Definition
Synergetics is defined by R. Buckminster Fuller (1895-1983) in his two books Synergetics: Explorations in the Geometry of Thinking and Synergetics 2: Explorations in the Geometry of Thinking as:
A system of mensuration employing 60-degree vectorial coordination comprehensive to both physics and chemistry, and to both arithmetic and geometry, in rational whole numbers ... Synergetics explains much that has not been previously illuminated ... Synergetics follows the cosmic logic of the structural mathematics strategies of nature, which employ the paired sets of the six angular degrees of freedom, frequencies, and vectorially economical actions and their multi-alternative, equi-economical action options ... Synergetics discloses the excruciating awkwardness characterizing present-day mathematical treatment of the interrelationships of the independent scientific disciplines as originally occasioned by their mutual and separate lacks of awareness of the existence of a comprehensive, rational, coordinating system inherent in nature.
Other passages in Synergetics that outline the subject are its introduction (The Wellspring of Reality) and the section on Nature's Coordination (410.01). The chapter on Operational Mathematics (801.00-842.07) provides an easy to follow, easy to build introduction to some of Fuller's geometrical modeling techniques. So this chapter can help a new reader become familiar with Fuller's approach, style and geometry. One of Fuller's clearest expositions on "the geometry of thinking" occurs in the two part essay "Omnidirectional Halo" which appears in his book No More Secondhand God.
Amy Edmondson describes synergetics "in the broadest terms, as the study of spatial complexity, and as such is an inherently comprehensive discipline." In her PhD study, Cheryl Clark synthesizes the scope of synergetics as "the study of how nature works, of the patterns inherent in nature, the geometry of environmental forces that impact on humanity."
Here's an abridged list of some of the discoveries Fuller claims for Synergetics (see Controversies below) again quoting directly:
- The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity.
- The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.)
- The rational identification of number with the hierarchy of all the geometries.
- The A and B Quanta Modules.
- The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration.
- The identification of the nucleus with the vector equilibrium.
- Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors.
- Omni-60-degree coordination versus 90-degree coordination.
- The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical.
Read more about this topic: Synergetics (Fuller)
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