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.

Symbolic Density

Let me begin with a more general point of view on Jung regarding the importance of his early work on the word association test and on the linguistic patterns of dementia praecox [Schizophrenia]. Jung’s work in these areas is, in my experience, too easily overlooked in preference for the later materials on archetypes, typology, and the alchemical writings. It is important for our purposes in thesetwo areas that the word association test revealed important foundational elements of psychological functioning in the phenomenology of associative networks, particularly the affective content of these networks.

As Spitzer (1992) argues in his historical review of the word association experiment, Jung significantly enlarged the scope of the test and, more importantly for psychiatry, used it to argue for the deep coherence of psychotic discourse, thereby influencing Bleuler’s model of schizophrenia. Jung’s understanding of schizophrenic discourse emphasized the presence of relatively coherent associative paths connecting the manifest elements of the discourse, but large portions of that connective network were obscured. This point of view on psychotic discourse has been investigated more recently by Rebeiro (1994) among others, who mapped the subterranean – or unconscious – networks of association that exist in the often seemingly disjointed ramblings of severely psychotic patients.

The essential element in this early work of Jung is the centrality of associative relationships among elements that we can reasonably call symbols, or at least symbolically significant markers in the individual’s psychic world. For an example, I recommend reading Jung’s masterful unpacking of thesymbol of the linden tree in his study of dementia praecox. What I now want to do is begin to tie Jung’s work on symbolic networks to a larger body of research on the nature of the symbolic, beginning with the American pragmatist and founder of semiotics, Charles Sanders Peirce (1839–1914). Peirce divided sign systems into three essential levels, the icon, the index and the symbol. Deacon (1997), in his essential study The Symbolic Species, draws directly on Peirce’s work as part of his discussion of the emergent nature of truly symbolic systems.

We do not need linger on icons, as they are relatively direct representations of the object of concern, such as a portrait of Louis XIV or a photograph of Jung. Where matters become interesting is in the move to the indexical level of signification. At this level, a sign begins to aggregate instances into larger sets such as monarchs or famous psychologists. There remains, however, a known, and essentially unquestioned referential relationship between the sign stimuli and the object or action in question.

Deacon identifies a critical transitional stage to a more complex arrangement of tokens, where the tokens, still largely indexical in relation to their objects, begin to arrange themselves in patterns of token-to-token combination. Importantly, these indexical combinations of token interactions still do not relinquish their referential relationship to objects or actions – monarchs who exercized great power throughout Europe.

As we move to the fully symbolic level, the relationships that matter shift to those between the tokens themselves, and only by abstraction to their physical or pragmatic referents. At this point one could thematize the nature of kingship, or, perhaps, the archetype of the king. Without elaborating on this in detail, I would suggest that Deacon’s approach is a useful illustration of what Jung was beginning to observe in the word association test, and in his work with dementia praecox and the discourse of the psychotics. These observations formed the foundation for what would eventually be his theory of archetypes.

Another brief comment to set the stage for what is perhaps the most difficult part of my argument. We are all aware of the importance of Jung’s close relationship with Wolfgang Pauli and their extended discussion of synchronicity in relation to quantum physics. Pauli was, in many ways, the only interlocutor to whom Jung paid actual attention and even deference. Pauli reciprocated with an extraordinary level of engagement in topics that he was aware could easily marginalize him in some scientific circles.

That said, when we read their correspondence, it is clear that one of Pauli’s greatest challenges in the exchange was getting Jung to understand the statistical nature of quantum mechanics. I raise this historical bit of the discussion of synchronicity because, with the advent of quantum mechanics, much of theoretical physics became statistical in nature, and that process has continued to the present. The aspect of this development that concerns us here is the application of the statistical methods developed by physicists, as well as some other disciplines such as economics, to domains beyond their normal purview, including the study of language and the nature of symbols. One way in which my own argument over the last several years might be framed is that Jung, as well as Pauli, with some of this research at hand, might have arrived at a very different understanding of archetypes and synchronicity.

Zipf’s Law

Had he known of them, Jung might have appreciated a set of mathematical formulations that have the important quality of describing a wide variety of phenomena with no intrinsic connection to one another. There is, if you will, something transcendental about them, in the philosophical sense of being universal conditions of the world, without reference to specific states of affairs. The ones I am particularly interested in, in relation to the symbol, are power-law distributions, particularly Zipf’s law, but also including the fractal geometry of Mandelbrot (1981, 1997) and scale-free structures of networks. Let me note that all of these patterns involve, amongst other characteristics,a relationship to scaling phenomena, or what is usually referred to as scale-invariance. This means that these patterns apply regardless of the scale at which the phenomena are analyzed.

