Thursday, 26 May 2011 16:35


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Having over the last month revisited some of the transforming systems I have explored by folding and joining circles has me rethinking movement. You can see videos of a few of the torus systems at; http://www.facebook.com/wholemovement?sk=app_2392950137 There will be more videos coming about variations on the torus and other kinds of moving and transforming systems inherent in the folds of the circle. Until I get a better understanding of moving videos around, here are a few thoughts.


We are all familiar with any number of geometrical transforming toys, many that appeared in the market after the rush of the Rubik's cube in the 70's, followed by a glut of “transformer toys,” and of course now the simulation of transformation through computer imaging. There is a long history of geometric and folded paper transforming and movement systems; the hexaflexagon and origami cranes commonly known to many. We all have curiosity about and are fascinated with movement. What is it to move, to be moved, to change and be changed? What happens as forms change is intimately connected to our ideas about time and space and form as the ordering of relationships that reveal interconnections between local and other.


We can trace movement through layers of infinitesimally smaller organized subsystems of individualized moving parts; beyond the atom to even smaller imagined parts and systems, about as successfully as we understand movement at speeds beyond our capacity to comprehend. Movement appears relative, so we assume a binary position of movement and non-movement, giving ourselves a standard to measure the space between things, which is only scaffolding to move from the physical mechanical to the transcendental mechanical.


As all children no doubt, I remember looking at trees moving and wondered where the wind comes from, who started it; what was that first push? What is it that is moving? I still wonder about movement and where things come from. Most explanations are imagined stories, elaborations in science about how things happen, not where it comes from or why. This moves into a larger context, into religion which has been around as long as we have been aware of forces existing outside of ourselves. Are we not suppose to ask these questions? There is no dogma in questions, or in faith; only in the formalize answers and the fixed stories we tell to others, expecting them to believe our story when they have their own stories to believe. No two pictures can have the same frame; and every picture tells a different story. You can bet we have been framed, for movement is not caught in static images.


I am intrigued that we have used the circle as a static symbol for both everything and nothing. Today we agree on mostly nothing, zero, yet desiring everything. We really don't understand either. Together is suggested an evolutionary integration towards understanding from limited movement towards increased capacity to move. A circle is a complete, inclusive, and self-referenced concentric movement system indicating there is no inner or outer boundary. There is no such thing as a one way movement except in the static image of conceptual framing. The circle is the compressive movement of the sphere from a spherical form to a planer form without a break in unity. The sphere looks the same weather moving or not, unless it is compressed into a form change. Only in origin will we find necessity and understanding the need for movement and change.


Compressing the sphere changes its form in two primary directions of symmetry; perpendicular to the expanding centrifugal plane, similar to how galaxies are formed, and the decreasing depth of dimensionality. Three circles are revealed in transforming spherical unity to a planer triunity. There is no separation of surface only a redistribution of volume. Nothing is added or taken away, the circle/sphere is Whole. Between the two circle planes is a circle ring, the dynamic agent of differentiation. Triunity of the circle is structural pattern revealed through precessional movement and is principle for all subsequent realization of potential formation; thus is prologue for another creation story:

Wholeness through movement causes division becoming duality in triangulation with each part consistent to movement and totally inner-dependent to the Whole. The individual nature of part to Whole regulates the interactions between all formed and unformed parts on all scale, in all time, with purposeful movement. This is how one story begins.


This still does not answer my question about the first push of wind, it only shows that movement is the first action that happens out of what we imagine to have no movement. From a supposed spherical non-movement compression into a time space continuum followed by the line of division into the triunity of been, doing and still doing. That first

movement can not be understood by describing a diameter or drawing line between there and here, the information is in the conscious experience of moving.


Folding is not to just demonstrate what you can do with the circle, it is about what you can discover by observing movement and what information is revealed in movement of the circle to itself. Folding is not about the skill, inventiveness or creativity expression of the folder, rather it is in understanding the nature of what the circle can do and what is revealed that is instructive for increasing folder capacity. Only through observation of moving do we know what we are doing. Circle unity does not change, but movement changes the form, so it is not about the form, rather to understand the movement between the forms, directional and with alignment. The circle is both context and the content; it is the folders perception and understanding that changes and moves.


