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
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.
Why am I spending so much time talking about this?
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 junk, this bad stuff that we don't like. 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
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 concept comes from the idea that the actions of others
can adversely affect everyone else. 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
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
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.
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
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
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.
(1), (3) Images from Design Science Toys web site at www.dstoys.com
(2) Picture from Chris Rywalt's Synergetics Photo Page at http://www.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
information, click here