Synchronicities

To flesh out the significance of this point of view, and more directly connect the symbolic and synchronicity to the ideas of amplification and dragon kings, I need to review, again drawing on Deacon, the fundamentals of emergent structures in complex systems. There are a number of ways in which emergent processes can be carved up and distinguished from one another. In many discussions of emergence, the notion of supervenience plays an important role.

The emergent properties of water are an example. Simply put, the combination of two gases, hydrogen and oxygen, at normal temperatures and pressures form a liquid when a large group of molecules are aggregated. The “liquidness” of an aggregation of water molecules is an emergent, supervenient property of the aggregation. The fact that you need an aggregation of water molecules is important precisely because a single molecule does not possess the qualities of liquidness. Those properties emerge due to interactions among the molecules at the aggregate level. The thermodynamic property of liquidness supervenes on the behavior of the water molecules. But even at this level, some of the potential interactions are amplified by other interactions, while still others are damped. In Deacon’s formulation of emergent processes, this combination of amplification and damping plays an important role.

Above the thermodynamic level of emergence, Deacon (2006) argues that we can see processes of what he calls morphodynamic emergence, such as crystal formation in supersaturated solutions. At this level of emergence the thermodynamic properties themselves are being amplified and damped such that new, higher-level structures, such as snowflakes, are formed. Moving still further up the scale of emergent processes, Deacon suggests that, as the morphodynamic processes stabilize into persistent molecular structures capable of self-replication, a new level of emergent amplification is established with such molecules as DNA. They shift the frame of time in the process of emergence by introducing a form of memory.

What has gone before is carried forward but, at the same time, this memory within the system creates a sense of movement toward some futurestate, and we begin to have what Deacon calls teleodynamic emergence. It is at this level that the symbolic itself emerges and, in turn, becomes part of the workings of complex systems with their own emergent properties. However, the symbolic in a sense detaches itself from the indexical and establishes the primary structures of symbolic systems within the symbolic domain itself. As a result, the potential for the formation of emergent structures is no longer bounded by reference to objects but rather by associative symbol-to-symbol reference.

Deacon captures this last point by reference to the Taoist metaphor of the empty hub of the spoked wheel, a metaphor that Jung also enlists. This passage from the Tao-Te-Ching reads, in Deacon’s (2006, p. 119) rendering:

Thirty spokes converge at the wheel’s hub to an empty space that makes it useful. Clay is shaped into a vessel, to take advantage of the emptiness it surrounds. Doors and windows are cut into walls of a room so that it can serve some function. Though we must work with what is there, use comes from what is not there.

Richard Wilhelm, who rendered “empty” as “nothing,” introduced Jung to this passage. Jung comments in the essay on synchronicity (Jung 1952,par. 919):

“Nothing” is evidently “meaning” or “purpose,” and it is only called Nothing because it does not appear in the world of the senses, but is only its organizer.

This Nothing, or emptiness, is what in complex systems theory would becalled an affordance that provides the space within which emergence takes place. Deacon remarks, in relation to the passage from the Tao-Te-Ching, that (Deacon 2006, p. 120):

The Western mind sees causality primarily in the presence of something, in the pushes and resistance that things offer. Here we are confronted with a different sense of causality, in the form of an “affordance”: aspecifically constrained range of possibilities, a potential that is created by virtue of something missing.

At this point it is appropriate to refer to Jung’s conceptualization of the symbol as the best possible representation of something we do not understand (Jung 1971, par. 816): “The symbol is alive only so long as it is pregnant with meaning”. We can play on this definition in the context of Jung’s comment on the Tao-Te-Ching in his synchronicity essay to argue that the symbol is alive insofar as it references “nothing” or “emptiness,” i.e. the affordance necessary for emergence to take place.

We are, however, not quite in a position to connect the scarab beetle incident to the emergence of dragon kings. To make this move I have to introduce a distinction that Sornette draws within the world of self-organizing systems. As emergent phenomena came to be more carefully studied, par-ticularly after the development of chaos and complexity theory, it became evident that some self-organizing processes developed to a point referred to as self-organized criticality (Bak 1996). Bak compared the formation of self-organized criticality to the avalanches in a child’s sand pile, in which small avalanches form as the pile grows, but at some point a critical level of sand will form a much larger avalanche – the pile has reached a point of self-organized criticality.

Importantly, the sand pile also illustrates the significance of loose coupling in the system. The large outlier avalanche in this example would fallnear the top of a power-law distribution, within the frame defined by Zipf’s law. It would be an unusual event, but not a dragon king. Researchers incomplexity theory have come to refer to these events as black swans. To use the notion of dragon kings as a way of thinking about synchronicity, we need to understand their relationship to black swans. I do now believe that I was wrong in previous work (Hogenson 2004) to argue that synchronicities lay directly on the path of a power-law distribution.

Archetypes may be black swans in the symbolic domain, but, if Sornette’s argument is correct, it may be better to see synchronicities as related, but different at critical points. It is here that some of what I said at the beginning about the scarab beetle incident becomes important. To flesh this out let us look at the diagram in Fig. 3 after Sornette (2009).

The horizontal axis of the graph in Fig. 3 is a measure of the heterogeneity of interacting elements in a self-organizing system, and the vertical axis measures the interaction strength of the elements of the system, their coupling. What appears to be the case in some systems – high-speed computer-driven stock market trading is one important example – is that the system develops into an almost entirely homogenous structure, where the parts are very tightly coupled. The collapse of the system takes the form of a dragon king. The system is basically driven to an extreme position. The black swan, on the other hand, forms in a more heterogeneous environment, with looser coupling, rather like the child’s sand pile.