This model represents another of the important concepts underlying Synergetics; the relationship of the various members of the Cosmic Hierarchy.
Here we are showing the relationship between the tetrahedron and the vector equilibrium. As the faces of the tetrahedron collapse (we’ll discuss why in a bit), the stable tetrahedron transforms into the VE. This process occurs continuously in a positive and negative fluctuation which generates all sorts of frequency and wave conditions as we will see. For now we are just investigating the basics.
Keep in mind that the tetrahedron represents the minimum structure in Universe. 4 vertices, 6 edges and 4 faces, an inside and an outside. We will also show in later posts how the tetrahedron is an excellent model for the photon which has been particularly enigmatic in the hands of traditional physicists. It acts like a wave or a particle, very predictably, depending on how you look at it. We can demonstrate why it can act as both and also, in the process give a workable model of quantum mechanics which any 12 yr old high school student with an interest in science may easily grasp.
Here we have one of the most important figures in Synergetics; the Vector Equilibrium. [FULL AMIMATION]
It’s based on the closest packing of twelve unit radius spheres around a nuclear sphere. The vectors (lines connecting the centers of the spheres} are all of equal length. The figure is not stable and represents a “Zero State,” a phase which is passed through but never paused at. Because of this, this figure is rarely seen in nature.
For now, I just want you to see how this figure is derived because it is the basis of much of what we are doing here.
Here we have a little closer look at what is a common occurrence in nature. As we have stated previously a cube is inherently unstable. It requires triangulation for stability. From the Syergetic POV what is happening is that 2 tetrahedra tend to combine to form the cube. Once we provide the necessary triangulation with the two tetrahedra the external vertices form the cube. If we consider the edges of the tetrahedron as unit length (2), then the edge of the cube becomes the square root of 2, an irrational number!
Now consider this; all of the geometric shapes you have seen here are related to each other by simple integer multiples, except the cube. The cube is related to the other figures through an irrational number. And, here’s the point; our entire system of mensuration is based on that single unit, square edge, x,y,z coordinate system. So every time we do any measuring of virtually any physical quantity we require compromises like “rounding off” which leave miniscule left over amounts unaccounted for. How does a soap-bubble round off and what does it do with the leftover?
Next we’ll see why a 60 degree, 4 dimensional system can help us avoid some major pitfalls.
This is a model of what Fuller titled “Cosmic Hierarchy for Omniinterrationally-phased, Nuclear-centered, Convergently-divergently Intertransformable Systems.” We’ll get into the details as we progress. For now we’ll just take a look at it. [FULL ANIMATION]
It could be that this model embodies the soul of Synergetics. Could these 6 geometric figures comprise the entire structural system of our Universe? Fuller seemed to think so. Think of the hologram. As these figures nest and recombine they follow the same rules of geometry at every level and repeat every 6 levels. I think this system can be used to model anything in a way much closer to the way nature does.
Now, in many areas Fuller went into much greater detail as to how these figures can be subdivided and rearranged to explain many physical phenomena. I’ll leave that to others. I am going to try to use my own models to illustrate as many physical principles as I can, as they occur to me.