stated that all natural movement arises out of a state of imbalance, of non-equilib- rium. Non-equilibrium is a pre-requisite for movement and evolution in all its forms, and a state of equilibrium is therefore impossible in Nature. Yet we find that certain symmetries do occur, nevertheless. The pine cone shown in fig. 4.7 represents a condition of 'balanced imbalance'. The apparent symmetry of the
pine cone at the same time embodies a dis- symmetry in that from the left-hand side to
the right, its form encompasses five spirals descending and eight spirals ascending.
In terms of integers or whole numbers themselves, uneven numbers are generally considered male and even numbers female, since even numbers are divisible by two (mother + offspring). In the pine cone this gender aspect or duality on the one hand is represented by the five descending spirals of male energies or higher rotational velocities, since within the overall length, or cycloid- spiral-wavelength as it were, of the pine cone, they achieve more rotations. The eight ascending spirals of female energies, on the other hand, gradually being aroused by the male forces, are slower moving, making only one full rotation over their common wave- length. Between them a state of harmony, or resonance, comes into being in relation to their respective energies. Where the two sys- tems of spirals cross; where they combine or negate each other, the seed of future pine trees, the new life, is formed.
The actual proportion of five male spirals to eight female spirals or 5:8 forms part of the
The symmetry of the pine cone demonstrates the condition of "Balanced Imbalance" which arises out of the harmonic interaction of two antithetical, complementary, but oppositely charged forces. The 5 positive male spirals of energy descend towards the 8 rising negative female spirals of energy. Where these cross each other a union of both forces occurs and there the seed of the new life is to be found. The male forces decelerate and the female forces accelerate to arrive at a mutual state of resonance.
66 Living Energies
so-called Fibonacci series, which progres- sively and with increasing accuracy, mathe- matically defines the proportion of the 'Golden Section', also known as Phi, or which becomes almost constant in the ratio of 1:1.618033988. Together with Pi the 'tran- scendental number' describing the circumfer- ence of the circle, this is one of the so-called 'Perfect' or 'Divine Proportions'.
Pi has been given the term 'transcendental', because no end to the sequence of numbers after the decimal point has yet been found, even though computers have been working on it for years. It is assumed to be of infinite length and therefore in this sense is a magni- tude beyond time and space. Phi on the other hand, is more down to earth and is also found in the linear proportions of the pentagon (fig. 4.8). Phi is frequently expressed in many of Nature's creations, and by varying the angle between the adjacent radii (their relative lengths conforming to the Phi proportion), a number of natural spirals (fig. 4.9) and leaf- shapes (fig. 4.10) can be created.
Phi is also manifested in the structure of the human body. If the length of the hand has the value of 1, for instance, then the com- bined length of hand + forearm has the approximate value of 1.618033988. Similarly the proportion of upper arm to hand + fore- arm is in the same ratio of 1:1.618033988, or In my studies of Phi from an energetic point of view, it seems always to be associ- ated with the transmutation of energy into form, since this proportion is reflected in so many of Nature's creations. In recognition of this peculiarity, I have come to call it the
'Transmutation Number'.
From another angle, the two spiral systems in fig. 4.11 have a common wavelength, dynamically viewed as cycloid-spiral-space- curves, since they curve out from their com- mon axis and eventually return to it over the full length of the pine cone, the eight female spirals having a slower rotational period than the five male spirals. Within this wavelength, there are points where they interconnect cre- atively. Such a point I call the zero-point, since it is the point where both male and female energetic attributes die or are temporarily sus- pended in order that new life can be created.
The zero point is where all motion ceases and where all motion begins. It is a point of extremely high potential in the same way that the string of a musical instrument is still in a state of tension, of sound-creating potential, even though it is not vibrating.
Here, therefore, we have two systems of opposing, but complementary energy which create a symmetry, although this is created out of unequal forces. Referring to the func- tion of the dialectic magnitudes set out in fig. 4.6 (p. 63), generally speaking those in the right hand column should prevail over those on the left for evolution to proceed produc- tively. That is to say, the effect and function of the right hand aspects of each dialectic unity should predominate. Viktor estimated the correct proportion between them to be 1/3rd to
2
/3rds respectively. The ancient Chinese also considered an unequal relation to be the one most propitious for the harmonious unfold- ment of life, their ratio being 2/5ths Yin to 3/5ths Yang. However in view of the manifestation of Phi in so many of Nature's creations, the proportion of 1:Phi is probably the more cor- rect, since as a proportion of slightly more than 1:1%) it lies between the two other ratios of 2/5:3/5 (= l:1 1/2) and 1/3:2/3 (= 1:2). In fig. 4.12
the relative magnitudes of these forces are represented by Weight B = 1 kg (left hand col- umn aspect) and Weight A = 1.618033988kg (right hand column aspect). Weight A is at a distance of l/Phi m or 0.618033988 cm from the pivot and weight B is 1 m away. Weight B exerts a moment about the pivot calculated as lkg x lm = 1 kgm. Weight A exerts the same moment, however, since 1.618033988kg x 0.618033988m also equals l kgm. The seesaw of life, as it were, is thus in a state of balance even though the absolute force of one magni- tude is greater than the other. The resultant downward force is the sum of these two weights and equals 2.618033988kg, which equals (1.618033988)2 or Phi2.
Through the interaction of these two pro- portions the unstable dynamic balance in Nature and her energetic processes is achieved. Were it not for this tentative bal- ance no forward progress would be possible, much in the same way that tightrope walkers cannot actually put one foot in front of the
70 Living Energies
other unless they are in a state of balance. At a more sublime level this also represents what the Buddhists call the 'Golden Middle Way', the path of tranquillity, compassion and contemplation unassailed by the vissi- tudes and extremes of life.
Viktor Schauberger attached a great deal of importance to this relation, stating that the extreme egg-form suited to his apparatuses was to be found within the pentagon, which is the Phi polygon. Viktor never actually stated how he obtained this egg-shape. Fig. 4.13 shows how it may be drawn using six pins and a loop of string, although any variety of egg-shape can be precisely determined using Walter Schauberger's hyperbolic mathematics.