The Topological Imagination

Spheres, Edges, and Islands

ISBN 9780674504561

Publication date: 04/04/2016

Boldly original and boundary defining, The Topological Imagination clears a space for an intellectual encounter with the shape of human imagining. Joining two commonly opposed domains, literature and mathematics, Angus Fletcher maps the imagination’s ever-ramifying contours and dimensions, and along the way compels us to re-envision our human existence on the most unusual sphere ever imagined, Earth.

Words and numbers are the twin powers that create value in our world. Poetry and other forms of creative literature stretch our ability to evaluate through the use of metaphors. In this sense, the literary imagination aligns with topology, the branch of mathematics that studies shape and space. Topology grasps the quality of geometries rather than their quantifiable measurements. It envisions how shapes can be bent, twisted, or stretched without losing contact with their original forms—one of the discoveries of the eighteenth-century mathematician Leonhard Euler, whose Polyhedron Theorem demonstrated how shapes preserve “permanence in change,” like an aging though familiar face.

The mysterious dimensionality of our existence, Fletcher says, is connected to our inhabiting a world that also inhabits us. Theories of cyclical history reflect circulatory biological patterns; the day-night cycle shapes our adaptive, emergent patterns of thought; the topology of islands shapes the evolution of evolutionary theory. Connecting literature, philosophy, mathematics, and science, The Topological Imagination is an urgent and transformative work, and a profound invitation to thought.

Praise

In Angus Fletcher’s fascinating, deliciously abstract, but literally down-to-earth meditations on the topological imagination, we are given a subtle new synthesis, new insights into our site and situation, and, at least in this reader, an incitement to poeticize. Like his master figure, the sphere, Fletcher wraps up what was never really apart.

—Dorion Sagan, author of Cosmic Apprentice
Angus Fletcher’s new book brings the mathematical richness of topological connectivity to bear on our understanding of the literate power of imagination and its potential for metaphor. Synthesizing insights from the arts and sciences, Fletcher offers a visionary proposal for navigating our contemporary condition. With brilliance and brio, The Topological Imagination charts the flow of our life along the edges of our biosphere.

—O. Bradley Bassler, author of The Pace of Modernity
Angus Fletcher’s new book The Topological Imagination is a visionary work of literary criticism. In the tradition of Kant’s thought on the ‘schematizing’ function of the imagination, Coleridge’s ‘esemplastic’ powers of imagining, and Wittgenstein’s and Einstein’s meditations on ‘picturing,’ Fletcher explores the many ways shapes, surfaces, and edges are the playground of consciousness. Asking ‘how spectral is any apparently single thing? What if a single object is actually an odd combination of smaller objects? What happens when shapes are actually compound?,’ he demonstrates a fundamental affinity between the history of mathematics, geography, and cosmology and works of poetry and speculative thought. Along the way he illuminates, with his usual brilliance, writings by Ovid, Shakespeare, Donne, Browne, Vico, Clare, Emerson, Rachel Carson, Walker Evans, and many others. In a blinkered and divisive era, Fletcher has written a self-help book for our planet.

—Susan Stewart, author of The Poet’s Freedom