adex theory how the ade coxeter graphs unify mathematics and physics 57 series on knots and everything

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Adex Theory

Author : Saul Paul Sirag
ISBN : 9789814656504
Genre : Mathematics
File Size : 52. 74 MB
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"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."--Provided by publisher.

Mereon Matrix The Everything Connected Through K Nothing

Author : Kauffman Louis H
ISBN : 9789813233577
Genre : Mathematics
File Size : 36. 31 MB
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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. Contents: Prologues: Sustainability: Mathematical Elegance, Solid Science and Social Grace (L Dennis and L H Kauffman) Lynnclaire Dennis & R Buckminster Fuller Investigation (R W Gray) The Matrix We Call Mereon (L H Kauffman) First Things First: Building on the Known: A Quintessential Jitterbug (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Methodology (J Brender McNair and L Dennis) Philosophical Thoughts and Thinking Aloud Allowed (L Dennis) Belonging -- Education as Transformation (L Dennis) Meme, Pattern and Perspective (L Dennis, N J Woolf and L H Kauffman) Including and Beyond the Point: The Context -- Form Informing Function (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Flow and Scale (L Dennis and L H Kauffman) The Core -- Sharp Distinctions to Elegant Curves (L Dennis and L H Kauffman) Connections, Ligatures and Knots: Mereon Thoughts -- Knots and Beyond (L H Kauffman) The Mereon Trefoil -- Asymmetrical with Perfect Symmetry (L Dennis) Applying Mereon to Knowledge Domains: Exploring the Mereon Matrix (and Beyond) with the CymaScope Technology (L Dennis and P McNair) The Origin of Matter: Life, Learning and Survival (N J Woolf and L Dennis) ATCG -- An Applied Theory for Human MoleCular Genetics (J Brender McNair, P McNair,

New Horizons For Second Order Cybernetics

Author : Muller Karl H
ISBN : 9789813226272
Genre : Language Arts & Disciplines
File Size : 60. 84 MB
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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 application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines. Contents: Prologue: A Brief History of (Second-Order) Cybernetics (Louis H Kauffman & Stuart A Umpleb)Mapping the Varieties of Second-Order Cybernetics (Karl H Müller & Alexander Riegle)Part I: Exploring Second-Order Cybernetics and Its Fivefold Agenda: Second-Order Cybernetics as a Fundamental Revolution in Science (Stuart A Umpleby)Obstacles and Opportunities in the Future of Second-Order Cybernetics and Other Compatible Methods (Allenna Leonard)Connecting Second-Order Cybernetics' Revolution with Genetic Epistemology (Gastón Becerra)Shed the Name to Find Second-Order Success: Renaming Second-Order Cybernetics to Rescue its Essence (Michael R Lissack)Beware False Dichotomies (Peter A Cariani)Second-Order Cybernetics Needs a Unifying Methodology (Thomas R Flanagan)Viva the Fundamental Revolution! Confessions of a Case Writer (T Grandon Gill)Author's Response: Struggling to Define an Identity for Second-Order Cybernetics (Stuart A Umpleby)Cybernetics, Reflexivity and Second-Order Science (Louis H Kauffman)Remarks From a Continental Philosophy Point of View (Tatjana Schönwälder-Kuntze)Finally Understanding Eigenforms (Michael R Lissack)Eigenforms, Coherence, and the Imaginal (Arthur M Collings)Conserving the Disposition for Wonder (Kathleen Forsythe)Author's Response: Distinction, Eigenform and the Epistemology of the Imagination (Louis H Kauffman)Cybernetic Foundations for Psychology (Bernard Scott)Wielding the Cybernetic Scythe in the Blunting Undergrowth of Psychological Confusion (Vincent Kenny)To What Extent Can Second-Order Cybernetics Be a Foundation for Psychology? (Marcelo Arnold-Cathalifaud & Daniela Thumala-Dockendorff)The Importance — and the Difficulty — of Moving Beyond Linear Causality (Robert J Martin)Obstacles to Cybernetics Becoming a Conceptual Framework and Metanarrative in the Psychologies (Philip Baron)The Social and the Psychological: Conceptual Cybernetic Unification vs Disciplinary Analysis? (Eva Buchinger)Second Thoughts on Cybernetic Unifications (Tilia Stingl de Vasconcelos Guedes)Cybernetics and Synergetics as Foundations for Complex Approach Towards Complexities of Life (Lea Šugman Bohinc)Author's Response: On Becoming and Being a Cybernetician (Bernard Scott)Consciousness as Self-Description in Differences (Diana Gasparyan)On the Too Often Overlooked Complexity of the Tension between Subject and Object (Yochai Ataria)Where Is Consciousness? (Urban Kordeš)Theorizing Agents: Their Games, Hermeneutical Tools and Epistemic Resources (Konstantin Pavlov-Pinus)How

Geometry Language And Strategy

Author : Gerald H Thomas
ISBN : 9789814719940
Genre : Mathematics
File Size : 32. 22 MB
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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 consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the Prisoner's Dilemma, which extends the resonant behavior of Vol. 1 to more general time-dependent and transient behaviors.

Explorations In Topology

Author : David Gay
ISBN : 9780124166400
Genre : Mathematics
File Size : 75. 37 MB
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Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

The Roots Of Consciousness

Author : Jeffrey Mishlove
ISBN : 1569247471
Genre : Body, Mind & Spirit
File Size : 57. 56 MB
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Attempts to unify a variety of supernatural phenomena with leading physicists' understandings of the universe

Knots And Links

Author : Dale Rolfsen
ISBN : 9780821834367
Genre : Mathematics
File Size : 61. 44 MB
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Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book"".

Novikov Conjectures Index Theorems And Rigidity Volume 1

Author : Steven C. Ferry
ISBN : 0521497965
Genre : Mathematics
File Size : 38. 93 MB
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The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes give a snapshot of the status of work on the Novikov conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, and analysis. Volume 1 contains a detailed historical survey and bibliography of the Novikov conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg. Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area.

The Quantization Of Gravity

Author : Claus Gerhardt
ISBN : 9783319773711
Genre : Science
File Size : 57. 53 MB
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​A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.

Physics And Number Theory

Author : Louise Nyssen
ISBN : 9783037190289
Genre : Mathematics
File Size : 88. 28 MB
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