Infinity, Flow Forms and the Lemniscate

The power of infinity

by Christine Paul on 07 December 2009. Posted by WellBeing Natural Health & Living News

In nature there is wisdom. The repeating patterns found in a pine cone, an uncurling fern and the fruitlets of a pineapple were well established before mathematicians recognised it and called it the Fibonacci sequence, thus creating a perfect design blueprint for structures such as the Parthenon and the Eden Project in the UK.

Likewise, the way in which a river meanders, causing water to move and flow around natural objects, has recently excited scientists and shown them an efficient design to revitalise and recycle water.

Flowforms, based on a mathematical and philosophical concept called a lemniscate, whose symbol represents infinity, have been developed to make better use of water in agricultural systems, for use as water features for creative expression or personal healing and to revitalise drinking water for sustainability purposes.

But what is a lemniscate and why is its use in flowforms so effective in revitalising nature?

In 1655, mathematician John Wallis devised the infinity sign, named lemniscus (Latin for “ribbon”) by mathematician Bernoulli about 40 years later. The lemniscate is similar to the device known as a Möbius strip (named after a 19th-century mathematician), a strip of paper that is twisted and attached end to end, forming an “endless” two-dimensional surface.

Spiritual beginnings

Religious and philosophical aspects of the infinity symbol predate its mathematical origins. In Tibet, similar symbols to the infinity symbol have been found in rock carvings while the ouroboros, or infinity snake, is often depicted in this shape. The Greek word ouroboros means “tail swallower” and the symbol is usually portrayed as a snake swallowing its tail. Although usually circular, it is also often depicted in a lemniscate shape.

In the Tarot, the sign for infinity represents the balance of forces and is often associated with the Magician card. The card depicts the Magician standing behind a table on which lie a cup, a coin and a sword. The Magician’s hat is in the form of the Cosmic Lemniscate, signifying the first motion of creation. His right hand points to the earth while his left holds aloft the rod of Jacob and also the staff that budded — the human spine crowned with the globe of creative intelligence.

In the pseudo-Egyptian Tarot, the Magician wears a uraeus or golden band around his forehead, the table before him is in the form of a perfect cube and his girdle is the serpent of eternity devouring its own tail. The double-zero or lemniscate symbol of the Holy Spirit over the Magician’s head represents the ancient doctrine that in creating, Spirit divides itself, so that the One becomes Two.

The lemniscate symbolises the endless, infinite nature of energy. Energy cannot be created or destroyed and the Magician is intimate with this knowledge. The infinity symbol above the Magician’s head also illustrates that he understands the energy of his thoughts always leads to infinite consequence. Some decks depict an additional lemniscate at the Magician’s throat: this symbolises the infinite power of the spoken word.

Legendary mystic and educator, the Austrian-born Rudolf Steiner, observed that the lemniscate was evident in nature where it is freely expressed in the swirling vortices of a running stream, the whorl-like patterns described by planetary motion, the chambers of a seashell and the growth of plants — and even in the human body.

In a lecture to his students, he writes: “Yesterday I showed that wheresoever we may look in the human body, we shall find the formative principle of the looped curve or lemniscate. This is essential: you must imagine the plane in which I am drawing the lemniscate to be rotating about the lemniscate axis; ie, about the line joining the two foci. I should therefore have to draw the lemniscate in space. This is the projection of it.

“Such is the drawing of the lemniscate you must have in mind … so, for example, when you are tracing the bony system or the nervous system in Man. Even the blood circulation can be traced in this way.

“You must imagine it all not in a plane but in space. The figure eight — the lemniscate — is therefore legitimate, but … you are really dealing with geometrical figures of rotation. The forms of our inner organisation, in the nerves-and-senses system and in the metabolic and limb-system respectively, are mutually related upon the principle of a lemniscate of rotation.”

What are flowforms?

English inventor and sculptor John Wilkes, who originated the Flowform Principle in 1970 as an ecologically sound method to revitalise water, further researched the properties of the lemniscate. Other luminaries in the field include Viktor Schauberger, George Adams and Theodor Schwenk.

Flowforms are vessels that seek to emulate the swirls and vortices of the mountain stream, enabling water to re-oxygenate, revitalise and rejuvenate itself to bring it back to its more natural state. Flowforms generally form a cascade of water that flows into a tank or pool. The water can be recirculated as many times as desired.

“Vortex” flowforms create pattern-of-eight movements in the water as it flows downward. Water entering each form flows rhythmically left and right between the two vortices, creating a lemniscate — an energy configuration recognised as one of the foundation patterns of all life. The marriage of these two opposing vortex energies imparts a powerful dynamism to the flowing water, noticeable after 20-40 minutes. This dynamism is imparted to both flora and fauna.

