Patterns of Relational Paradigm

Twofold Operators-Known/Random


Random Chaos Divergent
    • Existing: Assumes random. Things are independent.
    • Emergent: Assumes known. Things are interconnected.
    • Existing: Assumes increasing chaos (entropy). 2nd Law of Thermodynamics.
    • Emergent: Assumes increasing order. Prigogine's dissipative structures.
    • Existing: Assumes light is convergent.


    • Emergent: Assumes light is divergent.


    • Existing: Assumes resources diminish with use.
    • Emergent: Assumes data increase with use.
    • Existing: Assumes convergent events.
    • Emergent: Assumes Divergent events.

         Known/random is a twofold operator whose pattern can also be represented by the words order/chaos and convergent/divergent. In the relational paradigm, if one part of the twofold operator is present, then the other must also be included to have a complete picture of reality. In our existing Western world view, there are many areas from which one or the other part of this twofold operator has been excluded. The list in Exhibit 2.2.5 and the following brief discussions are but a few of the areas effected.



         All of our statistical theories and applications are based on the assumption that things are random. This assumption is usually stated by the injunction, "Take an independent sample." Connected / independent is just another set of words for the pattern of the known / random twofold operator. If from one view things are independent, from another equally valid view things are connected.

         I have seen the successful application of statistical theory based on the assumption that things are connected or known. In some cases, the applications have produced superior results to those which can be obtained from conventional statistics. However, these techniques and results have never seen the light of day. They are a great threat to the dominant paradigm and have been ignored.


          The concept of entropy as stated in the 2nd Law of Thermodynamics is one of the basic concepts of the Western scientific world view. This law states that the world is running down. The interaction between any two systems always increases chaos. Chaos is a little too strong a word, so they called it entropy. A common complaint among physics teachers is that students don't seem to understand this concept. This misunderstanding is not surprising since, through the choice of words, the pattern is obscured. Also, I believe that people intuitively know that the interaction between all systems does not always produce increased chaos. They have personal experience with the opposite reaction -- an increase of order.

         The Theory of Dissipative Structures by Ilya Prigogine provides the emergent counterpart to the 2nd Law of Thermodynamics. The Theory of Dissipative Structures states that living systems run up rather than run down. The interaction or exchange of energy in living systems can create increasing order.

Theory of Relativity

         According to stories, Albert Einstein as a young man had a vision in which he rode a beam of light. Through this experience he gained an intuitive understanding of the nature of light. He was unable to express this understanding in mathematical terms until he found Reimannian geometry. This geometry assumes that parallel lines are elliptic, contrary to the assumption of Euclidean geometry that parallel lines never meet. Einstein used elliptic geometry to describe the Theory of Relativity. The theory states that light is curved; it is elliptic or convergent.

         The emergent assumption would use a hyperbolic rather than elliptic geometry and would assume that light is hyperbolic or divergent. My understanding of the equations of Einstein's theory is that they do not exclude the possibility that light is hyperbolic. Likewise, they don't state that matter can't travel faster than the speed of light. They do state that matter can't travel at the speed of light. The problem is the transition.

         The emergent hypothesis is that light or space is curved with a twist. It has the pattern of the Klein bottle. On one side it is elliptic, on the other hyperbolic. The transition is a discontinuity through the still point and is part of the fifth business patterns of the relational paradigm.


         All of the economic theories in use by major nations of the world are based on the assumption that resources decrease with use. All pricing is based on this fundamental axiom.

          Today, the driving force of world economies is information. We have shifted from an industrial to an information age. Information increases with use. If I give you information, I still have it. And the fact that you now have it is itself information, and if I set up a feedback loop, the information increases exponentially.

          None of the existing economic theories, whether capitalism, communism, socialism, etc., can tell you how to price something which increases with use. This is not a complex concept, and it does not require a degree in economics to understand; however, even those with a degree in economics cannot draw a simple supply and demand curve for something which increases with use. The basic axioms of existing economic world views simply do not support the reality of information.

