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Geometric Algebra for Physicists
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.
Uncertainty in Geometric Computations
This book contains the proceedings of the workshop Uncertainty in Geomet ric Computations that was held in Sheffield, England, July 5-6, 2001. A total of 59 delegates from 5 countries in Europe, North America and Asia attended the workshop. The workshop provided a forum for the discussion of com putational methods for quantifying, representing and assessing the effects of uncertainty in geometric computations. It was organised around lectures by invited speakers, and presentations in poster form from participants. Computer simulations and modelling are used frequently in science and engi neering, in applications ranging from the understanding of natural and artificial phenomena, to the desig...
Applications of Geometric Algebra in Computer Science and Engineering
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic gr...
Making the World Safe for Capitalism
The Iraq War defined the first decade of the twenty-first century – leading to mass protests and raising profound questions about domestic politics and the use of military force. Yet most explanations of the war have a narrow focus either on political personalities or oil. Christopher Doran provides a unique perspective, arguing that the drive to war came from the threat Iraq might pose to American economic hegemony if the UN sanctions regime was ended. Doran argues that this hegemony is rooted in third-world debt and corporate market access. It was protection of these arrangements that motivated US action, not Iraq's alleged weapons of mass destruction or a simplistic desire to seize its oil. This book will provide new insights on the war which still casts a shadow over global politics, and will have wide appeal to all those concerned about the Middle East, world peace, and global development.
Integral Ecology for a More Sustainable World
Laudato Si’ insists on a revolutionary human response to the public challenges of our time concerning the ecological crisis. The volume takes up the revolutionary spirit of Pope Francis and speaks to the economic, technological, political, educational, and religious changes needed to overcome the fragile relationships between humans and Earth. This volume identifies various systemic factors that have produced the anthropogenic ecological crisis that threatens the planet and uses the ethical vision of Laudato Si’ to promote practical responses that foster fundamental changes in humanity’s relationships with Earth and each other. The essays address not only the immediate behavioral chang...
Science and Religion
This collection offers new perspectives on the study of science and religion, bringing together articles that highlight the differences between epistemological systems and call into question the dominant narrative of modern science. The volume provides historical context for the contemporary discourse around religion and science, detailing the emergence of modern science from earlier movements related to magic and other esoteric arts, the impact of the Reformation on science, and the dependence of Western science on the so-called Golden Age of Islam. In addition, contributors examine the impacts of Western science and colonialism on the ongoing theft of the biological resources of traditional and indigenous communities in the name of science and medicine. The volume’s multi-perspectival approach aims to refocus the terms of the conversation around science and religion, taking into consideration multiple rationalities outside of the dominant discourse.
Guide to Geometric Algebra in Practice
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
Unlocking Divine Action
Provides a sustained account of how the thought of Aquinas may be used in conjunction with contemporary science to deepen our understanding of divine action and address such issues as creation, providence, prayer, and miracles.
Foundations of Geometric Algebra Computing
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applic...
