Volume 2 Issue 6 Feature article

Embracing Chaos and Complexity for a Saner World  

Caroline Smith

View the pdf version here.

This article makes accessible reading of very complex scientific concepts and offers an avenue for understanding some of the very basic patterns of life. It is an exercise in wonder about the Mystery at the heart of chaos and also offers some insights into what makes for good education.

Chaos. An emotive and fearful word, speaking of disorder, anarchy, destruction, madness, mess, loss of control, fear. More mundanely it describes the everyday annoyances of the traffic in the rush hour  – ‘traffic chaos’, your child’s bedroom or, in my case, my desk. And then there’s chaos theory itself, whatever that may be.

In the ancient world, Chaos, from the Greek ‘Khaos’ referred to a formless chasm or void, but a void imbued with potential, the source of all creativity from which all matter sprang. The concept of an ordered material universe arising from Chaos is common to many cultural cosmologies, anticipating the present day science of the big bang from which poured forth all energy and all matter.

In the Greek worldview natural events were also personified and deified as arising from the pantheon of the gods. The poet Hesiod (800-700 BCE) in his poem Theogony, gives a description of the creation as the springing forth as dark, light and love from Chaos:Verily at the first Chaos came to be … From Chaos came forth Erebus and black Night; but of Night were born Aether (air) and Day, whom she conceived and bore from union in love with Erebus…  The same idea provided the foundation of the Christian biblical notion of the void, so beautifully expressed in Genesis 1:1: In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God moved on the face of the waters. And God said, Let there be light: and there was light.

In present day everyday English, the link between chaos, order and creativity has been lost. Our present day notion of a ‘void’ is merely a vacuous nothingness, and ‘chaos’ is a description of disorder. But new insights are emerging.  Fast forward to the 19th century where we find the precursors of the extraordinary chaos theory. Chaos theory is a branch of mathematics called nonlinear dynamics, whose foundations were laid in the 1880s by the French mathematician Henri Poincaré. Nonlinear dynamics describe those changes that occur over time in unpredictable ways, and which are highly sensitive to and respond disproportionately (nonlinearly) to initial conditions.

Some nonlinear systems exhibit the characteristics of chaos. A good example is the weather which is notoriously difficult to forecast accurately more than a few days ahead. Tiny fluctuations (called ‘perturbations’) in weather conditions on any one day can result in dramatic, unpredictable and magnified differences after a few weeks. In trying to describe this in 1972, meteorologist Edward Lorenz used the term ‘the butterfly effect’  – a whimsical description of a hypothetical butterfly flapping its wings in the Amazon forest that sets in motion ever amplifying winds that eventually result in the turbulence of a tornado on the other side of the world.

Chaos theory itself was formulated as late as the 1960s with the name ‘chaos’ itself only being added in 1975 by mathematician Jim Yorke. And it was not till the invention of superfast computers that the breathtakingly beautiful patterns of order and complexity in the heart of chaos came to be known. The most famous of these is the Mandelbrot set. Into his home computer, mathematician Benoit Mandelbrot fed a particular (and quite simple) mathematical equation whose answer was re-fed back into the equation (a process called ‘iteration’). When the results were graphed the first grainy images of the chaotic dynamical system called the ‘Mandelbrot set’ emerged. Faster computers have since refined and coloured these images to reveal the now well-known extraordinary patterns of unimaginable complexity.  Each part of the set reveals the same complex pattern repeated over and over at seemingly infinite levels. The wonderful film ‘The Colours of Infinity’ uncovers the magnificence of the Mandelbrot set and has recently been updated and published as a book of the same name (Lesmoir-Gordon, 2011).  There are now many Mandelbrot set generators on the internet.

The Mandelbrot set and other mathematical representations of order and complexity in chaos provide profound insights into the nature of our universe. They teach that complexity can arise from simplicity, and that chaos can contain hidden order and complexity. These new insights have been variously applied to cosmology, economic systems, population fluctuations, ecosystem changes and even education. In cosmology, chaos theory has helped understand how small perturbations in the evolution of the universe after the Big Bang gave rise to ever more complex, intricate and beautiful structures and patterns as the stars and galaxies were brought forth, culminating in life itself.

Systems that are stable can become unstable. Systems that are unstable can return to new stability. We lose biodiversity when a natural system becomes degraded, but its renewal though likely a different biodiversity, can emerge if the system is left to recover over time. One of the few positive gains from the insanity of human aggression is the flourishing of biodiversity in the no-man’s lands of Cyprus and Korea. Hope perhaps for a climate-changed world.

Mandelbrot called the repeating patterns in his set ‘fractals’ in his work ‘The Fractal Geometry of Nature’ (1982). To illustrate fractals in nature Mandelbrot had previously published a paper called ‘How Long is the Coast of Britain’? This apparently simple question reveals that the answer can never be exactly known, but rather depends on how closely and at what scale the coastline is examined.  The fractal nature of the universe can be seen in the repeating structure of a fern leaf, the branching of the blood system, the shapes in a cloud, swirls in turbulent water and in galaxies. Fractals teach us that just as the whole contains each part of the image, so too does each part contain the form of the whole. Fractal interconnectedness is fundamental to nature.

The great gift of chaos theory is the revelation of the deep complexity at the heart of our universe. Many people see the divine mystery in these patterns of nature, and some have even called this the mind of God at work. Complex fractals are not new. They have been part of human spiritual practice from antiquity. Buddhism and Hinduism create Mandalas – intricate, circular or square fractal images painstakingly created out of various materials, to focus the spiritual self. The Hindu symbols of the Chakras resemble the fractal patterns of chaos. According to Jackson (2004), the repeating and iterative fractal patterns of religious music as well as architecture, from the temples of India to the Mosques of Islam, the cathedrals of Christianity and pagan art forms, depict infinity and abundance.