Zipf’s law is named after the American linguist George Kingsley Zipf (1902–1950). He was something of a polymath or a dilettante, depending on your point of view, who began by examining variations in the size of cities. He discovered that, within a given geographic area, the size of population concentrations, from small villages to large cities is governed by a so-called power-law distribution. In the case of cities the abundance (or frequency) of agglomerations of sizes followed a deceptively simple 1/s distribution.

The outcome of this calculation looks like a graph schematically depicted in Figure 1a. However, when the results are converted to a doubly logarithmic graph (log-log plot), the chart looks like Fig. 1b, which exhibits the characteristic linearity of a power-law distribution. Zipf’s next step, and the result for which he is remembered, was to examine the frequency of words in a text. He found that the frequency of words in a text, ranked according totheir abundance, fell like 1/r as a function of their rank r. In a log-log plot, the slope of the resulting linear function is then minus one.

In addition to his work on the statistics of word frequency, Zipf proposed a model for the generation of lexicons, or symbol systems, that he referred to as the principle of least effort. Briefly, the idea here was simply that both the listener and the speaker in an exchange of signs would seek to minimize their expenditure of energy – that is, put in the least effort (Zipf 1949). This means that a kind of negotiation would take place between the parties of an exchange, in which each sought the greatest level of understanding for the least effort.

Needless to say, the simplest way to achieve this goal is to have a shared lexicon of exact one-to-one relations between the elements in the lexicon and the objects referenced by the lexicon. However, this approach entails massive memory requirements to insure the least ambiguity. It is the way in which most animals, other than humans, communicate. The monkey cry that designates the presence of a snake is distinct from the cry that designates an eagle. But while some animals can learn fairly large lexicons in captivity, and under well controlled conditions, we also know that in the wild the upper bound for say the bonobo chimpanzee, perhaps the most cognitively advanced primate short of humans, is on the order of about 40 “words”, with little or no syntax. These lexicons are essentially indexical rather than symbolic, in the terms used by Peirce and Deacon.

Explicitly drawing on Deacon’s and Peirce’s distinction between symbols and indexes, Ferrer-i-Cancho and Sole (2003) simulated the development of a lexicon beyond the indexical level and concluded that Zipf’s law was not simply a descriptive tool. Rather, it was actually a necessary emergent property of symbolic systems which, they also demonstrated, exist in what is known as a phase transition – a condition such as what happens as water turns to steam or freezes into ice.

However, the symbolic phase space in this instance has the added feature that the symbolic system proper remains in the phase space and does not resolve either into indexicals or into meaningless randomness. This feature, which entails a significant degree of referential ambiguity, was, they speculate, a likely contributing factor in the evolution of language, because it allows a limited lexicon to refer to a larger set of objects. In the presentation of their findings one can see how a phase transition emerges where the effort of the speaker becomes roughly equal to the effort of the listener Fig. 2.

The model of Ferrer-i-Cancho and Sole (2003) created a very abstract and idealized understanding of a language or symbol system. They have gone further in other papers, to examine the emergence of syntax and also to argue that semantic content may follow Zipf’s law as well. This is a more controversial claim, but it has received some support from other researchers. For instance, Vogt (2004) adds a dimension to this discussion in that he enlarges the set of possible symbolic structures by examining the ways in which referential tokens can be aggregated into categories. Once again, the principle of least effort is at work, but the objective is to locate the category that best discriminates one reference from others.

Vogt refers to the conceptual structures of symbolic systems in terms of their density: symbolic density. He argues that in a search for appropriate categorical structures, the principle of least effort will motivate movement through a hierarchy of increasingly dense categories. Furthermore, this hierarchy of category density can be subsumed under a Zipf-Mandelbrot power law. This is exactly my argument regarding Jung’s system; the complex, the archetype, synchronicity and even the notion of the Self are scale-invariant symbolic structures of increasing density that should, by virtue of their symbolic nature, as well as the curious fact of the scope of power-law like phenomena, fall under Zipf’s law.

A question can be raised at this point, however. If synchronicities are simply at the high end of a power law, why do they carry the level of meaning and affective impact that they typically do? A large earthquake, after all, is, as Sornette (2003) has remarked, simply a small earthquake that keeps going. But, if the same principle applies to synchronicities, why do you havethe experience of a “rupture of time” (Main 2004)?

Ironically, part of the answer is already available in the work of Ferrer-i-Cancho and Sole (2003), in their discussion of the emergence of language. As was mentioned, this process consists in the formation of a phase transition in which an entirely new and distinct regime emerges as symbols overwhelm the earlier simple indexical reference. This transition is, in no small measure, a catastrophe, in the technical sense of the word – and perhaps in practice as well, insofar as it likely catapulted the genus homo into an entirely different life-world to the general detriment of other organisms.