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The Fourth Dimension and Non-Euclidean Geometry in Modern Art

The long-awaited new edition of a groundbreaking work on the impact of alternative concepts of space on modern art. In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception -- the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space -- were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence. That iconoclastic idea encouraged radical innovation by a variety of early twentieth-century artists, ranging from French Cubists, Italian Futurists, and Marcel Duchamp, to Max Weber, Kazimir Malevich, and the artists of De Stijl and Surrealism. In an extensive new Reintroduction, Henderson surveys the impact of interest in higher dimensions of space in art and culture from the 1950s to 2000. Although largely eclipsed by relativity theory beginning in the 1920s, the spatial fourth dimension experienced a resurgence during the later 1950s and 1960s. In a remarkable turn of events, it has returned as an important theme in contemporary culture in the wake of the emergence in the 1980s of both string theory in physics (with its ten- or eleven-dimensional universes) and computer graphics. Henderson demonstrates the importance of this new conception of space for figures ranging from Buckminster Fuller, Robert Smithson, and the Park Place Gallery group in the 1960s to Tony Robbin and digital architect Marcos Novak.
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Linda Dalrymple Henderson is the preeminent scholar of geometry, physics, and the occult in the history of twentieth-century art. Her classic book meticulously presented a new perspective on the spatial imagination at the heart of modern art, and it is here strengthened by a substantial 'reintroduction.' Time has been very good to the book. Given subsequent developments in the computational modeling of complex space, theories of multidimensionality, and, most important, increased interactions among the arts, mathematics, and sciences, it is a classic whose relevance keeps on growing. -- Douglas Kahn, Research Professor, National Institute for Experimental Arts, University of New South Wales, Sydney The first edition of this book was a monumental achievement in the scholarly recuperation of one of modern art's most compelling and influential obsessions, the fourth dimension and non-Euclidean space. Extending her analyses of these strands of scientific thought on art and artists up to the later twentieth century, Linda Dalrymple Henderson not only provides a deeper understanding of this paradigmatic art-science interaction, but also demonstrates that her classic book remains highly pertinent. -- Mark A. Cheetham, Department of Art, University of Toronto

About the Author

Linda Dalrymple Henderson is David Bruton, Jr., Centennial Professor in Art History and Regents Outstanding Teaching Professor at the University of Texas at Austin. She is the author of Duchamp in Context: Science and Technology in the Large Glass and Related Works and Reimagining Space: The Park Place Gallery Group in 1960s New York and coeditor of From Energy to Information: Representation in Science and Technology, Art, and Literature.


Reading this book enriches our knowledge about the interrelation between the different fields of science, culture and art. It is a whole new world waiting to be discovered. * Mathematical Reviews * I think I can say without fear of contradiction that this book is the definitive work on the relationship of non-Euclidean geometry, the fourth dimension, however conceived, and modern art. -- Rob Harle * Leonardo *

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