George B. Hogenson
Chicago, Illinois, USA
Chicago Society of Jungian Analysts
Abstract: Jung’s theory of synchronicity is seen as a step in the development of a complete theory of the symbol. In so doing, a number of proposals are made for modeling the symbolic process along lines already in use for modeling a variety of other phenomena, ranging from language to the behavior of earthquakes. These modeling techniques involve processes of self-organization, and raise issues of scaling in systems, including symbolic systems. The proposal is made that symbolic systems obey the same rules of scaling that these other systems obey, and that symbolic systems can therefore be understood as exhibiting the characteristics of a power law distribution — a concept that is explained and developed in the paper. It is finally proposed that synchronicity is an aspect of the symbolic that can be characterized as exhibiting a high degree of “symbolic density.”
My objective in this paper is to present an outline of a way of thinking about several of Jung’s signature concepts, including the complex, the archetype, and the theory of synchronicity. My objective is to suggest a way to unify these elements of Jung’s system under a single dynamic principle.1
We can begin with the following quotation from the theoretical physicists, Ramon Ferrer I Cancho, and Richard Solé, of the Universitat Pompeu Fabra, in Barcelona, and the Santa Fe Institute, respectively. In their recent examination of the dynamics of the emergence of language, they conclude that “Our results strongly suggest that Zipf’s law is required by symbolic systems” (Ferrer I Cancho and Solé 2003, p. 791). One objective in this paper will be to explicate this conclusion within the context of the symbolic as conceived of in analytical psychology. My argument will be that if we grasp the significance of Zipf’s law for the structure of symbolic systems we will have gone a considerable distance towards understanding the relationionship between the symbolic and synchronicity. This argument rests on the proposition that fundamental advances in our understanding of pattern formation in nature have provided us with tools for reconceptualizing the structure of Jung’s entire system of psychology. The operative concepts in this reconstruction include dynamic self-organization, self-organizing criticality, fractals, and power laws. While these concepts may, at first sight, seem remote from analytic discourse and dauntingly obscure, I believe that they are no more so than the use of such abstract concepts as quantum field theory and related notions from micro-physics, the field Jung first thought would yield insight into synchronicity, a topic Jungians have been discussing for some time now. Additionally, I maintain that the concepts I will be making use of in this paper enjoy a degree of generality in relation to phenomena at all levels that exceeds the utility of concepts from micro-physics, and therefore cast a more illuminating light on synchronicity. Thus I also believe it is possible to offer a unified understanding of Jung’s system in which one can see a direct connection between the observations of his early research on the word association test to the theory of synchronicity. Put another way, I hope to demonstrate that synchronicity, far from being a radically alien phenomenon which departs decisively from the natural order, is in fact continuous with Jung’s earlier observations, and indeed, with the most commonplace and familiar of human behaviors, language. The issue, I will argue, is one of scale, and a more comprehensive understanding of the nature of the symbol under conditions of scaling. I hope that this last, rather Delphic, formulation will become clear by the end of the paper.
The distinguishing features of a synchronistic event can be found in Jung’s account of the dream of the scarab beetle (Collected Works, Vol. 8). To briefly review the event, an analysis Jung was conducting with a woman had reached a point where they were both feeling stuck in the process. The woman then had a dream that featured an Egyptian scarab beetle. As she was recounting this dream, Jung heard a tapping at his window. Turning, he saw a small beetle trying to get into the room. He opened the window, caught the beetle, and presented it to the woman with the words, “here is your beetle.” Following this event, the analysis opened up, and progress was again possible.
