The Mereon Matrix

The following sections are included:

• Dedication
• In Memory of
• Acknowledgements
• Preface to the First Edition
• Preface to the Second Edition
• Introduction
• Prelude
• Prologue
• The Authors’ Shared History
• Contents

Part I begins by presenting the fundamentals of the Mereon Matrix; it offers a new perspective on dynamic, whole and sustainable systems, and continues to inform the reader by communicating the basics necessary to understand the rest of the book. Included is the educational application that is in operation.

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.

This chapter presents two topics related to the application of the Mereon Matrix and interpretation of observations:

• A revealing demonstration of how the Mereon Matrix resolves paradox, exposing how difference can be a reflection of perspective, and
• A methodology for application, the Mereon Matrix used as a template for information modelling within a knowledge domain.

Presented as an inclusive model, readers are shown how well-known modelling techniques may be applied to support the application efforts. Included is the usage of strategic (S), tactical (T) and operational (O) elements that are related to planning and action, as employed in military decision-making and a quality management approach to an organisation.

This chapter provides glimpses of the historical, cultural and scientific elements that serve as the philosophical and scientific foundation for exploring and interpreting the Mereon Matrix, in particular the Mereon Trefoil. Numbers, symbols and forms found in natural systems were investigated relative to how they have been employed throughout history to communicate or encapsulate knowledge, helping to form or dismantle social systems. This review ranges from Galilei to Hawkins, linking Euler to Fibonacci and Φ. It reveals overlaps in philosophy and form, connecting astrology to cymatics and linking a 70,000-year-old stone carved in geometry to the architectural rule of Sullivan’s Law. The Mereon Matrix offers a new perspective on completeness and sustainability, and therefore, a call is made for transdisciplinary investigations to improve how humans use the resources that our universe provides and how we must expand our ability to preserve them.

Education is how lifelong progress is achieved through learning, unlearning and relearning. This chapter summarises the pilot of a social application based on the Mereon Matrix, and closes with an addendum that updates the original social application based on the Mereon Matrix. BELONGING was designed to rebuild the hearts and minds of teachers, strengthening their relationships with administrations, parents and learners. It provides a tool for addressing classroom management that was intentionally developed to fully support, yet operate independent of the curriculum. The results of this programme, implemented in an Italian school district since 2004, exceed what one might have dared to dream: BELONGING builds authenticity, develops character, and nurtures relationship skills, all of which are essential to learning and learning to lead. In a world driven by competition, separating winners from losers, BELONGING reveals connections and grows cooperation and empathy. This project indicates how authenticity, responsibility and accountability foster survival. It makes it clear why competent, creative, freethinking individuals who work together in a cooperative endeavour, strengthen stability to increase the possibility that a system can transcend survival. In 2017, the BELONGING brand was established and updated; design betas took place in the US and Indonesia; and global marketing efforts are underway in the fall of 2017.

This chapter initiates the study of the basic details of the Mereon Matrix. Starting with Euler, links are made to the connections between unique and diverse forms. The Mereon Matrix lifts planar geometry into harmonious and elegant three-dimensional geospheres and reveals that a cluster of complex forms function with clockwork precision. It is shown how the regular Platonic and Kepler solids dynamically fit together in a vertex-to-vertex configuration; similarly, vertex-to-edge connections and ‘dual’ relationship between one form and another are studied for the solids appearing in the Mereon Matrix. In conclusion, a simple link to personal transition and social transformation is revealed.

Part 2 presents the details of the Mereon Matrix’s dynamic geometry, and points out the links to physical, psychological and sociological systems.

Chapter 6 lays out the complex details of the Matrix’s outermost polyhedron, a geosphere that iterates between 120 and 180 faces as it opens and closes, expands and contracts. Image intense, it reveals how localised environmental energy is received and processed to produce new systems and/or product, and place it into a global environment.

This chapter reveals the depth of the transformational nature inherent in the Mereon Matrix showing how clusters and singles of polyhedra, 33 unified forms, scale to infinity, internally and externally. This chapter suggests significant physical, psychological and sociological implications inherent in the structure and dynamics of the Matrix’s outermost polyhedron. Referred to as the Context, this geosphere iterates between 120 and 180 faces as it opens and closes, expands and contracts. Image intense, it is revealed how localised environmental energy is required, received and processed to eventually produce new systems and/or product that expands the global environment.

