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.

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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.