The Mereon Matrix

Everything Connected through (K)nothing

Jytte Brender McNair, Lynnclaire Dennis, Louis H Kauffman

• Publisher: WSPC
• Year: 2018
• ISBN:
  9789813233577
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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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:

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• 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, L Dennis and Z Tümer)
  • A Unifying Theory of Biological Evolution (J Brender McNair)
  • Epilogue: Divine Architecture & the Art of Becoming Human (L Dennis)
• Reference Material:
  • Definition of Key Concepts (L Dennis and J Brender McNair)
  • The Emergent Science of Cymatics (J S Reid)
  • Bibliography

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--> Readership: Researchers in knot theory, geometry and systems theory. -->
Keywords:Knot Theory;Jitterbugs;Mereon Matrix;Platonic Solids;Kepler Solids;Topology;Dynamics;Pre-Life-Evolution;Biological Evolution;Genetics;Cymatics;Template Information Model;Information Modelling;System Theory;Classroom Management Model Review: Key Features:

• It elaborates on several important aspects of General Systems Theory including nonlinearity
• Offers a new way of modelling that can be applied across the sciences. For instance, it has been applied to explain pre-life evolution from the Big Bang, and it enabled a unification of all theories on biological evolution from Lamarck and Darwin till today
• Each chapter is self-contained and explained relative to Mereon. Throughout, it provides references to scientific findings that are congruent with or expanded by Mereon; no contradicting evidence has been found

Part 1

First Things First

Chapter 1

Building on the Known: a QuintEssential Jitterbug

L. Dennis^a), J. Brender McNair^b), N. J. Woolf^c), P. McNair^d) and L. H. Kauffman^e)

a)Director, The Mereon Legacy, CIC, Herefordshire, United Kingdom

b)Emeritus Assoc. Professor, Dept. of Health Science and Technology, Aalborg University, Aalborg, Denmark

c)Emeritus Professor of Astronomy, Steward Observatory, LAPLACE, University of Arizona, Tucson, AZ, USA

d)Retired director of the Medical Genetics Laboratory, Kennedycenter, Glostrup, Denmark; and Director, The Mereon Legacy, CIC, Herefordshire, United Kingdom

e)Professor of Mathematics, Dept. of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, IL, USA

Abstract: This chapter presents the First Principles with supportive assertions. First Principles are a translation of the fundamental laws and present a schematic that can be used to build or rebuild a sustainable system of any kind. These principles were determined by abstracting rules from the dynamics of discrete forms that shape the process, the simple and complex symmetries that mechanistically inform all functions. First Principles define seven sequential functions, each transform resources into an emergent property that is essential for the next function. The dynamics of the Mereon Matrix are shown to be applicable to sustainable systems of any kind as its fractal nature enables one to deal with immense complexity over time.

Keywords: Asymmetry; definition of key concepts; dynamics; emergent property; First Principle; function; geometry; geosphere; Jitterbug; Mereon; pattern; symmetry; time

1.1Essentials Regarding the Mereon Matrix

Almost two decades of working to identify the fundamentals of the Mereon Matrix has led to our current state of understanding. The dynamic of this geometric model is a pure mathematical structure that allows for the construction of a simple, quantitative and qualitative approach to any system. Repeatedly, the investigative process has led to a new understanding of the Mereon Matrix as a universal model that is applicable to systems in general, and to ourselves as a team and individuals in particular.

Figure 1.1. The Mereon Matrix Polyhedral Mix and Mereon Trefoil(s).

In Figure 1.1 a) and b), you see the primary geostructures that make up the Mereon Matrix. The outermost edges in Figure 1.1a reveal the ‘context’; a polyhedron that oscillates between 120 and 180 faces (therefore named Mereon120/180, or its shorter name: Context). Both phases present three types of vertices. The centre image shows the core, a geosphere that oscillates between 144 and 300 faces (therefore named Tau144/300, or its shorter name: Core) and has four types of vertices. These illustrations provide a sense of the embedded nature of the Matrix and the relationship and scale between these forms. In Figure 1.1c, the Context is represented with faint dotted lines and shows two of the five chiral Mereon Trefoil Knots that are defined by the vertex-to-vertex dynamics of the Matrix.

For years the Mereon Trefoil’s energetic ligature has invoked strong responses from children. In the same way, the geometry has resonated as ‘familiar’ with many adults. The knotted path is generated by the interaction of the two embedded geospheroids; its dynamic is a ‘dance’ that many are well acquainted with; the ‘Jitterbug’ made famous by R. Buckminster Fuller.