In his discussions of synchronicity, Jung is at pains to distinguish between chance events and synchronistic events. All too often, however, we tend to lose sight of this distinction and claim synchronicity when all we really have is chance. Jung’s distinction between the two phenomena rests on the creation of meaning, or the meaningfulness of the juxtaposed events. He also remarks that synchronistic evens are usually associated with archetypal materials, that they have profound affective and symbolic characteristics, and that they change the order of life, as in the breakthrough in the analysis of the woman in his paradigmatic case. Unfortunately, Jung’s account of this case is too brief to provide the degree of detail needed to fully understand the nature of the analytic moment. From my own experience, however, and that of other analysts, I believe we can say that synchronicity is associated with very strongly constellated symbolic material and that it carries unusually powerful meaning structures in its wake. Also, as Jung made clear, it has a transformative impact on those who feel themselves participating in the synchronistic moment. If this is not a procrustean caricature of what is loosely conceived of as a synchronistic experience, I believe that I will be able to illuminate why we ought to take synchronicity seriously, and see it as an organic and in fact perfectly reasonable element of a system of psychology that takes the symbolic and the creation of meaning as its central and guiding principles.
We are all familiar with the extraordinary ways in which words can be combined. Indeed, our very livelihood often depends on the level of discernment we are able to bring to the strange combinations our patients bring to us. Jung’s early work on the word association test offered some of the first insights into how these peculiar associative connections could be formed. In his discussion of associative networks, Manfred Spitzer, Professor of Psychiatry at the University of Ulm, highlights Jung’s contribution, which he considers to have set the standard for rigorous research on word association until recent technological advances finally surpassed his investigations (Spitzer 1999). Spitzer gives a variety of examples of how semantic networks operate. For example, a person concerned about a career in art may remark that “A career in art has drawbacks.” We are all familiar with this sort of expression, a minor parapraxis. Spitzer argues, however, that the development of semantic networks, such as those Jung analyzed, are best understood as self-organizing networks.
Self-organization is a concept that was first introduced by the Nobel Laureate in Chemistry, Illia Prigogene. Prigogene’s proposal was that many phenomena in nature had characteristics that did not exhibit straightforward causal relations, but rather came to be by virtue of the dynamics of the system in which they were imbedded and which they helped form. Self-organized systems, while made up of many elements – commonly referred to as a complex system – nevertheless display high levels of organization regardless of the scale at which they are examined.
Let us turn to another system that displays self-organizing features, the stock market. Anyone who has invested in the market will have had the experience of getting a “tip” from a friend regarding a particular stock or the direction of the market. Investors also tend to follow the behavior of other investors. In a remarkable example of cross- disciplinary analysis, the French geo-physicist, Didier Sornette, has analyzed stock market bubbles and crashes using the tools of dynamic systems analysis and the concept of self-organization (Sornette 2003). What he found in his analysis is that in large scale market behavior the network of association among major traders lends itself to a process of self-organization. This means that there need not be any particular cause for a major inflation of the market, a bubble. Rather, as each investor watches the behavior of their fellow traders the self-organization of the system entrains the collective behavior in such a way that bidding behavior escalates exponentially. This kind of exponential expansion in behavior defines a power law distribution, a concept that I will explain more fully below. As Sornette analyses the process, the trading behavior within the market will progressively self-organize itself to the point where all of the traders are behaving in a tightly defined – and tightly coupled – pattern at all levels.
The problem with this process is that if the self-organizing dynamics of the system go on long enough, they reach a point known as self-organizing criticality, or what Sornette refers to as a singularity, a felicitous term that I believe we can apply to those moments when we are approaching a synchronicity. Sornette argues it is this characteristic of intensely organized systems that leads to stock market crashes. Briefly, what happens is that in a system at the point of self-organized criticality, even a small deviation from the organizational pattern can cause the entire system to reorganize itself in an abrupt and unpredictable, even catastrophic, manner. In the case of the market, if one investor suddenly changes his or her pattern of trading the rest of the system will enter a state of cascading collapse that results in a crash.
The classic analysis of this phenomenon was carried out by the physicist Per Bak with his colleagues at the Brookhaven laboratory on Long Island, New York (Bak 1996). Bak and his colleagues began with a simple child’s play model in which they began to slowly pour grains of sand on a table to form a pile. As the pile grew into its characteristic conical shape, the falling grains would gently slide down the sides, enlarging the pile in what appears to be a well ordered manner. However, at some point, which cannot be predicted in advance, the falling grains set off a much more dramatic “avalanche” on the side of the pile. The pile had reached a point of self-organizing criticality where the introduction of one more grain set off a “catastrophic” reorganization of the pile. It is important to note here that in the controlled environ ment of the sand pile experiment the rate at which grains of sand were piled upon one another remained constant. There was no sudden alteration of the rate at which sand was deposited. Also, there was no way of predicting which grain of sand would set off the avalanche. The event emerged from the self-organizing properties of the system. Once again, however, the distribution of small, gradual cascades down the pile and the occasional, but catastrophic, avalanches can be plotted on a power law distribution.2 What is this concept, and what does it have to do with Jung and synchronicity?
