3 ENERGETIC AND SYNERGETIC GEOMETRY

2AT first the whole; comprehensiveness. In college at Harvard, Fuller’s intuitive mind soon forced him to reexamine the validity of the Euclidean-imagined straight line, and of a geometry built upon static concepts. Instinctively he felt the need to find a real, not an imaginary, starting point. Imagination is all well and good, but let it spring from a real base, not one that imagination itself, uninformed, has contrived. That base, to Fuller’s mind, must be broad, and, to be truly comprehensive, should consist of nothing less than the ‘‘totality of human experience.’’ A large order, but the faculty for comprehensive thinking could settle for nothing less. The truth impulse must be uncompromising, and ‘‘uncompromising’’ in present context is merely a synonym for ‘‘comprehensive.’’ In any case, Fuller’s comprehensive mind refused compromise with Euclid’s imaginary, static world straight line. Out of this staunch refusal was born a new-world geometry, aptly termed ‘‘Energetic and Synergetic Geometry.’’ It began, not with an imaginary straight line, but with a comprehensive sweeping view of the universe around us, moving, dynamic, orbiting, complete.

3 Students in universities throughout eastern and western worlds were introduced to a new world of mathematical concept when the man they would grow to think of with affection simply as ‘‘Bucky’’ commanded their minds to fresh vigor of creative effort. Beginning his explanation of the new geometry, he would say, holding before his class a simple model consisting of three triangles hinged together in a chain,

4 ‘‘One equilateral triangle…

5 ‘‘Hinged to two others…

6 ‘‘Can be folded into a three-sided ‘tent’ whose base is a fourth triangle.’’

7 Having suited action to the words, he tilts the tent backwards to show the base triangle.

8 ‘‘Now,’’ Bucky continues with mounting excitement, ‘‘The inadvertent appearance of this fourth triangle is a demonstration of ‘synergy,’ which is the behavior of a system un

9 predicted by its parts:

10 1 + 2 = 4

11 Then, to drive home to his students the essential need for them to comprehend the totality of a problem, he would say,

12
13‘‘A triangle drawn on the Earth’s surface is actually a spherical triangle bounded by great circle arcs.’’ (Think of the Equator; it is a ‘‘great’’ circle as distinguished from, say, the fortieth parallel of latitude which is a ‘‘lesser’’ circle; all great circles of the earth, be they the Equator, the meridians, or otherwise, would be equal in measurement to the nominal 25,000 miles of earth’s circumference.)¹

14 ‘‘If the triangle is drawn large enough,’’ Fuller continues, ‘‘its edges will reach an ‘equator’ which will divide the surface of the earth into two triangles enclosed by common edges.’’ And right here Fuller comes to the point of his proof of the need to comprehend the totality of a problem:

15
16‘‘Now, because every spherical surface has two aspects—¹ convex if viewed from outside, concave if from within—each of these triangles is, in itself, two triangles.’’

17 And then, eyes sparkling, Fuller would say, ‘‘Thus one triangle becomes four when the total complex is understood’’ Fuller’s excitement was contagious as the students’ minds were tethered to his in search for broader understanding of the total complex. Now, if we ourselves can join minds with Fuller’s as he explains the rudiments of energetic and synergetic geometry, we may succeed in laying aside some of our Euclidean certainties and enjoy the exhilaration of stretching those brain cells of ours to gain comprehension of totality.

22 It was not that Fuller wanted to find fault with Euclid. After all, that was a pre-Copernicus geometry and in its inception could not avail of a round-world concept. An imagined flat world naturally would incubate an imaginary flat plane, Euclid’s built-up second dimension. It was simply that Fuller was somehow intuitively compelled to clear his mind of the mathematical precepts which had stood for so long in their deceptive simplicity that they had become almost beyond strength of challenge.

