Synergetics (Fuller)
His two-volume work Synergetics: Explorations in the Geometry of Thinking, in collaboration with E. J. Applewhite, distills a lifetime of research into book form.
Despite mainstream endorsements such as the prologue by Arthur Loeb, and positive dust cover blurbs by U Thant and Arthur C. Clarke, along with the posthumous naming of the carbon allotrope "buckminsterfullerene",[5] synergetics remains an off-beat subject, ignored for decades by most traditional curricula and academic departments, a fact Fuller himself considered evidence of a dangerous level of overspecialization.
Among Fuller's contemporaries were Joe Clinton (NASA), Don Richter (Temcor), Kenneth Snelson (tensegrity), J. Baldwin (New Alchemy Institute), and Medard Gabel (World Game).
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.
[2] Amy Edmondson describes synergetics "in the broadest terms, as the study of spatial complexity, and as such is an inherently comprehensive discipline.
Its emphasis on visual and spatial phenomena combined with Fuller's holistic approach fosters the kind of lateral thinking which so often leads to creative breakthroughs.".
[11] Cheryl Clark points out that "In his thousands of lectures, Fuller urged his audiences to study synergetics, saying 'I am confident that humanity's survival depends on all of our willingness to comprehend feelingly the way nature works.
This tetrahedron anchors a set of concentrically arranged polyhedra proportioned in a canonical manner and inter-connected by a twisting-contracting, inside-outing dynamic that Fuller named the jitterbug transformation.
Whereas "height, width and depth" have been promulgated as three distinct dimensions within the Euclidean context, each with its own independence, Fuller considered the tetrahedron a minimal starting point for spatial cognition.
Geometers and "schooled" people speak of length, breadth, and height as constituting a hierarchy of three independent dimensional states -- "one-dimensional," "two-dimensional," and "three-dimensional" -- which can be conjoined like building blocks.
(326.13, 1009.92) Fuller took an intuitive approach to his studies, often going into exhaustive empirical detail while at the same time seeking to cast his findings in their most general philosophical context.
As an example of "dot connecting" he sought to relate the 120 basic disequilibrium LCD triangles of the spherical icosahedron to the plane net of his A module.(915.11Fig.
913.01, Table 905.65) The Jitterbug Transformation[14] provides a unifying dynamic in this work, with much significance attached to the doubling and quadrupling of edges that occur, when a cuboctahedron is collapsed through icosahedral, octahedral and tetrahedral stages, then inside-outed and re-expanded in a complementary fashion.
(Fig 986.411A) "Synergetics" is in some ways a library of potential "science cartoons" (scenarios) described in prose and not heavily dependent upon mathematical notations.
His demystification of a gyroscope's behavior in terms of a hammer thrower, pea shooter, and garden hose, is a good example of his commitment to using accessible metaphors.
His focus is reminiscent of later cellular automaton studies in that tessellating modules would affect their neighbors over successive time intervals.
He remained concerned that humanity's conditioned reflexes were not keeping pace with its engineering potential, emphasizing the "touch and go" nature of our current predicament.
Coxeter (with permission) and by citing page 71 of the latter's Regular Polytopes in order to suggest where his A & B modules (depicted above), and by extension, many of his other concepts, might enter the mathematical literature (see Fig.
