Ultimately, I haven’t been able to gain much traction on tangible implications beyond highlighting the impact of physical environment and infrastructure as contexts for learning, which is essentially where I have left off with this blog, moving over thence to Language & Literacy.

That said, I remain fascinated by complexity theory and interdisciplinary noodling. After listening recently to a podcast interview on Simplifying Complexity with Geoffrey West, I added his book, Scale, to my to-read list. I found it to be an interesting book that bears some relevance to my desire to bring something more tangible to examining schools as complex adaptive systems.

What is compelling about Scale is that West brings empiricism derived from physics to the study of complex adaptive systems – and he lays out a case that power law scaling can be demonstrated across widely disparate systems, from animals to cities.

Power Law Scaling

Power law scaling refers to a mathematical relationship where a relative change in one quantity results in a proportional relative change in another quantity.

Some key quotes from the book on power law scaling:

• "These systematic scaling relationships are highly counterintuitive. They show that almost all the physiological characteristics and life-history events of any organism are primarily determined simply by its size"

• “power law scaling is the mathematical expression of self-similarity and fractality."

• “because animals obey power law scaling both within individuals, in terms of the geometry and dynamics of their internal network structures, as well as across species, they, and therefore all of us, are living manifestations of self-similar fractals”

In addition to examining how scaling applies both internally and externally across animal species, West also examines how power law scaling applies to businesses and cities. One of the interesting distinctions he explores is that of sublinear vs. superlinear forms of scaling.

Superlinear scaling relates to a greater than proportional change, while sublinear scaling indicates a less than proportional change.

Sublinear Scaling

Both animals and companies reflect sublinear scaling in that as their size increases, other aspects will increase at a slower rate. So for example, consider a whale.  A blue whale, the largest animal on Earth, doesn't need to consume food at the same rate as a much smaller fish, even though it has significantly larger body mass. This is because an organism's surface area, which is more crucial for heat exchange and nutrient absorption, increases proportionally less than its volume as size increases.

In companies, doubling the number of employees does not mean there is a need for doubling office space or computer resources. Communication channels and management structures will need to adapt, but not at a 1:1 ratio with employee growth. This sublinear scaling allows for larger systems, whether a blue whale or a multinational corporation, to function more efficiently despite their size.

Yet while sublinear scaling allows organisms to grow larger and function efficiently, it also plays a role in the inevitable process of aging and death. As creatures grow, the advantages of sublinear scaling become challenges. Distributing resources and eliminating waste become increasingly difficult, cellular maintenance becomes a more difficult task, and harmful byproducts accumulate. These factors lead to the gradual decline of an organism, ultimately setting a natural limit on size and lifespan.

What West found surprising was that these very same sublinear factors also apply to businesses. Like people, companies experience increasing challenges as they age. Communication bottlenecks create information silos and slow decision-making, hindering their responsiveness to changing market conditions. Management complexities stifle innovation and agility, making it difficult to adapt to new threats. These inefficiencies accumulate, leading to a company's decline, acquisition, or bankruptcy.

Superlinear Scaling

Unlike the sublinear scaling in a closed system, superlinear power law scaling describes a situation where a system's output or a certain property increases at a faster rate than the size of the system itself. Examples include our brains, social networks, and ant colonies. Emergent properties that were not present in the smaller versions arise as the systems get larger.

Our economy is driven by the superlinear scaling of innovation and markets. This leads West to provide strong caution on the ecological limits that we are hitting due to the properties of superlinear scaling. I hadn’t expected to encounter environmental advocacy in this book, given West’s preoccupation with mathematical calculations and large scale ideas – but his sustained and wide ranging focus on the implications of power law scaling inevitably led him to confront the brutal facts: as a species wielding powerful technologies that require outsized resources to drive, we are hitting the upper limits of our ability to innovate our way out of ecological constraints.

He provides a tangible way of understanding this by explaining how much metabolic energy we consume each day to keep our bodies going. As with any other animal, this is determined by our physical size. He then contrasts that by how much we consume beyond our biological needs due to the technologies we wield:

• "Thinking of us as an animal using thirty times more energy than we 'should' given our physical size, the effective human population of the planet accordingly operates as if it were much larger than the 7.3 billion people who actually inhabit it."

• "In a very real sense, we are operating as if our population were at least thirty times larger, equivalent to a global population in excess of 200 billion people"

The Power of Cities

As West explains it, cities are an especially fascinating case to study the properties of power law scaling, as they simultaneously demonstrate aspects that are sublinear, and others that are superlinear.

Two key quotes on these twin aspects of super- and sub-linear scaling coexisting in cities:

• In a city, "the sublinearity of infrastructure and energy use is the exact inverse of the super linearity of socioeconomic activity. Consequently, to the same 15 percent degree, the bigger the city the more each person earns, creates, innovates, and interacts ...and the more each person experiences crime, disease, entertainment, and opportunity and all of this at a cost that requires less infrastructure and energy for each of them. This is the genius of the city. No wonder so many people are drawn to them."

