Abstract
Discussions of synchronicity tend to focus either on the meaningful content of the experience, or on speculation about possible mechanisms underlying the phenomena. The present paper suggests that the symbolic or meaningful content of some synchronistic phenomena are themselves governed by identifiable dynamics associated with the emergence of symbol systems generally. Specifically, these dynamics are associated with complex dynamical systems theory and give rise to phenomena governed by power laws such as Zipf’s law. It is suggested that synchronicities, which display distinctly symbolic features, behave in ways that conform to power-law distributions in which highly coupled systems form rare outlier aggregations referred to as "dragon kings". This terminology is explained and related to the experience of synchronistic phenomena.
:mao-shining:
Dragon Kings
The term “dragon king” was originally coined by Didier Sornette at ETHZurich, where he studies financial bubbles (Sornette 2003). Sornette began as an earthquake researcher, which involved him in the study of power laws, particularly Zipf’s law and its variant, the Zipf-Mandelbrot law. While examining other systems that fail catastrophically, most notably the global financial system, he recognized the emergence of a separate class of events that should fall within the classic Zipf power-law distribution, but for some reason did not. One example, which uses Zipf’s original research topic of city size, is the existence in some countries of one exceptional outlier city, such as Paris in France.
Sornette, in a series of papers, gives many examples of dragon king phenomena, but they are, as I will discuss in a moment, united by one dynamic process. It is at this point that I believe we may begin to address the question of synchronicities as psycho-symbolic dragon kings. Sornette (2009) remarks that he chose the term dragon in part because dragons are rather mystical and mysterious creatures, much like a synchronicity. The notion of the king, on the other hand, refers to the characteristic vast wealth of kings, a feature that we might want to associate with the meaning-ladenness of a synchronistic experience.
So how do we address synchronicities in this context? In Sornette’s discussion of the emergence of dragon-king phenomena, one critical element is the degree of coupled interactions within a synchronized system, and the impact degrees of coupling have on amplifying the characteristics of the system. In the case of a massive city such as Tokyo, for example, the great Shogun Tokugawa Ieyasu consolidated his power by forcing the other great lords to conduct elaborate progressions between Tokyo and their own fiefdoms, as well as maintain courts in both places. This arrangement also playedto the competitiveness the great lords felt toward one another, and led to ever-greater concentration of resources in Tokyo.
As we will see, this became, as was the case in Paris, and to a degree London, a tightly coupled system of amplification with limited damping mechanisms that would regulate the system’s development. Compare this to the United States, where a variety of early and explicit political decisions prevented any one city from attaining a similar level of cultural hegemony. The looser coupling of the amplification and damping process resulted in a distribution of city populations that follows Zipf’s law far more closely.
To work this part of the argument out in greater detail, we need to understand a bit more about the role played by amplification within complex systems, partly for its explanatory importance, but also because Jung made amplification, as opposed to reductive analysis, the cornerstone of his method. I want to be clear that I do not think of this similarity in terminology as a simple analogy; rather, it is a matter of substance. Jung’s method, in other words, is directly associated with the perspective I am proposing. This takes us into questions related to emergent phenomena, an area to which I want to turn once again before concluding this paper.
My argument (Hogenson 2001) has been that archetypes, and related phenomena such as synchronicities, are emergent phenomena rather than pre-existing structures. I even went so far as to argue that “the archetypes of the collective unconscious, as either modular entities in the brain or as neo-Platonic abstractions in some alternative ontological universe, do not exist, in the sense that there is no place where the archetypes can be said to be” (Hogenson 2001, p. 606). Jung’s notion of the archetype-in-itself was, therefore, mistaken, and archetypal phenomena, as emergent, derived from the systemic interaction of brain, culture and narrative.
I have, since then, become even more convinced that when we talk about archetypal images we are dealing with complex dynamic systems within which the symbolic itself plays the most important role. Attempting to imbed the archetypal in evolutionary theory, neuroscience or developmental achievements is to put the cart before the horse. While all of these elements are part of the system taken as a whole, they have, if you will, become subsidiary to the workings of the symbolic environment that human beings inhabit – the environment to which we have become adapted (cf. Hendricks-Jansen 1997).
This means, and here I return to Deacon’s use of Peirce’s semiotic model, that amplification as a force within the emergent processes of the symbolic world can manifest in extraordinarily complex ways. This gives synchronicity, as a particular manifestation of archetypal emergence within the symbolic world, equally extraordinary scope. As Deacon himself comments in an important paper on emergence, to which I will refer in what follows, “asymbolic species such as Homo sapiens” occupies an ecological niche that is characterized by processes of “symbolic self-organization and by evolutionary processes that are quite different from those at lower levels” (Deacon 2005, p. 149)
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:
Richard Wilhelm, who rendered “empty” as “nothing,” introduced Jung to this passage. Jung comments in the essay on synchronicity (Jung 1952,par. 919):
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):
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.
Conclusion
Let me finally return to the remarks I made about Jung’s interest in scarabs, as well as the patient’s dream and the advent of the chaffer. The scarab beetle event, in essence, resembles a tightly coupled, homogeneous system thatis about to undergo a process of catastrophic self-organization: a synchronicity. As Sornette (2009, p. 11) remarks regarding the emergence of dragon kings: “The key idea is that catastrophic events involve interactions between structures at many different scales that lead to the emergence of transitions between collective regimes of organization.” These interactive processes, as Sornette and Ouillon (2012) explain, create amplifying feedback loops in the aggregate system that push the system into a global phase transition.
In the case of the scarab, we have Jung and his patient evidently under considerable pressure – she is very rational, the work is not progressing, they are stuck. In this situation, the dream introduces a symbolism that captures not only the patient, but, importantly, Jung as well or even in particular. With the appearance of the chaffer, the aggregate system of Jung-patient-symbolism produces just such an undamped tightly coupled amplifying feed-back loop that pushes the systems into a global phase transition. As Jung remarks, this rearranges the entire structure of the analysis. This is the process, I would suggest, that makes at least this synchronistic event, but perhaps others as well, into a dragon king.
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