An Index of Relevant Topics

Bullet Concentric Hierarchy of Polyhedra
Concentric Hierarchy

Synergetics centers around a set of inter-related polyhedra. Their relationships are both static (e.g. relative volumes) and dynamic (e.g. the jitterbug transformation). Because synergetics defines the tetrahedron to serve as the prime unit of volume, instead of the cube, other polyhedra, traditionally presented with irrational volumes, have whole number or simple fractional volumes in the context of the concentric hierarchy.

Bullet Sphere Packing
Sphere Packing

Synergetics focuses on polyhedral agglommerations of dense-packed spheres (e.g. the tetrahedron, octahedron and cuboctahedron). For example, canon balls and grocery store oranges are typically stacked in a tetrahedral conformation. The number of intervals between spheres along an edge is identified with the concept of Frequency in synergetics, and formulae relating Frequency to sphere counts provide a quick way of counting canon balls and oranges.

Bullet Isotropic Vector Matrix

Synergetics embeds polyhedra in a space-filling grid pattern known as the isotropic vector matrix. In contrast to the xyz coordinate system, the ivm is more 60-degree than 90-degree oriented: it defines complementary tetrahedral and octahedral volumes and is known as the octet truss in architecture. This matrix, or lattice, is also coincident with a sphere-packing arrangement well-known to crystallographers (fcc).

Bullet Geodesic Domes and Spheres
Fly's Eye

Fuller derived geodesic spheres and domes within the context of more general geometric investigations. Domes, along with other "livingry artifacts" play a central role in "anticipatory design science". Artifacts make a tremendous difference to living standards, both positively and negatively. A design science approach to econospheric evolution is about accentuating the positive. Synergetics aims to support design science toward this end, along with any other self-disciplines aimed at boosting humanity into a sustainable, high living standards phase.

Bullet Fuller Projection

The Fuller Projection, like the geodesic dome, derives from synergetic geometry. It features very low distortion and shows all the earth's landmasses in a continuous layout, without any interruption by the map's edges. Fuller hoped this map would serve as a 'game board' for teams of players committed to finding workable strategies aimed at raising the living standards of humans as a whole, and not at the expense of the environment (to trash the environment is to lower living standards, obviously). To assist humans to break loose from their more parochial viewpoints, he copy-protected his map against being used to display political boundary data, i.e. the Fuller Projection is inherently nationless.

Bullet Desovereignization

Corresponding to an apolitical view of Spaceship Earth, as conveyed by the Fuller Projection, is a geopolitical analysis of humanity's plight: the world's sovereignties have by now become integrated into supranational commercial and financial networks, at the basis of which we find a lot of buggy, only quasi-functional code, frustrating our initiatives to create more humane, satisfying and comprehensible operating systems. Design science diagrams the global infrastructures which prop up our nation-states and looks to global networking (e.g. the internet) as a tool for bringing better designs online.

Bullet General Systems Theory
Sun & Earth

General Systems Theory challenges the historically monopolistic hegemony of Economics (as a discipline) over life and death matters of resource allocation. GST recognizes that the economy is coincident with the ecology, and that ecology extends beyond the planet to the solar system, wherein the fusion reactor we call Sun is clearly the primary driver of our econosphere. In bookkeeping terms, Earth is like a not-for-profit, centrally depending on grant funding from the Sun to sustain and power its operations. Wealth (life support) accumulates as a result of humans applying eternal principles to the task of local circuit design and energy-channeling, and doing so increasingly intelligently on many fronts over time.

Bullet Quadrays
QCOLOR2.gif - 3.5 K

Quadrays provide an alternative to the standard XYZ coordinate system by mapping space with only positive numbers using an omnisymmetric schema consisting of four rays pointing from the center of a regular tetrahedron to its four vertices. The information at this site includes algebraic and computer language methods for operating this gizmo, providing students with partially overlapping exposure to time-honored mathematical ideas, as well as an introduction to object oriented programming and ray tracing software. Methods for converting spatial location addressed between XYZ 3-tuples (x,y,z) and quadray 4-tuples (a,b,c,d) are also provided.

Synergetics on the Web
maintained by Kirby Urner