Thanks to all who joined us for part one of our analysis of Batman in terms of chaos, order, and randomness. And thanks again to Clint Sprott (University of Wisconsin, Madison) for the 'fractal of the day' to the left. I'm still very new to blogging (3rd week), so I've been considering how best to slice up this long post. What I'm going to do is post part II and III right now, and then take next Monday off (I'll be on vacation anyway, so...). That way, if anyone would like to just read all 3 parts, they may. Or for those who like serials, they may choose that instead. I was glad to see that the numbers did not drop off from the first post. But there were far fewer comments. Perhaps people were waiting for the remaining installments? But just in case the content is getting too tricky - please keep in mind - the goal here is to make chaos theory in psychology understandable and relevant to all of you. This will be a very hard thing to do, so questions and feedback even if it is "huh?!!!" is very welcome. I'm going to be developing a course on this topic for our undergrads at Chapman University, and may someday want to do a general reader book on this topic. So your feedback is really going to help me, especially negative feedback.

Okay, so where we left off in part I: we now know the basics of what chaos is, from "chaos theory," and we are wondering if this really relates to the character Joker, from the new Batman film. And on a broader level, I want to explore whether or not this type of chaos is bad, as people (Westerners at least) do typically think that chaos is bad. Is ‘deterministic chaos' like the force of the evil Joker, the bad Anarchist (there are good anarchists by the way - like Noam Chomsky)?

In some ways, chaos may seem good, and in some ways it may seem bad. Some simple systems move from being very ordered, like a homeostatic system (i.e., a thermostat) that tries to stay at the same level all the time, to an oscillator (a single pendulum swinging), to a complex oscillator at the "edge of chaos," and then on to full blown chaos (see picture to the left of such an evolution of dynamics in the example of simple population fluctuations from work done by May in the mid 1970's).

For population dynamics, such chaotic fluctuations are probably good. If you are from Wisconsin (my home state), it is good that the deer population fluctuates chaotically. That way, each season is different, and if too many die off one winter, you will typically get nice bounce back the next year. Actually - the deer may appreciate this too (not the dying part, but the bounce back part). And more broadly, if the deer population was homeostatic, unchanging from year to year, then they would be less able to adapt to changing conditions, like available food, other animals that depend upon them, and the number of good hunters out there trying to get them.

Along the same lines that "chaos is good," Prigogine won the Nobel Prize in chemistry in the 1980's for his discoveries that self-organizing chemical clocks could emerge to more complex orderly states by moving through a period of chaos, like a nice refreshing dip in the chaotic pool, which rejuvenates a system.

In psychology, one finds in the rhythms of certain neural firing patterns, low dimensional chaos (chaos with more of the predictability in it), which seems to be a healthy state of affairs. And there is some evidence that it is good for the heart as well (though there is some controversy here, see Glass for some of the best research in this area). In psychotherapy, Adele Hayes has shown some evidence that things tend to fall apart (i.e., greater fluctuations in symptoms, emotions and more erratic behavior) prior to positive changes in therapy for depression. Tony Tang has done similar work, showing that sudden gains tend to be common in therapy, with abrupt (perhaps chaotic seeming) positive shifts in symptoms and functioning being pretty commonplace in various approaches to therapy. Yet, Tschacher and others have found that coherence (less chaos) within the therapeutic relationship is good, predicting better treatment outcomes. Nevertheless, there is a growing body of research showing that too much order in intimate relationship systems is a bad thing, like the work of Granic, Dishion and others who have been showing that rigid and predictable social interactions in families, and also in teen peer relationships, lead to psychopathology over time (depression, anxiety, and conduct disorders). Finally, Gottman has demonstrated clearly that rigidity in marital interactions, behavioral and also physiological, is a strong predictor of unresolved conflict and eventual divorce. All of this relationship research suggests that rigidity is bad, implying that moving toward chaos is good. But is any of this "good chaos" really the chaos from chaos theory? Is it the same chaos that the Joker was trying to instigate? To address this question, we need to look at chaos theory's less popular, but more successful cousin: Complexity theory.

Complexity theory: The Batman Incarnate

In this blog, we will be using "complexity theory" and the related concepts of "emergence" and "self-organization" to understand psychology much more often than chaos theory. Although chaos theory seems "sexier" (at least for math geeks), complexity theory has had more utility in psychology thus far. The best lesson I ever had on complexity versus chaos pointed out the ways they are like opposites in the way that they are created. Chaotic dynamics come from the relatively simple interactions of a few variables (i.e., a few swinging pendulums tied together). Complexity involves the interactions of many different variables, the more the better in fact (see Per Bak, Stuart Kauffman, or Herman Hakan for more information).

Furthermore, chaotic dynamics rest within an attractor (see the 'strange attractor' from Lorenz in last week's post); they are bounded. Complex dynamics are creative; they are unbounded in a certain sense, even though they are technically more structured than chaos. Both produce fractal outputs - self-similarity and infinite complexity across different scales of size or time. The simple branching pattern to the left is a fractal - and "sure" it does look like almost every complex structure in nature. All of these structures are known as "power-laws" - structures with exponentially more small branches than big ones (see the graph on the left from if you are interested in the mathematical relation between size and frequency in a fractal).

