Systems Theory & Chaos

by Chris Clarke

 

GreenSpirit is a movement which celebrates all existence as deeply connected and sacred. For a long time the sciences have presented a mechanistic picture of a universe consisting of particles in motion determined by external forces. It is now realized, however, that the universe is self-organizing and self-creative. In the new picture everything in the universe is radically interlinked. This section of the resource pack will cover the key ideas of this new scientific understanding, drawing from Quantum Theory and the theories of Chaos, Dynamical Systems and Complexity.

Indeterminism

Newtonian physics introduced the idea that the universe was made up of a mass of individual particles obeying fixed laws which absolutely determined the motion of each one. In principle, once the state of the universe was known at any one instant, then its state at all other times could be determined. At face value, there seemed no room for novelty, free will, or creativity. The aim of Newtonian Dynamics was to predict exactly what would happen, in numerical terms. The systems regarded as typical of the nature of the universe were those where explicit mathematical prediction was possible, such as the pendulum and the system consisting of a single planet in orbit round a star. 

Two things changed this: quantum theory and dynamical systems theory .Quantum theory revealed that, at least on the very small scale, things did not happen predictably. Imagine, for instance, the case of a beam of light passing through the lens of a pair of polaroid sunglasses. On a large scale, it seems as though the beam of light is predictably dimmed. On a small scale, however, the light is found to be made up of particles (called photons) each of which either goes through the lens unchanged, or does not get through at all, at random. 

In this particular case, random behaviour on a small scale averages out to deterministic behaviour on a large scale. But it need not be like that. Imagine a stream of water flowing over a weir. The slightest change in the water at the top of the weir gets magnified more and more and the water goes down, becoming a large change when it reaches the bottom. A dynamical system with this property is called dynamically unstable. People sometimes talk about the butterfly effect, in which a butterfly flapping its wings in Brazil can cause a hurricane over India in two weeks time. If now one combines quantum theory with an unstable dynamical system, the random behaviour at a very small scale gets magnified to give a random behaviour of the whole system. Since most dynamical systems are in places unstable, this means that most of the universe is unpredictable.

An unpredictable universe is open to new things breaking in at every moment. Creativity and the action of free will now become possible.

Structure formation

Life is the process of the generation, reproduction and elaboration of forms/structures – whether we are talking at the biological level of social level. But what is “structure”? Do we require a notion of meaning in order to distinguish the structured from the unstructured? Is structure the same as “order”, and does this make a link with entropy, which is traditionally thought of as “disorder” – or chaos? If that is so, does life violated the second law of thermodynamics, which says that entropy increases? Answers are now emerging to many of these questions, with dynamical systems theory lying at the heart of the ideas.

The philosophy of dynamical systems theory (which recognizes indeterminism as a practical reality, if not a fundamental one) is that pattern is more fundamental than exact specification. A system is understood through the patterns that it manifests. These can be expressed completely precisely, but they are not single numerical quantities. A well known example is a very simple model of convection in a fluid (such as the convection that drives the weather systems on our planet) described by a set of equations called the Lorentz equations. These produce a behaviour which shifts unpredictably between two different types of almost regular motions. This changes ones methodology. Instead of trying to predict exactly what is going to happen – the paradigm of control – one recognizes the pattern that is dominating at anyone time and operates within that pattern. Co-operation with an existing pattern replaces control and forcing into a pre-conceived goal. A new world view emerges no longer based on the ethics of domination.

As well as patterns forming in time, patterns can also form in space. The simplest “toy systems” to see this in are systems like those in the “game” of Life invented by the mathematician John Conway and the systems known as Langton’s Ant. These, and many other more realistic models of processes from chemical reactions to gravitational collapse, suggest that pattern and structure can emerge very naturally from the simplest systems, if the conditions are right. Seemingly barren deterministic laws can be amazingly fertile, opening up the possibility of a universe in which creativity is the norm, not the exception.

Linking the two disciplines is the study of the non-equilibrium thermodynamics: the behaviour of physical systems with heat flowing constantly through them, which exhibit all sorts of structure formation. The paradigmatic experiment in the study of non-equilibrium thermodynamics is the observation of the onset of convection cells in a shallow liquid where heat is flowing upwards. When the temperature difference (and hence the heat flow) rises to become greater than a critical value, the system becomes unstable: any small perturbation will shift the state to one where convection is taking place. This is because at this stage convection results in a greater flux of heat, so that the transition to convection releases energy.  In mathematical terms, the emergence of the new structure of convection is loosely analogous to the onset of dynamic instability.  This motivates the idea that structure is associated with a transition to chaos. If the temperature difference increases further, boiling takes place, which is even more “chaotic”. The unpredictable environment caused by greater chaos seems to have much to do with the development of life.

