Duality and polarity
In these two fundamentally different forms – circle and square, sphere and cube –, which do not seem to have any inner connection, there is a basic law, which we can find in everything that exists: the polarity as the two in one, as the male and female force, as day and night, as the two sides of a coin. This living principle of polarity is often mixed up with duality which antagonistically splits two complementary, but contrary qualities in good and bad.
Good and bad
Bad is not the equivalent opposite of good, but it is a secondary occurrence thereof. Like death is not the opposite of life, but a part of life. Hate is not the equivalent opposite of love, but it is a secondary reaction, which can, however, become very powerful. The shadow is not the equivalent opposite of light, but a reaction, which comes about through an opaque body. The polarity of light and shadow is true for every dense body, however not for the light as such.
Polarity as an effective nature law contains complementary forces, which work towards a three-unity and are focused onto a greater whole. Only when judgement interferes and raises one part to being good and demonises the other to being bad, an unfruitful struggle begins, which blocks the creative cooperation and thus the joy of each other and directs the gushing spring force to mills of disputes and war. „Polarity must, as a fruitful opposite, be strictly differentiated from an antagonistic and destructive dualism. What it is about is a two-unity, an opposition, which is encompassed by a higher unity.” 1
The polar opposites of circle and square are used as floorplans in many buildings. Also, in the symbolic meaning, there is a connection between the circle and the square as a perfect, eternal being and a dynamic development in time, like heaven and earth.
Human eyes have always seen the most original circle form as a sun star. This is by no means a still form, but a very dynamic one. It is a rolling celestial cart. The rays that emanate from it, are arrows of force, warmth and light.
Every form in nature as well as in culture arises from the polar opposites of the circle and the straight line which become effective and visible in the sun. Circle and straight line are the mother and father of all forms. The straight line arises from the circle. If the circle and the straight line connect, evolutionary basic forms emerge. Firstly, the egg as a sphere with a directional tendency and moreover the manifold figures of the spirals, which are manifested in the double helix, the snail shell and the galaxies.
The form as an expression of forces
Inner correlations can be recognised between streaming forms and solid forms, as, for example, between a water vortex and the shell of a snail. The energy and movement that are built in the solid forms, come to a halt. They show precisely by what forces they were created.
The Swiss doctor, painter and scientist, Hans Jenny, made this connection of invisible energy, vibration and visible forms convincingly visible in his experiments, which he called „cymatics“. The vibrations of certain frequencies create standing waves, sometimes of a surprisingly geometrical precision and wonderful complex order in sensitive materials like water. Some of these vibrating figures are similar to flowers, others to skeletons and organs. In the water sound pictures of Hans Jenny and Alexander Lauterwasser it becomes clear how sound and form mesh. We could call them living water picture metaphors for the „incarnation“ of the creative word and the primal tone „Bindu“, through which the universe was created.
The water researcher Theodor Schwenk also shows the connection of streaming forms and solid forms in his book Das sensible Chaos (The sensitive chaos, 1965). Here we see that the visible is an expression of the invisible. Seeing a bird as compressed air, a fish as compressed water, a snake as compressed earth, becomes obvious. What might the human being be, though? A compressed cosmos? A two-legged universe? In fact, every human being harbours a universe under his skullcap. This is held together by a skeleton, whose proportions refer to a harmonic law: the golden section.
The golden section
This is a geometric law with astounding characteristics and numerical proportions, which can be found in rich diversity in the forms of nature. You can see these laws very distinctly in flowers, which reflect the planetary trajectories in their forms. Hartmut Warm visualises the orbits of the planets in his book Die Signatur der Sphären (The signature of the spheres). He shows that the Earth and Venus draw a precise pentagram into the cosmic space, as a trace of their invisible movements during their respective journey around the sun and their dance around each other in the course of eight years. It is difficult to scientifically prove that the planetary movements have a form-building influence on the Earth, however, it becomes manifested through the correspondences and proves itself: If we look at flowers, we look at the cosmos at the same time, with whose forces and rhythms the flowers interact.
In the golden section the smaller part (the „minor“) is in the same proportion to the larger one (the „maior“) like this one is to the whole. This means that the minor and the maior are divided in such a way that they contain the whole. No other point on a line can do this.
Apart from the golden section there is a second universal law of division: symmetry. Pure symmetry is the original division. It is always identical with itself. There would be no development from it alone. The golden section divides unlike symmetry, but in such a way that the proportions remain the same. Through it development is possible through the harmonious-dynamic interaction of quality and quantity. By doing so, it does not fall from its wholeness and sprawls into the arbitrary.
Nature works with symmetry as well as with „constant division“ as the golden section is also called. The purest figure of this harmonious-dynamic order is the pentagram.2