What is it about Mother Nature that has a calming effect on people? Why do they feel at peace and at one with the natural world? Could it have something to do with the geometrical patterns exhibited by trees and flowers of breathtaking beauty? Could it be nature’s magical sounds – the wind in the treetops or the chuckling of a mountain stream?
Trees can have a strange effect on the human psyche. Have you ever sat in wood listening to the gentle rustling of the treetops as the light wind lives and dies, or marvelled at the beautiful branching forms of an ancient oak or pine? The proportions of trees seem to possess a harmony that is bewitching to the eye and the soughing of the leaves can soothe the most vexed and tired of spirits. But why is this?
Let us first look at their form. In the words of Aristotle, “The chief forms of beauty are order and symmetry and precision”, and this can clearly be seen in the remarkable design of trees. The mathematical patterns of tree branches are in fact fractal in nature. Fractals refer to geometric shapes, which can be split into smaller and smaller parts such that each part is identical to the original i.e. a reduced size copy of the whole at all levels of magnification. Although fractals in mathematics can have infinite levels, in nature they tend to display self-similarity on a large but finite scale. Thus a branch from a tree, whether large or small, is a miniature replica of the complete tree, not identical but similar in nature.
Mathematical fractals are based on iterative equations. Such equations can be used to model trees on a computer and are currently being used to determine how much carbon they contain.
As well as their shapes trees possess a combination of strength and flexibility that is unequalled in nature. We may often marvel at their sheer size, feel protected while walking beneath them, or watch in awe at their energy and movement as their branches dance and sway during a storm. Their remarkable design has enabled them to become the world’s tallest, bulkiest and longest living organisms. California’s General Sherman sequoia, for example, is over 270 feet tall and is believed to weight at least 2,500 tonnes. The oldest sequoias are more than 4,000 years old, and if left undisturbed trees may remain standing for decades after their death.
As well as great strength trees possess tremendous elasticity. This is why tree trunks sway and branches bend in the wind without buckling. Wood’s remarkable lightweight strength comes from its structure. The majority of its cells are hexagonal in shape, and their arrangement resembles a “honeycomb pattern” that occurs frequently in nature. It forms a perfect tessellation with no gaps between joining cells. The cell walls are composed of cellulose fibres whose ability to store energy like a spring gives great strength and resilience.
Plants in general need to compete for space and sunlight. Their structure has evolved so that they can take advantage of any competitive edge, the arrangement of branches being such that there is minimum overlap of leaves and maximum absorption of sunlight, ideal for shading you on a sunny day or keeping you dry in the rain. As a tree grows leaves tend to emerge along a stem in a 3-dimensional spiral, such that each leaf follows the one before at a fixed angle (the angle of divergence), so that the points of attachment of successive shoots mark out upon the stem a helical line. If the eighth leaf were to be exactly above the starting leaf after completing three complete rotations then the angle of divergence would be 3/8 x 360 . The numbers 3 and 8 occur very frequently in such observations while those such as 7 and 11 are rare. Most numbers tend to belong to the Fibonacci series 0 1 1 2 3 8 13 21 etc.
Oak = 2/5 Beech = 1/3 Elm = 1/2 Willow, Rose = 3/8.
This implies that there is a principle behind the mechanical design of trees. Their branching forms serve the needs of the trees themselves, but at the same time their aesthetic arrangement is deeply pleasing to us and adds stability, restfulness and dignity to our surroundings.
This explains the fantastic design of trees, but what about listening to their beguiling voices. Why do we find them so relaxing and can trees really talk to us. Aeolian tones are the audible sounds created by the wake-eddy vortex induced air pressure fluctuations as air flows around obstacles such as leaves.
The pressure in the air in the vortex is not quite equal to the pressure in the air, which is flowing smoothly. Therefore, as vortices break away alternately from each side of the obstacle it experiences alternating forces. If vortices are shed at the natural frequency of the body then resonance occurs causing it to vibrate strongly and the sound to increase. The pitch (height or depth of a note) depends on the frequency of these vibrations i.e. on the rate at which vortices break away alternatively from each side of a body. In forests needles, leaves and twigs all act as such obstacles and as the structure of each tree is different they all produce Aeolian tones specific to their species. The large twigs and branches of a beech will shed larger vortices, have a lower frequency and produce much lower tones than the numerous small needles of a pine tree. Thus a forest acts like a band of musicians each with their own instrumental sound. John A. Adam explains in his book Mathematics in Nature that:
“the whisper of a tree will have more or less the same pitch as that of its individual leaves or needles just as a swarm of bees is pitched to that of the average bee, whereas the intensity (which is related to the loudness) is approximately the sum of the individual intensities. Thus, the pitch of the Aeolian whisper of a pine tree is about the same as its average needle, but while the sound of an individual needle may be inaudible that of the tree itself may be heard some distance away. By the same arguments the numerous leaves, twigs and trees of a wood will merge into the famous, ‘murmur of the forest’’’.
