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The term "pattern integrity" is a product of Fuller's lifelong commitment to vocabulary suitable for describing Scenario Universe. He explains,
When we speak of pattern integrities, we refer to generalized patterns of conceptuality gleaned sensorially from a plurality of special-case pattern experiences... . In a comprehensive view of nature, the physical world is seen as a patterning of patternings... (505.01-4)
Let's start with his own simplest illustration. Tie a knot in a piece of nylon rope. An "overhand knot," as the simplest possible knot, is a good starting point. Hold both ends of the rope and make a loop by crossing one end over the other, tracing a full circle (360 degrees). Then pick up the end that lies underneath, and go in through the opening to link a second loop with the first (another 360-degree turn). The procedure applies a set of instructions to a piece of material, and a pattern thereby becomes visible.
What if we had applied the same instructions to a segment of manila rope instead? Or a shoelace? Or even a piece of cooked spaghetti? We would still create an overhand knot. The procedure does not need to specify material. "A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists" (505.201). The knot isn't that little bundle that we can see and touch, it's a weightless design, made visible by the rope.
The overhand-knot pattern has integrity: once tied, it stays put. In contrast, consider directions that specify going around once (360 degrees), simply making a loop. This pattern quickly disappears with the slightest provocation; it is not a pattern integrity. (Even though the overhand knot depends on friction to maintain its existence, a single loop will not be a stable pattern no matter how smooth or coarse the rope.) Notice that it requires a minimum of two full circles to create a pattern integrity. 2 × 360 = 720 degrees, the same as the sum of the surface angles of the tetrahedron (four triangles yield 4 × 180 degrees). Minimum system, minimum knot, 720 degrees. A curious coincidence? Synergetics is full of such coincidences.
A similar example involves dropping a stone into a tank of water. "The stone does not penetrate the water molecules," Fuller explains in Synergetics, but rather "jostles the molecules," which in turn "jostle their neighboring molecules" and so on. The scattered jostling, appearing chaotic in any one spot, produces a precisely organized cumulative reaction: perfect waves emanating in concentric circles.
Identical waves would be produced by dropping a stone in a tank full of milk or kerosene (or any liquid of similar viscosity). A wave is not liquid; it is an event, reliably predicted by initial conditions. The water will not surprise us and suddenly break out into triangular craters. As the liquid's molecular array is rearranged by an outside disturbance, all-embracing space permeates the experience. Because liquids are by definition almost incompressible, they cannot react to an applied force by contracting and expanding; rather, the water must move around. In short, the impact of any force is quickly distributed, creating the specific pattern shaped by the interaction of space's inherent constraints with the characteristics of liquid.
The concept thus introduced, Bucky goes on to the most important and misunderstood of all pattern integrities: life. "What is really important... about you or me is the thinkable you or the thinkable me, the abstract metaphysical you or me, ... what communications we have made with one another" (801.23). Every human being is a unique pattern integrity, temporarily given shape by flesh, as is the knot by rope.
... All you see is a little of my pink face and hands and my shoes and clothing, and you can't see me, which is entirely the thinking, abstract, metaphysical me. It becomes shocking to think that we recognize one another only as the touchable, nonthinking biological organism and its clothed ensemble. (801.23)
Our bodies are physical, but life is metaphysical. Housed in a temporary arrangement of energy as cells, life is a pattern integrity far more complex than the knot or the wave. Remember that all the material present in the cells of your body seven years ago has been completely replaced today, somehow showing up with the same arrangement, color, and function. It doesn't matter whether you ate bananas or tuna fish for lunch. A human being processes thousands of tons of food, air, and water in a lifetime. Just as a slip knot tied in a segment of cotton rope, which is spliced to a piece of nylon rope, in turn spliced to manila rope, then to Dacron rope (and so on) can be slid along the rope from material to material without changing its "pattern integrity," we too slide along the diverse strands supplied by Universeas "self-rebuilding, beautifully designed pattern integrities." No weight is lost at the moment of death. Whatever "life" is, it's not physical.
The key is consciousness. "Mozart will always be there to any who hears his music." Likewise, "when we say 'atom' or think 'atom' we are... with livingly thinkable Democritus who first conceived and named the invisible phenomenon 'atom'" (801.23). Life is made of awareness and thought, not flesh and blood. Each human being embodies a unique pattern integrity, evolving with every experience and thought. The total pattern of an individual's life is inconceivably complex and ultimately eternal. No human being could ever completely describe such a pattern, as he can the overhand knot; that capability is relegated to the "Greater Intellectual Integrity of Eternally Regenerative Universe." (2)
If we seem to stray from the subject of mathematics, resist the temptation to categorize rigidly. Synergetics does not stop with geometry. Fuller was deeply impressed by a definition in a 1951 Massachusetts Institute of Technology catalog, which read "Mathematics is the science of structure and pattern in general" (606.01): not games with numbers and equations, but the tools for systematic analysis of reality. To Fuller this meant that mathematics ought to enable the "comprehensivist" to see the underlying similarities between superficially disparate phenomena, which might be missed by the specialist. Rope may not be much like water, but the knot is like the waveis like the tetrahedron.
Our emphasis thus far has been on pattern. What about structure?
Let's go back to the regular polyhedra. On constructing the five shapes out of wooden dowels and rubber connectors, it is immediately apparent that some are stable and others collapse. The "necklace" demonstrates that only triangles hold their shape, and so the problem becomes quite simple.
Picture a cube. Better yet, make one out of dowels and rubber tubing, or straws and string. Whatever material you choose, as long as the joints are flexible, the cube will collapse. Connectors with a certain degree of stiffness, such as marshmallows or pipecleaners, are misleading at first, because the cube appears to stand on its own. However the shape is so easily rearranged by a slight push that the illusion does not last.
The six unstable windows must be braced in order for a cube to be rigid. So six extra struts, inserted diagonally across each face, would be the minimum number that could stabilize the system.
Six struts? Just like a tetrahedron! And not only are there the right number of struts, but they can also be arranged the same way. A regular tetrahedron fits inside a cube with its six edges precisely aligned across the cube's faces (Fig. 5-3). We can therefore state that there is an implied tetrahedron in every stable cube. Nothing in our investigation thus far would predict the precise fit of a cube and a tetrahedron. This and many other examples of shared symmetry among polyhedra (as seen in the previous chapter) are powerful demonstrations of the order inherent in space.
If the cube is unstable without a scaffold of triangulation, what about cardboard models? They stand up by themselves with no trouble. The key word is cardboard. A polyhedron constructed out of stiff polygon faces, rather than edges and connectors, is effectively triangulated. Cardboard provides the necessary diagonal brace. It provides a lot of extra material too, but the untrained eye will not recognize the redundancy at first.
Likewise, the stiffness of marshmallows or pipecleaners provides triangulation, in the form of tiny web-like triangular gussets at the corners, strong enough to stabilize the whole window. Furthermore, stiff material is itself rigid because of triangulation on the molecular level.
Only when polyhedra are considered as vector systems is stability an issue. Construction is one method of determining stability, but a simple formula utilized by Loeb can also be used to check: E = 3V - 6. (3) If the number of edges is less than three times the number of vertices minus six, the system will be unstable. But the criterion is really even simpler: for polyhedra without interior edges, a stable system is always triangulated and a triangulated system is always stable. 3V - 6 = E holds true for a polyhedral shell if and only if that system consists exclusively of triangles.
The other option is to establish internal triangles; an unstable shell can be stabilized by interior edges, or body diagonals. Instead of triangulating the surface, the bracing members create triangles inside the shell to maintain the system's stability.
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