What does scaling have to do with schools?

There are no implications for schools yet based on what was presented in the book. And yet, it was exciting to see how consistent mathematical properties can be derived that can inform how we can understand a wide diversity of animals, businesses, and cities across different scales.

I hope that as more of this type of analysis grows, more study of how schools as complex adaptive systems, both in terms of the social networks and communications within and around them, and in terms of their physical infrastructure, can be taken on with empirical data. The book was published in 2017, and scaling laws continue to be studied, such as in this recent article on how superlinear scaling relates to crime in NYC.

How do power laws apply to schools as they increase or decrease in size, both physically and in terms of the number of students and teachers? How does power law scaling relate to student learning? What are the opportunities and challenges afforded by social networks in different sizes of schools?

With the right level of knowledge and data, these things can be studied empirically! If you are aware of any research along these lines, please share.

When I first started this blog, I hoped--as my younger, more idealistic and grandiose self--that we would uncover ecological principles of complex adaptive systems that could be applied in everyday practice.

While I have certainly uncovered many interesting themes and patterns along the way (such as obliquity, or the influence of unconscious bias on behavior), my slightly more hoary-eyed self can say, in an honest moment, that I have not discovered an alchemical praxis that will transmute principles of self-organizing systems into pedagogy or school organizations. Sorry!

A blog post, "Life Is Complexicated," by Benjamin Goertzel helped me to clarify a reason why it might be so difficult to distill principles of complex adaptive principles into readily applicable practices.

Goertzel critiques the "Santa Fe Institute" concept of complexity, which has examined complex adaptive systems that have qualities of self-organizing emergence to identify universal principles. For Goertzel, the problem is not that there aren't such systems, but rather that the real world systems that we wish to most understand aren't simply complex—they are an admixture of both complex and complicated:

They are complex (in the Santa Fe Institute sense) AND complicated (in the sense of just having lots of different parts that are architected or evolved to have specific structures and properties, which play specific roles in the whole system). . . . They are messy in a lot of different ways.  They have lots of specialized parts all working together, AND they have complex holistic dynamics that are hard to predict from looking at the parts, but that are critical to the practical operation of the parts.

When considering a school or a school system, this messy confluence of self-organizing emergence and highly specialized roles and frameworks sounds like a more apt description. Our analogy of a school to an ecosystem is meant to push back against the linear thinking that many apply to schools—but I will readily acknowledge that a school is far from an actual ecosystem (really, it's perhaps more akin to a garden). Schools are institutions embedded within a wider complexication of bureaucracy, policy, culture, economics, and politics.

So perhaps I shouldn't feel bad about having difficulty in simplifying the realm of education based on an analysis of schools as complex adaptive systems. Schools are complexicated.

In facing complexity, institutions that seek to represent some form of authority can no longer count on simple mechanisms of control, nor can they claim to hold the sole, proprietary keys to critical information. The information most critical to their success lies within the minds of those they would seek to influence.

Knowledge from the community, as we've discussed here before, is critical information to the flourishing of successful enterprises, whether a business, school, government, or—as recent statements by NYC Police Commissioner William Bratton and FBI Director James Comey have made clear—a police force.

In "Another Bratton revolution for the New York City police" by Kevin Cullen in the Boston Globe, Bratton addresses the significant tension between the police and the communities they work most within: “The biggest challenge. . . is that the neighborhoods where our approval is the lowest are the same neighborhoods most plagued by violent crime.”

To address the great rift that lies between the perception of the communities they serve and the police officers, Bratton wants to tap into the expertise of veteran cops by pairing them with rookies. This apprenticeship model gives cops an opportunity to learn from those who have long served the communities they work within:

Basically, it’s getting back to the beat cop paradigm, freeing them from the tyranny of responding to radio calls. Cops will learn, from the community itself, who the troublemakers are, reducing the need for the random stops and frisks that engender so much resentment. “For years,” Bratton said, “we’ve been asking our officers to engage with the community, but we’ve never given them the time to do it.” [bold added]

There's parallels to teaching here. Most teachers are thrown into any school they can find employment at, with little apprenticeship, and little induction into the community their school serves. Teachers are left stranded in an isolated classroom, struggling to support students whose everyday lives may be so foreign to that of their teachers that may be little opportunity to connect new academic learning to prior knowledge or social aspects of students' lives.

When you add racial and socio-economic differences into this mix, situations can become toxic. Though everyone talks about high expectations in the education sector, at the ground level, in that isolated classroom, who is to say that this teacher is equipped with the context and understanding to work positively with students that may look, talk, and live in a manner completely foreign to her own experience? What kind of training and support has she received to prepare her for the specific social, cultural, linguistic, and emotional reality of the students who sit before her?

The FBI Director, James Comey, also addressed the deep tension that can lie between law enforcement officers and the communities they serve. In "F.B.I. Director Speaks Out on Race and Police Bias" by Michael Schmidt in the New York Times, Comey refers to the "significant research showing that all people have unconscious racial biases."

