Bøger i Series on Knots & Everything serien

Based on Einstein's static universe model, this work presents technically viable alternative interpretations to all pillars of Big Bang cosmology in the context of a new 'continuous-state' cosmological paradigm able to elucidate many contemporary problems plaguing the standard model of particle physics.

Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.

A collection of essays that stand on their own but are also connected. Part I examines how numbers and geometry arise in nature and several cultural contexts. Part II shows how many of the same numbers and number sequences are related to the study of numbers, dynamical systems, chaos and fractals.

The well-known observations of the flat rotation curves of spiral galaxies and of the gravitational lensing effect greatly exceeding the expectations based on the classical GRT can be explained without bringing in the notion of dark matter. This book offers a new approach to the challenging problems of modern physics, astrophysics, and cosmology.

Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and "Golden" Paradigm of Modern Science. "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony," the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and "Golden" Paradigm of Modern Science. "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony," the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory.

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 first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.

This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics.

This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

This text brings together 20 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 science of knots, and decorative knots.

The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration

- Introduces the concept of bipolar feedback, a mathematical and natural process that generates bios, a pattern beyond chaos- Demonstrates biotic patterns in cosmological, physiological, meteorological, and economic processes- Introduces new methods for time series analysis, and includes programs for them- Proposes a research program based on the concept of creative development as an alternative to deterministic and random models- Advances a new theory of biological evolution

Presents a summary of the results of a research project on discreteness in modern physics. This book argues that in contrast with the expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this basic treatment builds up the world from the discrimination of discrete entities.

A comprehensive reference in design science, bringing together material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations.

Features classical papers on algebraic and differential topology published in the 1950s - 1960s. This title documents methods and constructions from these works.

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. This title is intended to be a graduate text as well as a research monograph.

Gives a description of one of the most beautiful and complicated examples in low-dimensional topology. This text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers.

Consists of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. This book contains lectures on the many aspects of applications of knot theory. It gives an in-depth survey of the advances of knot theory and its applications.

The Maxwell, Einstein, Schrodinger 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 reveal their richness and continued importance for advancing fundamental Physics.

Features works in topology written during the 1950s-1960s. This book book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated singular homologies of fiber spaces.

In this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management.The importance of the book comes in the following ways:The dynamics of the geometry unites all Platonic and Kepler Solids into one united structure and creates 11 unique trefoil knots. Its topology is directly related to the dynamics of the polyhedra.The Mereon Matrix is an approach to the unification of knowledge that relies on whole systems modelling. it is a framework charting the emergence of the Platonic and Kepler solids in a sequential, emergent growth process that describes a non-linear whole system, and includes a process of 'breathing' as well as multiplying ('birthing');This dynamic/kinematic structure provides insight and a new approach to General Systems Theory and non-linear science, evolving through a new approach to polyhedral geometry. A set of 11 First Principles is derived from the structure, topology and dynamics of the Mereon Matrix, which serve well as a template information model.The Mereon Matrix is related to a large number of systems, physical, mathematical, and philosophical, and in linking these systems, provides access to new relationships among them by combining geometry with process thinking. The new perspective on systems is hypothesized as universal — this is, applicable in all areas of science, natural and social. Such applicability has been demonstrated for applications as diverse as pre-life evolution, biological evolution and human molecular genetics, as well as a classroom management system for the educational system.Care has been taken to use images and languaging that are understandable across domains, connecting diverse disciplines, while making this complex system easily accessible.

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and "Golden" Paradigm of Modern Science. "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony," the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

Serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. This second edition introduces two new chapters - twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition.

Provides an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. This title covers frictional properties of knots, relations with combinatorics, and knots in dynamical systems. It includes articles Khovanov Homology.

Offers a different way of thinking about two 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 prevailing approach to these questions, this book demonstrates the need for more than just a different theory.

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 title deals with 'diamond', a logic of paradox. It resolves paradoxes by Russell, Cantor, Berry and Zeno.