The Shape Of Inner Space

The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist

In this long-out-of-print counterculture classic, Dr. John C. Lilly takes readers behind the scenes into the inner life of a scientist exploring inner space, or “far-out spaces,” as Lilly called them. The book explains how he derived his theory of the operations of the human mind and brain from his personal experiences and experiments in solitude, isolation, and confinement; LSD; and other methods of mystical experience. It also includes glimpses into Lilly's friendship with such 1960s' notables as Oscar Ichazo, Ram Dass, Timothy Leary, Albert Hofmann, Fritz Perls, and Claudio Narajo. Written for the non-specialist, Center of the Cyclone shows an important, modern thinker at his most personal and profound.

Collection of reports from men and women who have taken mystical journeys in an altered state of consciousness.

The study of human body measurements on a comparative basis is known as anthropometrics. Its applicability to the design process is seen in the physical fit, or interface, between the human body and the various components of interior space. Human Dimension and Interior Space is the first major anthropometrically based reference book of design standards for use by all those involved with the physical planning and detailing of interiors, including interior designers, architects, furniture designers, builders, industrial designers, and students of design. The use of anthropometric data, although no substitute for good design or sound professional judgment should be viewed as one of the many tools required in the design process. This comprehensive overview of anthropometrics consists of three parts. The first part deals with the theory and application of anthropometrics and includes a special section dealing with physically disabled and elderly people. It provides the designer with the fundamentals of anthropometrics and a basic understanding of how interior design standards are established. The second part contains easy-to-read, illustrated anthropometric tables, which provide the most current data available on human body size, organized by age and percentile groupings. Also included is data relative to the range of joint motion and body sizes of children. The third part contains hundreds of dimensioned drawings, illustrating in plan and section the proper anthropometrically based relationship between user and space. The types of spaces range from residential and commercial to recreational and institutional, and all dimensions include metric conversions. In the Epilogue, the authors challenge the interior design profession, the building industry, and the furniture manufacturer to seriously explore the problem of adjustability in design. They expose the fallacy of designing to accommodate the so-called average man, who, in fact, does not exist. Using government data, including studies prepared by Dr. Howard Stoudt, Dr. Albert Damon, and Dr. Ross McFarland, formerly of the Harvard School of Public Health, and Jean Roberts of the U.S. Public Health Service, Panero and Zelnik have devised a system of interior design reference standards, easily understood through a series of charts and situation drawings. With Human Dimension and Interior Space, these standards are now accessible to all designers of interior environments.

A complete guide to creating planetary yantras to access their healing and centering benefits • Provides easy-to-follow instructions to create the yantras • Serves as an introduction to active meditation, which focuses the mind while the body is engaged in a meditative activity The tantric art of drawing or painting the nine designs known as yantras is an ancient practice of active meditation that releases positive healing and centering effects. Each of the nine designs corresponds to one of the nine qualities of body and mind essential to well-being: radiance, nourishment, passion, intellect, expansion, bliss, organization, uniqueness, and spirituality. From the basic elements of the square, the circle, and the triangle, dynamic visual meditations unfold as the practitioner works clockwise from the outer elements inward toward the central point of stillness, or bindu, the source of happiness within. An accompanying mantra is recited while preparing each yantra to fully engage the senses in the meditative process. Creating the design that “speaks” most to the practitioner enables its unique healing quality to be transmitted. For example, working on the yantra named “Radiance” cultivates optimism and the self-confidence to succeed in one’s endeavors, while “radiating,” or imparting, one’s inner light to others. This workbook provides an important resource for active meditation, a practice revered for its effectiveness in revealing the spiritual underpinnings of everyday life. The active participation of the body in meditation while creating the nine planetary yantras raises to the level of spiritual ritual the practitioner’s intention toward wakefulness and gives access to profound states of healing integration.