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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
Musings About Strange Attractors
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
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 (http://en.wikipedia.org/wiki/Feigenbaum _constants and http://mathworld.wolfram.com/FeigenbaumConstant.html)
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
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 http://www.simplypsychology.org/cognitive-dissonance.html.
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.
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.
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 http://www.scholarpedia.org/article/ Mirror_neurons.
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
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
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
Efficient and sustainable learning,
Dementia and other memory-related matters,
Ongoing anxiety, and
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,
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
Polyvagal theory, including its connections to epigenetics. (Sylwester and Moursund, 2013).
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.
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: firstname.lastname@example.org.
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