By the mid-nineteenth century, social observers were commenting on the rise of large cities and their relationship to small towns. The first truly systematic analysis of this phenomenon, however, was carried out by a linguist at Harvard University, George Kingsley Zipf (Zipf 1949). Zipf determined that the distribution of populations in relation to the frequency of different scales of population organization could be graphed on what is called a double logarithmic graph. The graph will display many villages with few people in each, and few large cities with huge populations. Zipf went on to apply the same analytic techniques to his own specialty, language, demonstrating that in any give body of text the relative frequency of word occurrences, from the most common – usually “the” or “a” – to the least common, would fall on the same graph line. Again, there will be many instances of words with relatively little semantic content, and a few with a large semantic content. This linguistic observation has come to be known as “Zipf’s Law.” What is interesting about a double logarithmic graph is that the pattern of distribution does not form a normal distribution, or bell curve. In fact, a bell curve would not capture the double registration of people and organizational form. Rather, one would likely have to place very small villages and very large cities at either end of the curve, and conclude that they are statistical outliers of increasingly greater improbability. Thought of in this way, one recognizes, I believe, that there is something oddly counter intuitive about the notion that Mexico City or Shanghai are “statistically improbable” events. And, in fact, the work of Zipf initiated an approach to understanding certain scale related events as falling into a pattern known as a power law.3
Power law distributions are important because, as analyses using these equations have proliferated, it has become clear that a wide variety of phenomena, from ion transfers in the brain to word frequencies in a text to volcano eruptions and earthquakes can all be shown to fall along a double logarithmic distribution.
It should be clear by now that my argument to this point leads to the question of what Jung would have done had he approached synchronicity from the point of view of power laws rather than from the point of view of conventional statistical analysis. If one reads the essays on synchronicity, one immediately confronts Jung’s determination to place the phenomena outside the range of statistical probability. This even before he gets to synchronicity’s other defining characteristics such as the deep sense of meaning that accompanies these phenomena, as opposed to the mere sense of interest that may accompany less improbable coincidences and accidental happenings. Jung’s understanding of synchronicity is critically dependent on a traditional statistical analysis. This is one aspect of Jung’s approach that we will have to re-evaluate going forward.
Returning, then, to power laws we must identify one more important aspect of nature that they reveal in both mathematically rigorous and aesthetically beautiful fashion. This aspect of the power law was first developed by the mathematical economist, Benoit Mandelbrot in the form of what we know as the Mandelbrot set or fractal (Mandelbrot 1983; Mandelbrot 1997).4 Working from Zipf’s law between the late 1950s and the 1960s, Mandelbrot realized that the exponent in a power law defined a pattern of self-similar structure in the phenomenon under investigation that was “scale invariant.” What this meant was that regardless of the scale at which one examined a phenomenon, the same basic structure would be revealed. As Sornette summarizes Mandelbrot’s insight, “Power laws describe the self-similar geometrical structures of fractals. [F]ractals are geometrical objects with structures at all scales that describe many complex systems, such as the delicately corrugated coast of Brittany or Norway, the irregular surface of clouds, or the branched structure of river networks.” (Sornette 2003, p. 366) Or, I will want to add, the symbolic and the synchronistic.
In a paper delivered at the last conference hosted by the Journal of Analytical Psychology, I suggested that the symbolic world of the analytic encounter displayed characteristics of phase transitions (Hogenson 2004). Phase transitions occur at the threshold of phenomenal transformation. The phase transition that we are probably most familiar with is when water freezes, changing abruptly from liquid to solid. All of the phenomena that I have described in the context of power law distributions also display the features of a phase transition. In the case of the sand pile the transition occurs when the gradual sliding of the accumulating grains of sand suddenly gives way to an avalanche.
