Adex Theory

"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.

' 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. Contents:IntroductionThe Octahedral GroupThe Octahedral Double GroupThe McKay CorrespondenceLie Groups and Lie AlgebrasCoxeter''s Reflection GroupsThom–Arnold Catastrophe StructuresALE Spaces and Gravitational InstantonsKnots and Links and BraidsTwistors and ALE SpacesTwo-Dimensional Conformal Field TheoriesElliptic Curves and the Monster GroupSphere Packing and Error-Correcting CodesQubits and Black HolesThe Holographic PrincipleCalabi–Yau Spaces and Mirror SymmetryHeisenberg AlgebrasSummary and OutlookBibliographyGlossaryIndex Readership: Researchers in mathematical physics. Keywords:ADE Graphs;ADE Groups;ADE Lattices;ADE Lie Algebras;ADE Singularities;ADE Catastrophes'

In this richly illustrated book, Dr Jorma Kyppö explores the history of board games dating back to Ancient Egypt, Mesopotamia, India and China. He provides a description of the evolution and various interpretations of chess. Furthermore, the book offers the study of the old Celtic and Viking board games and the old Hawaiian board game Konane, as well as a new hypothesis about the interpretation of the famous Cretan Phaistos Disk. Descriptions of several chess variations, including some highlights of the game theory and tiling in different dimensions, are followed by a multidimensional symmetrical n-person strategy game model, based on chess. Final chapter (Concluding remarks) offers the new generalizations of the Euler-Poincare's Characteristic, Pi and Fibonacci sequence.

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.

Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter famillies of diagrams and which are invariant under 'higher' Reidemeister moves. Luckily, knots in 3-space, often called classical knots, can be transformed into knots in the solid torus without loss of information. It turns out that knots in the solid torus have a particular rich topological moduli space. It contains many 'canonical' loops to which the invariants for one parameter families can be applied, in order to get a new sort of invariants for classical knots.

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,

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

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.