## The Geometry of Harmony

Geometry is the most fundamental subject in the universe, for it describes the relationships between all things. The application of geometry to life can help us to better understand life.

This article will be looking at harmony and geometry, particularly, tensegrity, and it's relationship to life. Tensegrity is a word coined by R. Buckminster Fuller in his masterwork Synergetics. A tensegrity structure is one which is defined by tensional forces, not compression member forces. In a standard building, you start with posts and beams which absorb the forces placed on top of them. A post or a beam will fail if there is too much stress locally on one part of it. It is rigid and cannot flex or adapt holistically to forces placed locally on any one point of the structure. But a tensegrity structure balances the forces around and within it. It is dynamic and can respond to change, just as life can.

Bucky says that all structures in the Universe, from the solar system to the atom, are tensegrity structures.

We will see how tensegrity relates to harmony, and by looking at these structures, discover the true definition of harmony.

These are examples of tensegrity structures.

Picture 1 A basic tensegrity structure. (1)

Picture 2 A geodesic dome. The Geosphere at Disney World (2)

Picture 3 Showing tensegrity struts with attached tension wires and caps. Also showing more clearly how the struts are independently islanded within the structure. (3)

Picture 2 is a geodesic dome, the famous geosphere at Disney World in Florida. Picture 1 is an icosahedron, the base geometry from which Class I geodesic domes are constructed.

Picture 3 shows how each strut has a tension wire connected to it, and how the struts have notches in them to connect to other tension wires on other struts, and are capped at the ends. (These pictures are models only. A tensegrity strut could be manufactured differently, but the principles are the same as shown here).

Look at Picture 1 again. None of the struts ever touch each other. They are independently islanded so that if forces act upon it, the entire structure immediately finds balance. When a structure is built in this way, it can withstand tremendous forces upon it. If you push on one end of it, there will be an immediate, uniform and symmetrical response around the entire structure. It is dynamic and can flex inwardly and outwardly, always finding equilibrium within itself. In other words, it can easily adapt to change. (A conventionally built structure, with all of the ends connected to each other, is brittle and will collapse under stress at the localized point of pressure.)

3 strut tensegrity vertex (4)

4 strut tensegrity vertex (5)

5 strut tensegrity vertex (6)

You can see here that the ends of the struts in a tensegrity design do not come together. This picture doesn't show it very well, but the ends of the struts do not lay upon each other, they are held by the balanced tensional forces of the structure apart from one another. (See picture 1 and 3 at the beginning of the article.)

The wires are shorter than the struts, so that when a strut is inserted into the structure, the wires stretch a little, providing tension. The struts pull upon the stretched wires and the tension wires provide an inward force which the more rigid struts resist. All of the struts want to fly radially outward, but they are resisted by the tensional force which tries to push it together. The inward and outward forces generated by the structure is a synergetic combination of ALL of the struts and tension wires, so that, in a large structure with lots of struts, even if you removed a bunch of them the system would not fall apart. It would immediately re-balance internally all of the forces acting upon it. The tensegrity system is in perfect balance.

This is a brilliant innovation because if you work with tensegrity you can see that the structure INTERNALLY GENERATES ALL OF THE FORCES UPON IT AND WITHIN IT. It generates its own energy and dynamically balances it. It does not require energy from the outside. It is self-contained, independently energy generating and self-balancing. If you built one of these things out in space it would operate the same way as when subjected to a gravitational field. In fact if you study a tensegrity structure for a while you can see that it generates its own gravitational force, circumferentially, upon itself, and also generates an outward, anti-gravitational, force which balances the inward force.

If you play with one of these things you can FEEL the energy within it and can see immediately how it can come quickly to balance when subjected to outside forces. It's almost as if the thing were alive.

Tensegrity is the epitome of the holistic idea.

The brilliance of tensegrity comes from one simple, but powerful idea: each strut has attached to it a tension wire which is shorter in length than the length of the strut. This is the source of the energy generated within the structure. The tension wire is forced to stretch a little when attached to another strut. So every individual element is contributing equal energy to the entire structure. The combined forces generated by each element are in no way predictable by simply saying that each strut has a tension wire connected to it. When such a tensegrity system is put together, many forces are created which combine effortlessly to create something much greater than the sum of its parts.

Because life itself is similar to tensegrity.

We look around on planet earth and see contrast and diversity everywhere, which provides tension. The contrast provides tension, because there is so much out there that we don't like. There are so many ideas, so many opinions, so many different activities going on that we wouldn't in a million years want to have anything to do with. The natural impulse is to say: "OK, lets get rid of all of this garbage. Lets create a world of harmony and peace so that all can be comfortable."

That's a great idea, except that it doesn't work!!

Like a tensegrity structure, IT IS THE TENSION PROVIDED BY THE CONTRAST THAT GIVES LIFE ITS DYNAMIC QUALITY.

It's the tension that provides the dynamic, self-balancing energy for the tensegrity structure, and its the contrast of opinion and action that provides the dynamism for life itself to exist, to be in balance, and to grow. Without tension, without contrast, there is weakness, brittleness, non-responsiveness to change, stagnation, and yes, if carried far enough, death.