The discovery of high levels of organisation within chaotic systems was taken further by Ilya Prigogine and his colleague Isabel Stengers through their work on chemical systems that they termed ‘the edge of chaos’, for which Prigogine won the 1977 Nobel Prize for chemistry (Prigogine and Stengers, 1984).  Prigogine worked on what he termed ‘dissipative structures’ which are able to maintain identity far from equilibrium by engaging in active exchange of energy with the environment for growth and renewal. These systems are creative, self-organising and adaptive, capable of maintaining identity while changing form. This is the stuff of the evolution of the universe – the formation of stars and galaxies, and the cells, living organisms and ecosystems of life itself.

Does this understanding have any relevance for our everyday lives? Many believe it does, and chaos theory is increasingly being applied to many areas. As human social interactions are nonlinear in nature, chaos theory is highly relevant in understanding human behaviour. Staying unchallenged in our comfort zones is the human equivalent of being in non-dynamic equilibrium. By deliberately creating an uncomfortable ‘edge’ with others, we have the potential to spark creativity in each other. These concepts are now being applied in education. When he was a school principal, Peter Harney achieved this in his school by deliberately mixing young enthusiastic teachers with older teachers who were more set in their ways. While such encounters may result in mere disorder they also have the potential to spark creativity and stimulate new learning for all.  Mentoring also has this potential.

Teachers are beginning to experiment with chaos theory in the classroom. The process of learning is highly nonlinear, occurring in highly individualistic ways according to the inner processes of the learner, as well as through complex interpersonal dynamics. The idea of intimate interconnectivity means that learners cannot be seen as separate from their learning context. Chaos theory suggests that learning is sensitive to initial conditions, so educators must pay special attention to the learning environment and to the introduction of new topics. Learners are often spontaneous in their reactions to new experiences — experiences that are critical in stimulating long-term learning. We know that we need a diversity of teaching approaches to reach as many students as possible, thus providing layers of complexity in the learning situation.

Chaos theory reveals the conflict between the spontaneity of young minds and the rigidity of hierarchical structures in traditional teacher-controlled classrooms. In classrooms with low levels of energy input, boredom and disengagement can occur. Chaos theory implies a more hands-off approach, so that the far-from-equilibrium associated with confusion and rich tasks, is an essential phase of learning. When higher energy levels flood the system through stimulus and creative edges, behaviour may become unpredictable. But deeper learning may emerge through the tension of chaotic conditions and the system’s tendency towards self-organization. To be realistic, this is not an invitation to create chaotic classrooms without giving considerable thought to the process. The danger is always that simple disorder will result. However these insights inject exciting new directions for learning that schools may wish to explore.

The science of chaos and complexity are now tipping us into a major paradigm shift in our worldview – the way in which we view the organisational principles of the universe.  Gone forever is the mechanistic, reductionist view of nature. In the west, centuries of imposition of the mechanistic worldview has constructed our social structures and our very way of thinking as simple either-or polarities, linear cause-and-effect thinking, dominating power and dogmatic hierarchies. Our Enlightenment inheritance has made us crave certainty in an increasingly uncertain world. The plethora of graphs, predictions and forecasts which form part of the daily media diet (and are frequently wrong) construct the appearance that someone actually knows what’s going on and is in control (this is grimly ironic given the elephant in the room – climate change – is itself a product of chaos as a small perturbation in carbon dioxide levels in the atmosphere is resulting in amplified chaotic weather events). Our universe is nonlinear, dynamic, turbulent, unpredictable, ecological, complex, open, chaotic, fractal, adaptive, self-organising, flowing, networked, connected, abundant, evolving, transformative, emergent … and totally awe-inspiring.

It is daunting but also liberating to embrace chaos, nonlinearity, complexity, uncertainty and paradox.  Western history has made these insights seem overwhelming, alien and challenging. But if we relax into them, let go of our need to control, and trust in the inherent self- organising capacity of the universe, we may find we become more accepting and less needing to control. With the wisdom of the ancients and the gift of the new sciences, humanity may at last be on the way to more deeply knowing ourselves as intimately interconnected into the great evolution of the universe, and so to a saner world.

References

Harney, P.J.(1997). Changing the social system of a Catholic secondary school: An examination of salient design features pertinent to the change process from a permacultural perspective. Unpublished PhD Thesis, Department of Educational Foundations, Australian Catholic University.

Hesiod ll. 116-138, translated by Hugh G. Evelyn-White (1914) Retrieved July 4th 2013 from [http://www.sacred-texts.com/cla/hesiod/theogony.htm].

Jackson, W.J. (2004). Heaven’s fractal net: Retrieving lost visions in the humanities. Bloomington: Indiana University Press.

Lesmoir-Gordon, N. (1995). (Director). The colours of infinity  (Film). UK: Gordon Films.

Lesmoir-Gordon, N. (2010). (Ed.).  The colours of infinity: The beauty, the power and the sense of fractals. New York: Springer

Mandelbrot , B. (1967). How long is the coast of Britain?  Statistical self-similarity and fractional dimension. Science 156, pp 636-638

Mandelbrot, B. (1982). The fractal geometry of nature USA: Freeman and Co.

Prigogine, I. and Stengers, I. (1984). Order out of chaos. London: Flamingo.

Caroline Smith is a regular contributor to EarthSong. With an academic background in science Caroline has been for many years an innovative teacher in Education for Sustainability and is currently a Research Fellow at the University of Tasmania. With her husband Aidan she is an enthusiastic promoter of Permaculture Design.