The Greeks were used to building with roughly cubic, stone blocks. They were stable, withstood compression well and were water-resistant, piled up nicely and were generally good for building. This concept was so inculcated in the Greek mind that as the field of mathematics was developing it seemed logical to use this 90°, 3 dimensional system and to see this as axiomatic. Unfortunately, it has an inherent flaw.Rene Descartes who invented the Cartesian coordinate system, and analytic geometry, and the Greeks before him, based all of mathematics on the edge of a cube, the most basic structure in cartesian geometry. The only problem is that a cube is not a stable structure and requires several diagonals to stabilize it. You see, nature doesn’t use this 3 dimensional system but instead uses a 60°, 4 dimensional system based on the closest packing of spheres as we shall demonstrate. This simply means that the diagonal necessary for triangulation becomes an irrational number. Now understand that this means it is a number which cannot be expressed as the ratio of any other two numbers. While this may not seem like much it requires that we do some heavy non-intuitive mathematics to describe many of the phenomena we see everyday. Things like analytical geometry and calculus become requirements if we hope to understand our environment. How does a soap-bubble know when to round off PI? The answer: it doesn’t have to, nature has no need for irrational numbers nor does it require that a tree separate biology from chemistry from physics. Our contention is that nature uses a much simpler accounting system: Synergetics.

Now, since we can’t actually see into atoms we must deduce what is going on by shooting greatly accelerated, high energy particles at atoms and other particles and watch as time after time the so-called particle splits into other smaller particles and energy is released. Then, using the basic generalized principles discovered by Newton, we are trying to put together a Grand Unified Theory which will show us how everything works.

The problem here is that we are taking the wrong approach. We are throwing rocks at an airplane and trying to learn to fly. To further the complications, the only people doing the calculating are using an outmoded mathematical system, rather like using roman numerals on a calculator. In so doing science in the mid-20th century abandoned modelling which was basically impossible. This is what Fuller hoped to bring back to science; the ability to model the Universe. Einstein wished the same thing and was disappointed that the generalized principles he had discovered, very intuitively as a young man, could not be resolved with other aspects of physics especially at the sub-atomic level. Resolution of quantum mechanics (at the micro level) and relativity (at the macro level) has proved elusive. Connections to other fields; biology, chemistry, psychology were not considered relevent, a product of specialization.

Fuller’s approach enables us to model many complex events and systems simply, intuitively and without resorting to calculus, integrals or Pi. There are several additional areas where the Greeks made assumptions such as the choice to consider the surface of the planet flat, at least locally i.e. that there are 360° around any point on a sphere. It is a provably false assumption which we labor under to this day.

So let’s make a few bold points which may appear arguable but have shown to be true time and again.

- Science has never demonstrated a “particle”. Every “indivisible” particle has been split to give off energy and other smaller “particles.”
- Science has never demonstrated a flat surface (or plane), a continuous curve, a sphere. These are all metaphysical concepts which exist only in mind, nature doesn’t use them.
- Nature doesn’t use irrational numbers, doesn’t need them. Anyway how does a soap-bubble know where to round off Pi and what happens to the little bit left over?
- If the Universe started as a “big bang” and is expanding at an accelerating rate, where is the energy coming from? And where is the center.

Since nature doesn’t use squares or cubes, other than as products of triangulation, we are stuck with the following dilemma; when we attempt to model things like areas and curves mathematically we are constantly having to triangulate our dimensions through the hypotenuse which is the triangulation necessary for stabilization of the 90° angle. So if we use the edge of the square or cube as our unit of measure we find that the triangulation required becomes an irrational number.

So everything we find in nature, which we will show uses a 60° 4-dimensional system, must be adjusted using elaborate constants and machinations on all but the most basic calculations of the movement of rocks. Modelability is gone! Stephen Hawking says, “It’s impossible to imagine a 4-dimensional space.” I beg to differ! We exist in a 4-dimensional space, it can be visualized. It is “real” in that it is part of an eternal, timeless integral unity which we as conscious minds divide and sub-divide for an evermore complex layering of detail upon detail, the wellspring of Synergetics doing ever more with less and less. It’s here right before our eyes but you must remove those silly 3D glasses, they’re making you squint.

Why all the morons are still stuck to the 90 degree coordinates?

Why not we have still a softwares and graphs available for 60degree plane and solid angles?

Where is mutually tangent spheres drawing CAD?

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