Picture 4 A structure where all of the elements are touching at the vertices. (7)

This is a smaller version of Picture 1 (icosahedron). The struts are constrained to come together at every point. This structure will fall apart when subjected to stress, because the blue compression struts have nowhere to go and so will break at the point of pressure.

A harmonious, peaceful world is like a structure when it is made out of materials that all come together at the vertices (Picture 4).

It falls apart under stress, because there is no self-generated energy from within the structure. There is no holistic balance of forces. There is no room for change. This kind of structure can be beautiful, but it cannot adapt. It is fixed in position, and cannot change.

It cannot change because the individual pieces of which it is composed have no freedom to operate.

They are constrained to come together.

The tensegrity structure, remember, is composed of individual struts which never touch each other, yet all of these struts are connected by the tension wires and share the entire energy of the structure. In fact, each member is responsible for CREATING the energy of the whole. Without any one individual element, the structure could not exist in wholeness. Of course, it would still exist, but it would be less than complete. That is why in life every being is so important. Every individual is creating and balancing the energy of the whole. All individual members of the structure are intimately connected, yet have the freedom to go their own individual way. All of the elements of the structure are happy to see every other member doing their own thing, completely and fully allowing independent expression and action!

This is the true meaning of harmony.

HARMONY IS THE COMPLETE ALLOWANCE OF INDEPENDENT EXPRESSION.

So in order to have true harmony, there must be dynamic tension. There must be contrast. There must be complete freedom of expression. And there must be complete allowance. Unconditional allowance is the same thing as unconditional love.

Each person must be allowed to go his or her own way, while still being part of the whole.

So many think that if only the world could be one of peace and harmony, then all would be perfect. But it would be just the opposite. When most people think of a world of peace and harmony, they think of a world where 'all of the bad stuff' has been eliminated. This is a flawed concept because it requires other beings to constrain their actions in order to satisfy others who may not like those actions. The warrior likes to fight. A world of peace and love is not something to which he or she will agree to at all. The history of mankind is the history of the struggle to get people to think and act in a way which one or another group finds non-threatening. It cannot possibly work because it requires all to agree to a certain set of ideas and actions which all beings can find acceptable. It constrains freedom and limits expression, something which no being will put up with for very long! A world where all ideas and activities have been whittled down to those which everyone can agree upon is stagnant. It is static, not dynamic. There is no diversity providing the tension which gives birth to new ideas, new desires, new ways of doing things. Like the brittle structure, it falls apart when buffeted from the outside, or from within . It has less integrity, it cannot respond to changing conditions.

HARMONY IS NOT EVERYONE AGREEING WITH EACH OTHER. HARMONY (AND LOVE) IS ALLOWING.

The tensegrity structure shows perfectly how this is accomplished. If you want to build one, study it, and test it out you will see for yourself and it will blow your mind. (You can buy tensegrity kits at

www.dstoys.com.)

Harmony and love is allowing all of our wonderful fellow beings to create in any way they would wish, even if we disagree vehemently with what they are doing, even if it is obvious, from our point of view, that their actions are egregious.

For example, if the tensegrity structure were to become more harmonious, struts would have to be removed from their unique, separated positions and placed closer to each other. This would destroy the perfect balance of forces and distort the whole. In the tensegrity structure every one of the struts is independently acting, yet creating the perfectly balanced whole.

And so in life as well.

The desire for harmony within each being is strong. But the desire for freedom is stronger. The desire for freedom is the single strongest desire that any being has. If you have lived long enough and observed enough, you can see that this is true. You can't constrain freedom in the desire for harmony. That's where the idea of allowing comes in. Harmony can be created and maintained even among the most glaring diversity as long as everyone agrees not to limit thought or conduct!

No one can create in your experience, no one can affect you negatively in the slightest way, unless you place your attention upon it and resist it. When you place your attention on something that is not wanted, you include it in your vibrational mix and the universe responds by Law of Attraction to that signal. Thus the conditions around you change to match the vibrational signal you have sent out, a signal which is bringing into your life all of those unwanted conditions you dislike so much.

The solution?

Place your focus upon what you want, don't push against what you don't want. Know that even if the actions of others seem abhorrent, it is all part of the tension that creates the dynamics of life. It cannot affect you, unless you resist it.

Like the tensegrity structure, each being must be allowed freedom while still being connected to the whole.

Create your life the way you would like, and allow others to do so in their own way, knowing that their energy is just as vital to the overall structure as yours is.

Work to change conditions in the world, but do it from a position of creating positively, not resisting negatively.

Like the tensegrity structure, this universe is creating its own energy through dynamic tension. The universe is perfectly balanced, ever-expanding, infinitely responsive to change, filled with new ideas and activities, and above all, overflowing with well being.

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(1), (3) Images from Design Science Toys web site at www.dstoys.com

(2) Picture from Chris Rywalt's Synergetics Photo Page at westnet.com/
~crywalt/photos/photos.html

(4), (5), (6) Images from Holistic Geometry, by Marvin Solit,Foundation for New Directions, at www.fnd.org/geo.htm

(7) Image from George W. Hart's awesome web site at www. georgehart.com