Sunday, 27 July 2014 01:44

Paradigm Shift From Part To Whole

To change a paradigm is to change one's frame of beliefs about the world to another. Is it possible in a world of infinite parts to think about an inclusive Whole? Is this even desirable in a world seemingly bounded by infinite  boundaries?

The circle is fundamental in math as a 2-D image concept. Can we believe the circle is more than this image we draw, more than a defined circumference? Can we equally accept the circle as a 3-D form that comprehensively demonstrates through folding the idea of spherical unity that is inclusively whole?

Traditionally the idea of the circle is demonstrated by cutting a sphere in half. By compressing a sphere a 3-D circle is generated without destroying the wholeness of the only form that represents absolute unity. When the sphere is compressed the volume of the circle remains equal to the sphere. The surface boundary of the sphere changes properties. The sphere/circle is whole; nothing is taken away or added, it is transformed through movement from a spherical form to a circular form through compression. The circle/sphere functions as both Whole and discrete part simultaneously.

Euclidean construction of a circle is based on the definition of a point. Using a compass to draw a line that is considered as a set of points on an imaginary plane at a given distance from a single point, we draw and thus define a circle, calling the center point  'origin'. The small circle point contains even smaller equally concentric circles in the same way circles get progressively larger through opening the compass. There is no fixed outside or inside boundary, only unseen circles in alignment. The radius measures the openness of a compass used to draw a circle. It does not fully measure a circle, although we generalize and use it that way in the abstract.

The property of the image shows one continuous curved line defining a given area; we imagin individualized points. The properties of the 3-D circle show five distinct circles with volume. Think of a disc, such as a coin. Circles are dynamic, they move, can be moved; and through a consistent and systematic sequence of folds will self generate proportional relationships that are not possible with other shapes, yet contain all shapes.

If there is uncertainty about the difference between a 2-D and a 3-D circle then do the following:

Draw a circle, use a compass or trace around a circular object.

Cut the circle from the paper you drew it on.

Observe the difference between the image you drew, the hole that is left in the paper, and the circle in your hand.

Each of these must be understood for what they are in able to understand the interdependent nature of one to the other. There is nothing to suggest throwing out traditional understanding about the circle; on the contrary we are moved to enlarge what we believe by embracing the full nature of the object the picture represents.

This shift of perspective can be understood by looking at the word ‘geometry.’ Geometry means earth measure, measuring things of the earth. Geo refers to the earth. The earth is spherical and the sphere is whole. Metry means measure, keeping track through movement in space. We can now understand geometry comprehensively as wholemovement; a self-referencing system of the whole. This better describes, giving demonstration of our presently evolving worldview in a universe among many where much of what we see and know now was a short time ago unimagined. We can no longer afford to hold a geocentric view about ourselves, anymore than we can sustain the belief that the sun and celestial bodies revolve around the earth. We are a small part of something much larger and far more complex that yet imagined.

This suggest maybe it is time to consider shifting from a commonly held parts-to-whole thinking to a Whole–to-parts perspective. To start with the Whole in the form of the circle/sphere and observe information as  revealed through movement, the order and proportional arrangements, the appropriateness of interactive systems,  is perhaps worth considering. Through observation of what is generated from the circle, through folding and joining reveals what is not possible using other shapes or forms. The circle is its own center; an alignment of inner and outer boundaries. The whole is origin to all seen and unseen parts, realized and unrealized, revealing ongoing potential. The origin, both center and outer boundary, is already whole and cannot be constructed or deconstructed.

Broadening our perspective does not deny any mathematical value. What temporary benefits progress will eventually drop away being replaced by greater knowledge that elevates value towards a greater realization of human potential as we begin to see the finer reality of further abstraction. We need a more inclusive and comprehensive way of thinking about our universe, our place in it, and how we negotiate the inequalities and fragmentation, the separation that are no longer sustainable given our present understanding of the interrelated and interdependent nature of parts and systems. There is a fear of the unknown that isolates and keeps us from reaching out on a cosmic scale. Fear keeps us from reaching outside of the circle we have draw around ourselves.

Comparing properties of the image and the circle/sphere compression shows differences between 2-D & 3-D. The 3-D circle shows five discernable circles; three circle planes and two circle edge lines that contain a volumetric location. It all starts with a spherical point. Tradition shows two points making a relationship formed by connecting with a line. Three non linear points form three lines forming the edges of a triangle area. Similar components in both 2 & 3-D are points, lines, and planes. Folding the circle by touching any two points will generate two more points at the end of the crease, an axial line of division perpendicular to the distance between points that shows six relationships. These four points can be form into six edges that define four solid triangle planes. There are two solid planes and two open planes defined by five edges you can see, one edge you cannot see. Minimum description of a tetrahedron is for points in space. Edge relationships and planes are inherent in this spatial movement of two points of the circle. The first fold of the circle around the creased line/diameter/axis, in both directions forms two tetrahedra, one the inverse of the other at the same time showing a spherical pattern of movement as origin.

For those that like pictures with their words, I have included some photos of an old folded circle piece that bares relationship to this discussion. These pictures, “The Transient of Venus” show different views of an idea about Venus as it moves in a slow spiral around the sun observed from earth where for a short time appearing as a dark spot moving across the sun. This object is made using seven paper plate circles, four are folded to an open tetrahedron and joined with string holding them together, and the fifth is left unfolded, the other two form Venus and its path. It is painted conforming to the folded equilateral triangular grid matrix, indicating the activity between the surface and interior of the sun as Venus passes giving a temporary linear alignment of three spheres in space.




























This form becomes an expression of multiple parts and by adding string, the black square box, and paint gives design to the discrete parts of the folded matrix. Here we have made in “parts” a multiple expression of the whole. Parts and whole are folded one into the other.

The circle/sphere is the only form that demonstrates, with some degree, the idea of a comprehensive Whole. In that regard no other form can be observed that is principle to all symmetries, and all subsequent generations of parts. What is principle is what comes first, not what is believed at the time to be most important. The whole, even defined as “nothing,” for lack of boundary, binds all potential to the principles of first movement. Does our compass open wide enough and will it close small enough to construct all circles contained in the one that can not be drawn?






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