Fuller exhibition

Buckminster Fuller portrays the Tetrahedron as the fundamental geometrical component of nature's structure. In fact Fuller strongly believes in the perception of a universe structured on a "simple" code. These experts are part of his lectures held back in the 1970's arguing on these and other really interesting fields concerning the "Spaceship Earth", as he puts it and it's "Operating manual". Fuller has been an inspiring personality for generations of scientists and designers and his work and ideas seem to be coming again in the foreground. I had the opportunity to watch an exhibition at the Whitney Museum of Modern Art on Buckminster Fuller and buy a collection of essays under the general title "Utopia or Oblivion", edited by Jamie Snyder and published by Lars Muller. The abstracts come from this collection.

_"I said to myself back in 1917  "Inasmuch as the planar force diagrams which we were taught are, to say the least, inadequate, is it not possible to find an adequate model for us- an omnidirectionally interacting, minimum set of vectors?" We have to deal always in the reality of an omnidirectional physical universe, so how many forces are really operating on us?"

Through experiments Fuller points out there are always a minimum of 12 restraints(vectors) for the universe to completely immobilize a body, as for example you need the minimum of 12 spokes to make a wire wheel. So there are always 12 fundamental vectors which converge at the angular degrees of freedom in the universe : 6 positive and 6 negative, which, when symmetrically interacting, represent the 6 edges of the positive phase of the tetrahedron and the 6 edges of the negative, or vertexially inside-outed phase of the same vectorial tetrahedron.

Fuller takes examples from our everyday experience to draw our attention on the stability of the tetrhedron. Such is the pilling up of oranges, assuming them as balls, in the supermarket cases.  Because the "spheres" are the same size, equilenght vectors may connect each and every adjacent sphere, with the vectors running from the centers of the spheres through the points of tangency to the adjacent sphere's centers. Remove the spheres and leave the vectors and you've got the tetrahedron-octahedron complex.

 The "isotropic vector matrix" is a structure that I discovered independently back in kindergarten in 1899, says Fuller and seems to believe that all humans, once children, have an inherent, built-in, understanding of nature's most basic functions. By the way the isotropic vector matrix is the official scientific name for the tetrahedron-octahedron complex. Fuller explains to us that besides the tetrahedron, the octahedron and the icosahedron are the only three basically stable omnitriangulated, omnistructural systems. When he begins to explore the relation of volume between the tetrahedron, the octahedron and the cube he points that if the tetrahedron has a volume value of 1, then the octahedron has a volume of 4, and the cube a volume of 3. As the tetrahedron is inherently more stable than the cube,which represents the Cartesian ideal of the structure of the Universe, had we replaced our familiar coordinate system with a new based on the tetrahedron, we would end up with a much more "economical", in terms of representation, system, as well as a system that could deal with equations on the fourth and fifth power, the one's Einstein was dealing with at the end of his life. Fuller argues that it's a scientific fallacy that the forth dimension came to be so widely recognized as the parameter of time. And that it was exactly due to the Cartesian coordinate system's inability to portray a fourth dimension that this came to be.

Fuller's theory are further supported by findings in the science of Chemistry of that time and before. Van't Hoff is the first chemist to receive a Nobel Prize back in 1901 for his work with solutions. He was the first to claim, and prove, the tetrahedronal configuration of carbon, the combining master of all organic chemistry. Since the time of Van't Hoff and until the lectures of Fuller organic chemistry had been tetrahedronally coordinated. The way the tetrahedra bonded defined whether the result was gas,liquid, crystals, etc. Half century later Linus Pauling with the use of  X-Ray machine discovers that all metals which he analyzed where tetrahedronally coordinate but instead of being linked vertex to vertex they were linked midledge to midledge with common centers of gravity. Two leading virologists of the time as well, again through X-ray difraction found the shape of the protein shells of the virus to be similar in appearance to Buckminster Fuller's geodesic domes [which are a product of the tetrahedronal "geometry"]_