Complexification

Given that everything in the world is relative, contemporary societal organization is based on social absolutes that are considered self-evident. This type of system invariably introduces central polarization into society, leading to class divisions, with transitions between the classes becoming increasingly difficult as polarization intensifies. Throughout human history, various forms of centrally polarized societies have been established, referred to by different names in different eras, such as slavery, feudalism, capitalism, or socialism. However, these societies can only endure as long as transitions between their social strata remain possible. Once these transitions become unattainable, the society inevitably crumbles. The escalating central polarization of society and its subsequent division become impediments to progress and development and can only be overcome through decentralization. Historically, transitions from one societal structure to another have resulted in a temporary decentralization of society. Nevertheless, the new societal structure invariably deteriorated due to the emergence of fresh central polarization, albeit founded on different polarization criteria. This book offers a deep exploration of the phenomena of relativity, complexity, and complexification, proposing a new approach to the critical analysis of capitalism as a societal structure. It elaborates on the foundational principles of distributed society as the only sustainable alternative to centrally polarized society.

This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.

Memory Evolutive Systems; Hierarchy, Emergence, Cognition provides comprehensive and comprehensible coverage of Memory Evolutive Systems (MEM). Written by the developers of the MEM, the book proposes a mathematical model for autonomous evolutionary systems based on the Category Theory of mathematics. It describes a framework to study and possibly simulate the structure of living systems and their dynamic behavior. This book contributes to understanding the multidisciplinary interfaces between mathematics, cognition, consciousness, biology and the study of complexity. It is organized into three parts. Part A deals with hierarchy and emergence and covers such topics as net of interactions and categories; the binding problem; and complexifications and emergence. Part B is about MEM while Part C discusses MEM applications to cognition and consciousness. The book explores the characteristics of a complex evolutionary system, its differences from inanimate physical systems, and its functioning and evolution in time, from its birth to its death. This book is an ideal reference for researchers, teachers and students in pure mathematics, computer science, cognitive science, study of complexity and systems theory, Category Theory, biological systems theory, and consciousness theory. It would also be of interest to both individuals and institutional libraries. Comprehensive and comprehensible coverage of Memory Evolutive System Written by the developers of the Memory Evolutive Systems Designed to explore the common language between sciences

This volume contains the proceedings of the international conference ""Ordered Algebraic Structures and Related Topics'', held from October 12-16, 2015, at CIRM, Luminy, Marseilles, France. Papers contained in this volume cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.

Based on a conference held in Trento, Italy, and sponsored by the Centro Internazionale per la Ricera Matematica, this work presents advances in several complex variables and related topics such as transcendental algebraic geometry, infinite dimensional supermanifolds, and foliations. It covers the unfoldings of singularities, Levi foliations, Cauchy-Reimann manifolds, infinite dimensional supermanifolds, conformal structures, algebraic groups, instantons and more.

Discusses the relationship between Chomskyan syntactic theory and the evolution of language.

The geometry of Jordan and Lie structures tries to answer the following question: what is the integrated, or geometric, version of real Jordan algebras, - triple systems and - pairs? Lie theory shows the way one has to go: Lie groups and symmetric spaces are the geometric version of Lie algebras and Lie triple systems. It turns out that both geometries are closely related via a functor between them, called the Jordan-Lie functor, which is constructed in this book. The reader is not assumed to have any knowledge of Jordan theory; the text can serve as a self-contained introduction to (real finite-dimensional) Jordan theory.

This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.