Mary Swenson

The Circle symbolizes the Public Realm and relates to Quasi-research or the mixed design approach.  The process used refers to subtle nuances illuminating what is not readily evident. It culminates in the Business, intuitive, or cultural component. Historically, the sphere has represented infinity, perfection, and the eternal. It is blue and indicative of the cosmic universal flow which is a representation the interpretive data recycling germane to all research style which occurs in any investigative effort. The sphere is the symbol of connectivity and change, or the manifestation of collective creativity. When each of the geometric elements are strategically focused toward an objective, restrictions can become instrumental, and the quotidian or everyday becomes incredible. To circle something implies an area of action or influence; or to move or revolve around a fixed point of reference. The combination of each geometrical construct when used together in a specific procedure, results in an algorithm for resolving conflict that can be used as a cipher, or in symbolic logic. The etiology of any problem and the necessary decision required creates a need for resolution between two opposing forces.

A series of circles, one inside the other, is widely accepted as a representation of the cosmos. It is a universal symbol of extensive meaning representing notions of totality, wholeness, the self, eternity, infinity and cyclic movement. It is a manifestation of both the feminine and masculine principle in addition to the perpetual motion of what generates change. The circle is also absolute zero symbolizing the emptiness of the embryo and the potential of what is not there that can be potentially brought into reality. The sphere is said to possess magical properties as a protective agent and indicates the end of the process of individuation, or the striving of psychic wholeness and self-realization (Julien, p. 71). For Jung, it was the ultimate state of oneness or the antithesis of the square (lowest state of humanity that has not achieved inner perfection) with the octagon as a composite between each entity. This is known as the sacred “squaring of the circle” in ancient alchemy which has psychological import in self-integration and actualization.

The series of models offered at interpretive leadership, offers the triangle as the meeting ground of two contrary concepts. In our strategic planning template, the circle is but one level of the triangle forming the intersection between the two poles of reality which comprises the physical and spiritual poles and between them, or the observable empirical reality. Empirical theory as we define it houses a combination of what is, how much (frequency), and what is not, thereby producing an evaluative form where weight or gravity can be contemplated to illicit action. In this process, meaning and understanding are obtained through the contrast and reconciliation of opposites. According to the Psychoanalytic theorists one’s inability to integrate opposites results in all manner of illness, both mental and physical. However, the circle has many associations and appears in numerous forms in various artistic creations. As a symbol of the infinite timelessness, without beginning (alpha) or end (omega), it is the ultimate and perfect geometric symbol used to depict halos, rings, wheels and seasons. Just as a structure’s shape, color, and essence denotes its best use, so these elements configure to manifest optimum outcomes.

The half circle is a symbol of incompleteness while conversely is the promise is evidenced in the rainbow shape which touches or communicates between the realms of heaven and earth Rings have been used as symbols of union, eternity, magic, and of authority and status. The Koran says King Solomon had a magic ring that could transport him to a celestial sphere where he could rest from the affairs of state. The snake or dragon with its tail in its mouth continually devouring itself and being reborn from itself, symbolizes eternity and the cyclic nature depicting process and the unity of all things which never disappears but simply changes form in the never ending cycle of destruction and re-creation (Carter, 1998). This process is the symbol for chemical change and a representation of mobility as in the form of a wheel. Rose windows for example, use the circle geometry three ways:

• Manifest- impact of the structural composition
• Hidden-relationships and proportions of the parts
• Symbolic- a representative shorthand where figures represent different things.

Retrieved from Paul Carter, Dartmouth College, 1998.

Vesicas, or mandorlas, are the ellipse figures that occur when circles overlap or intersect such as what occurs in a Venn diagram or series of rings. In symbolic logic, the Venn diagram represents the intersection of two sets as a unification of Art and Science. A horizontal vesica is depicted as the all seeing or omnipresent eye that leads to the soul, while the vertical position is typically employed as an almond shaped aureole. The wheel, because of its ability to turn, has been associated with chance and fortune assuming the form of inherent instability. This sector relates to intuition and the merging of both logic and creativity in a symmetrical approach to thinking which uses triangulation, categorization and interpretation in various combinations to reconfigure something new. Utilizing both modes of thinking and research is a fundamental leadership attribute that sets it apart from others. Appropriately, in basic mathematics to round something off (such as a number) implies that it is made complete or finished.

