We are beginning to see, and to draw clearer images of what this most basic of systems; consisting of only rational numbers and angles; vectors, indicating only mass times volume, can show. Here we are demonstrating the relationship of closest packed spheres with the 60 deg Synergetics coordinate system we are espousing.
A sphere is defined as the locus of all points equidistant for given point. Unfortunately, science has never demonstrated a perfect sphere. Any object we have that looks like a sphere is at best an approximation. A steel ball bearing when viewed under a scanning electron microscope displays massive imperfections. A better example may be our own planet Earth. We can see mountains (up to 5000 ft high) and undersea trenches( up to 3000 ft deep) but if we were to see the Earth as the size of a billiard ball it would appear to be as smooth as that billiard ball. A true sphere exists only as a metaphysical principle. It is timeless, sizeless and exists irrespective of who, or indeed if, anyone conceives of it. So what is the real sphere? We see approximations of spheres throughout nature and the Universe, it appears to be the very basic shape of nature. As light and energy radiate out, the shape generated is a sphere. Stars, planets and atomic particles most often appear spherical and as these spheres interact they follow the rules of closest packing of spheres which is exactly what Synergetics is based on. Now, these spheres vary greatly in scale but most atoms are similar enough in size, as are many planets, to be able to interact in a very structured pattern which varies significantly as these scales vary. In Synergetics we choose to model these interactions and disclose these rules based on the metaphysical concept that these spheres are all of unit radius, a state which rarely exists in nature but allows us to determine these universal rules while also allowing for the huge variations we see in nature.
So, rather than seeing lines and areas extending to an inconceivable infinity we should try to realize that nature uses this spherical closest packing as the basis of all of her mathematics and that these spheres tend to vary from certain minimum/maximum limits in a vibratory dance never pausing at a zero state which we see as a metaphysical concept which remains timeless and sizeless. Still with me? Good, it gets better.