Chapter 7 covers the connections between the Mereon Matrix and the work of R. Buckminster Fuller and Ron Resch are explored in detail, deepening the knowledge found in the Context. The Context’s dynamics defines five “Jitterbugs’, a process described by Fuller. The concept of scalability is expanded to include horizontal and vertical, inside and outside, up and down; it is shown how these characterisations are essential for application in natural and social systems. Fuller’s impact on the world is realised today through his ongoing influence on engineering, design, architecture, science and the arts; the foundation he laid is used to those committed to creating sustainable systems. Authors suggest that in many ways this work rests on Fuller’s foundation and evolves it, that applying the Mereon Matrix will catalyse further positive change, stable and long-lasting benefits. Evidence is also presented to demonstrate comparisons between the Context and the 120 Cell Dodecaplex.

This chapter reveals how a core geosphere known as the Tau144/300 forms within the Context. Referred to as the Core, it is shown how a complex aggregation of points form edges and meet to give rise to three-dimensional interacting elements. Image intense, this chapter demonstrates how the Context and Core of the Matrix synchronise and sequentially harmonise discrete forms. The Core is also revealed to dynamically unify all forms, and generate a cluster of six Jitterbugs as compared to the five found in the Context. The relationship of the Core’s architecture, a dynamic, face-centred crystalline lattice, is explored with connections found in common with the atomic nucleus, quantum mechanics, diamonds, Earth’s planetary core and cell biology.

Part 3 presents the Mereon Matrix’s knot that is known as the Mereon Trefoil.

Chapter 9 addresses basic topological issues as they relate to the Mereon Trefoil in particular and the Mereon geometry in general. The non-alternating ligature tied by the Matrix is shown to be topologically equivalent to a 2,3 torus knot (with a three-crossing diagram) but the Mereon version of this knot is a higher energy version of the alternating weave of the 2,3 trefoil knot and a direct relative of the 3,2 version of the same knot. Associations are made to the pentagon, Petersen graph, the Chinese mythology of the Five Elements and Fourier knots, and the Mereon Trefoil is shown to be formed by double helices. Connections are established between the pattern of DNA recombination, Spencer Brown’s ‘Laws of form’ and Shea Zellweger’s Logical Garnet. The theory regarding the shape of the Universe as Dodecahedral is linked with how such a construction can arise from the trefoil knot as the unfolding of a five-fold symmetry. Making such a simple knot would generate a ‘cosmic loop’ around the universe, and make knot theory universally applicable.

Chapter 9 addresses the foundational issues as they relate to the topological distinctions found in the Mereon Trefoil in particular and the Mereon geometry in general. Kauffman presents how the non-standard version of the trefoil knot seen tied by tracing the arcing angles of the Matrix is a higher energy version of the alternating weave of the 3,2 trefoil knot. Geospherical in nature, links are made to the pentagon, Petersen graph, the Five Elements. So too, connections are made to Fourier knots, and how the Mereon Trefoil form by connecting double helices. Connections are established between the pattern of DNA recombination, Spencer-Brown’s ‘Laws of Form’, and Shea Zellweger’s Logical Garnet. The assertion that the shape of the universe is dodecahedral is linked with how its construction might arise from the trefoil knot as the unfolding of a five-fold symmetry. It is presented how this would make the Mereon knot a complex but simple ‘cosmic loop’ around the whole universe, thus making knot theory universally applicable.

Creating direct and dramatic visual use of the Mereon Trefoil as time and a knotted fold in space-time, the dynamics are imagined as geometric lines of force that turn the Mereon Matrix inside out. It is shown that Mereon’s toroidal dynamics are reflected in nature’s patterns and human social patterning. This chapter presents how the Matrix’s 33 planar ‘landshapes’, similar to Russian dolls, imprint the knot with particular symmetries that define the Mereon Trefoil as a knotted ‘timeshape’, all aspects time and space connected to and embedded with prior ‘time-slices’. Chirality is shown to be implicit in the knot, and us revealed to have a fundamental relationship with the smallest 3D polyhedra, two types of tetrahedron. The Mereon Trefoil is demonstrated equal to a minimal Enneper surface; all polyhedra are shown to ‘tie’ the knot, and like the geometry, the topology scales to infinity.

