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Ideas In Practice

When you put an idea into practice in a place-time context, things get complicated. Bucky likes the example of drawing a triangle on the ground (on the earth). When we draw a triangle on any surface, it divides the surface into two triangles, one on the inside of the triangle and the other on the outside of the triangle. And because the triangles are on a surface,  the dirt triangles are concave and the air triangles are convex .

Bucky describes the tetrahedron with 4 sides as the minimum structural system that you can point to. In other words, any thing in a place-time context must have at least 4 sides. If you cut a triangle out of a piece of paper, it has 3 very thin edges. plus 2 sides of the paper, so it is really just a very thin wedge with 5 sides. And of course a cube is even more complicated with 6 sides. And sphere is at least 12 sides.

Fourness

This implies we need to look for fourness when describing anything real. What about "the three pillars of ..." which uses the analogy of a three legged stool, the simplest stable platform you can stand on. Without the seat (or roof) the three pillars or legs would be very unstable. That fourth component is vital for the integrity of the system.

In the standard 3 dimensional Cartesion coordinate system, one point is at the origin, and x,y,z are vectors at right angles to each other in relation to the origin point. Bucky says in Synergetics [527.703], ...people speak of length, breadth, and height as constituting a hierarchy of three independent dimensional states—"one-dimensional," "two-dimensional," and "three-dimensional"—which can be conjoined like building blocks. But length, breadth, and height simply do not exist independently of one another... 

The Universe is Four Dimensional

If we add a 5th point in the centre of a regular tetrahedron as the origin of a 4 dimensional Quadray coordinate system, then the 4 vertex points mark the ends of four vectors at 60 degrees to eachother in relation to the origin. 5 points can define a tetrahedron in place-time which is 4 dimensional.

Bucky says [527.712], All conceptual consideration is inherently four-dimensional. Thus the primitive is a priori four-dimensional, being always comprised of the four planes of reference of the tetrahedron. There can never be any less than four primitive dimensions.

Check out Ask Bucky, the world’s first and most powerful AI dedicated to making the world work for 100 % of humanity in the shortest possible time.

A Cycle becomes a Spiral in a Place-Time Context

Take the cycle of the four seasons for example. The seasons repeat every cycle, but that is just an idea. Every season is different from the previous year, so a cycle in a place-time context is really a spiral. As Emmanuel Vaughan-Lee says, And for me, the seasons at their core are an expression of the cyclical nature of reality as it unfolds. And as the cyclical nature of reality unfolds, it unfurls. And it unfurls as a spiral.

Next: Context and Perspective

Metaphor opens our minds to changing perspective AND context. Aristotle said being a master of metaphor is a sign of genius. Perhaps most indigenous teachers would agree.

Emérgéntly as a Fractal

This illustrates how a fractal (repeating pattern) of a triangles with a huge diversity of sizes and angles can create an image of Nature. But it is only two dimensional. Perhaps a three dimensional fractal of tetrahedrons with a huge diversity of sizes and angles could model the structure of Nature — the tetrahedron is the minimum structural system possible:

Nature is a totally efficient, self-regenerating system. If we discover the laws that govern this system and live synergistically within them, sustainability will follow and humankind will be a success.
R. Buckminster Fuller

Two dimensional triangles have no opposite sides or angles. The Emérgéntly triangles fold up into a three dimensional tetrahedron, a triangular based pyramid, which also has no opposite sides or angles. Each face of the tetrahedron shares an edge with every other face, so they are all equally interconnected - equally interdependent. According to Buckminster Fuller, the tetrahedron is the way Nature works. In fact, there is an Emergence Theory that reality is built from tetrahedrons.

Carbon is the basis for all life on Earth and the carbon atom always has four relationships with other atoms (it is tetravalent). Carbon is an extremely abundant element by mass in the universe (after hydrogen, helium, and oxygen) so the repeating pattern of fourness probably pervades the entire universe. Every system exists within a context, except perhaps the universe itself (assuming the multiverse is fictional). 

These tree images were generated with software. The fractal used is a varied dragon curve. See Wikipedia	Hubble-Space-Telescope-Galaxy-Collection. See Wikipedia

Four-Phase Dynamics in Complex Systems

According to a Review in the August 2019 issue of, Ecological Complexity, panarchy (nested adaptive cycles) has been used as a metaphor and conceptual tool for understanding long-term dynamics of change in complex systems like ecosystems and social–ecological systems.