Wilkes saw that the secret of water’s vitality lay in its rhythmical movement. The fact that all living things depend on water implied for him that regenerative processes are continually at work within it — otherwise it would be unable to maintain its function as a life-sustaining element.

Restoring water’s life-sustaining properties, the process streams water through a rhythmical, repeating figure-of-eight, lemniscate flow path so that oxygenation and clarification are enhanced. The swirling action evokes similarities to the way blood flows through the heart in order to absorb a fresh supply of oxygen, which then travels to cells throughout the body.

According to Wilkes, flowforms are preferable to spray systems used in some standing pond sewage systems: “We are always technologically trying to force things. When you force oxygen or air under pressure through the water, it will mainly try to bubble out again and about five per cent may really dissolve. And besides, when using pressurised sprays, you may run the danger of mutilating organisms.

“The question is, can we learn ways of bringing water into a situation where it will draw oxygen in its own right, as it does in a mountain stream?” he asks.

Today, at the John Wilkes’ Flow Design Research Institute in the UK, research work on flowforms and the sustainable approaches to the engagement of water continues. In 2002 Philip Sedgman, CEO of a flowform company, visited the institute and met with Wilkes. Prior to this Philip spent 20 years in Tasmania exploring the natural environment and farming the land, during which time his love of nature and inquiring mind led him to biodynamics. Intrigued by flowforms, he became acquainted with moulds, forms and plugs and, in 1996, developed his own flowform design.

”In a mountain stream, nature provides a complex bed through which water flows,” Philip says. “As gravity pulls it in, around and over rocks, sand and vegetation, water constantly creates within itself patterns and vortices, the action of which creates winding river beds.

“Water in its natural state does not travel in straight lines; it loves to meander and spread itself out. When water moves too fast, as it does in a ‘straightened’ river, or when it is forced out of its natural meander patterns, as in hydroelectric dams or in water pipes, or when it is polluted, it loses its vortex patterns and, some would say, its vitality.

“Flowforms seek to emulate this vital pattern of water,” he says.

As Schwenk had observed, rhythmical motions are evident in many water phenomena: rising and falling tides, the repeated crashing of waves on a beach, the alternating left and right curves of a river’s meander, even the Earth’s hydrological cycle. Yet the orderly form exists only fleetingly and then quickly dissolves. It would seem that water can manifest its potential of creating orderly forms within itself only momentarily before returning to the state the poet Novalis called “sensitive chaos”, the name Schwenk also chose for his book on fluid movement.

Wilkes’ goal was to design a sequence of forms through which water could fulfil its capacity to manifest orderly metamorphic process, to create artistically what he calls an “organ of metamorphosis” for water. He postulated that such a sequence of forms had the potential to physically manifest the delicate potential for ordered movement that appears to be inherent in the nature of water.

Following painstaking research and experimentation, the flowform was created — a water lemniscate whose movement of water in a figure-of-eight rhythm has been the basis of a revitalising effect on water.

According to flowform advocates, a second benefit is that the rhythms of water, enhanced by flowform proportion and shape, create an environment, which supports the rhythmical processes in which micro-organisms are always involved.

“When you look at these organisms through a microscope, you see that they are pulsing and spinning and moving spirally in their environment,” Wilkes observes. “The rhythms created in the water by the flowforms are intended to relate to these micro-movements.”

Encompassing an array of water fountains and waterfalls, flowform water sculptures are prized for their both artistic form and functional value. Broadly divided into two categories — for landscape and agriculture — flowforms can be used for many purposes, including the revitalisation of drinking water, in dams, for stirring biodynamic preparations, sewage and grey water treatment, dairy and piggery effluent. Other applications include nurseries, ponds in zoos for aquatic birds and wildlife, aquaculture, swimming pools, in office buildings, air-conditioning plants and in parks and gardens where their sheer aesthetic beauty complements and harmonises with the environment.

“The rhythmical, relaxing sounds of falling water through flowform sculptures have distinctive water therapy qualities with a deeply calming, reassuring effect on people, rather similar to restful gazing into a flickering fire,” Philip says.

“Many clients, from water garden feature owners to those who have commissioned commercial water feature, have found flowforms to be fascinating, peaceful and deeply touching on a level they can hardly describe.”