Figure 1.2. The Mereon Matrix as defined by Jitterbugs and the VE.

A set of twelve vectors in space is defined by a centre and the vertices of a Cubeoctahedron that Fuller called the Vector Equilibrium that will hereafter be referred to as the ‘VE’. The Jitterbug is a spatial configuration whereby the length of the polyhedral edges is equal to the radial distance from its centre of gravity to any vertex. Fuller built a moveable stick model to demonstrate how the twelve vertices of the VE move symmetrically. A Cuboctahedron is smoothly transformed into a regular Octahedron with an Icosahedron appearing in the intermediate space during the process. While it may seem convoluted, animations will be presented to demonstrate how this is actually a complexly simple unifying motion between the octahedral and icosahedral symmetries; see Figure 1.2.

While difficult to see in grayscale, Figure 1.3 demonstrates the Mereon Trefoil’s relationship to the VE. It forms ‘arcs’, each made from four line segments. In Chapters 8 and 9, it will become clear how this pattern appears by tracing the movement between all polyhedra within the Matrix.

Figure 1.3. The Mereon Trefoil and the VE.

The Mereon Matrix is novel in the following respects:

(1)It is a complex, active and sustainable system that is descriptive of self-organisation and propagation. We should remark that for years for one of us (Dennis) the Mereon Matrix has been an on-going dynamic internal visualisation. However, while the Mereon Matrix has long ‘existed’ in the realm of mathematics, it is now cymatically observable and thus, transcends the purview of ‘conceptual’.

(2)It is an inter-connected geospherical system that is comprised of unique embedded geospheroids, whose dynamics define chiral knots.

(3)Its external structure is a 120/180 faceted polyhedron (Mereon 120/180, also called the Context) comprised of three-, four- and five-fold symmetry: i) The three-fold symmetry defines the quantity and type of resources that a system can receive from its environment in order to initiate materialisation; ii) The four-fold symmetry in the Mereon Matrix is stable and remains closed; it determines that the system and its resources are stabilised and able to undergo transformation in time and space, and internally and externally; and iii) The five-fold symmetry regulates how the Matrix sustains itself through the regeneration of progeny as it contributes potential new systems or products to its environment.

(4)The Context unites all forms; determines the Matrix’s maximal contraction.

(5)The core of the Mereon Matrix is a 144 faceted polyhedron that is called the Tau 144/300 (or simply the Core) due to how its dynamics transform it into a 300 faced geosphere; ‘Tau’ means 300 in Greek. Like the Context, it also unites the Platonic and Kepler solids.

(6)The symmetry of the Context and the Core generate an infinitely repeating asymmetrical pattern that has perfect symmetry.

(7)This unitive patterning is an energetic vertex-to-vertex language.

(8)The Mereon Trefoil is a spherical torus; a 2,3 expression of the Trefoil Knot.

(9)The dynamics in the Context define five interconnected, independent and non-interfering Jitterbugs, four rotated with respect to the first. The critical connection is identified in the reciprocity between the structure of a Cube and an Octahedron as defined by their vertex-to-face centre relationship. The general dynamics relative to the Matrix will hereafter be referred to such as the “QEJ”, a Quint-Essential Jitterbug.

(10)Dynamics in the Core define six Jitterbugs; they too are interconnected, independent and non-interfering with five rotated with respect to the first.

(11)All measures, integers, points, planes, 3D structures and dynamics in the Mereon geometry are rooted in and connected by the Golden Ratio

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(12)The dynamics of Input, Throughput, and Output mimic the biological features of birthing and reproduction.

Albert Einstein said,

“The most incomprehensible thing about our universe is that it is comprehensible.”

By engaging cognition and intuition, the logic inherent in the Mereon Matrix illuminates possibilities that may lead to new levels of scientific comprehension. However, harnessing such possibilities requires understanding the first radical fundamental that this Matrix demonstrates: unity is found within diversity and requires multiple perspectives.