Part 4 presents a total of four applied science investigations on the Mereon Matrix. This includes three applications of the Mereon Matrix as a template information model and the outcome of pilot application of the CymaScope technology described in Appendix B.

By means of frequencies derived from the mathematics of the Mereon Matrix, the CymaScope (a sonic visualising technology presented in Appendix B) was used to make the matrix visible in the predicted medium, water (see the Preface to the First Edition). It revealed minute details of the complex structure and the dynamics of Mereon Matrix. This chapter summarises a series of related investigations made using the CymaScope. This technology revealed how the difference of only 1/100th of a hertz makes a remarkable distinction; cymatic images of living matter are shown to display the Mereon symmetry, expanding our understanding and increasing our ability to consider how this vibratory pattern relates to how everything is connected.

This chapter turns the idea that life evolves from life on its head and reveals that life evolved from non-living processes. Using the Mereon Matrix as an information template of functional operations, authors present a new perspective on how it re-answers some of the old questions in the search for the origin of matter. It explores possible beginnings and how transformation over time led to the development of life-forms. Charting how the Matrix’s sequential functions fit the functional aspects that gave rise to life, authors address the emergence of membranes, proteins and RNA from the development of simple monomers to complex polymers with each other and their role in the origin and evolution of life forms. They assert why metabolism and reproduction are not the distinctive aspects of life but are rather the means for utilising them.

The team’s initial hypothesis states that the Mereon Matrix’s First Principles constitute a unitive template generally applicable as an information model. For verification of this premise, the knowledge domain of human molecular genetics was used in a study called ATCG. The Matrix’s seven functions and its fractal principle were applied using the latest (at the point of writing, i.e. up to the beginning of the year 2013) original scientific literature as the source of domain information. ATCG was elaborated through all seven functions with each further explored through its level of micro-functions. The Mereon Matrix was extremely useful in modelling as it constantly forced authors to pose specific questions with respect to the topics inherent at different micro-functions. This allowed searching for answers in the literature using an iterative and incremental modelling process. Upon completing the project it was concluded that the Mereon Matrix as a template for modelling human molecular genetics met and exceeded what was anticipated.

This chapter is an extract of the model on biological evolution reported in the book [Brender McNair, 2016a]. The focus here is on presenting the Mereon-related aspects of the outcome rather than the book’s details of a variety of theories on biological evolution, from Darwin and Lamarck till today. The most important outcome of the study is how the Mereon Matrix’s template information model solved decades of combat between seemingly antagonistic theories on evolution; it demonstrates that and how all the evolutionary theories are independent, cooperative theories.

In conclusion of the study as a whole, it seems plausible that the template information model of the Mereon Matrix might be the General System Theory that von Bertalanffy called for.

This chapter closes the book with a personal perspective that addresses issues directly related to the sentiments of cultural anthropologist Margaret Mead who said, “If we are to achieve a richer culture, rich in contrasting values, we must recognise the whole gamut of human potentialities, and so weave a less arbitrary social fabric, one in which each diverse human gift will find a fitting place.”

Like a handwoven tapestry, it is hoped that you will find inspiration, beauty, and wisdom woven through these words and images. We acknowledge they are formed by human hands, meaning there will be imperfections as well. Using the Mereon Matrix as the loom, these strands are ideas that when woven together reveal connections that let you think about how conscience arises, and leads to the blossoming of conscious awareness. A perspective is presented regarding why only in the presence of coherence and human willingness to act does that which we consider ‘Divine’ willingly participate in the work of regeneration. This chapter’s design uses the natural scaling of the golden ratio to further define the relationship between a system’s ‘invironment’, and its local and global environments, its micro and macro field of ‘Consciousness’.

Like our understanding of everything, including the Mereon Matrix, these thoughts are subject to time and these ideas will most surely evolve.

The following sections are included:

• Appendix A Definition of Key Concepts
• Appendix B The Emergent Science of Cymatics
  • The History of Cymatics
    • Sound in the Early Universe
    • Cymatic Seeds
  • Experimental Sound Imaging Instrument
    • Water Membranes – Imaging Sound in ‘Quasi-3D’
    • CymaScopic Equivalent to “GIGO: Garbage In, Garbage Out”
  • Imaging Unifying Frequencies
    • Glimpse of a Trefoil Knot
    • Imaging the Schumann Cavity Resonance
• Bibliography
• Index