Complex systems like forests, cities, customers or teams follow repeating cycles of four phases

• Exploitaton/Growth
• Conservation/Accumulation
• Release/Collapse
• Reorganization/Renewal

And these cycles happen at many nested scales at once e.g. small patches inside a whole landscape, teams inside a company, etc. Understanding these cycles helps predict when a system is becoming fragile and how it might change after a shock. Resilience depends more on how the system is organized and how parts interact across scales than on any single component — systems can keep working even if individual parts change.

 Forest:
- Growth — young trees rapidly fill open space after a fire.
- Accumulation— mature forest stores lots of biomass and seeds.
- Collapse — a big fire or pest outbreak suddenly clears canopy.
- Renewal— new seedlings and different species colonize, starting a new growth phase.

Action: monitor tree age structure, fuel buildup, and seed sources to detect rising fire risk and guide controlled burns or planting.

Small business:
- Growth — rapid customer and staff expansion.
- Conservation — stable processes, accumulated cash, less innovation.
- Collapse — sudden market change or loss of a key client causes sharp decline.
- Reorganization — pivoting to a new product or restructuring staff, then growing again.

Action: track cash flow, customer churn, and innovation rate to notice fragility and trigger changes earlier.

More:

• Article: Fractal Leadership Just as in a mathematical fractal, the organization as a whole must work on alignment, its departments must work on alignment, its groups must work on alignment, and so on down the chain.
• Article: A System Engineering and Fractal Approach to Leadership Viewing leadership fractally emphasizes how self, team, and organizational leadership are interconnected and interdependent.
• Research:  Fractals of strategic coherence in a successful nonprofit organization Complexity theory and fractal processes help us understand the generation of strategic coherence.
• Research: Fractality in Four Dimensions: A Framework for Understanding Organizations as Fractal Entities The correct level of dimensionality is essential to the aim of building a robust conceptual model. Nevertheless, despite the difference in complexity, fractal processes in human organizations are fundamentally the same as those in the natural world.

Next: Ideas in Practice

When you put an idea into practice in a place-time context, things get complicated. Bucky likes the example of drawing a triangle on the ground (on the earth).

Who Are We?

Yoshimi Brett is a third generation Japanese-American-Kiwi. Jon Brett is a born and bred Kiwi. In 1978 they sailed the Pacific, then lived in Japan and Australia. Fast forward 46 years - they’re now in Tāmaki Makaurau (Auckland) on the whenua (land) where Jon grew up. Together they designed and built a Petal Certified Living Building sanctuary that reflects their life’s work and love of Nature.

In 2000 Yoshimi & Jon birthed TetraMap, a model that explores the nature of behaviour. They authored the book: TetraMap: Develop People and Business the Way Nature Intended. In 2020, their mokopuna (grandchild) Emérgéntly, emerged as a framework and approach to explore the behaviour of systems. Like TetraMap, Emérgéntly is a metaphor of Nature’s Elements reflected on an unfolding tetrahedron. Emérgéntly is developing well, already supporting individuals, teams and communities to listen and learn from Te Taiao (Nature). Reconnecting with her teaches us about gratitude, trust and reciprocity. Yoshimi & Jon strive to facilitate the healing and restoration of our relationships with Te Taiao and with each other. 

Kataraina Pipi (Ngāti Porou, Ngāti Hine) is a mother of two and nanny of four. Kataraina provides skilled evaluation, facilitation, and coaching services. Kataraina has completed the Post-Graduate Diploma in Social Sector Evaluation Research (2009) and is a PhD candidate with Te Whare Wānanga o Awanuiārangi in the field of music and healing. Kataraina has been working in the field of evaluation for over 15 years with extensive experience within whānau, hapū and Iwi kaupapa and contexts, with a focus on health, social services, sexual and intimate partner violence, youth justice, and Māori leadership. Kataraina is a highly sought after facilitator who works with whānau, organisations, businesses, iwi and communities supporting teambuilding, organisational development, iwi development and conflict resolution.