Phi Space

Blancmange Curve. First described by Teiji Takagi in 1903, this curve has no tangents anywhere; it is uniformly continuous but nowhere differentiable, and is a special case of a de Rham curve.

Thank you for joining me as I continue to sketch the most basic underpinnings of my interactive geometric model for organizational and network design. I am proceeding with the premise that the merits of the model will not become readily apparent until individual users can interact with the virtual environment and with other users. Once users begin to observe the effects of their actions in controlling virtual workspaces and adjusting their strategy to increase the value of their space through “work,” they will quickly understand the value of geometry in shaping environment and interactions. Until that time, the best course is to keep moving forward.

In “The Geometry of Meaning,” Arthur M. Young identifies the blind spot of science since Newton has been inquiry into nonobjective patterns. After Henri Bergson and others, Young insists that the forces that oppose the objects must be more closely observed. Thus, Young elegantly lays out how Actions affect States and, consequently, Relations via multiplication and division that square and cube relations. Young recognized that increasingly complex scenarios require higher dimensions to solve (the “squared” area of the plane, the “cubed” space within a solid), and that generative organizing structures manage complexity by combining layers of different dimensions. It is simply enough when developing a semiotic model to freight line segments with simple concepts and to assign polygons and eventually polygons to manage the meaning of increasingly complex ideas. But we are still left with the challenge of relating these disparate shapes.

Fortunately, R. Buckminster Fuller envisioned and articulated a comprehensive and finely detailed system describing spherical dynamics in “Tensegrity.” Fuller carefully lays out a complete coordinate system based on four coordinates (rather that the three axes of the polar coordinate system) of self-polarizing, mutually comprehending points. In other words, the geodesic structures exist via the diametric opposition of its constituent points. Thus, “awareness of otherness involves mutually intertuned event frequencies.”

Fuller then provides the means to place the observer at any point within the tensegrity system, and further, to empower that observer to act and transform the local environment. Like Young, Fuller describes the tetrahedron as the simplest unit for delineating space, being marked by four points drawn from at least two planes. The tetrahedron is composed of two triangles, which are shown to be simple spirals, with two opposing spirals drawn together to form the tetrahedron as one quantum of action. Thus, the tetrahedron is the ideal basic unit upon which my model is built.

Although simple, the tetrahedron still has four vertices, four faces, and six edges, and each of these edges may be said to have two directions. Further, Fuller immediately places these structures within synergetic systems composed of multiple other tetrahedrons and connects them via inward-flowing pulses of energy and outward-flowing waves. Within the synergetic system, the polarity of the various components become “tuned” with one another, primarily via Fuller’s most dynamic construct: the vector equilibrium.

Diagram: Vector Equilibrium

More a map of flowing energy than a shape or a solid, the vector equilibrium represents the intersection and balancing force of components of different locations, complexities, and energy levels. Once again, we see technology where the mathematics is daunting, but the natural effects of its actions are intuitive and easily anticipated and influenced by the average knowledge worker. This sets the stage for the observer/participant to take their place and begin to anticipate and influence events: “All local events may be anticipated by inaugurating calculation with a local vector-equilibrium frame and identifying the assymetric pulsing of the introduced resonance.”

Thus, by placing knowledge workers within a workspace that has been algorithmically equipped with relevant data, information and control mechanisms, the organization sets them up to conduct meaningful inquiry and to adjust the variables within the workspace to effectuate meaningful changes that enhance the work product. The model will immediately adjust in accordance with the changes made, giving the knowledge worker more information to guide further actions.

Tomorrow we will take a closer look at the composition of the individual workspace and the method by which geometry is instrumentalized to populate myriad workspaces with specific settings representing local conditions within the greater synergetic system. Again, thank you for persisting through these layers of abstraction as I strive to ground these principles in actual human activity over the next few days!

Sources and resources:

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