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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Inner Space/Outer Space brings together much of the exciting work contributing to a new synthesis of modern physics. Particle physicists, concerned with the "inner space" of the atom, are making discoveries that their colleagues in astrophysics, studying outer space, can use to develop and test hypotheses about the events that occurred in the microseconds after the Big Bang and that shaped the universe as we know it today. The papers collected here, from scores of scientists, constitute the proceedings of the first major international conference on research at the interface of particle physics and astrophysics, held in May 1984. The editors have written introductions to each major section that draw out the central themes and elaborate on the primary implications of the papers that follow.
Kjell Espmarks The Inner Space (Den Inre Rymden, 2014) is the culmination of an oeuvre ranging over more than a half century. His previous book of poetry, Vintergata (2007), in English called Lend Me Your Voice, was a success. One of the leading Swedish newspapers, Svenska Dagbladet, called it the best Swedish poetry in the new millenium and it was promptly translated into ten languages, including Chinese and Arabic. This new book The Inner Space is to appear in Sweden in the autumn of 2014, but is simultaneously published in Italian, Spanish, and Arabic. A Chinese version is on its way. Vintergata - literally Milky Way - is a constellation of a hundred small mono-logues in which the dead from all ages, some famous, most of them anonymous, appeal to our attention. They could be said to form a modest history on the margin of History. The Inner Space is more personal and has a light mood. It brings us a further hundred monologues but this time there is a continuous shift between autobiographical moments and the voices of the dead. The earlier book finished in the picture of an ego on a bench at the bay, hit by an obviously fatal heart attack.The Inner Space starts there, in a new attempt at life, recreating prehistory and family chronicle, childhood and formation, work and love, up to "the final vertigo of childrens voices." The ages appear unhampered by logic, one beside the other - your head is "full of memories of all that hasnt happened yet." At the same time urgent voices from outside break in, voices that carry essential, often harrowing messages, contributing to form the life they invade. This poetry is direct, clear-cut and dramatic, presenting "the second simplicity" that one of the poems talks about. It addresses a wide audience.
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
A series of mental exercises designed for group participation focuses on the roles of reasoning and imagination in achieving sensory perception
The sixth man who walked on the moon shares his journey to the stars, into the mind, and beyond. In February 1971, as Apollo 14 astronaut Edgar Mitchell hurtled Earthward through space, he was engulfed by a profound sense of universal connectedness. He intuitively sensed that his presence and that of the planet in the window were all part of a deliberate, universal process, and that the glittering cosmos itself was, in some way, conscious. The experience was so overwhelming, Mitchell knew his life would never be the same. For the next thirty-five years, he embarked on another journey, an inward exploration of the ineffable mystery of human consciousness and being. Mitchell left NASA to form the Institute of Noetic Sciences (IONS). There he initiated research in areas of study previously neglected by mainstream science and constructed a theory that could explain not only the mysteries of consciousness, but also the psychic event—what spiritualists call a “miracle” and scientists dismiss altogether. Mitchell also created a new dyadic model of reality, revealing a self-aware universe not predetermined by the laws of physics, preordained by deities, or infinitely malleable. While human actions are generally subject to the laws of physics, these laws are also influenced by the mind. From Outer Space to Inner Space traces two remarkable journeys—one through space and one through the mind. Together they fundamentally alter the way we understand the miracle and mystery of being, and ultimately reveal humankind’s role in its own destiny. Previously published as The Way of the Explorer, this edition includes a new foreword by Avi Loeb, an afterword by Dean Radin, and a postscript chapter by the author.
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