Patterns of Relational Paradigm

Twofold Operators-Form/Process






  • They are co-evolutionary.

  • Without process there is no form.

  • Without form there is no process.

  • Can distinguish, but cannot seperate.





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         Without form there is no process. Without process there is no form. You cannot have one without the other; they are co-evolutionary concepts. You can distinguish and name the two concepts, but you cannot separate them.

         The concepts of form and process are present in all world views; however, different philosophies treat them in different ways. In general, existing philosophies emphasize one as being above or more important than the other.

         Western philosophies have placed the form—God or the Ideal—above the process. Eastern philosophies have placed the process—the Tao or Way—above the form. The male emphasizes form, “How does she look?” The female emphasizes process, “Will he be a good provider?” The male produces goods, the female provides services.

         The relational paradigm recognizes that process and form are of equal status; they are balanced. The form may be placed above the process or the process above the form. Both are valid views and both are necessary for a complete understanding of our reality.

         In applying the twofold operator form/process to other twofold operators, e.g., Western / Eastern or male / female, it is important to recognize that both form and process are always present. To say that the male emphasizes form does not mean that he does not have process. It does imply that he normally places the form above the process in his world view. If we analyze any system, e.g., Western science or Eastern science, we will always find both process and form.

         In physics the particle is form and the wave is process. In language the noun is form and the verb is process. In arithmetic the numbers are form and the arithmetic operators are process. The form is structure and is spacial in nature; the process is function and is temporal in nature.

         A major problem with existing world views is that a continued emphasis on either form or process will eventually result in unforeseen consequences. Western industry is very efficient in producing things; it is not efficient in determining the impact of these things on society or the environment. Industry understands form but not process.

         A good example of the introduction of process to an existing paradigm which emphasizes form, is the work of Christopher Alexander in the field of architecture. In the books The Timeless Way of Building and A Pattern Language he effectively incorporates function or process into a discipline that concerns itself primarily with only structure or form.

         In introducing process, Alexander asked two basic questions: “How does it feel?” and “Does it last?” I believe that these questions are, respectively, subjective and objective evaluations of process. The comparable evaluations of form are: “Does it work?” and “What are the results?” These four questions are fundamental to the effective evaluation of any world view.

         One of the reasons that the relational concept has been difficult to explain is that a description of the relational doesn’t make sense unless accompanied by a description of the user view. The hierarchy and the network are often explained through a description of their form or of their process. To explain the relational, a description of both form and process is required.


          A visual picture of the process and form can be obtained from two geometric shapes: the double helix and the Klein bottle. These figures and their interaction are depicted in the exhibit below. I believe that the shapes themselves are a twofold operator (Klein bottle/double helix); you can distinguish the two shapes but you cannot separate them. They are two different views of the same basic phenomenon—the building blocks of our reality. All of what we now call reality has the basic pattern of the Klein bottle/double helix. It is a holographic effect in that no matter how small or large a segment we examine, it has the same basic pattern.





Double Helix
          The double helix is the most familiar of the two figures. It is the basic shape of the DNA molecule, the building block of all things which we call living.

          The helix is a coil-shaped curve traced on a cylinder or conical surface in such a way that there is uniform distance between adjacent coils. The thread of a screw is a helix. A double helix is two helixes together, like a spiral staircase. The double helix can move in either a clockwise or counterclockwise direction.

Klein Bottle
          The Klein bottle is an elusive shape. It is named after the German mathematician, Felix Klein, and is a topological shape of which only imperfect models can be made in three-dimensional Euclidean space. The Klein bottle has only one side and no edges. It can be obtained by connecting two ends of a cylindrical surface in the direction opposite that necessary to obtain a torus (a donut-shaped figure). The Klein bottle is a donut with a twist. A representation of this construction follows.

          The Klein bottle is closed but unlike the torus or sphere it is possible to move from the inside to the outside without crossing a boundary. A non-Euclidean geometry is needed for the actual construction of the Klein bottle.

          The Klein bottle is a non-orientable shape in that there is no objective way to determine where you are. All reference systems are arbitrary; they are necessary, but they are arbitrary and relative to the observer. There is an inside and an outside of the Klein bottle, but which is which is relative. An analogy is the earth—no objective reality says that the north pole is up and the south down. The map makers lived in the north and up was a preferable position. Right and left in a mirror image is another example of a non-orientable phenomenon. Orientation as to which is right and which is left can only be made in relation to some other figure. There is no objective way to determine right from left.

          Non-orientable is not a good word to describe the phenomenon. There is orientation; however, all orientation is subjective rather than objective. The high priests of Western science often take the view that if it isn’t objective, it doesn’t exist. Subjective orientation becomes “non-orientable.” Fortunately for them, Einstein called his theory the theory of relativity rather than the theory of subjectivity or we would have seen earlier that this scientific mentality was in the “dark.” “The speed of light is constant, relative to the position of the observer,” means that there is no objective measurement of the speed of light.

          My personal visualization of a Klein bottle is of an hourglass with the large ends connected, and rather than a small hole through which the sands of time pass, the hole is a “singularity” point where the inside of the hourglass becomes the outside. Another way to visualize a Klein bottle is to imagine the roots of a tree connected to the branches and the singularity point where the trunk enters the ground.

Möbius Strip
          Most of the basic characteristics of the Klein bottle are common to the Mobius strip, and since the Klein bottle cannot be constructed in three-dimensional Euclidean space, the Mobius strip can be used to demonstrate basic concepts. A Klein bottle can be cut into two Möbius strips.

          A Möbius strip can be constructed from a long narrow strip of paper. Give the strip a half-turn or a 180-degree rotation and connect the two ends to form a closed ring.

          From a geometric or topological point of view, the Möbius strip has only one edge and one side. This can be easily demonstrated by placing a pen on the surface or edge and tracing around the strip until returning to the starting point. Upon examination you will find that both physical sides or edges of the strip have been covered.

          The topological perspective of a one-sided figure emerges only when one considers the Möbius strip as a whole. From a limited or common sense perspective, there are two physical sides. When we attempt to totally explore these two sides we find that we have trouble determining where one ends and the other begins; however, from a limited perspective we can make a clear distinction between the two sides.

          Normally we see only one-half of the Möbius strip or one physical side at a time. To see the other half or the complete strip we must change perspectives. This change in perception can be easily demonstrated by traveling around the Möbius strip visually in your mind. At some point you must change your perspective to complete the trip. Another way to demonstrate this is to hold the Möbius strip with one hand and trace around it with a finger of your other hand. If you keep your finger flat, at some point you will have to become a pretzel or lift your finger to complete the trip.

          The usual path is to travel only on one-half of the strip by making a switch where the Möbius strip naturally crosses. We take the “sloshen cut-off” rather than making the complete trip. To obtain a balanced or complete perspective we must experience both halves or both physical sides.

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