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J. J. Sakurai's treatment of various elementary particle phenomena, is written for those not completely familiar with field theory who wish to gain insight into theoretical problems. Since the manuscript for his book was completed, a very important development has taken place in particle physics-the discovery of the p, w, and n mesons: in view of this development, the author has added a new section devoted exclusively to these new mesons and resonances.Originally published in 1964.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Recent scientific advances have placed many traditional philosophical concepts under great stress. In this pathbreaking book, the eminent philosopher Robert Nozick rethinks and transforms the concepts of truth, objectivity, necessity, contingency, consciousness, and ethics. Using an original method, he presents bold new philosophical theories that take account of scientific advances in physics, evolutionary biology, economics, and cognitive neuroscience, and casts current cultural controversies (such as whether all truth is relative and whether ethics is objective) in a wholly new light. Throughout, the book is open to, and engages in, the bold exploration of new philosophical possibilities.Philosophy will never look the same. Truth is embedded in space-time and is relative to it. However, truth is not socially relative among human beings (extraterrestrials are another matter). Objective facts are invariant under specified transformations; objective beliefs are arrived at by a process in which biasing factors do not play a significant role. Necessity's domain is contracted (there are no important metaphysical necessities; water is not necessarily H2O) while the important and useful notion of degrees of contingency is elaborated. Gradations of consciousness (based upon "common registering") yield increasing capacity to fit actions to the world. The originating function of ethics is cooperation to mutual benefit, and evolution has instilled within humans a "normative module": the capacities to learn, internalize, follow norms, and make evaluations. Ethics has normative force because of the connection between ethics and conscious self-awareness. Nozick brings together the book's novel theories to show the extent to which there are objective ethical truths.

Recent scientific advances have placed many traditional philosophical concepts under great stress. In this pathbreaking book, the eminent philosopher Robert Nozick rethinks and transforms the concepts of truth, objectivity, necessity, contingency, consciousness, and ethics. Using an original method, he presents bold new philosophical theories that take account of scientific advances in physics, evolutionary biology, economics, and cognitive neuroscience, and casts current cultural controversies (such as whether all truth is relative and whether ethics is objective) in a wholly new light. Throughout, the book is open to, and engages in, the bold exploration of new philosophical possibilities. Philosophy will never look the same. Truth is embedded in space-time and is relative to it. However, truth is not socially relative among human beings (extraterrestrials are another matter). Objective facts are invariant under specified transformations; objective beliefs are arrived at by a process in which biasing factors do not play a significant role. Necessity's domain is contracted (there are no important metaphysical necessities; water is not necessarily H2O) while the important and useful notion of degrees of contingency is elaborated. Gradations of consciousness (based upon "common registering") yield increasing capacity to fit actions to the world. The originating function of ethics is cooperation to mutual benefit, and evolution has instilled within humans a "normative module": the capacities to learn, internalize, follow norms, and make evaluations. Ethics has normative force because of the connection between ethics and conscious self-awareness. Nozick brings together the book's novel theories to show the extent to which there are objective ethical truths.

Recent scientific advances have placed many traditional philosophical concepts under great stress. In this pathbreaking book, the eminent philosopher Robert Nozick rethinks and transforms the concepts of truth, objectivity, necessity, contingency, consciousness, and ethics. Using an original method, he presents bold new philosophical theories that take account of scientific advances in physics, evolutionary biology, economics, and cognitive neuroscience, and casts current cultural controversies (such as whether all truth is relative and whether ethics is objective) in a wholly new light. Throughout, the book is open to, and engages in, the bold exploration of new philosophical possibilities.Philosophy will never look the same. Truth is embedded in space-time and is relative to it. However, truth is not socially relative among human beings (extraterrestrials are another matter). Objective facts are invariant under specified transformations; objective beliefs are arrived at by a process in which biasing factors do not play a significant role. Necessity's domain is contracted (there are no important metaphysical necessities; water is not necessarily H2O) while the important and useful notion of degrees of contingency is elaborated. Gradations of consciousness (based upon "common registering") yield increasing capacity to fit actions to the world. The originating function of ethics is cooperation to mutual benefit, and evolution has instilled within humans a "normative module": the capacities to learn, internalize, follow norms, and make evaluations. Ethics has normative force because of the connection between ethics and conscious self-awareness. Nozick brings together the book's novel theories to show the extent to which there are objective ethical truths.

