This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper lang…
This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitude…
This book presents two new mathematical techniques: nonstandard logics and nonstandard metrics. The techniques are applied to current problems in physics, i.e. the hidden variable problem, the local and nonlocal problems, etc.
This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing scie…
This book consists of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: the ancient musical scale, proportion in architecture, ancient geometry,…
This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes…
This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully incl…
This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. Th…
This book is a Festschrift for the 90th birthday of the physicist Pierre Noyes. The book is a representative selection of papers on the topics that have been central to the meetings over the last three decades of ANPA, the Alternative Natural Philos…
The Maxwell, Einstein, Schroedinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to…
This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distan…
We could be on the threshold of a scientific revolution. Quantum mechanics is based on unique, finite, and discrete events. General relativity assumes a continuous, curved space-time. Reconciling the two remains the most fundamental unsolved scienti…
LinKnot - Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The b…
This book is about "diamond", a logic of paradox. In diamond, a statement can be true yet false; an "imaginary" state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic…
Every hundred years or so, a unique groundbreaking Copernican class volume arises unexpectedly. From ashes long thought cold of Einstein's static universe model, for the first time technically viable alternative interpretations to all pillars of Big…
This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference.Knot theory is a very special topological subject: the classification of embeddings of…
This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the…
This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the…
This is the first of three volumes collecting the original and now classic works in topology written in the 50s-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book co…
The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a…
This volume gathers the contributions from the international conference "Intelligence of Low Dimensional Topology 2006," which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus…
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces…
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a co…
The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular f…
There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon-Luecke work on surgeries on knots, Jones' work on invariants of lin…
This book is about "delta", a paradox logic. In delta, a statement can be true yet false; an intermediate state, midway between being and non-being. Delta's imaginary value solves many paradoxes unsolvable in two-valued Boolean logic, including Russ…
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in "Mathematics, Chemistry, and Astronomy - Professional and Reference" in 1991. It has been a comprehensive reference in design science, br…
Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations for physics to date. The author proposes a fundamental description of process in a universal computational rewrite system, le…
This book is about dealing with 3-manifolds using computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind…
This book discusses the origins of ornamental art - illustrated by the oldest examples, dating mostly from the paleolithic and neolithic ages, and considered from the theory-of-symmetry point of view. Because of its multidisciplinary nature, it will…
The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the…
The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classic…
The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the c…
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Th…
This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. inva…
This volume is a collection of papers on various areas of current interest in mathematical biology, such as epidemic disease modeling, including the effects of vaccination and strain replacement; immunology, such as T-Cell dynamics and the mechanism…
In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its a…
The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams repla…
This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simp…
This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants…
This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No ex…
Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been…
The aim of the book is to provide a new and fruitful approach to the challenging problems of modern physics, astrophysics, and cosmology. The well-known observations of the flat rotation curves of spiral galaxies and of the gravitational lensing eff…
This book focuses on a prototype of creative causal processes termed BIOS and how the concept can be applied to the physical world, in medicine and in social science. This book presents methods for identifying creative features in empirical data; st…
The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and co…
This book is about "diamond", a logic of paradox. In diamond, a statement can be true yet false; an "imaginary" state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued Boolean logic…
This volume is the result of the author's many-years of research in this field. These results were presented in the author's two books, Introduction to the Algorithmic Measurement Theory (Moscow, Soviet Radio, 1977), and Codes of the Golden Proporti…
In this second edition, the following recent papers have been added: "Gauss Codes, Quantum Groups and Ribbon Hopf Algebras", "Spin Networks, Topology and Discrete Physics", "Link Polynomials and a Graphical Calculus" and "Knots Tangles and Electrica…