Narrow Results

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 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.

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.

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.

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.