Patterns of Relational Paradigm

Twofold Operators-Balance/Relationship











Still Point





User View









  • Twofold operators are balanced.
  • Balance is a one-to-one mapping.
  • Balance is diferent than symmetry. Equality is different than sameness.
  • Systems balance at fine levels before jump.
  • Once jump is made, balance becomes boring.



  • Relationship is comparison.
  • Without comparison there is no perception.
  • Shift in perception-always and inverted view.
  • Experience or sequence is a relationship.
  • Swing of pendulum. Spice of life.





Patterns of Relational Paradigm


Twofold Operators







Summary of Emergent Axioms

Threefold Operators

Fourfold Operators

Fifth Business

Relational Organization

Relational Structure & Root Language

         Balance/relationship is a twofold operator with properties similar to those of the other twofold operators. However, this operator works in conjunction with form/process, hierarchy/network, sequence/jump, measure/count, and known/random to form fourfold operators. The fourfold operator is the basic pattern through which our physical reality is manifest and will be discussed in a following section. 

        The basic pattern of the balance/relationship operator is also represented by the words still point / change, potential / experience, relational/user view, iteration/compare, and identification/relationship. This twofold pattern is how the other twofold operators can be perceived. For example, there is a balance between form and process; they are part of the same thing. At the same time there is a relationship or contrast between form and process which makes perception possible. Without this contrast or comparison there is no perception.

         Balance/relationship can be analyzed as a twofold operator, i.e., without balance there is no relationship and without relationship there is no balance. It can also be analyzed as it applies to the other twofold operators -- the balance and relationship of the twofold. Both balance and relationship require the twofold before they make any sense. There is no balance or relationship of the one.

         Every aspect of the physical universe has a relationship with a balancing aspect. If you can't identify both sides of the balance or relationship, then you don't have a complete map of the territory. This axiom applies to itself -- the twofold operator balance/relationship.

         Relationship can be viewed as an imbalance. The balance/imbalance pair is a relationship which is balanced. It's self-referencing.

         Balance is equality -- a one-to-one mapping. It is not sameness. Process and form are balanced. For every form there is a process, a one-to-one mapping. An equality exists between every process and form, but they are not the same thing. They can be distinguished but not separated.

         Balance is different than symmetry. Symmetry is a special case of balance, a balance of form or space. In the Western world view, symmetry or mathematical equality is often assumed to be necessary for a system to be balanced. This assumption seems to be based on the view that the system or world can be totally described by its form. It ignores process. An illustration of balance which is not symmetrical can be obtained from some Oriental paintings. The figure itself is often not symmetrical but there is a balance between figure/ground.

         Relationship is the comparison between two things. There are always at least two in every relationship. In comparing two things, we must by necessity put one of them first ( A compared to B ), or one of them over the other (space / time). A relationship demands an order to the things being compared, but the order is arbitrary or subjective. If we can compare A to B, then we also can compare B to A. If we analyze space/time, then we can analyze time/space. In relationships, there is always an inverted view. Either party in a relationship can be on top.


         The threefold operator is necessary to understand the twofold operator balance/relationship. Of course the twofold operator is also necessary to understand the threefold. The self-referencing nature of reality makes the starting point arbitrary, but one has to make a choice and I've started with the twofold.

         In analyzing the twofold operators, there are always three basic views or perceptions which can be made. You can think of these three perceptions in terms of allocation between the twofold operators.

         As an example, we can say that the hierarchy and the male have all the power in our society. They set the directions and do the planning. The network and the female have no power.




         From another perception, an inverted view, it's easy to see that in reality the network and the female hold the real power in our society. They maintain the course, and are the ones who are in control. The power of the hierarchy and the male is bankrupt.




         There is always two perceptions, always an inverted view. And this perception of the two ways of allocating power is itself a third perception. From this perception the hierarchy and the male are balanced with the network and the female, each side being allocated equal power. After several swings of the pendulum, they just call it a tie.




         All three perceptions are valid, and all are necessary for a complete perception of our reality. This fourth perception -- the three perceptions as parts of a whole -- completes the picture and is in fact the fourfold operator and the manifestation of our reality.

         These perceptions of our reality are a very powerful tool. They apply to everything which is a part of our physical universe. The identification of the twofold operator and the mapping of our perception onto the two sides will go a long way toward providing us with an accurate map of our reality.

          Male and female -- the yin and yang -- are always in balance. For every male characteristic there is a counterbalancing female characteristic. For every competitive male there is a cooperative female. For Industrial Man there is Domestic Woman.

