The Fourth Dimension and Non-Euclidean Geometry in Modern Art, revised edition


Book Description

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.




From Space in Modern Art to a Spatial Art History


Book Description

This book traces artists’ theories of constructive space in the first half of the twentieth century. Drawing on these concepts and recent theories on space, it develops a methodology termed ‘Spatial Art History’ that conceives of artworks as physical spatio-temporal things, which produce the social, to overcome the reductive understanding of art as a mere mirror or facilitator of society.







The Emergence of the Fourth Dimension


Book Description

The Emergence of the Fourth Dimension describes the development and proliferation of the idea of higher dimensional space in the late nineteenth- and early twentieth-centuries. An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and influenced a number of important Modernist writers and artists. Providing a context for thinking of space in dimensional terms, the volume describes an active interplay between self-fashioning disciplines and a key moment in the popularisation of science. It offers new research into spiritualism and the Theosophical Society and studies a series of curious hybrid texts. Examining works by Joseph Conrad, Ford Madox Ford, H.G. Wells, Henry James, H. P. Lovecraft, and others, the volume explores how new theories of the possibilities of time and space influenced fiction writers of the period, and how literature shaped, and was in turn shaped by, the reconfiguration of imaginative space occasioned by the n-dimensional turn. A timely study of the interplay between philosophy, literature, culture, and mathematics, it offers a rich resource for readers interested in nineteenth century literature, Modernist studies, science fiction, and gothic scholarship.




Shadows of Reality


Book Description

In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.




Imagine Math 8


Book Description

This eighth volume of Imagine Math is different from all the previous ones. The reason is very clear: in the last two years, the world changed, and we still do not know what the world of tomorrow will look like. Difficult to make predictions. This volume has a subtitle Dreaming Venice. Venice, the dream city of dreams, that miraculous image of a city on water that resisted for hundreds of years, has become in the last two years truly unreachable. Many things tie this book to the previous ones. Once again, this volume also starts like Imagine Math 7, with a homage to the Italian artist Mimmo Paladino who created exclusively for the Imagine Math 8 volume a new series of ten original and unique works of art dedicated to Piero della Francesca. Many artists, art historians, designers and musicians are involved in the new book, including Linda D. Henderson and Marco Pierini, Claudio Ambrosini and Davide Amodio. Space also for comics and mathematics in a Disney key. Many applications, from Origami to mathematical models for world hunger. Particular attention to classical and modern architecture, with Tullia Iori. As usual, the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture.




The Spiritual Dynamic in Modern Art


Book Description

This book demonstrates that numerous prominent artists in every period of the modern era were expressing spiritual interests when they created celebrated works of art. This magisterial overview insightfully reveals the centrality of an often denied and misunderstood element in the cultural history of modern art.




The Mathematics of Harmony


Book Description

Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."




A Course in Modern Geometries


Book Description

Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".




Hyperspace


Book Description

Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe.