Complexity – “a chaos of behaviors in which the components of the system never quite lock into place, yet never quite dissolve into turbulence either” (Waldrop, 1992, p. 293)
Complexity lies at the edge of chaos
Chris Langton at the Santa Fe Institute, proposed the following interesting equation:
order -> complexity -> chaos
Nicolis and Prigogine (1989), for example, define complexity as the ability of a system “to switch between different modes of behavior as the environmental conditions are varied” (p. 218).
According to Prigogine and Stengers (1984), “the models considered by classical physics seem to us to occur only in limiting situations such as we can create artificially by putting matter in a box and then waiting till it reaches equilibrium” (p. 9). Classical physics, then, makes too many assumptions. Matter in its natural state contains randomness and irreversibility. Chaos theory says that matter is not the passive substance of the mechanistic world view of our forefathers. Rather, it is spontaneously active. Deep within this random activity, is the creation of order.
According to Jung, individuation, the process of becoming whole, is a series of spontaneous psychic processes (Jung, 1959). In his view, life processes are “complicated and difficult …. in this respect, they may be compared with all other biological processes” (pp. 350-351). He was well aware that order can come from chaos. This, he claimed, was the purpose of the mandala:
“Experience shows that individual mandalas are symbols of order, and that they occur in patients principally during times of psychic disorientation or re-orientation. As magic circles they bind and subdue the lawless powers belonging to the world of darkness, and depict or create an order that transforms the chaos into a cosmos” (Jung, 1959/1978, pp. 32-33).
Quantum Foam–A Creative Matrix.
Nuclear particles are known to enfold and unfold in endless processes within their quantum fields. Elementary particles have self-referential iterations (repetitions) which create and/or destroy themselves from a vacuum state. According to modern quantum mechanics, there is no such thing as a vacuum. What was once considered a vacuum is now known to be seething with the creation and destruction of virtual particles. (Davies, 1984, p. 105).
Virtual particles cannot be detected directly, but scientists know them from their effects. They are born and they die so fast that they cannot be detected. In essence, they represent a quantum foam where chaos and order struggle together ceaselessly, the one coming out of the other, over and over, forever. Experimentalist, Willis Lamb, was actually able to measure the vacuum polarization in the vacuum between the electron and nucleus of the hydrogen atom. He measured a small change in the orbit of the electron due to the inherent background charge in what was previously thought to be empty space. His observations compared favorably to those calculated theoretically by using the equations of quantum electrodynamics (Pagels, 1982, p .277).
Modern science has discovered that chaos and cosmos exist together even at the quantum level. The quantum foam of science is comparable to the chaos of alchemy. Translating an alchemical work, Jung describes chaos as an “assortment of crude disordered matter …. [which nevertheless contains the] divine seeds of life” (Jung, 1953, pp. 144-145). This chaos-order relationship is also embedded in the Chinese symbol of yin-yang.
Chaos theory demonstrates how order can be produced from chaos. The chaos that appears to exist on the macroscopic level (to our eyes) is order when seen at the molecular level (through a microscope).
Chaos theory also recognizes that systems can cascade toward chaos through a series of bifurcations. The Feigenbaum sequence (named after the physicist, Michael Feigenbaum, who discovered it) is a good example. In this sequence, for a range of parameter values, a system is orderly and has a period with a fixed value T. Beyond this range of values, the system is chaotic until the period reaches 2T (this is called period doubling). Beyond this value, chaos begins again until we reach another threshold–the system becomes orderly again when the period reaches 4T. This sequence can then be repeated at 8T, and so on. The system undergoes a series of bifurcations having successive period doubling. In this way we see incidents where order is sandwiched between chaos, and where chaos is sandwiched between order (Prigogine and Stengers, 1984, p. 169).
A bifurcation is a crisis point in the life of a system, in which the future of that system is uncertain. It is usually depicted as a fork in the time sequence of a system, in which a system can take two possible branches, one or both leading to chaos. All dynamic systems go through bifurcations, most of which are irreversible. The ego and psyche also undergo bifurcations, especially when attracted by an archetype of the collective unconscious. An archetype, acting as a strange attractor in the phase space of the psyche, can create an uncertain decision point for the psyche. The psyche must then either assimilate the experience or else exhibit neurotic behavior. According to Jacobi (1949), the consciousness of every human being is attracted by archetypes in the collective unconscious at one time or another else we must pay the penalty in the form of a neurosis.
In his On the Nature of the Psyche, Jung says that the psyche actually lies in an objective continuum, one parallel to our spacetime continuum, which he calls “a psychically relative space-time continuum” (de Laszlo, 1959, pp. 98-101).