Symmetry plays an essential role in science - not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in condensed-matter physics, thermodynamics, chemistry, biology, and others. This text discusses the concept of symmetry and its application to many areas of science. While it includes a detailed introduction to the theory of groups, which forms the mathematical apparatus for describing symmetries, it also includes a much more general discussion of the nature of symmetry and its role in science. Many problems serve to sharpen the reader's understanding, and an extensive bibliography concludes the book.
When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. Written by a renowned expert, this book will convince all interested readers of the importance of symmetry in science.
The perception of symmetry in art and in nature has been appreciated since antiquity, with development of the underlying laws tracing back at least to Pythagorean times. By the end of the eighteenth century it was realized that the immense variety of natural crystal shapes could be accounted for on the basis of a rather small number of symmetry operations, of which some were equally applicable to biological systems. The mathematical theory of symmetry continued to mature throughout the last century, culminating in the independent discoveries in Russia, Germany, and England that a total of only 230 independent ways exist in which the operations of rotation, reflection, and translation can be combined to transform three-dimensional geometrical objects into themselves. Derivation of the 230 space groups depends ultimately on restricting the meaning of symmetry to that of a property of purely geometrical figures. A. V. Shubnikov and his collaborators, over the past three decades, expanded this concept of symmetry to include the sign of transformation operations.
An engaging exploration of beauty in physics, with a foreword by Nobel Prize–winning physicist Roger Penrose The concept of symmetry has widespread manifestations and many diverse applications—from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics—one of the greatest chapters in the intellectual history of humankind.
Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
From the Publisher: "What does it mean to be lonely?" Thomas Dumm asks. His inquiry, documented in this book, takes us beyond social circumstances and into the deeper forces that shape our very existence as modern individuals. The modern individual, Dumm suggests, is fundamentally a lonely self. Through reflections on philosophy, political theory, literature, and tragic drama, he proceeds to illuminate a hidden dimension of the human condition. His book shows how loneliness shapes the contemporary division between public and private, our inability to live with each other honestly and in comity, the estranged forms that our intimate relationships assume, and the weakness of our common bonds. A reading of the relationship between Cordelia and her father in Shakespeare's King Lear points to the most basic dynamic of modern loneliness-how it is a response to the problem of the "missing mother." Dumm goes on to explore the most important dimensions of lonely experience-Being, Having, Loving, and Grieving. As the book unfolds, he juxtaposes new interpretations of iconic cultural texts-Moby-Dick, Death of a Salesman, the film Paris, Texas, Emerson's "Experience," to name a few-with his own experiences of loneliness, as a son, as a father, and as a grieving husband and widower. Written with deceptive simplicity, Loneliness as a Way of Life is something rare-an intellectual study that is passionately personal. It challenges us, not to overcome our loneliness, but to learn how to re-inhabit it in a better way. To fail to do so, this book reveals, will only intensify the power that it holds over us
When scientists peer through a telescope at the distant stars in outer space or use a particle-accelerator to analyze the smallest components of matter, they discover that the same laws of physics govern the whole universe at all times and all places. Physicists call the eternal, ubiquitous constancy of the laws of physics symmetry. Symmetry is the basic underlying principle that defines the laws of nature and hence controls the universe. This all-important insight is one of the great conceptual breakthroughs in modern physics and is the basis of contemporary efforts to discover a grand unified theory to explain all the laws of physics. Nobel Laureate Leon M. Lederman and physicist Christopher T. Hill explain the supremely elegant concept of symmetry and all its profound ramifications to life on Earth and the universe at large in this eloquent, accessible popular science book. They not only clearly describe concepts normally reserved only for physicists and mathematicians, but they also instill an appreciation for the profound beauty of the universe’s inherent design. Central to the story of symmetry is an obscure, unpretentious, but extremely gifted German mathematician named Emmy Noether. Though still little known to the world, she impressed no less a scientist than Albert Einstein, who praised her "penetrating mathematical thinking." In some of her earliest work she proved that the law of the conservation of energy was connected to the idea of symmetry and thus laid the mathematical groundwork for what may be the most important concept of modern physics. Lederman and Hill reveal concepts about the universe, based on Noether’s work, that are largely unknown to the public and have wide-reaching implications in connection with the Big Bang, Einstein’s theory of relativity, quantum mechanics, and many other areas of physics. Through ingenious analogies and illustrations, they bring these astounding notions to life. This book will open your eyes to a universe you never knew existed.