Creativity

The previous sections show that we live in a universe where each moment is open to the unpredictable, and where the formation of pattern is the norm. This has echoes of creativity, and yet this is an elusive term. In conventional science, either things are determined, in which case there are no surprises and everything that happens is, as it were, already given in the initial conditions; or else things are indeterminate, meaning random, and nothing can be said about what does or does not happen, apart from giving statistics about different possibilities. There is nothing in between complete predictability and complete randomness.Yet when I make a creative act, what I produce is, I feel, neither predictable nor random. It is unpredictable but meaningful. Creativity, I suggest, is an undetermined act which simultaneously brings into being its own meaning. But what is “meaning”? An answer to this will have to come in the future from a much deeper understanding of physics and of consciousness. Clues, however, come from quantum theory, which suggests that living organisms may be governed by a more flexible sort of logic than mechanical systems, allowing a new category of creativity to come into being.

Connectivity

The biggest change that modern physics might bring to the way we look at the world is the change from being a passive onlooker to being a participant immersed in the dynamism of a universe of which we are an integral part. The idea that we are intimately connected with every part of the universe has actually been with us for a long time – since Newton’s proposal that every particle in the universe attracts every other particle by gravitation. But ranged against this has been the idea that all our interaction with the world is indirect: according to Descartes, our soul is influenced mainly by the innermost parts of our brain; these respond only to heavily coded signals from the outside world, which are carried to us by particles impinging directly on our sense organs …  we perceive the world at many removes from it.

Now, however, a different story is being told. In quantum theory all matter can manifest as waves – that is, it has an aspect that is akin to the gravitational field in the way it penetrates everywhere. More significantly, every particle in the universe is connected with every other in a way that is unique to quantum theory: through quantum entanglement, a process in which two distant particles can respond to outside influences as if they were a single system, confirmed in the last ten years by the Aspect experiment. Whether or not the particular phenomenon of this experiment can play a role in organic life is still a matter of debate. But the significance of the experiment goes far beyond the particular phenomenon. It confirms the basic way of thinking about the universe that workers in quantum mechanics are used to: the idea that matter is no longer located in space, but is a manifestation in space of something that is more fundamental than either matter or space – or time. The idea is still too radical even for most physicists to entertain, and the emphasis in physics still on understanding how we can get back to traditional Newtonian space and particles as soon as possible. But what if life has evolved to make use of the connectivity revealed by the Aspect experiment? What if consciousness is not limited to the particular manifestation of matter in space and time, but is rooted in those aspects of matter that go beyond space and time? We do not have the conceptual tools yet to investigate such ideas scientifically, but the shift in our fundamental understanding of matter is already having a profound influence on how we think of ourselves in relation to the universe. We are in communion with the universe as a whole, and not merely a temporary resident in a small corner of it.

 

 

Further Reading

Dynamical systems

James Gleick, Chaos (Paperback Minerva, 1996) ISBN: 074938606
Still probably the best general introduction to the ideas of dynamical systems theory and chaos.

Sally J Goerner, After the Clockwork Universe: the Emerging Science and Culture of Integral Society  (Floris Press,1999) ISBN 0-86315-290-2
An inspiring tour through the social implications of thinking in a dynamical systems manner about the society we live in, which she believes is leading to a major shift in human culture.

Connectivity

Mae-Wan Ho The Rainbow and the Worm: the Physics of Organisms (2nd Edn) (World Scientific, Singapore, 1998) ISBN 981-02-3426-0
A key book: applies ideas from quantum theory and thermodynamics to argue that the nature of life lies in coherence. 

Lynn Margulis The Symbiotic Planet  (Phoenix Press, 1999) ISBN: 0753807858
Support from a new conception of evolutionary biology for the main implication of connectivity: that cooperation rather than competition is the dominant tendency in the universe.

Quantum theory

Gribbin, John  Schrödinger’s Kittens. ( Weidenfeld and Nicholson, 1995) ISBN 1-85799-4027.
Perhaps the best popular exposition of the mainstream physicists’ approach. Well written, very readable and reliable as far as it goes.

Stapp, Henry P  Mind, Matter, and Quantum Mechanics. (Springer-Verlag, 1993) ISBN 3-540-56289-3.
A collection of non-mathematical essays, forming a good compromise between rigour, scope and imaginative extension. Surveys with philosophical care the history and main versions of the subject as well as the author’s own personal approach. Not the easiest text, but the most reliable.

Zohar, Danah  The Quantum Self. London: Bloomsbury.(1990). ISBN 0-7475-0271-4.
Highly readable and inspiring account of why quantum theory is important for the way we live. Conveys the inner spirit of quantum theory, though a lot of the details would be contested by the mainstream.

Omnès, Roland  Quantum Philosophy Princeton, NJ: Princeton University Press.(1999) ISBN 0-691-02787-0.
I think this is the only non-mathematical account of the consistent histories approach to quantum theory, which has now taken over from older versions as the most promising candidate for a generally applicable interpretation. He takes a very individual philosophical and interpretative position, however, which should be allowed for. [END]

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Read about the following:

Conway’s Game of life

Langton’s Ant

Dynamical Systems

Emergence

Quantum Entanglement

Quantum Theory

A Brief History of Chaos Theory 

Unpredictability