As we observe the initial sphere/circle transformation where information is generated, that upon reflection and consistent development of systematic symmetrical folding leads to an equilateral triangular grid of creases. This triangle grid is the primal matrix for moving the circle; for forming, reforming, transforming, and in-forming the circle/sphere. After all the circle is a generalized flat plane, albeit the only one of its kind. Reconfiguring this grid is the means to informing the possibilities inherent in the circle. Endless interrelated movement and joining in multiples gives expression to what otherwise remains potential.


This is only part of the story. It does not answer my question about the first push of wind, but it does move the story forward off of the flat plane and out into space where the movement from one location to another requires time and consideration.


Wednesday, 06 April 2011 15:16

Properties Of The Circle

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It is important to understand the origin and the properties of what we are working with. In this case the 3-D circle needs to be differentiated from the circle image we draw. The circle, the subject of the image, has spatial properties that are unique from all other 3-D forms. We need to observed the differences in properties between 2-D and 3-D if there is to be any clarity and understanding about each.


If we do not know the properties of what we are working with we do not know what it is or what to do with it beyond arbitrarily imposing our will that frequently ends up violating the nature of what it is, often being counter to expected results. Lack of understanding properties has proven over time to cause unforeseen problems. Properties of the circle set the foundation for all subsequent folding (see previous blogs).




This picture shows a circle and the image of a circle.

The circle originates through spherical compression. Both circle and sphere demonstrate a dual function as individual unit and unity simultaneously. The non-differentiation of spherical surface is transformed by a right angle movement to the direction of an centrifugally expanding circle that reveals a triunity of three circles

The image shows one circle where as the 3-D circle shows three circles, one on each side and a circle ring. (Think of an extremely flattened cylinder.) There are two edges where the three planes meet. There is an inside volume and an outside space. Three planes, two edges, two spaces; (3+2+2=7.)

The circle is a triunity of three interdependent circles that can not be separated one without the other. In order to conceptually take them apart unity is destroyed, being left with three abstracted, isolated, and imaginary units. The association of three anythings is a structural pattern and reflects unity. All number of units will never equal unity, for unity is always singular. Units is always plural and infinite in number. Three is the first active number and seven is the most possible associations of three.


One set of three (ABC)

Three sets of each individually (A) (B) (C)

Three combination of sets of two each (AB) (AC) (BC)

Drawing a diameter divides the image in two halves. When folding the circle in half the diameter changes the properties where instead of two semicircles on one plane there are six semi-circle planes; six half circles. While this make no rational sense using a 2-D model, it is observationally logical to the folded circle. The circle remains whole, retaining unity even as folded into six half circles. ( If we decided to count the two edge circles it would change the possible combinations of associations.)

There is no conflict between folding and drawing circles; they are two very different systems; one is an image/idea of the other. Knowing the difference in properties helps clarify some confusion and greatly expands our understanding of the circle. It introduces a new area of dynamic exploration that in no way denies the theoretical or 2-D mathematics that has been developed. There are well over a hundred relationships, functions, and math concepts in this one fold of the circle into six halves. This is not to suggest one is better than the other, but rather to understand the difference and benefits of both folding and drawing circles and the connections between them. We know the value of drawing circles but there is no precedent for folding the circle and that means we have no experience or understanding about it. Only through the direct experience of folding will we understand the difference.

Besides the information and the beautiful objects that are revealed by folding, it is fun, interesting and engaging. We have a prejudice of not wanting to have too much fun learning something we have already decided should be difficult; if it is serious we must work at it. We are at our most open to learning when we are having fun and engaged in what holds our interest and simulates curiosity. Long ago we decided that mathematically the circle as image is a symbol for nothing, a place holder to later be replaced by something of value. It is now time to look at the information value of the circle beyond the image and the mechanical advantage we find in using it.

The information and reformation possibilities by folding circles demonstrates we can no longer afford to disregard circle/sphere unity. Because we have not done it before is no reason to continue to ignore it. I am writing these blogs in an attempt to give some understanding about the importance of the circle and that it might possibly simulate you to want to fold the circle and to find out for yourself and discover things there to be observed, and connections to directions not yet seen.