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This book presents a new economic theory developed from physical and biological principles. It explains how technology, social systems and economic values are intimately related to resources. Many people have recognized that mainstream (neoclassical) economic theories are not consistent with physical laws and often not consistent with empirical patterns, but most feel that economic activities are too complex to be described by a simple and coherent mathematical theory. While social systems are indeed complex, all life systems, including social systems, satisfy two principles. First, all systems need to extract resources from the external environment to compensate for their consumption. Second, for a system to be viable, the amount of resource extraction has to be no less than the level of consumption. From these two principles, we derive a quantitative theory of major factors in economic activities, such as fixed cost, variable cost, discount rate, uncertainty and duration. The mathematical theory enables us to systematically measure the effectiveness of different policies and institutional structures at varying levels of resource abundance and cost.The theory presented in this book shows that there do not exist universally optimal policies or institutional structures. Instead, the impacts of different policies or social structures have to be measured within the context of existing levels of resource abundance. As the physical costs of extracting resources rise steadily, many policy assumptions adopted in mainstream economic theories, and workable in times of cheap and abundant energy supplies and other resources, need to be reconsidered. In this rapidly changing world, the theory presented here provides a solid foundation for examining the long-term impacts of today's policy decisions.
This book presents a framework for resolving some of the crucial paradoxes that trouble thoughtful physicists and philosophers of science. Central to the work is a symbolic object-language (originated by the author) comparable to such other object-languages as computer programs, engineering flow-charts & chemical formulas. It differs from them, however, in being vigorously derived from one of the simplest & least controvertible of ideas: the otherness of any two entities, even identical ones (if two, then one & another, otherwise, just one). It therefore admits only those representations, expressed in the symbolism, that are strictly compatible with the idea -- unlike computer programs, which can represent any concept, however absurd or physically impossible. The author employs his symbolism to construct models of physical processes. He shows how these models make it possible to resolve the paradoxes at the heart of contemporary physics, including particularly those implicit in the recent definitive demonstration of the violation of "Bell's Inequality." Among these implications is that past events can be influenced by present acts of observation. This radical departure from traditional conceptions of causality has caused a crisis in physics. With that crisis, this book is basically concerned.
Topology is the mathematical study of the most basic geometrical structure of a space. Mathematical physics uses topological spaces as the formal means for describing physical space and time. Tim Maudlin proposes a completely new mathematical structure for describing geometrical notions such as continuity, connectedness, boundaries of sets, and so on, in order to provide a better mathematical tool for understanding space-time. He begins with a brief historicalreview of the development of mathematics as it relates to geometry and an overview of standard topology, and goes on to develop his original Theory of Linear Structures.
Winner of the 1987 Pfizer Award of the History of Science Society "A majestic study of a most important spoch of intellectual history."—Brian Pippard, Times Literary Supplement "The authors' use of archival sources hitherto almost untouched gives their story a startling vividness. These volumes are among the finest works produced by historians of physics."—Jed Z. Buchwald, Isis "The authors painstakingly reconstruct the minutiae of laboratory budgets, instrument collections, and student numbers; they disentangle the intrigues of faculty appointments and the professional values those appointments reflected; they explore collegial relationships among physicists; and they document the unending campaign of scientists to wring further support for physics from often reluctant ministries."—R. Steven Turner, Science "Superbly written and exhaustively researched."—Peter Harman, Nature
The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

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