Well before structuralist linguistics and surrealist aesthetics, the Victorian revolution in mathematics ushered in a set of epistemological shifts more disconcerting even than Darwinism. Symbolic logic, non-Euclidean geometry, set theory, differential calculus all elevate abstractions and signs from a description of the world to a projection of hypothetical realities and thus, in Kornbluh¡¯s words, ¡°establish mathematics as formalism¡±. In her dazzling book, formalist mathematics crystallises what forms can do, introducing new ways of organising thought and relationships.

Maths enables Kornbluh¡¯s argument about 19th-century fiction more as a guiding style of thought than a topic for analysis (this isn¡¯t a book about how literature adopts mathematical protocols). Instead, The Order of Forms uses formalism to explain how realist novels ¡°model¡± the social. In virtuoso close readings of Wuthering Heights, Bleak House and Jude the Obscure, as well as Alice, Kornbluh insists that realism does more than simply reflect or represent the conditions and contexts of production ¨C art acts upon relations, especially when it projects relations?that don¡¯t exist. In her previous book, Realizing Capital ¨C on the psychological framing of economics in the Victorian novel ¨C she refers to this as ¡°aesthetic thinking¡±. The Order of Forms pursues this thinking to its culmination, finding in aesthetic projection inspiration for new figuring, modelling, building.

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To approach politics and aesthetics thus is to turn away from hitherto dominant methods in literary and cultural studies, such as deconstruction,?that exult in unmaking, fragmentation, the supposed liberation of formlessness. For Kornbluh, ¡°Formalism should study how to compose and to direct ¨C rather than ceaselessly oppose ¨C form, formalization, and forms of sociability¡±.

The Order of Forms is unashamedly a manifesto for theory, so it¡¯s a challenging read. But its potential goes beyond literary criticism. Formalism here is not just an aesthetic method but an epistemology and a political theory. ¡°Embracing form¡±, declares Kornbluh, ¡°serves as the foundation for projects to constitute and institute collective values.¡± Humans cannot exist without forms that scaffold sociability (institutions, law, sovereignty), although the particular forms are not fixed and ¨C her rallying call ¨C can be reformed. Thinking about the co-emergence of aesthetic and mathematical formalisms in the 19th century alongside 21st-century psychoanalysis and Marxism, Kornbluh boldly gives shape to a new set of strategies for thinking politically in the humanities.

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Charlotte Jones teaches English literature at King¡¯s College London.

The Order of Forms: Realism, Formalism, and Social Space
By Anna Kornbluh
University of Chicago Press, 240pp, ?62.00 and ?22.00
ISBN 9780226653204 and 9780226653341
Published 25 November 2019