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The first comprehensive book on the topic in half a century explores recent symmetry – and symmetry breaking – related discoveries, and discusses the questions and answers they raise in diverse disciplines: particle and high-energy physics, structural chemistry and the biochemistry of proteins, in genetic code study, in brain research, and also in architectural structures, and business decision making, to mention only a few examples.
A professor of physics and astronomy studies a theory that time is reversible, and explains how physicists have generally been reluctant to accept the reversibility of time because of the implied causal paradoxes. Illustrations.
The two volumes together offer readers a new window into the communicative importance of design."--Jacket.
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in ?Mathematics, Chemistry, and Astronomy ? Professional and Reference? in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.
In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. Michael Leyton's arguments about the nature of perception and cognition are fascinating, exciting, and sure to be controversial. In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. He elaborates a system of rules by which the conversion to memory takes place and presents a number of detailed case studies--in perception, linguistics, art, and even political subjugation--that support these rules. Leyton observes that the mind assigns to any shape a causal history explaining how the shape was formed. We cannot help but perceive a deformed can as a dented can. Moreover, by reducing the study of shape to the study of symmetry, he shows that symmetry is crucial to our everyday cognitive processing. Symmetry is the means by which shape is converted into memory. Perception is usually regarded as the recovery of the spatial layout of the environment. Leyton, however, shows that perception is fundamentally the extraction of time from shape. In doing so, he is able to reduce the several areas of computational vision purely to symmetry principles. Examining grammar in linguistics, he argues that a sentence is psychologically represented as a piece of causal history, an archeological relic disinterred by the listener so that the sentence reveals the past. Again through a detailed analysis of art he shows that what the viewer takes to be the experience of a painting is in fact the extraction of time from the shapes of the painting. Finally he highlights crucial aspects of the mind's attempt to recover time in examples of political subjugation.
The systematic bottom-up approach provides the appropriate framework for interpreting measurements that will be performed to better understand the physics of mass generation in the universe. No knowledge of quantum field theory is required other than familiarity with effective Lagrangians and Feynmann diagrams.
The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
The authors, world-renowned scientists, have already produced a dozen books on symmetry for professionals as well as lay persons, for grownups as well as children, in English, Russian, German, Hungarian, and Swedish languages. They provide this attractive account of symmetry in few words and many oOe1/4OCO as many as 650 oOe1/4OCO images in full color from the most diverse corners of our globe. An encounter with this book will open up a whole new experience for the reader, who will never look at the world with the same eyes as before."
It is gratifying to launch the third edition of our book. Its coming to life testi?es about the task it has ful?lled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the ?rst and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from ch- istry as well as from other ?elds to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pl- sure in addition to learning experience. In our ?rst Preface we paid tribute to two books in particular from which we learned a great deal; they have in?uenced signi?cantly our approach to the subject matter of our book. They are Weyl’s classic, Symmetry, and Shubnikov and Koptsik’s Symmetry in Science and Art. The structure of our book has not changed. Following the Int- duction (Chapter 1), Chapter 2 presents the simplest symmetries using chemical and non-chemical examples. Molecular geometry is discussed in Chapter 3. The next four chapters present gro- theoretical methods (Chapter 4) and, based on them, discussions of molecular vibrations (Chapter 5), electronic structures (Chapter 6), and chemical reactions (Chapter 7). For the last two chapters we return to a qualitative treatment and introduce space-group sym- tries (Chapter 8), concluding with crystal structures (Chapter 9). For the third edition we have further revised and streamlined our text and renewed the illustrative material.
An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.