First published in 1986. Routledge is an imprint of Taylor & Francis, an informa company.

Recent scientific advances have placed many traditional philosophical concepts under great stress. In this pathbreaking book, the eminent philosopher Robert Nozick rethinks and transforms the concepts of truth, objectivity, necessity, contingency, consciousness, and ethics. Using an original method, he presents bold new philosophical theories that take account of scientific advances in physics, evolutionary biology, economics, and cognitive neuroscience, and casts current cultural controversies (such as whether all truth is relative and whether ethics is objective) in a wholly new light. Throughout, the book is open to, and engages in, the bold exploration of new philosophical possibilities. Philosophy will never look the same. Truth is embedded in space-time and is relative to it. However, truth is not socially relative among human beings (extraterrestrials are another matter). Objective facts are invariant under specified transformations; objective beliefs are arrived at by a process in which biasing factors do not play a significant role. Necessity's domain is contracted (there are no important metaphysical necessities; water is not necessarily H2O) while the important and useful notion of degrees of contingency is elaborated. Gradations of consciousness (based upon "common registering") yield increasing capacity to fit actions to the world. The originating function of ethics is cooperation to mutual benefit, and evolution has instilled within humans a "normative module": the capacities to learn, internalize, follow norms, and make evaluations. Ethics has normative force because of the connection between ethics and conscious self-awareness. Nozick brings together the book's novel theories to show the extent to which there are objective ethical truths.

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.

MYTH OF INVARIANCE explores the unifying symbolism of music and number so the reader can understand the secrets from Babylon, Egypt, Greece and the Bible - secrets hidden for centuries.

Octavo. 5.75 x 9 in. xxi, 216 pp. Profusely illustrated with black & white reproductions of images and diagrams. Very good in pictorial wrappers with general rubbing to covers and mild foxing to edge of text block.

Ernest McClain's book constitutes an intellectual breakthrough of utmost significance. It offers a persuasive explanation of crucial passages in texts of world literature - the Ṛg Veda, the Egyptian Book of the Dead, the Bible, Plato that have defied critics of the separate concerned disciplines. All these passages deal with numbers. What sounds like mathematical nonsense or literary gibberish has been given life and meaning by McClain's incisive thoughts. The recurrence, moreover, of identical and similar numbers in Babylon, Egypt, Greece, and Palestine confirms ever growing speculations on the historical continuity and direction of a basic spiritual tradition. Dr. McClain's method is simple enough: he recognizes music as the one force capable of projecting a philosophic synthesis. For this approach he is not likely to learn the immediate approval and support of theologians, philosophers, philologists, mathematicians, and others who have become too specialized to view the whole rather than the detail. Nor is he likely to find on his side musicians who consider their art primarily a branch of amusement and musicologists who are instinctively afraid of numbers. Yet his approach, neglected for centuries, is anything but new. He learned it by taking Plato literally. Plato insists on the superior role of music in the education of the whole man. In antiquity musical symbolism was understood directly. When in the course of history the role of music as a spiritual force was increasingly sacrificed to that of individual expression or entertainment, the interpretation of once very clear texts suffered. McClain's great accomplishment lies in his recognition of music as the spiritual model par excellence throughout antiquity and in his courageous and self-critical application of this insight to other fields. He has provided philologists, philosophers, theologians, historians, mathematicians, and musicians with a sound basis for further explorations in their own fields

These twenty-three contributions focus on the most recent developments in the rapidly evolving field of geometric invariants and their application to computer vision. The introduction summarizes the basics of invariant theory, discusses how invariants are related to problems in computer vision, and looks at the future possibilities, particularly the notion that invariant analysis might provide a solution to the elusive problem of recognizing general curved 3D objects from an arbitrary viewpoint. The remaining chapters consist of original papers that present important developments as well as tutorial articles that provide useful background material. These chapters are grouped into categories covering algebraic invariants, nonalgebraic invariants, invariants of multiple views, and applications. An appendix provides an extensive introduction to projective geometry and its applications to basic problems in computer vision.

