Information Age Education
   Issue Number 123
October, 2013   

This free Information Age Education Newsletter is written by Dave Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is one component of the Information Age Education project.

All back issues of the newsletter and subscription information are available online. In addition, three free books based on the newsletters are available: Consciousness and Morality: Recent Research Developments, Creating an Appropriate 21st Century Education, and Common Core State Standards for Education in America.

This newsletter is the ninth in a series on complexity. Our informal and formal educational systems, and our everyday life experiences, help us learn to deal with the complexities of complexity.

Understanding and Mastering Complexity:
Musings About Strange Attractors

Bob Sitze
Author and Consultant

Previous articles in this IAE Newsletter series focused on the central role that analogy (and then caricature) play in cognitive processing. This article illustrates the intriguing possibilities that can develop when we push an analogy to the edge of its rational utility. It uses the primarily mathematical concept of “strange attractors” to demonstrate analogy-stretching.

Understanding Strange Attractors

You are familiar with gravity and magnetism. Gravity is a force that attracts two physical objects to each other. Magnetism is a force that can attract or repel certain objects. Attractors have been studied by physicists and mathematicians. Some behave in an unpredictable, chaotic manner. Mathematicians named these strange attractors.

In strictest scientific terms, strange attractors are mathematical constructs that help explain phenomena whose patterns seem complex or chaotic. An “attractor” is a durable theorem about the physical world that becomes “strange” because it interprets or connects ostensibly disparate events or facts. Strange attractors are scientifically useful because they can describe seemingly unconnected processes in simple terms. Defined operationally, strange attractors are intriguing because they may predict the seemingly unpredictable and invite or motivate further actions.

My Attraction to Strange Attractors

My interest in strange attractors came almost at the moment when I first discovered that this scientific/mathematical phenomenon existed. I remember reading in Scientific American about Feigenbaum’s Constants (
and and being awed that a decades-old mathematical formula might be helpful in understanding disparate parts of the physical world. I was also amazed that scientists were hopefully fitting these ratios to phenomena important to their research.
Over the years I began to see other strange attractors (such as those described below) that emerged as scientific/mathematical attempts to bring order to complexity. Most were mathematical, but at their roots these formulas or constructs skated right up to the edge of the meaning of “analogy.” It occurred to me that “strange attractors” could be useful in more places if they were considered more broadly and perhaps less mathematically in other areas of daily life. I started playing with such questions as, “Where else in life does something ‘strange’ attract attention or make sense?” or “Stripped of their math, what are strange attractors really like?”
Because my professional work has always involved making sense out of social systems, I began using “strange attractors” as a way to describe new axioms in education, ecclesiology, and social change. It seemed that my audiences and readers instinctively understood how “strange attraction” described bedrock matters that were applicable across a broad spectrum of their work.

That’s why I have come to see the value of “strange attraction” as a helpful way to understand and master complexities in a variety of fields of human endeavor. Thus it has not been difficult to extend this possible analogy into the field of applied neuroscience. What follows is the result of those years of happy noodling with an intriguing concept.

An Example from Physics

To see strange attraction in action, imagine a pile of various metal filings, showing no pattern or purpose other than to collectively take up space. Now think of what happens when a strong magnet passes through that metallic collection. Some filings—iron, steel, cobalt, and nickel—are drawn to the magnet’s forces, oriented toward the lines of energy the magnet has presented. In time, each of the magnet-oriented slivers can become its own mini-magnet, displaying an additional identity imparted by the magnet’s presence. Those filings not drawn to the magnet’s force field can be described in other ways, but “magnetized” is not one of them. What previously seemed to be an indescribable collection of metal is now explained and understood by virtue of the magnet’s presence.

In this illustration, the magnet becomes the strange attractor because it enables a specific description of direction, purpose, unity, and similitude where none existed without its presence. (When magnetism was first discovered, of course, it was wonderfully and oddly strange, and therefore attractive. The same thing happens in our times, when quirky bits and pieces of science emerge as newly powerful and accurate descriptors of much of what we had previously not understood that well.)

Moving Strange Attraction into Behavioral Sciences

As suggested above, the function of strange attractors has not been completely limited to math and the physical sciences. Leon Festinger’s theory of cognitive dissonance burst into the fledgling science of social psychology in the 1950s. It's the discomfort one experiences when simultaneously confronting conflicting concepts. His ideas were attacked as unprovable or vaporous. See But as the applications of the theory started to multiply and gain traction in actionable science, the influence and connectivity of this body of knowledge began to emerge. Today, cognitive dissonance theory is a bedrock principle in the applied behavioral sciences. It has added cohesive, durable meaning, thus functioning as a strange attractor in the explanation of seemingly unpredictable behavior. For example, imagine the cognitive dissonance experienced by a terminal patient's caregiver. To provide the patient with food and medicine extends a terrible and often painful life. Conversely, to consciously deny food and medicine seems hopelessly cruel to a person one loves.

Claiming Strange Attractors in Neuroscience

It seems defensible that several of the lodestone concepts of neuroscience may also function as strange attractors. Three familiar examples: Dunbar’s Number, mirror neurons, and movement. In each case the initial discovery or theorem eventually coalesces to form a wide variety of useful applications that the original discoverer would probably not have known.

Dunbar’s Number

Expressed as the ratio between the size of the human neocortex and the size of the entire brain, Dunbar’s Number (147.8, rounded up to 150) may predict the optimum number of cooperative and trusting relationships that can be sustained in human societies. Published more than 20 years ago, the original research by British anthropologist Robin Dunbar (1992) showed similar correlating ratios among other primate relational groupings.