The vesica, conversely, is the overlap between two circles as is termed a mandorla (or almond shaped vesica) and is the universally recognized shape for a portal or doorway, and has many references to the fish as in Christianity, or the all-seeing eye when positioned horizontally. The shape overall implies an intersection between this world and the next. The circle is the ultimate action figure. The squaring as such, occurs in the Indian and Tibetan mandalas, and is a vehicle for concentrating the mind that often contains a square. Carl Jung suggested that the circle symbolizes the processes of nature and the cosmos as a whole, while the square is the universal projection of “man”. However, if the cosmos represents the universe and the square represents the physical earth, then the role of the triangle between them assumes a place in its own right as a representation of humanity throughout the ages.

As a bold empirical median, trigonometry provides the integrated connection between the corporeal (circular) and temporal (angular) planes, or the joining of both arc and angle. This combination is realized in biology on a cellular level between organic and inorganic substances. As with any true dynamic force, descriptors for the circle or oval can be considered as change, movement, and a process that occurs over time offering perceptions for multiple determinations. The recycling of creation results in the evolution of reality and develops verification comprised of both induction and deduction linking imperative constructs together in an order that works both unilaterally and bilaterally evoking an imperative by which to address and navigate existence.

The assertion of this system is that the combination of the three shapes elicits innovation by enhancing imagination and fostering perceptual intuition. The result is an integration of the opposing concepts that together generate imagination. This conceptual analogy is evident in the mathematical operations used to find answers using known values to obtain what is not apparent. Combining two has special significance as the reconciliation of the infinite and that which is finite. The squaring of the circle is the quintessential attempt to rationalize the irrational. Therefore the rounding of the triangle offers a method to access direction, knowledge and ability. In Sanskrit the literal translation of mandala means circle, center, or Holy Realm which disciplines the mind.

A mandala often contains a square as well as a circle, even if the square does not square the circle the symbolism is there. Triangles are also used. The circle symbolizes nature or the cosmos (collective unconscious) and the square as its opposite refers to the universe perceived and projected by humanity (consciousness). For Jung, the ultimate squaring resulted from the self collectively manifested in universal archetypes. The circle as it symbolizes the universe and the cosmos while the square is the limits of nature. Between them lies the triangle as the ultimate resolution. The great pyramids interestingly enough, were considered to square the circle and reconcile both triangle and square as does the function of mixed method research.

Carl Jung proposed that the artistic function of creating a mandala each day provided a snapshot view into the psyche and that through the act of creating the figure and altering it as a matter of course, the health or balance of individual could improve in a creative dialogue of self-healing. The golden ration is the successful integration of two extremes representing the golden mean or reconciliation between two opposing extremes.  A vesica pictorially, demonstrates the intersection or the duality of the two circles (or more) as depicted by a Venn diagram integrating duality and revealing common ground.

These shapes represent each research application providing an axiom template for individuals and groups to address concerns, realize dreams, and resolve conflicts. The power of words and numbers has always been a subject of introspection and interest to scholars for a multitude of reasons. When those two elements are combined, signs or indicators as well as symbols as representations become critical to understanding hieroglyphs which are bilingual in nature. The power of symbolic logic is present everywhere in ancient and modern times and manifests itself in campaign slogans, business logos, short hand, artistic expression and mathematics.

Torrance (1979) has identified three thinking and behavioral styles with respect to individuals and groups as left, right, and integrative. This demonstrates the promise of the transcendence available when utilizing opposing constructs of both paradox and balance. Considerable interest continues to develop with psychologists, educators, and businesses with the styles associated in the anatomical physical structures of both right and left hemispheres. The use of geometrical shapes as representations of a related conceptual construct enhances abstract cognitive maps yielding an application for extensive applications across disciplines. A procedure can be applied and used as a planning algorithm to solve problems, make decisions, or resolve conflict (crisis control) and requires a set structure that individuals can use to interpret information and make determinations about leadership. For example, each shape can be visualized in the following three ways.