Critical phenomena arise in a wide variety of physical systems. Classi­ cal examples are the liquid-vapour critical point or the paramagnetic­ ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur­ bulence and may even extend to the quark-gluon plasma and the early uni­ verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal­ ing, provided only that angles remain unchanged.

A fundamental reason for using formal methods in the philosophy of science is the desirability of having a fixed frame of reference that may be used to organize the variety of doctrines at hand. This book—Patrick Suppes's major work, and the result of several decades of research—examines how set-theoretical methods provide such a framework, covering issues of axiomatic method, representation, invariance, probability, mechanics, and language, including research on brain-wave representations of words and sentences. This is a groundbreaking, essential text from a distinguished philosopher.

MYTH OF INVARIANCE explores the unifying symbolism of music and number so the reader can understand the secrets from Babylon, Egypt, Greece and the Bible - secrets hidden for centuries.

A fundamental reason for using formal methods in the philosophy of science is the desirability of having a fixed frame of reference that may be used to organize the variety of doctrines at hand. This book—Patrick Suppes's major work, and the result of several decades of research—examines how set-theoretical methods provide such a framework, covering issues of axiomatic method, representation, invariance, probability, mechanics, and language, including research on brain-wave representations of words and sentences. This is a groundbreaking, essential text from a distinguished philosopher.

Critical phenomena arise in a wide variety of physical systems. Classi­ cal examples are the liquid-vapour critical point or the paramagnetic­ ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur­ bulence and may even extend to the quark-gluon plasma and the early uni­ verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal­ ing, provided only that angles remain unchanged.

Ernest McClain's book constitutes an intellectual breakthrough of utmost significance. It offers a persuasive explanation of crucial passages in texts of world literature - the Ṛg Veda, the Egyptian Book of the Dead, the Bible, Plato that have defied critics of the separate concerned disciplines. All these passages deal with numbers. What sounds like mathematical nonsense or literary gibberish has been given life and meaning by McClain's incisive thoughts. The recurrence, moreover, of identical and similar numbers in Babylon, Egypt, Greece, and Palestine confirms ever growing speculations on the historical continuity and direction of a basic spiritual tradition. Dr. McClain's method is simple enough: he recognizes music as the one force capable of projecting a philosophic synthesis. For this approach he is not likely to learn the immediate approval and support of theologians, philosophers, philologists, mathematicians, and others who have become too specialized to view the whole rather than the detail. Nor is he likely to find on his side musicians who consider their art primarily a branch of amusement and musicologists who are instinctively afraid of numbers. Yet his approach, neglected for centuries, is anything but new. He learned it by taking Plato literally. Plato insists on the superior role of music in the education of the whole man. In antiquity musical symbolism was understood directly. When in the course of history the role of music as a spiritual force was increasingly sacrificed to that of individual expression or entertainment, the interpretation of once very clear texts suffered. McClain's great accomplishment lies in his recognition of music as the spiritual model par excellence throughout antiquity and in his courageous and self-critical application of this insight to other fields. He has provided philologists, philosophers, theologians, historians, mathematicians, and musicians with a sound basis for further explorations in their own fields

OKart., paperback, 216 S. broschiert. Äußerl. Gebrauchs- u. Lagerspuren, Druckseiten unbeschadet. guter Zustand 352 gr

The papers in this volume reflect the renewed interest in the semantics of grammatical categories and the issues of invariance and variation in grammar. In particular, this collection presents the current understanding of invariance of grammar with respect to the synchronic and diachronic analyses of specific languages, and as realized in work on typology and universals.The book is divided into five sections: The Question of Invariance; Invariance and Grammatical Categories; Grammar and Discourse; Grammar and Pragmatics; Typology and Universals.

R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.