Angle vs. Frequency
Shape is defined by angles irrespective of scale. A regular tetrahedron has unchanging surface and central angles regardless of its size — and so for any object, no matter how complex. This angular aspect of experience links metaphorically to the idea of eternal principles. The ideally angular is only fleetingly grasped through intuition however. Our actual communications of eternal verities inevitably appear aberrational — idiosyncratic even — doomed to become nonsense in the long (or short?) run.
The concept of Frequency identifies the cyclic aspect of experience. An object persists in space and time as an aggregate of repeating energy events. The electromagnetic spectrum separates angular identities according to their different energy involvements. With the addition of frequency, the hitherto only-angle-defined becomes special case, temporal, mortal.
Or, borrowing computer terminology, we could say that eternal principles define the template class hierarchy, and special case events represent instantiations of these templates, as application objects with a finite life span, measurable in clock cycles.
For further reading:
4D in synergetics does not allude to 3D-space plus 1D-time. Space is experientially volumetric in synergetics: no Euclidean objects of zero, one or two dimensions (e.g. points, lines, or planes) are defined as such i.e. “planes” have thickness. Fuller argued that volume (space) is intuitively four dimensional (4D) because the tetrahedron is the simplest shape, the most primitive model of space. The tetrahedron has four faces, four corners, six edges. The “4D” tag derives from the tetrahedron’s inherent 4ness.
Synergetics also defines time/size as a unitary concept — persistence in time is not inherently separable from extension in space. Timeless, sizeless shapes, defined solely by their angles, take on the added attribute of frequency once made real in the form of special case experiences.The Cartesian XYZ axes do not delineate three independent dimensions — height, width and depth are not mutually separable aspects of experience. The mutually orthogonal arrangement of 3 positive and 3 negative vectors penetrate the 6 mid-edges of a tetrahedron — the “3” in “3D” relates to either open-triangle “zig-zag” from which a tetrahedron is comprised.
In place of the 90-degree-based XYZ lattice of Cartesian geometry, synergetics invests in a primarily 60-degree-based isotropic vector matrix (IVM), a lattice defined by the centers of closest packed spheres of equal radius.
For further reading:
No Race, No Class
Western science originally portrayed race and class as characteristics of a person’s blood which, as such, could be subdivided in proportion to a person’s ancestry, “blood” being treated as a mathematical quantity, contributed in equal proportions by one’s parents. Hence such terms as “octamaroon” (one eighth black). Whereas “class” is no longer regarded as a genetic entity, “race” has remained a popular concept for grouping genetic characteristics, even if the link to blood is no longer made. Like anthropologist Ashley Montague, Fuller felt the concept of “race” had outlived its usefulness, that the cross-breeding of the world’s people, especially evident in North America, was exposing the old racial categories as mere snap-shots of genetic traits thrown together by the exigencies of time, but available in any number of permutations from that vast grab bag of traits known as the human gene pool. In the Fuller lexicon, a racist is perhaps most straightforwardly defined as someone who believes in races.
For further reading:
Structure by Kirk Van Allyn
Fuller conceived of Design Science as an application for synergetic geometry: the geodesic dome and Fuller Projection (a world map) were examples of putting general principles to work as a source of practical artifacts. Design Science, which draws on many sources for its content, including software engineering, architecture, and the visual arts, is an approach to problem solving which looks at redesigning processes and/or inventing new tools, rather than trying to convince people to change their beliefs. “Don’t change people, change their environment” was one of Fuller’s favorite encapsulations of this approach. Fuller hoped that by means of a design science revolution, humans would be able to dramatically improve their living standards while coming into a sustainable long-term relationship with their ecosystem context. He insisted this revolution would need to be bloodless and artifact-centered, as opposed to violently political.