Physical examples of complex, self-organizing structures include: plants, neurons, bronchial tubes, coastlines, cloud outlines, and river systems. Change-over-time examples include heart beat intervals (one point of controversy with the idea of chaos in the heart mentioned above), wait times in stop-and-go traffic, and earthquake magnitudes. Examples in psychology include: visual search patterns, speech production, reading for meaning, reading single words, memory - nearly every area of cognitive psychology. Even the internet has "self-organized" into a fractal. The graph above and to the left actually represents the relative popularity of blogs. Very few are highly popular (like the trunk of a tree) and many are rather obscure (small branches -like this one). The connections among web-sites works the same way, as do things such as social popularity (few people are most connected in social networks and many are on the outskirts), and the relative size of cities.

In my own research, I have found repeatedly that social interactions are complex and fractal. Specifically, if you look at repetitions in the order of who talks to whom and when during conversations, you will find branchlike structures, with very few patterns that repeat a lot, and many more that happen once or twice. Furthermore, the fractal patterns you find in verbal turn-taking as people talk correlates with control, closeness and conflict among the members. So if you have a strong leader, lots of repetitions will happen in conversation patterns involving the leader; if you have very close members of a group they will talk in more repetitive ways; and in conflict we all know that we get stuck and go round-and-round. We all know the familiar repetitions in the conversations of our families of origin, right? The more rigid and repetitive they are, the more enmeshed our family is, or the more lopsided it is in terms of power, or the more conflict-driven it is. On the other hand, when things are more open and unpredictable, this means that people can tolerate more distance, are more democratic with each other, or that there is less unresolved conflict.

Conflict is a really important process, regulating control and closeness. In fact, most if not all conflicts are about control or closeness, like "quite telling me what to do," "do what I say," (control) "leave me alone," or "don't leave me" (closeness). Experimentally, I induced conflict into a single person in a group (told her the other members found her cold and abrasive) and found that the fractal turn-taking patterns shifted rigid - like the branches falling off a tree. When they resolved the conflict the conversation ‘fluffed back up again,' with new growth. I have replicated these fractal results on many types of relationships, from group therapy members and families to new friendships. The fractal structure is always there, clear as day statistically speaking.

Altogether, these results suggest that individual personality is structured as a fractal, and that there is some self-similarity between the individuals and the groups they are in, like snowflake personalities joining together to make larger snowflake groups and so on. When a person gets rigid from some internal conflict, the group gets rigid and vice versa. Just like other fractals, the part is in the whole, and the whole is in the parts, up and down in an infinite manner. And change in one part, spreads up down and across such systems. If we wanted to stretch the scales from biology to the entire world, you could theoretically suggest that Hitler had a chemical ‘imbalance' (rigid process of neurotransimitter flow), which made his personality conflicted (i.e., malignant self loathing), which led to a rigid political movement (Nazis), which started a world-wide conflict (WW-II). This is how complexity theory works. Occasionally, very small events propagate within the fractal structure to become very large events: the straw that broke the camel's back, avalanches out of a snow flake, earthquakes out of a tiny platonic shift, and marriage ending conflicts over a trifle. Of course, timing is all important.

Okay - a bit of a tangent from the movie Batman, but I do have a point. Allow me to address Gomez's comment from my first blog entry about control and intentionality in our lives. He asked: "My question now is if our brain is constantly experiencing what we feel is our subjective future, are we stuck on our own non-linear ride through life? It seems to be that we are hardly aware of this momentum we have built up, yet daily we ride it out in our minds with the illusory preface of control. Any thoughts?"

Gomez, I can reply now with a quote from Hollis, Kloos and Van Orden (2008). They wrote one of the cognitive psyc chapters in our forthcoming book, Chaos and Complexity in Psychology: Theory of Nonlinear Dynamical Systems, from Cambridge University Press: "Sources of constraint for purposeful action exist throughout the body, including anticipatory movements and excitations, as well as dynamical processes of the body such as head position, posture, respiration, and digestion. At the extreme, sources of constraints even include the details of capillary red blood flow and local oxidation in muscle tissue. All these constraints combine to reduce the degrees of freedom for cognitive behavior and thus contribute to the fractal variation in cognitive activity."

What they are saying is that when we make an act of will, we choose along a fractal path. There are typically many ways to go, but not an infinite number. "Yes" to Gomez, our view of the subjective future (what he has called "nexting") does limit us. Along with our experiences in memory, the intricacies of the situation, the states of our bodies and details right down to head position or eye gaze. All of this combines to provide constraint on free will.

However, Hollis et al (2008) review the available research in fractal cognition which suggests that although all levels of cognitive behavior involve constraint, this constraint paradoxically allows for purposeful creativity. Constraint and free will combine (yet another example of a yin yang type of co-creative process). When a whole lot of constraints combine together, exchanging information, relating - they create a maze of unlimited options on a more holistic level.

A relationship example may make this more understandable. When you begin interacting with others, you are limited by many aspects of the interaction, roles, customs, politeness, the topic of conversation and so on. But together, you and the other interactants have unlimited possibilities for creating new patterns of relating. There are infinite subtle shifts in branches that you may take. So "no" to Gomez, momentum and imagining our next moves does not preclude self-determination. Rather, it facilitates it by removing the paralysis of having too many options to choose from. The batman would be a prime example of a complex, yet integrated human being. And in becoming "The Batman" he is both constrained, but also supremely in charge of his own destiny and his place in the world.

If you've hung on this long, please stay tuned for part III below, where we'll try to put this all together and bring it on home to a conclusion....

About the Author

David Pincus

David Pincus is a licensed clinical psychologist and assistant professor of psychology at Chapman University in Orange, CA.

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