The tones of each forest are unique and have a mysterious harmonious nature that plays upon the mind lulling the listener into a relaxed reflective state.
The acoustic wave vortices in leaves are analogous to the wake eddies you would see in water on the downstream side of a rock in a river. These vortex induced vibrations were observed by the famous artist and innovator Leonardo da Vinci in 1504 AD, but now Jasper Copping in the Telegraph writes that a revolutionary new device is being used to use this effect to harness energy from slow moving rivers and ocean currents and some scientists believe it could one day produce enough energy to power the entire world.
It is generally accepted that just 0.1 percent of energy in the ocean could support the energy needs of 15 billion people. However, current methods of harnessing water energy are inefficient. They need waves, tides or currents moving at a speed around 5 knots to operate efficiently and most of the world’s water flows at less than 3 knots. They also require the construction of large dams across rivers or barriers in the sea. Studies are now being made of the flow of water around obstacles and the way fish swim curving their bodies so that they can glide between vortices shed into the slipstream of fish swimming ahead. Thus, they can reach greater speeds than those achieved by muscle power alone.
A new technology, vortex induced vibrations for aquatic clean energy, acronym VIVACE, is being researched. This involves placing cylinders in the water horizontal to the flow and attached to springs. As water flows the creation of eddies, wakes and vortices, just as observed by Da Vinci, cause the cylinders to rise and fall thus creating mechanical energy, which can be converted into electricity. The new system is more efficient, can work at slower rates of water flow and is less obstructive than traditional technologies.
Trees have long been known to respond to cosmic radiation, but can they really influence our minds and can they even help us to travel through the cosmos? Viktor Schauberger, a forester, who lived in Austria during the first half of the twentieth century, developed revolutionary new theories through observations based on nature in the woods and mountains where he worked. He believed that his ideas were the result of the direct influence of natural energies inside his beloved forest. Could trees really have influenced his ideas and inventions? After observing a trout maintaining its station in the midst of a turbulent forest stream, he was prompted to develop his theories on “living water”. He produced a number of impressive and highly innovative machines, which were destroyed in Germany during the war, and was even believed to have cracked the anti-gravity challenge. Gravity is believed to have waveforms like water and Schauberger was nicknamed the “Water Wizard”.
Current space travel methods would take us light years to reach the next nearest star to our sun so if space travellers are to reach us they must be using a form of technology we do not yet understand. One of our most famous scientists Albert Einstein’s general theory of relativity allows for the existence of wormholes and hence time travel. This is because mass is able to curve space-time. This effect can be seen if you were to place a heavy object in the middle of a tablecloth held tightly between two people and representing space-time. A marble placed on the tablecloth would then roll towards the centre due to the curvature caused by the heavy object. Now imagine the cloth representing space-time is folded over leaving a space between the top and bottom. If an equal mass were to indent the cloth at exactly the same point on the top and bottom where the curvatures meet would represent the formation of a wormhole. In space masses placing pressures on different parts of the universe could combine to create a kind of tunnel, which would in theory join separate times and allow passage between them. However, even if such tunnels could be created it is well known that if we were to artificially prolong the life of such a tunnel through folded space-time a radiation feedback loop might occur destroying the time tunnel in the same way audio feedback can wreck a speaker.
Can we now think again of the fish gliding between the vortices shed by the bodies of the fish in front of them and imagine not a wormhole, but a “fish that swims through space-time itself”. Instead of the wormhole being open at both ends joining two separate times a futuristic craft may be able to start in one space-time location and swim through the fabric of space-time curving it around it as it travels. To an observer it would appear to vanish in one place in space-time and then suddenly appear in another place in space-time. Many UFO sightings have revolved around vibrating cigar-shaped metallic objects that remain motionless in the air only to shoot forwards with amazing speed or disappear then suddenly reappear somewhere else. Sound familiar? The problem of feedback would be solved because as space-time was curved around the craft like water around a trout moving upstream it would immediately be re-closed behind the craft.
With Tokamak fusion energy still decades away who would have thought that da Vinci and the principal of music in trees may lead the way to a new source of energy for mankind? As for the consequences of time travel, England may still win the War of Independence.
For more on sacred geometry watch this clip from the brilliant Spirit Science series!
