Mereon Matrix The Everything Connected Through K Nothing

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 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.

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.

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.

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.

It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled 'Knots, Braids and Moebius Strips,' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.

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.