One of the more perplexing problems in the evolution of human beings is the apparently unique capability known as language. The problem with language is that unlike virtually any other characteristic – hands, food preferences, grooming behavior, infant care – language does not have any genuine analogs in other species. Even the most sophisticated chimpanzees do not naturally possess an analog of language. A variety of solutions to the problem of how language could emerge in evolutionary time in the absence of any evolutionary antecedents have been proposed, but by and large they have all ended up being circular. In the paper to which I referred at the outset, however, Ramon Ferrer I Cancho and Ricardo V. Solé at the Universitat Pompeu Fabra here in Barcelona have proposed a novel solution (Ferrer I Cancho and Solé 2003). Following the work of Zipf and the analytic approach of Mandelbrot among others, Ferrer I Cancho and Solé argue that the emergence of language represents a phase transition within a scaling process governed by a power law. That is to say, as the signaling capacity of the pre-linguistic organism expands, a linguistic avalanche will eventually occur, which radically reorganizes the entire system, including the brains of those who are engaged in the process. Based on this analysis, they argue that language does not emerge gradually, but rather appears abruptly, as a phase transition.6 Furthermore, in the phase transition from signaling, language immediately displays the characteristics of Zipf’s law.
With these background features in mind, I now want to argue that Jung’s entire system, insofar as it is a system based on the nature and function of the symbol, can be viewed as a continuum of self-similar, that is fractal, structures, distributed along a power law distribution. Furthermore, the variant elements of the system, namely the association, the complex, the archetype, the synchronistic event and the emergence of the Self, become evident as the system transitions through a series of self-organized critical moments that result in phase transitions within the symbolic system as a whole. In other words, all of these phenomena are self-similar moments in a scaling distribution characterized by what I will term symbolic density. To draw an analogy from the geo-physicist Sornette, who remarks that “there are no large earthquakes, only small ones that don’t stop,” we could say that there are no big symbols, only small ones that don’t stop.
It is at this point that I believe the notion of symbolic density is useful. As Spitzer makes clear in his study of semantic networks, associative structures can ramify over large semantic distances. But not all semantic networks have this quality. Spitzer does not address the impact that Zipf’s law has on his model. I believe, however, that its application is instructive, for we are all aware that for some patients single words or other symbols can have a range of associative connectedness that far exceeds that of any other symbol in their experience. Jung was aware of this, and in his work with psychotic patients we can see evidence of his ability to discern the immense associative networks of these patients as they elaborated their “fantasies.” The psychotic inhabits a symbolically dense environment, but one with a structure that eludes us. The development of the complex, on the other hand, can be conceived of as the formation of a structural pattern of associations in the individual psyche. It is not accidental then, that Jung could see the complex in the patterns of the word association test. What the test accomplishes is a simple display of the associative network that shapes the psychic reality of the individual.
In their important paper in the Journal of Analytical Psychology, Saunders, a mathematician, and Skar, a Jungian analyst, argue that the developmental forces usually thought to originate from the archetype arise instead out of the complexes, which are formed through self- organization in the brain/mind. In this view, the “archetype” is not something that forms the complexes; it is a class of complexes which fall into the same general category (Saunders and Skar 2001). I believe they see the archetype in a manner similar to what I am attempting here. In both their paper and in some of my work of the same period, we all make the claim that the archetype does not exist, in the sense of being a discrete ontologically definable entity with a place in the genome or the cognitive arrangement of modules or schemas in the brain. Rather, taken from the point of view I am now trying to develop, the archetype, like the complex, is an iterative moment in the self-organization of the symbolic world. From this point of view, one would encounter the archetypal at that point where the sand pile of the symbolic achieves a state of self-organized criticality and radically reorganizes while maintaining its fractal, self-similar structure – the complex and the archetype are fundamentally structured like the symbol, only the archetype exhibits itself at the point where symbolic density transcends the carrying capacity of the complex and moves into a more collective realm.