          To fit data and information into an existing economy we must perform all kinds of unnatural acts. Rather than data, we provide disinformation and hype; rather than information, we provide obfuscation; rather than allowing people to make their own models, we provide propaganda; and rather than feedback, we provide secrecy. Examples are everywhere and everyone has personal experience with the limits of the existing practices.

         Copying material which has a copyright, taping a television program on your VCR, and sharing copyright games on your personal computer are examples of how we get around the existing laws. Trying to find out what to buy, as well as where and when, is a major time-consuming activity for many people. Try understanding a basic insurance contract, legal document or medical report and you know about obfuscation.

         Attempting to find basic facts about industry or government becomes an art. One of the major political issues of the day for example, is a flat tax, yet the information on the actual taxes paid by various income groups has not been available. How can we make a policy decision when we don't know the information? It's like traveling in unknown territory without a map.

         The relational paradigm adds the axiom that data and information increase with use. The theories and practices which result from this axiom have yet to be developed.

Organizational Planning

         Planning in most organizations is based on the assumption that events are known or convergent. We plan for a designated group of people to take specified actions to arrive at a predetermined outcome. We do not plan for unknown or divergent events. Yet we can predict with absolute certainty that divergent events will occur.

         The result of planning only for convergent events can take one of two basic paths. In the first, the plans are made but never used. The elaborate planning document sits on the shelf and has little or no impact on what the organization actually does. In the second, the people who have to perform the activities learn from experience that divergent events do in fact occur. Since divergent events cannot be included in the plan, conservative estimates are made of the time required to accomplish the convergent events and then this time typically is doubled for the planning document.

         Allowing divergent events to be included with convergent events in the planning process should improve our understanding and the effectiveness of organizational planning.


Random Chaos

Klein Bottle

  • Chaos in space is order in time.
  • Chaos in time is order in space.

         A change in perception can result in a shift of the twofold operator known/random. Chaos from a spacial perception can become order from a temporal perception, and chaos from a temporal perception can become order from a spacial perception.

         I have not found an adequate description of the distinction between a space way and a time way of perceiving. Clearly there is a difference. Most of the Western world, particularly males, view the world from a spacial perspective. All of our education seems to be oriented toward this view. However, certain occupations have people who think from a different perspective. Process Engineering is one such occupation. Major companies is this field often do not hire people directly into positions of responsibility, but hire them at a low level and then determine whether they know or can be taught to think in a temporal fashion.

         One distinction between the two ways of perceiving is that temporal perception requires that the person visualize himself as part of the process rather than as an observer. A subjective rather than objective point of view.

         It seems that both perception processes can be learned, and that you can consciously shift from one to the other. I believe that the shift is discontinuous, in that you can't hold both views simultaneously. A similar experience is looking at the Necker cube.

         When one shifts perceptions, a simultaneous shift occurs in the twofold operator known/random. As an example, if I walk into my 3 year-old son's room after he has been playing for an hour, it appears to be in chaos. Things are everywhere. However, if I watch and listen as he plays, then the spacial chaos turns into a definite order in time.

         Another example from the other direction comes from watching an artist friend paint a picture. She cannot explain what she will paint next or even when she will do it. It appears to be chaos in time. However, viewing the finished picture shows a very clear order in space.

         Another example of this shift in perception can be obtained from the following lines.

         Looking from the right to left, the lines are convergent. Shifting to a left to right perception, the lines become divergent. An inverted image, such as can be obtained through a camera obscure or crystal ball, will produce the same switch. The switch in direction and corresponding switch in convergent and divergent appearing lines occurs while traveling around a Mobius strip or Klein bottle.

         I believe that the acknowledgment of both perceptions will be of significance. Not just from the improved knowledge, understanding, modeling and control of our reality, but also from our ability to educate ourselves and others. I believe that certain people and races have a time based perception that is in natural conflict with a solely spacial based education system.

Form/ProcessHierarchy/NetworkSequence/JumpMeasure/Count • Known/ Random • Balance/RelationshipSummary of Emergent Axioms




Patterns of Relational Paradigm


Twofold Operators







Summary of Emergent Axioms

Threefold Operators

Fourfold Operators

Fifth Business

Relational Organization

Relational Structure & Root Language

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