Worldwide applications

In Norway, water consultant and advocate, Will Browne has designed a highly successful sewage processing system using flowform-assisted ponds and reed beds. The system was devised for Vidarǻsen Camphill, a community of 160 people, including effluent from their dairy, food processing workshop, bakery and laundry facilities. Browne’s colleague, Petter D. Jenssen, Professor of Agricultural Engineering at the University of Norway, collected data and provided documentation of Vidarǻsen’s success.

The system comprised a sludge settlement pond, pre-treatment vertical-flow constructed wetlands, an advanced primary stabilisation pond, three smaller stabilisation ponds and a horizontal-flow constructed wetland filled with lightweight aggregate. The advanced primary stabilisation ponds were equipped with Flowform cascades that provided year-round aeration, rhythmical treatment and thorough mixing of wastewater in the ponds. During the first three years, treatment performance worked efficiently and continues to do so through changing climatic conditions.

In Wisconsin, USA, an organic dairy farm is at the centre of Martina and Christopher Mann’s Nokomis Farm promoting biodynamic and organic farming. The commercial farm works in close cooperation with an innovative educational and agricultural research centre, the Michael Fields Agricultural Institute, also in Wisconsin. For some time the farm had been labouring under a failing waste disposal system which began to contaminate fields downhill.

A system designed in a collaboration between Flowforms America and Industrial Design Professor William Becker of the University of Illinois resulted in the creation of a constructed wetland, replacing the mire and leaching of too many nutrients into local waterways. The challenge was to maintain adequate oxygen levels to support the aerobic bacterial action that broke down organic material from the cows and milk residues. This was where the flowforms got to work.

Once the solids were separated out, the liquid effluent travelled down a cascade of 12 flowforms, which began the renewal process. Moving through the cascade in the characteristic flowforming manner — forming a figure-eight pattern — the liquid became deeply aerated as it continually flowed over itself, the lemniscate effect adding oxygen to the layers of liquid.

After entering the primary treatment pond at the end of the cascade, the liquid underwent “root zone filtration” — an alchemical process whereby a balance of micro-organisms, plants, aerobic and anaerobic processes transform the nutrient into stable and usable forms, upon which the roots of plants thrive. In the first year, the wetlands were ready to be planted and to begin life as a bioremediation system for farm waste.

Through the help of flowform technology, Nokomis Farm’s physical landscape had been transformed and produced welcome revenue from the sale of harvest produce.

Elsewhere, at the Australian National Botanic Gardens (ANBG) in Canberra, a flowform sculpture serves as an interesting reminder to people that recycling and reinvigorating water can be both functional and appealing to the senses.

In 2003, a waterfall flowed into a pond below; however, a substantial structural leak formed and was deemed irreparable. This, compounded by subsequent drought and water conservation priorities, led to the waterfall being switched off completely. The water subsequently stagnated and pond life deteriorated. ANBG staff and volunteers raised the funds and prepared a project proposal to both restore the water cascade and provide ideal conditions for microorganisms to improve and restore water quality and pond life. The project was named Friends’ Cascades.

“Often flowforms are set up on an ‘industrial’-looking frame above the ground, when used commercially for treating effluent, grey water recycling, stirring bio-dynamic preparations and so on,” says an ANBG spokesman. “We wanted to have the cascade fit snugly into the immediate landscape and so constructed the series of flowforms using the slope to advantage — a stylised version of a creek bed if you like.”

The flowforms were set up at varying angles to give different effects, some strongly pulsing, others a very gentle movement.

“Topping up the pond from our water supply was not an option, so we had to ensure the system was self-sustaining in terms of replacing any water loss through evaporation,” he says. “The runoff collected from the adjacent building tops up the pond and we have an option of using rain-water tank storage for topping up in long dry periods.

“Today, many people are attracted to the sound and the mesmerising rhythm and water movement … What we are hoping is that people may be inspired by the flowform sculpture and see such ‘waterwise’ ideas as an interesting landscaping option, particularly when such a structure can be incorporated as part of the landscape.”

Rhythm of water

In the preface to his book, Flowforms, the Rhythmic Power of Water, John Wilkes states: “Water is the element of movement, functioning in nature as a universal mediator. Everything living is inevitably dependent upon water … the physical carrier of rhythm. Rhythm is a gateway. Moving water is inseparable from surface. It either influences surfaces over which it flows or is influenced by them and creates surfaces within its own volume.

“The flowform is a vessel, by virtue of its proportions, capable of inducing rhythms in water streaming through it.

“This book is directed to those people with an open mind, who are interested in our environment and are willing to admit that it is in need of our active support and participation … the more subtle aspects which nature is trying to show us, if only we are willing to see.”

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