Synergetics is Fuller's name for the geometry he advanced based on the patterns of energy that he saw in nature.
For him, geometry was a laboratory science with the touch and feel of physical models--not rules out of a textbook. He started with models of the closest packing of spheres. From that basic starting point he derived triangles as the most economical relationship between events.
He did not start with Euclid's lines in the sand or Descartes' cubes and square XYZ-coordinates. Fuller felt that the old classic approaches did not describe the way nature actually behaves. For instance, Euclid's lines were thought to go off to infinity. Fuller says lines are vectors of energy and he rejected the notion that anything physical could be extended indefinitely.
Descartes cubes are unstable forms. For Fuller, the world is built of stable, finite structures. His triangular coordination depends on tetrahedral models. (A tetrahedron is a pyramid with a triangular base.) Four spheres close pack into a stable tetrahedron: good. Eight spheres stack into an unstable cube: bad. His geometry hinges on the tetrahedron, the simplest structural system within insideness and outsideness: he advances it as the most economical way to measure space and to account all physical (and metaphysical!) experience.
This is what he calls synergetics: an empirical mathematical system in which geometry and number mesh without fractions. It gains its validity not from classic abstractions but from the results of individual physical experience. His two-volume work "Synergetics" has the subtitle: Explorations in the Geometry of Thinking.
E.J. Applewhite collaborated on the books Synergetics I and II with Buckminster Fuller. He recommends Kirby Urner's Synergetics on the Web for an excellent graphic introduction to Fuller's synergetic geometry, plus links to other sites describing synergetics--many with gorgeous color graphics.
Bucky missed this one- so close, yet so far. More ironic since he was able to deal with nucleons in the atomic nucleus.
My new model has a symmetrical arrangement of all the s, p, d, and f orbitals, and is able to account not only for traditional periodicity as depicted in the 2-dimensional representation most are familiar with, but it also manages to deal easily with less well-known connections such as secondary periodicity, diagonals, and the knight's mover relation. I'm now looking to see whether it can also take account of Aufbau anomalies in the transition metals, actinoids, and lanthanoids. If it works, then this new model will show that Fuller's tetrahedral emphasis was right on the mark.
Sadly, I came up with this idea originally several years before he died, but was rebuffed by the chemistry community- the current effort began only months ago after I found out that someone else had independently discovered the tetrahedral mapping. Had I known about Fuller's work back then, I might have had the opportunity to meet him. I think he would have loved this.
Jess Tauber
phonosemantics@earthlink.net
Synergetics
by E.J. Applewhite at:
The web site above says:
"Synergetics is Fuller's name for the geometry he advanced based on the patterns of energy that he saw in nature."
But Section 203.09 in Synergetics says:
203.09 A study of the microbiological structures, the radiolaria, will always show that they are based on either the tetrahedron, the octahedron, or the icosahedron. The picture was drawn by English scientists almost a century ago as they looked through microscopes at these micro-sea structures. The development of synergetics did not commence with the study of these structures of nature, seeking to understand their logic. The picture of the radiolaria has been available for 100 years, but I did not happen to see it until I had produced the geodesic structures that derive from the discovery of their fundamental mathematical principles. In other words, I did not copy nature's structural patterns. I did not make arbitrary arrangements for superficial reasons. I began to explore structure and develop it in pure mathematical principle, out of which the patterns emerged in pure principle and developed themselves in pure principle. I then realized those developed structural principles as physical forms and, in due course, applied them to practical tasks. The reappearance of tensegrity structures in scientists' findings at various levels of inquiry confirms the mathematical coordinating system employed by nature. They are pure coincidence__but excitingly valid coincidence.
The web site also says:
"He started with models of the closest packing of spheres. From that basic starting point he derived triangles as the most economical relationship between events."
But Sections 986.082 to 986.085 says:
986.082 I was born cross-eyed on 12 July 1895. Not until I was four-and-a-half years old was it discovered that I was also abnormally farsighted. My vision was thereafter fully corrected with lenses. Until four-and-a-half I could see only large patterns__houses, trees, outlines of people__with blurred coloring. While I saw two dark areas on human faces, I did not see a human eye or a teardrop or a human hair until I was four. Despite my newly gained ability__in 1899__to apprehend details with glasses, my childhood's spontaneous dependence upon only big-pattern clues has persisted. All that I have to do today to reexperience what I saw when I was a child is to take off my glasses, which, with some added magnification for age, have exactly the same lens corrections as those of my first five-year-old pair of spectacles. This helps me to recall vividly my earliest sensations, impressions, and tactical assumptions.
986.083 I was sent to kindergarten before I received my first eyeglasses. The teacher, Miss Parker, had a large supply of wooden toothpicks and semidried peas into which you could easily stick the sharp ends of the toothpicks. The peas served as joints between the toothpicks. She told our kindergarten class to make structures. Because all of the other children had good eyesight, their vision and imagination had been interconditioned to make the children think immediately of copying the rectilinearly framed structures of the houses they saw built or building along the road. To the other children, horizontally or perpendicularly parallel rectilinear forms were structure. So they used their toothpicks and peas to make cubic and other rectilinear models. The semidried peas were strong enough to hold the angles between the stuck-in toothpicks and therefore to make the rectilinear forms hold their shapes__despite the fact that a rectangle has no inherent self-structuring capability.
986.084 In my poor-sighted, feeling-my-way-along manner I found that the triangle__I did not know its name-was the only polygon__I did not know that word either-that would hold its shape strongly and rigidly. So I naturally made structural systems having interiors and exteriors that consisted entirely of triangles. Feeling my way along I made a continuous assembly of octahedra and tetrahedra, a structured complex to which I was much later to give the contracted name "octet truss." (See Sec. 410.06). The teacher was startled and called the other teachers to look at my strange contriving. I did not see Miss Parker again after leaving kindergarten, but three-quarters of a century later, just before she died, she sent word to me by one of her granddaughters that she as yet remembered this event quite vividly.
986.085 Three-quarters of a century later, in 1977, the National Aeronautics and Space Administration (NASA), which eight years earlier had put the first humans on the Moon and returned them safely to our planet Earth, put out bids for a major space-island platform, a controlled-environment structure. NASA's structural specifications called for an "octet truss" __my invented and patented structural name had become common language, although sometimes engineers refer to it as "space framing." NASA's scientific search for the structure that had to provide the most structural advantages with the least pounds of material__ergo, least energy and seconds of invested time-in order to be compatible and light enough to be economically rocket-lifted and self-erected in space__had resolved itself into selection of my 1899 octet truss. (See Sec. 422.)
And the web site says:
"This is what he calls synergetics: an empirical mathematical system in which geometry and number mesh without fractions."
Any polyhedron whose vertexes all have integer Synergetics coordinates has a whole number tetra-volume, I think.
Cliff Nelson
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