In this, the Mereon Matrix presents a panoply of questions that are waiting to be explored by natural and social scientists. Two animations will help provide a sense of the nature and characteristics of the Mereon Matrix:

Animation 1: Into the Matrix, see
http://www.worldscientific.com/worldscibooks/10.1142/10805#t=suppl

Animation 2: Into the Simplicity of the Mereon Matrix, see
http://www.worldscientific.com/worldscibooks/10.1142/10805#t=suppl

1.1.1Definition of Key Concepts

In making assessments and assertions regarding what we think we know about Mereon and applying the principles of this structure to both living and life-like systems, our learning was constant and the relearning curve was often steep. In this articulation, we feel we have sharpened Occam’s razor, see an account of this concept in [Bauer, 2007 (p. 155)], through finding and eventually agreeing on simple, logical and meaningful terms that both support and extend our understanding. Finding single terms or short phrases that could be understood across multiple domains was our primary goal, and a constant challenge. While we feel we have achieved a measure of success in our quest for trans-disciplinary interpretations and correlations, we ask the reader to bear in mind that neither words nor ideas are or ought to be dogmatised.

While we postulate Mereon to be a unitive model of form and functionality, it absolutely requires personal, interpersonal, professional and cultural distinctions when it comes to defining a knowledge domain, determining choices and articulating tasks. As inclusive, it transcends traditional ‘norms’ and ‘standards’, uniting the extremes at either end of the spectrum ‘abnormal’ or ‘untouchable’, or ‘superior’ or ‘miraculous’.

To minimise misunderstanding and misinterpretation, see Appendix A ‘Definition of Key Concepts’ in Part 4. Understanding that many words mean different things to different people and professions, this table is a list of words and their meaning as they relate to the Mereon Matrix. Particular terminology is used when our meaning deviates from a term that is well-recognised and has a common understanding. We have also invented specific words relating to the Mereon Matrix, the reason for doing so will become obvious both in context and when referring to the list.

For the same reasons, we intentionally chose not to use certain words, particularly as they apply to the dynamics in human relationship:

‘Collaborate’, ‘collaboration’ or ‘collaborative’: while often used as positive descriptors within organisations and their endeavours, the inappropriate use of these words has carved a deep negative imprint into the human psyche in many cultures and countries around the world. For this reason, we omit it from our languaging.

‘Consensus’: decisions within a socio-relational system founded on principles of the Mereon Matrix are based on prior understanding and agreement, unity found in shared values and a mutual vision. The organisation’s raison d’être is set, and then diverse and discrete functional decisions become the responsibility of those with the demonstrated competence to act and will be held responsible. This is the core of conscious cooperation.

‘Now’: you may be surprised to learn we have avoided this word in order to remain ‘current’ and in the flow, especially as we talk about temporal and spatial modelling. Raise your right index finger in the air and point to the elusive ‘now’. Yes. You’re it. It is not so radical a perspective as it may sound because as far as Time is concerned, the instant you whisper ‘now’ it is already long gone.

‘Never’ or ‘always’: from any perspective in the Mereon Matrix, when these terms are applied to human action and interaction, they are fundamentally devoid of logic.

Repeatedly, we are reminded how genuine understanding is found in a mutual context: a space in which words are relationally expressed. Even in best case circumstances, what we think we have stated clearly is subject to misinterpretation because others may define what we say by their past experiences; the time of day; the state of their emotions; and other contextual conditions. For these reasons, we have attempted to refrain from using slang and jargon while taking care to avoid our own assumptions as well.

1.1.2“Q²M²”: Quantitatively Measurable and Qualitative Meaningful

The First Principles underscoring the Mereon Matrix provide a systematic template to approach natural and social science. We find that this new model can be used to explore life functions and even redefine ‘quality of life’.

As such, it requires you to define the primacy of your life based on meaning rather than lifestyle. The Matrix provides a framework that helps articulate and activate pragmatic strategies; it enhances clear communication that is the foundation essential for all tactical and operational imperatives.

Without the union of logic, quantitative and qualitative measurement, the critical connections that insure stability, order, coordination and coherence are at risk, and a system is subject to breakdown. The process inherent in the Matrix occurs in Nature and through intentional implementation in a social endeavour can foster stability and harmony. Application of the Matrix has demonstrated to increase the probability of producing potential that is measurable, significant and sustainable....

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Contents
• Dedication
• Preface to the First Edition
• Preface to the Second Edition
• Introduction
• Prelude
• Prologue
• The Authors’ Shared History
• Part 1 First Things First
• Part 2 Including and Beyond the Point
• Part 3 Connections, Ligatures and Knots
• Part 4 Applying Mereon to Knowledge Domains
• Appendix A Definition of Key Concepts
• Appendix B The Emergent Science of Cymatics
• Bibliography
• Index