This last point is of the utmost importance for understanding the argument in this paper. While virtually everyone in the Jungian community explicitly recognizes the centrality of the symbol for the understanding of the psyche, it is less clear that we have as yet taken the symbol as seriously as we need to if we hope to fully ground and unify our theories. In this regard, I believe that the neuroscientist and anthropologist Terrance Deacon, of the University of California at Berkeley, provides important insight. Regarding the nature of the symbol, Deacon remarks:
I believe that [the notion that symbolic reference is arbitrary as in Saussure] is an unwarranted assumption based on the fallacy of generalizing from individual symbol-object relationships to systems of symbols. [T]here are indeed constraints that are implicit in symbol use. The point I want to emphasize here, however, is that such semiotic constraints as involve symbol systems are located neither in brains nor in society, per se. They are a bit like the formal constraints that have shaped the development of mathematics (and yield such curious universal phenomena as prime numbers). (Deacon 2003, p. 98)
Deacon’s analogy to the system of primes allows me to suggest that the argument of Ferrer I Cancho and Solé reveals one of the most fundamental formal constraints on the form and structure of symbolic systems in the apparent necessity of a Zipf’s law. Deacon’s argument, which has a realist quality to it, would hold that even if nobody ever calculated a prime number the system of primes would nevertheless be said to exist, and the process of mathematical investigation becomes one of discovery rather than construction, at least in part. In the sense that Deacon uses the system of primes as an analogy to the relative autonomy of the symbol when added to the argument of Ferrer I Cancho and Solé, it becomes possible to conceive of the world of the symbolic as a world that the psyche inhabits, realizes, or perhaps falls into, rather than as a world that the human mind creates. I take it that this approach to the symbolic has interesting, perhaps important implications for our understanding of the “process of symbolization,” at both the infant and the adult level.
This approach to the symbolic serves to shift the center of gravity for our understanding of synchronicity. At this point, I quite selfconsciously turn to a more speculative discussion in hopes of opening up the horizon of understanding regarding synchronicity within the context of the symbolic, which is where Jung originally located it.
Let us recall the most salient features of Jung’s theory. For Jung, the synchronistic defined a juxtaposition of a psychic state and a state in the material world that resulted in the emergence of meaning and a transition in the individual’s state or understanding of the world. Jung’s example is of the scarab-like beetle that flies through the window just as his patient is recounting a dream of a scarab beetle. Joe Cambray has given us an account of a severely disturbed patient who dreamed that Joe was lost in the Black Forest while he was on vacation, and only after talking with her on the telephone, at which point she recounted her dream, did Joe learn that a SCUBA diving class he was attending was scheduled to dive in a coral formation known as the “black forest.” A common element in both these instances, and in others that can be recounted, is that the patient or other party to the experience was in a heightened state of anxiety or, in Jung’s case, stuckness in the treatment. In the case of Joe’s patient, her psychotic states had frequently required hospitalization when Joe was away for any period of time. Seen from the standpoint of semantic networks, as in Spitzer, one can say that these women inhabit intensely self- organized symbolic spaces. From the point of view of the realist analogy to the status of the symbol, those symbolic worlds would be capable of self-organization without necessary reference to the person or to other states of affairs. These factors would lead us to ask whether and where on a power law continuum of symbolic density these women found themselves. The point of view I want to propose regarding synchronicity, in these cases, is that the density of symbolic activity, the steepness of the symbolic sand pile, if you will, for these individuals, had reached such a pitch that a phase transition, a symbolic avalanche, was precipitated and radically reorganized their worlds.
The notion that I am advancing here is that if we see the symbolic as more than simply a system of representations but rather a relatively autonomous self-organizing domain in its own right, then we can investigate the degree to which the symbolic conforms to the structuring dynamics of a double logarithmic power law, and by extension displays self-similar or fractal structures on a scale invariant basis, that is, at ever greater levels of scale. In other words, the complex, the archetype, the synchronicity and the Self all “exist” as moments in a scale invariant distribution governed by a power law. Like large cities, major volcanic eruptions, and catastrophic stock market crashes, synchronistic phenomena are extremely rare, as Jung himself argued, but they are not improbable in the sense one would assume to be the case under more conventional probability theory. They are rather the result of small symbolic developments that don’t stop.