The ancient Egyptians conceived life everlasting as beginning with a journey of death where the KA (life force) leaves the body for judgment of the BA (soul) to recombine them into the AKH, (spirit). This journey is most significant as the KA is a representation of the mind (EEG) and the BA is the physical manifestation of the heart which is weighed to see if it balances against the feather of MAAT (truth) to determine if things are the way they should be. If the scales balance, the two can combine together once again and re-enter the living world to enjoy its’ pleasures, obtaining heaven or nirvana, as this utopia is for all of eternity, ensuring immortality as opposed to oblivion (National Geographic, 2005).

These forces can be considered as the brain activity or intellectual essence of person in the KA or life force (IQ). The second force as the BA or emotional component (EKG) while identified as the soul by the Egyptians was thus represented by the heart (EQ or emotional quotient). The third component again is a combination of the two and is termed the spirit or AKH and is the drive force, instinct, guts and free will associated with higher powers (ESP). Combined there is a cohesive manifestation or Intuitive Extrasensory Quotient (IEQ) located in the abdomen as the area of visceral response and somatic energy. These terms utilize the mind, heart, and soul and together they serve one between the planes of a metaphysical or spiritual opposite.

Jung wrote extensively about the circle as a representation of the personality and stated that when an individual, through struggle, comes to themselves, they are able to accept who they are.  In doing so, they are able to become reconciled to themselves and are able to be reconciled to adverse circumstances and events.  A mandala has been said to represent an involuntary confession of a peculiar mental condition. People who have been through trial by fire that have obtained the peace one can feel only after a long and fruitless struggle has ended, describe their experiences in such a way as to evidence a centering of themselves within. Such a person knows that what is wrong within the world is wrong in them—if a person can deal with what is misaligned in their own psyche, they have done something real for the world. (Storr, 1983).  Jung proposed that when an individual fails to acknowledge a creator, egomania develops from this neurosis, (functional fixedness) and sickness ensues. To serve a mania is undignified and detestable, but to serve a higher power and purpose is full of meaning and promise. Therefore, submission is a willingness to serve as an invisible force outside the self.

The “soul spark” of humanity encompasses the inner most divine essence of life using symbols to characterize the deity within, in nature, and the world. The fact that images of this type have a significant therapeutic effect upon their authors or creators is well established and widely supported. Each operation represents a bold attempt to recognize and assemble opposing irreconcilable differences and the reconciliation of hopeless splits (Jung, 1961). This is also true of the fight or flight dilemma in which a person is either a victim or an aggressor who engages in violence. In finding a third alternative, victory from either extreme is assured. An attempt towards an integrated direction has a healing property and empowers an individual to take action and claim responsibility for their own outcome. Nothing of genuine integrity results from a replication or a deliberate imitation. 

For genuine and true outcomes are the sole products of sincere spontaneity. Jung puts it well when he described the recycling effect of the circle (as in action research) or the mandala as encompassing 1) formation 2) transformation 3) and recreation. This sequence is validated in the algorithmic formula used to cipher and navigate through adversity using each of the geometrical designs. By formulating items upon the triangle one can neutralize polarity. Using an open grid or text box, with closed borders as well as a spreadsheet (expanded truth table), the logic box transforms information dependent upon how it is to be utilized into the sensory system. In the process of revisiting information through a theory, practice, and research lens, invention results.

This series and process aligns with identifying the conditions or content by which to discern relevant issues. Secondly, the situation or the context in which something develops evidences and offers implementation of an action plan through the connections made during redefinition. For Jung, the circle was a living representation of the self—the path to the center, to individuation as the ultimate insightful expression. Jung utilized a geometric figure to combat the confrontational opposites implicit in nature that disorient and impair our ability to cope, manage, and deal with the challenges of life.

Finding it, pulling it all together, and putting it out there for others to use is the greatest of satisfactions. It is also representative of the essence of leadership behavior which always implies the guidance of others vicariously or directly. No one does it alone, at least not well. The following passage from Jung’s book Dreams sums up the relationship between the two opposing forces of the personality it a meaningful way. “It is evident that the human psyche possesses layers that lie below consciousness and that there could just as well be layers lying above consciousness. Thus the actual conscious mind can claim only a relatively central position and must accept that the unconscious psyche transcends and surrounds it on all sides. Pure unconscious content then connects it backwards with physiological states on one side and archetypal data on the other.

. Copyright © 2005 Interpretive Leadership Inc. Patent Pending, All Rights Reserved.

Learn more about the symbolism of: The Triangle - The Square