          The existence of a Western world view which says "it's external" demands the existence of an Eastern world view which says "it's internal." The existence of blacks who say "it's soul" demands the existence of whites who say "it's spirit."
Nothing exists in our reality without a balancing counterpart. If there are angels, there are devils. If there is peace, there is war. The particle is balanced by the wave, the process by the form.

         Some of the most interesting twofold operators which I have tried to understand are listed below.

Male / Female
Western / Eastern
North / South
Black / White
Space / Time
Photon / Neutrino

          The exhibit below contains a partial list of aspects of some of these twofold operators.




  • Individual
  • Group (The Many)
  • Vietnam
  • Afghanistan
  • Iron Curtain
  • Berlin Wall
  • 1984 Olympics
  • 1980 Olympics
  • CIA
  • KGB
  • "Evil Empire"
  • "We will bury you"
  • McCarthy purged minds
  • Stalin purged bodies

USA (White)

USA (Black)

  • Present Space, Futue Time
  • Present Time, Future Space
  • Harmony
  • Rythm
  • Do
  • Be
  • "He's good."
  • "He's bad."
  • Spirit
  • Soul
  • Discrimination
  • Quotas

USA (West)

USA (Black)

  • Hierarchy
  • Network
  • Pride
  • Face
  • Ballet
  • Martial Arts
  • The One
  • The Way (Tao)
  • Form
  • Process
  • Alphabet (Letters)
  • Characters (Pictures)




          Balance and relationship seem to have different roles in the process of change. One jumps from balance and experiences a relationship. If you attempt a discontinuous change while swinging on the pendulum, the result is seldom successful. If you are unbalanced and attempt to jump, you usually fall.

          The discontinuity of general systems theory, the jump to a new level of order by dissipative structures, and the introduction of a new paradigm all take place from a position of balance. The apparent chaos or destructing activity which takes place prior to the discontinuity seems to be an attempt by parts of the system to arrive at balance at a finer level.

          The feminist movement is an example of the balancing of systems at finer levels. Historically, the rational, aggressive and competitive nature of the male has been balanced by the intuitive, compassionate and cooperative nature of the female. As a result of the feminist movement, both male and female are moving toward a position in which reason and intuition, competition and cooperation, and aggression and compassion are equally present or balanced in each individual.

          In a neutral, balanced environment, new order will emerge.

          If a system stays balanced after the jump, it stagnates. Balance becomes boring. Relationship is the swing of the pendulum, the spice of life. Once a new level of order is established through the jump, the system naturally explores the limits of the new order. "No pain, no gain," and "Where's the party?" become the mottoes of the new.

          The steps in General Systems Theory correspond with this pattern. Stage 1 is formative where things are drawn to oneself -- an inhale. Stage 2 is replicative and outward directed -- an exhale. Stage 3 is perturbative and integrative -- a move to balance at a finer level. From this third stage the system jumps to a new level and the process begins again.

          Both balance and relationship are required, but they serve different purposes.

          A new paradigm changes the rules. It is part of the process which the universe is currently undergoing in preparation for a jump, the introduction of the new. The jump will be made from balance.


          One of the most obvious emergent concepts is a calculus which inverts the relationship of the existing calculus. The calculus of Newton and Leibniz, called "The Calculus," analyzes the relationship of space to time. The emergent, called "A Calculus," analyzes the relationship of time to space. It inverts the relationship of space and time.

          The applications of the emergent calculus of time/space are not yet clear. The existing calculus is a primary tool for the Industrial Man economy. It measures velocity and acceleration -- productivity measures. The new calculus may be a similar tool for the Domestic Woman economy which we do not at present measure. Rather than velocity, the emergent calculus measures pace. It is a measurement of comfort rather than of productivity. How does it feel? Does it fit?

          The basic relationships and derivatives of these two approaches to calculus are listed below where T is time and L is length or space.

The Calculus
A Calculus
L - position in space
T - position in time
L/T - velocity
T/L - pace
L/T2- acceleration
T/L2 - ?
L/T3 - control
T/L3 - ?


  • Existing: The Calculus

    Measurement of a change in space with regard to a change in time.

The ration of a change in space () to a change in time () as the change in time approaches zero. Velocity at a point.

  • Emergent: A Calculus

    Measurement of a change in time with regard to a change in space.


The Calculus
A Calculus
  • Space/Time
  • Time/Space
  • How many per hour?
  • How long did you stay there?
  • Productivity

    How many did you produce?

  • Comfort

How did it feel?

  • Measurement for industrial man.
  • Measurement for domestic woman.

Form/ProcessHierarchy/NetworkSequence/JumpMeasure/CountKnown/Random • Balance/Relationship • Summary of Emergent Axioms

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