Warped Space

How psychological ideas of space have profoundly affected architectural and artistic expression in the twentieth century. Beginning with agoraphobia and claustrophobia in the late nineteenth century, followed by shell shock and panic fear after World War I, phobias and anxiety came to be seen as the mental condition of modern life. They became incorporated into the media and arts, in particular the spatial arts of architecture, urbanism, and film. This "spatial warping" is now being reshaped by digitalization and virtual reality. Anthony Vidler is concerned with two forms of warped space. The first, a psychological space, is the repository of neuroses and phobias. This space is not empty but full of disturbing forms, including those of architecture and the city. The second kind of warping is produced when artists break the boundaries of genre to depict space in new ways. Vidler traces the emergence of a psychological idea of space from Pascal and Freud to the identification of agoraphobia and claustrophobia in the nineteenth century to twentieth-century theories of spatial alienation and estrangement in the writings of Georg Simmel, Siegfried Kracauer, and Walter Benjamin. Focusing on current conditions of displacement and placelessness, he examines ways in which contemporary artists and architects have produced new forms of spatial warping. The discussion ranges from theorists such as Jacques Lacan and Gilles Deleuze to artists such as Vito Acconci, Mike Kelley, Martha Rosler, and Rachel Whiteread. Finally, Vidler looks at the architectural experiments of Frank Gehry, Coop Himmelblau, Daniel Libeskind, Greg Lynn, Morphosis, and Eric Owen Moss in the light of new digital techniques that, while relying on traditional perspective, have radically transformed the composition, production, and experience—perhaps even the subject itself—of architecture.

This primer brilliantly exposes concepts related to special and general relativity for the absolute beginner. It can be used either as an introduction to the subject at a high school level or as a useful compass for undergraduates who want to move the first steps towards Einstein's theories. The book is enhanced throughout with many useful exercises and beautiful illustrations to aid understanding. The topics covered include: Lorentz transformations, length contraction and time dilation, the twin paradox (and other paradoxes), Minkowski spacetime, the Einstein equivalence principle, curvature of space and spacetime, geodesics, parallel transport, Einstein’s equations of general relativity, black holes, wormholes, cosmology, gravitational waves, time machines, and much more.

Epic verse and pulsating paintings merge to shed light on time travel, black holes, gravitational waves and the birth of the universe. Nearly two decades in the making, The Warped Side of Our Universe marks the historic collaboration of Nobel Laureate Kip Thorne and award-winning artist Lia Halloran. It brings to vivid life the wonders and wildness of our universe’s “Warped Side”—objects and phenomena made from warped space and time, from colliding black holes and collapsing wormholes to twisting space vortices and down-cascading time. Through poetic verse and otherworldly paintings, the authors explicate Thorne’s and colleagues’ astrophysical discoveries and speculations, with an epic narrative that asks: How did the universe begin? Can anything travel backward in time? And what weird and marvelous phenomena inhabit the Warped Side? Featuring more than 100 paintings, including a soaring Stephen Hawking, this one-of-a-kind volume, with its multiple gatefolds, takes us on an Odyssean voyage into and through the Warped Side of Our Universe.

A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson–Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson–Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.

Presents the current understanding of the nature of time and space, and an approachable explanation of Einstein's theory of special relativity; then goes on to connect these to possible time travel along with the accompanying paradoxes involved.

The universe has many secrets. It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now. Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.

In Black Holes and warped spacetime you'll discover a world of science fact stranger than science fiction.

Selected and introduced by Richard Dawkins, The Oxford Book of Modern Science Writing is a celebration of the finest writing by scientists for a wider audience - revealing that many of the best scientists have displayed as much imagination and skill with the pen as they have in the laboratory. This is a rich and vibrant collection that captures the poetry and excitement of communicating scientific understanding and scientific effort from 1900 to the present day. Professor Dawkins has included writing from a diverse range of scientists, some of whom need no introduction, and some of whose works have become modern classics, while others may be less familiar - but all convey the passion of great scientists writing about their science.