23 And so, with the whole of human knowledge and experience as his point of departure, Fuller was able to find a comprehensive geometry capable of bringing into congruence form, mass, external space, the energies of heat, electrostatics, electrodynamics, electric waves and, finally, ‘‘the atomic complexities demonstrated by the family of chemical elements.’’ Once freed from the unreal world of a static Euclid, the innate dynamics of Fuller’s mind not only brought forth this revelation of an exquisite congruence of form, mass and energy experience, but also led to the discovery of the inventor’s ‘‘closest packing’’ theory. A leading nuclear physicist, speaking of Fuller’s concept of closest packing, has acknowledged this theory to be ‘‘an indispensable aid to understanding the significance of advanced studies’’ in his field.² The new geometry begins quite simply and directly with an investigation of requirements for a minimum system within the universe. A ball on a string, the end of the string being held at a fixed point, is free to spin at the limit of its tether in a myriad of circular arcs. The fixed point at the end of the string furnishes what is functionally described as a single vector of restraint. The locus of the path of movement of the ball as tethered by this single vector of restraint defines a sphere—a three-dimensional system. With two vectors of restraint as provided where the ball is held by two strings fixed to anchorages at opposite sides of the ball (a pendulum plus its mirror image), a plane is defined—a two-dimensional system. Three vectors of restraint (three strings and three anchorages), and a line is scribed—a one-dimensional system. Four vectors, and a point is fixed with vectors define the tetrahedron, a polyhedron having four equal equilateral faces. This remarkable figure, the tetrahedron, is the first identifiable ‘‘system’’ as a primary or minimum division of Universe.

25 no displacement possible in any direction. Notice how completely Euclid has been turned upside down, Euclid beginning with the ‘‘straight’’ line and eventually building up to a solid, Fuller with die sphere which is the comprehensive whole that represents the totality of experience—the totality which is to be analyzed and comprehended.

26 Continuing beyond these initial thought structures, Fuller’s geometry of energy and synergy advances to concepts of ‘‘turbining’’ within the position otherwise fixed by the four vectors of restraint, and to the basic revelation that the four extension of the edges of the tetrahedron through any one vertex creates a kind of triangular hour-glass which forms what a complete understanding will describe as ‘‘positive’’ and ‘‘negative’’ tetrahedrons (a tetrahedron and its mirror image). This is another example of the two-ness of a system. The one noticed before was the two-ness of a spherical triangle which is both convex and concave.

27 The Universe must be the starting point for any study of synergetic phenomena. ‘‘Universe’’ is defined as the sum total of all man’s sensed and communicated experience. The within-ness and without-ness of a spherical (concave-convex ) surface suggests the inherent two-ness of the Universe.

28 Proceeding beyond the discovery of the first identifiable system, the tetrahedron, Fuller’s exposition demonstrates that the mathematical process of ‘‘squaring’’ is equivalent to ‘‘triangling’’ (edge times edge equals area), while ‘‘cubing’’ is equivalent to ‘‘tetrahedroning’’ (edge times edge times edge equals volume). A little thought about these two mathematical equivalents will quickly make apparent the intellectual block-busting potential of such revolutionary concepts to the mathematician and scientist.

29 Such is the enticing introduction to the geometry of energy and synergy; the new-school geometry of Universe. In its further development, this geometry reaches what has come to be known as geodesic structuring, according to which the largest free-span structures in the world have been erected. And it has found surprising points of congruence in the field of medicine, where such geodesic structuring has been identified by molecular biologists with the structure of the protein shell that surrounds every known virus. Logically, it can be imagined that a truly comprehensive system would in certainty create bridges across all of the chasms in man’s compartmented world. A comprehensive system should be valid in mechanics, electronics, chemistry, biology, medicine, astronomy…

30 Fuller’s method of comprehensive thought is to go behind the ‘‘known’’ theory and begin once more at the experimentally informed beginning, being careful to avoid distraction by scientific dogma, mind alert to examine fresh approaches and to formulate new interpretations of what men understood, or thought they understood, before. The strongest and most unique characteristic of Fuller’s mind is that it allows no thought that springs solely from any one point. ‘‘Intuitively,’’ as Fuller uses the term in self-analysis, the cocooning fabric of thought is spun between a complex of points as it inventories and reconsiders the broadest possible range of relevant experience in quest of universal truth, the truth of the whole. The purity and one-ness of the patterns evolved by such a method is itself a demonstration of the phenomenon of synergy, according to which the whole is equal to more than the sum of its recognized parts.