What can be said regarding the most characteristic aspects of a Jungian analysis? Here, important advances in the neurosciences provide insights into our work in ways that connect directly with the themes of this paper. The foundation of Jung’s approach to the symbol rests on the dream. Neuropsychologist Carl M. Anderson and his colleagues at the Harvard Medical School, as well as a number of other brain researchers, have recently conducted a series of experiments on the nature of REM sleep – the sleep pattern most associated with dreaming – and concluded that the time patterns of REM sleep display fractal organization, that is, the patterns of brain activity are scale invariant over time (Anderson and Mandell 1996). Regardless of the granularity of the test of brain activity, the pattern displayed appears identical. Anderson et al. have also investigated the impact of trauma on these patterns and are in the process of developing new intervention strategies based on the stimulation of oneiric – that is, dream based or symbol based – functions in the brain.
Anderson remarks, in one of his papers, that what is important about the fractal nature of the REM sleep brain patterns is that they follow a power law distribution with precisely the same mathematical structure as “the flow of the Nile, light from quasars, ion channel currents, neuronal firing patterns, earthquake distribution, electrical current fluctuations in man-made devices, inter-car-intervals in expressway traffic, and in variations in sound intensity in all melodic music.” (Anderson 1998, ca. p. 10). It seems to me that in research such as this we can begin to see the outlines of an understanding of the dream, the symbolic in general, and the interface of dream, symbol, and the material world that Jung intuited, but lacked the analytic tools to examine in depth. To the extent that this state of affairs can be worked out in greater detail, our understanding of the relationship of dream and reality will necessarily become deeper and analytically more powerful.
What of the even more overarching concepts in Jung’s system – the Self, and the trans-historical collective? Looked at from the point of view developed in this paper, the Self, defined by Jung as possessing the symbolic qualities of a god image, should stand at the far end of the symbolic power law distribution. And indeed, one would have to marvel at the degree to which the genuinely massive symbolic moments in human history, the emergence of the great religions, seem to possess a power of social organization that transcends anything that one would expect from a carpenter’s son, a displaced prince, or the son of a minor merchant family, to acknowledge only the most recent instances of the emergence of such powerful symbolic systems.
My purpose in this paper has been to argue that it is possible to unify Jung’s system of psychology by bringing the elements of his system into a framework that allows us to see the invariance of structure across different scales of experience. The analytic method I propose is one that is already well understood and widely applied in areas as diverse as geology, stock market behavior, and neuroscience. That it has only begun to be applied in a more thorough going manner to the symbolic world, and there only to analyze the patterns and emergence of natural languages, seems to me to be something of a scandal as well as an unprecedented opportunity for further development in analytical psychology.
In the course of making this argument I have maintained that we should view that most illusive of Jung’s theoretical constructs, synchronicity, as an element in a continuum of symbolically structured moments in the psyche and the psyche’s relationship to the world at large, rather than as a radical departure from the norms of nature and the otherwise ordered world of our experiences. Synchronistic events are rare, genuine moments in which the Self is present, perhaps even more rare. But they are not statistical outliers, or impossibilities, in the classic sense of statistical analysis. To the contrary, while they may be exceedingly rare, if the exponent of the power law governing the symbolic domain is sufficiently large, they will emerge almost out of necessity.
At the other end of the scale we are dealing with phenomena that while smaller in their own right, are nevertheless self-similar to the great events of the collective unconscious. At the risk of being unduly romantic about the day to day work of analysis, one can see that this relationship does add a certain dignity to the work of the individual. It is not a great reach to suggest that in the individual encounter in the consulting room one does encounter the god image in every symbolically defined moment.
All of this must for now be seen as an hypothesis. It is offered here as a call to think differently about the symbolic and our relationship to the symbolic. I hope that the hypothesis – that the symbolic can be understood as a part of nature, sharing the characteristics of other great processes in nature, from the ion transfers in the brain to the destructive force of a great volcano – will stimulate more thought and research, and lead us to new and important insights.