At its onset, Dunbar’s Number described:
  • The average number of villagers in 21 hunter-gatherer societies around the world (150),

  • The optimum number of soldiers in an effective fighting unit (under 200),

  • The historic cutoff point for Hutterite communities to split into new communities (150), and

  • The organizational philosophy of the GoreTex Corporation (a cap of 150 employees per manufacturing plant).
Today, debate and further application of the original research continue, harnessing its predictive usefulness to the size of online communities, shared purpose in social groupings, ideals in management theory (e.g., work team efficiency), and even the optimum size of churches. This neurobiological strange attractor could be a key to understanding as-yet-unknown elements of applied social science. Its emerging iterations may someday instruct algorithms or practices that guide the further development of social media, investment in entrepreneurial start-ups, neuromarketing (e.g., word-of-mouth approaches), monetizing of relational capital, and social psychology.

Mirror Neurons

What began as a casual observation by Italian researchers of monkeys imitating what they saw eventually led to the discovery of mirror neurons—several varieties of cells found throughout the nervous system that assist us in the valuable skills of imitation, imagination, and self-awareness. See
. Today, the science surrounding mirror neurons, which includes but is not limited to motor neurons, may also have strangely attractive implications for other facets of human behavior.

This possibility is amply illustrated in the inventive conjectures and experiments that V.S. Ramachandran describes in The Tell-Tale Brain: A Neuroscientist’s Quest for What Makes Us Human (2011). He explores how the “mirror neuron system” can explain autism, theory of mind, social systems, language development, and memory.
He suggests that mirror neurons assist our brains to determine the intentions of others, adopt their conceptual vantage points, become aware of others’ point of view about ourselves, construct and use abstractions (especially metaphors), and interpret the implied actions embedded in those metaphors—perhaps the basic stuff of consciousness.

If mirror neurons are implicated in autism, as Ramachandran's experimental work suggests, many of autism’s characteristics could be explained as mirror neuron system deficiencies. For example, persons in the autism spectrum have difficulty interpreting metaphors as action-prevalent expressions, connecting sensory/motor processes, understanding social cues, and acquiring and using language.

Since the 1992 discovery of mirror neurons, what initially seemed simple—the power of imitation and imagination in human brains—has found utility in fields of endeavor as diverse as sports coaching, learning/memory theory, neuro-linguistic programming, counseling, parenting, stroke recovery, research into neonatal development, addiction, prejudice, sociability, motivation, and habituation. Some of these applications may work, others may not. That’s the way things develop.

While remaining mindful of Ramachandran’s caution regarding “mirroritis”—mirror neurons explain everything!—we can nonetheless explore this piece of neuroscience as it continues to be useful and thus strangely attractive.


When I’m not sitting here writing, I move around. I practice tai chi, walk regularly, steward my suburban yard, and count twig-collecting as my hobby. (For disbelieving non-twiggers: This hobby requires lots of tricky twiggy moves!) I understand the value of exercise and movement for my body. When a friend suggested that “movement” be included in my book about the applications of brain science to ecclesiology (Sitze, 2005), I welcomed the valuable addition. His basic thesis: Movement is profoundly integral to our well-being because our brains are oriented toward movement.

That thinking turned out to be prescient when John Ratey published Spark: The Revolutionary New Science of Exercise and the Brain (2008), a wide-ranging synthesis of research regarding brain benefits of movement/exercise. Ratey proposed that movement of any kind, and especially regular exercise, could benefit people who wanted clarity about:
  • Persistent depression,

  • Continuing addictions,

  • Efficient and sustainable learning,

  • Dementia and other memory-related matters,

  • Ongoing anxiety, and

  • Attention-related difficulties.
In each case, Ratey focused on the proven value of exercise to brain-related difficulties that can hamper well-being. As he gathered together extant science around the idea of movement, Ratey was able to offer people facing life-altering circumstances a basis for reasoned, actionable hope.

The phenomenon of movement/exercise now functions as a neurobiological strange attractor. Today, the precepts of movement coalesce the attention and behaviors of educators, human resources managers, occupational and physical therapists, gerontologists, psychologists, psychotherapists, and pediatricians. Due in part to Ratey’s efforts, the neurobiology of movement has effected changes in entire school systems, clinical practices, regimes of rehabilitation and recovery, and the daily routines of ordinary people.

Emerging Strange Attractors in Neurobiology

Several other elements of cognitive neuroscience may soon qualify as strange attractors. The following newer discoveries are beginning to function as durable explanations of widely divergent phenomena in our lives:
And you?

You may be among those whose work in applied neurobiology generates or strengthens chunks of knowledge that affect people’s lives. I hope you have found reasons to take heart, to remain strong in your resolve about the value of your work. I hope that, because you are already fitting neurobiology into life’s fundamental behaviors, you will see yourself as part of a growing movement of people who can claim strange attractiveness as a part of their lifework—to understand and then to master complexity.


Dunbar, R.I.M. (1992). Neocortex size as a constant on group size in primates. Journal of Human Evolution.

Ramachandran, V.I. (2011). The tell-tale brain: A neuroscientist’s quest for what makes us human. New York: W.W. Norton.

Ratey, J. (2008). The revolutionary new science of exercise and the brain. New York: Little, Brown.

Sitze, R. (2005). Your brain goes to church: Neuroscience and congregational life. Herndon, VA: Alban Institute.

Steiner, C. (2012). Automate this: How algorithms came to rule our world. New York: Portfolio/Penguin.

Sylwester, R., & Moursund, D. (2013). Consciousness and morality: Recent research developments (Chapter 5). Eugene, Oregon: Information Age Education. Available at

Bob Sitze

Bob Sitze is a church consultant and Alban Institute author. He continues his active interest in the application of neurobiology to social systems, especially churches. He lives and works in Wheaton, Illinois. Contact information:

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