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Amy C. Edmondson
A Fuller Explanation
Chapter 7, Vector Equilibrium
pages 82 through 85


Vector Equilibrium

If you begin to suspect that the concepts hiding behind Fuller's intimidating terminology are often easier to understand than their titles, you will soon find that "vector equilibrium" is no exception. "The vector equilibrium is an omnidirectional equilibrium of forces in which the magnitude of its explosive potentials is exactly matched by the strength of its external cohering bonds" (430.03). If Fuller's description doesn't make it crystal clear, read on! The VE, as it is usually called, is truly the cornerstone of synergetics.

      Vectors are certainly familiar to us by now; but what is meant by equilibrium? The word is by no means esoteric; like "systems," it enjoys considerable popularity these days. That is no wonder, for the concept is at the root of all phenomena, both physical and metaphysical. Defined by The American Heritage Dictionary as "any condition in which all acting influences are cancelled by others, resulting in a stable, balanced, or unchanging system," equilibrium is not inactivity, but rather a dynamic balance. (1) This balance is not necessarily physical, but may be mental or emotional as well. In fact, so much of experience is characterized by fluctuation in and out of fragile balances, that it is easy to understand the word's frequent use covering everything from structural to emotional to financial equilibrium.

      A simple mechanical model of equilibrium involves a ball and a bowl. Allowed to roll around inside the open smooth surface, a ball will finally come to rest at the bottom of the bowl, requiring renewed force to set it back in motion. This state is called stable equilibrium. On the outside of an inverted bowl (or dome) the ball might rest briefly at the center, but the slightest disturbance will make it roll off—thus demonstrating metastable equilibrium. The third possibility is that the ball sits on a flat table, in a state of neutral equilibrium (Fig.7-1).

A ball and a bowl demostration of stable, metastable and neutral equilibrium
Fig. 7-1 Stable, metastable, and neutral equilibrium.
Click on thumbnail for larger image.

      Nature exhibits a fundamental drive toward equilibrium. Scattered pockets of varying temperatures will equalize at the mean temperature; opposing forces of different magnitude naturally seek a state of rest; these differences cannot remain imbalanced. Greater forces overpower smaller forces, causing motion until they balance out. Demonstrations of this universal tendency are provided by countless everyday experiences. For example, if a massive object sits on too weak a shelf, the force exerted by gravity toward the earth's center exceeds the strength of the shelf's restraining force and the object comes crashing through. Motion continues until a new equilibrium is achieved by the object landing on a sturdy floor capable of matching the gravitational force with an equal and opposite restraining force. Apparent motion then ceases, as a stable equilibrium is maintained.

      Invisible motion continues, however; atoms never stand still. The Systems approach encourages us to note that we can zoom in to observe the same event on another level of resolution.

      The front door is opened and quickly closed, allowing a rush of cold winter air into the living room. Freezing temperatures dorninate the corner of the room near the door, while the other side by the radiator is cozy and warm. However, the imbalance quickly disappears; the temperature soon becomes more or less consistent throughout the room.

      Nature's tendency to seek equilibrium is a spontaneous reaction; it is the path of least resistance.

      We have already seen that vectors model certain events and reactions of nature. In this discussion, we focus on one specific use of vectors: to represent forces. The application is straightforward. Forces push or pull on something. The strength or magnitude of a force is represented by the length of the vector, and its direction is of course specified by the orientation: frequency and angle, as Bucky says.

      It follows, then, that a balance of forces is geometrically modelable. We can create a spatial diagram of the concept of equilibrium, and in so doing learn more about space's inherent symmetry.

      Bucky's love affair with vectors dates back to his World War I Navy experience. Introduced to vector diagrams of colliding ships in the officer's training program, he discovered that the tiny arrows contained all the necessary information about the ships' masses and speeds and compass headings to predict the results of collisions or the effect of tail winds and other influential forces. Bucky was fascinated by the economical elegance of the system. These vectors actually modeled the energetic events of reality—a pleasant contrast to the mathematics teacher's "lines stretching to infinity." Bucky was hooked. "A vector is an experience," he reminisces in a 1975 videotaped lecture, "so I thought, if I could only have a geometry of vectors, that would be great." (2) This concept was introduced in the previous chapter, but now we must discern the specific shape of the configuration generated by vector diagrams and models.

"Nature's Own Geometry"

We periodically remind ourselves of the purpose behind this geometric journey. Trying to faithfully trace Bucky's footsteps, we seek to isolate the "coordinate system of nature": how Universe is organized. One of the essential parts of the mystery is how to account for structural similarities between totally unrelated phenomena, vastly different in both scale and material. The implication is that, rather than being coordinated, things coordinate themselves. This self-organization occurs according to a set of physical forces or constraints, absolutely independent of scale or specific interactive forces. In short, space shapes all that inhabits it.

      But how? Through what vehicles does nature adhere to this underlying order? Let's look at Fuller's fundamental operating assumption:

      It is a hypothesis of synergetics that forces in both macrocosmic and microcosmic structures interact in the same way, moving toward the most economic equilibrium packings. By embracing all the energetic phenomena of total physical experience, synergetics provides for a single coherent system of geometric principles. ...(209.00)

      Synergetics seeks to establish the natural laws through which the self-organization of systems in the most diverse fields of science occurs. Science, as we noted earlier, acknowledges a fundamental drive toward equilibrium, but what else can be observed about this tendency?

Container demonstrating entropy
Fig. 7-2
Click on thumbnail for larger image.

      Gas molecules buzzing around in a closed-container are suddenly allowed, by the removal of a barrier, into an adjacent empty compartment of the same size (Fig. 7-2). The molecules rapidly disperse, taking advantage of their new freedom by using the additional room to spread out and slow down. The reverse action—of all the gas molecules suddenly gathering in one half of a container—has never been observed, just as in the living room disparate temperatures equalize, but that room will never spontaneously become warm on one side while the other side suddenly cools off. The closed-container experiment is the classic model for illustrating nature's entropic tendencies. The Austrian physicist Ludwig Boltzmann (1844-1906), noted for his work in entropy theory, called the resulting dispersal disorderly behavior. A geometer, however, might observe the individual gas molecules vying for the most room—accomplished of course by a maximally symmetrical distribution—and not perceive such a progression as disorder. Both perceptions call it equilibrium.

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