The Space that Separates: A Realist Theory of Art radically challenges our assumptions about what art is, what art does, who is doing it, and why it matters. Rejecting the modernist and market-driven misconception that art is only what artists do, Wilson instead presents a realist case for living artfully. Art is defined as the skilled practice of giving shareable form to our experiences of being-in-relation with the real; that is to say, the causally generative domain of the world that extends beyond our direct observation, comprising relations, structures, mechanisms, possibilities, powers, processes, systems, forces, values, ways of being. In communicating such aesthetic experience we behold life’s betweenness – "the space that separates", so coming to know ourselves as connected. Providing the first dedicated and comprehensive account of art and aesthetics from a critical realist perspective – Aesthetic Critical Realism (ACR), Wilson argues for a profound paradigm shift in how we understand and care for culture in terms of our system(s) of value recognition. Fortunately, we have just the right tool to help us achieve this transformation – and it’s called art. Offering novel explanatory accounts of art, aesthetic experience, value, play, culture, creativity, artistic truth and beauty, this book will appeal to a wide audience of students and scholars of art, aesthetics, human development, philosophy and critical realism, as well as cultural practitioners and policy-makers.

This book explores the notions of space and extension of major early modern empiricist philosophers, especially Locke, Berkeley, Hume, and Condillac. While space is a central and challenging issue for early modern empiricists, literature on this topic is sparse. This collection shows the diversity and problematic unity of empiricist views of space. Despite their common attention to the content of sensorial experience and to the analytical method, empiricist theories of space vary widely both in the way of approaching the issue and in the result of their investigation. However, by recasting the questions and examining the conceptual shifts, we see the emergence of a programmatic core, common to what the authors discuss. The introductory chapter describes this variety and its common core. The other contributions provide more specific perspectives on the issue of space within the philosophical literature. This book offers a unique overview of the early modern understanding of these issues, of interest to historians of early modern philosophy, historians and philosophers of science, historians of ideas, and all readers who want to expand their knowledge of the empiricist tradition.

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

This is volume 1 of a 2 volume set.

This ambitious book investigates a major yet underexplored nexus of themes in Roman cultural history: the evolving tropes of enclosure, retreat and compressed space within an expanding, potentially borderless empire. In Roman writers' exploration of real and symbolic enclosures - caves, corners, villas, bathhouses, the 'prison' of the human body itself - we see the aesthetic, philosophical and political intersecting in fascinating ways, as the machine of empire is recast in tighter and tighter shapes. Victoria Rimell brings ideas and methods from literary theory, cultural studies and philosophy to bear on an extraordinary range of ancient texts rarely studied in juxtaposition, from Horace's Odes, Virgil's Aeneid and Ovid's Ibis, to Seneca's Letters, Statius' Achilleid and Tacitus' Annals. A series of epilogues puts these texts in conceptual dialogue with our own contemporary art world, and emphasizes the role Rome's imagination has played in the history of Western thinking about space, security and dwelling.

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

A unified survey of both the status quo and the continuing trends of various branches of number theory. Motivated by elementary problems, the authors present todays most significant results and methods. Topics covered include non-Abelian generalisations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. The book is rounded off with an overview of the major conjectures, most of which are based on analogies between functions and numbers, and on connections with other branches of mathematics such as analysis, representation theory, geometry and algebraic topology.

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.