Echoing Bratton's comments on beat policing, Comey suggestions the following:

"Law enforcement officers, he said, need 'to design systems and processes to overcome that very human part of us all. Although the research may be unsettling, what we do next is what matters most,” Mr. Comey said. . . . Mr. Comey said tensions could be eased if the police got to know those they were charged to protect. “It’s hard to hate up close,” he said. [bold added]

It's a constant refrain in education these days for a reason: getting to know our students and build positive relationships with them is critical. Furthermore, knowing their families and community is critical. Without this knowledge and understanding, unconscious biases and assumptions have free reign. And while that may have worked just fine for schools and law enforcement agencies in the past, it's no longer tenable in a day and age where individuals are equipped with advanced communications technology (smartphones).

We live in a time in which anyone with a phone can nearly instantaneously post a blog or a video and influence many others within their networks. This has changed the game for those who work for institutions that represent "authority," and who seek to influence the constituents they serve.

This recognition has also been made by the military. In "A refocus of military influence" by Vaughan Bell on Mind Hacks, Bell investigates the birth of the 77th Brigade, a new arm of the British military that "has been prompted by a growing realisation that the success of security strategy depends as much on influencing populations at home and abroad as it does through military force."

The formation of the 77th Brigade is a mostly reflection of a wider refiguring of global conflict that puts cognition and behaviour at the centre of political objectives. It is simultaneously more and less democratic that [sic] ‘hard power’. It makes the battle of ideas, rather than the use of force, central to determining political outcome but attempts to shape the information environment so some ideas become more equal than others. [bold added]

In schools, we have long shed disciplinary mechanisms of paddling and rapping knuckles with rulers. Yet we still cling to vestiges of this mentality, suspending kids right and left, rather than seeking to get to the heart of the psychological perceptions and emotional and social experiences that drive that behavior. But this, too, is changing, as concepts of "restorative justice," rather than suspension, become more widely propagated. Restorative justice sounds like a hippie thing. But when you consider that the method strategically taps into the perceptions and emotional experiences and social networks of those involved, it becomes more evident as a tactic for better coping with complexity by harnessing the knowledge of those who hold the most critical information.

All of this talk of police work as embedded within the community it serves brings to mind David Simon's "The Wire" series. One of the moments that most stood out to me from that show was when a police major, Colvin, laments the "warfare" mentality engendered by the "war on drugs," and recalls the "real police work" of the beat officer walking the streets of the community she serves.

Here's a short clip of his monologue [Warning: strong language use]:

http://youtu.be/BA5za4VsskM

We've investigated the concepts of randomness, disorder, and chaos and how they might relate to complex and dynamic systems here before. The obvious connection to a school, in case you've never worked in one, is that you can never quite anticipate what's going to happen on any given day. Schools are complex systems rife with social and emotional and cultural and political and psychological interdependencies and turbulence. Yet it is this very complexity that makes working within them so very compelling.

An interesting article on Nautilus by Kelly Clancy, "Your Brain Is On the Brink of Chaos," the concept of chaos is examined in its relation to the brain. Clark lays out some principles worth exploring further. For example, she lays out the following definition of chaos:

Chaos is not the same as disorder. While disordered systems cannot be predicted, chaos is actually deterministic: The present state of the system determines its future. Yet even so, its behavior is only predictable on short time scales: Tiny differences in inputs result in vastly different outcomes. Chaotic systems can also exhibit stable patterns called “attractors” that emerge to the patient observer. Over time, chaotic trajectories will gravitate toward them. Because chaos can be controlled, it strikes a fine balance between reliability and exploration. Yet because it’s unpredictable, it’s a strong candidate for the dynamical substrate of free will [bold added].

This made sense to me based on some other ideas on chaos we've examined before. For example, in a quote from Simple Really: From Simplicity to Complexity — And Back Again by John D. Barrow, an essay within a compilation of essays on the Royal Society, Seeing Further: Ideas, Endeavours, Discoveries and Disputes — The Story of Science Through 350 Years of the Royal Society, edited by Bill Bryson, Barrow states the following:

An important feature of chaotic systems is that, although they become unpredictable when you try to determine the future from a particular uncertain starting value, there may be a particular stable statistical spread of outcomes after a long time, regardless of how you started out. The most important thing to appreciate about these stable statistical distributions of events is that they often have very stable and predictable average behaviors. . .[bold added].

So through careful observation and analysis, chaotic systems can be predictable, even if they are quite unpredictable on an immediate basis. I thought Clancy's explication of chaos as actually deterministic was also enlightening. This idea that it's present state determines its future also lines up with what we've examined in terms of the possibility of an underlying mathematical simplicity of complex systems.

In that post, "A Self-Organizing Criticality, Somewhere Between Boredom and Chaos," we also examined Per Bak's concept of a "self-organized criticality," in which complex systems spontaneously transition between states of order and disorder, which Clancy echoes in the following quote about the brain:

The critical state can be quite useful for the brain, allowing it to exploit both order and disorder in its computations—employing a redundant network with rich, rapid chaotic dynamics, and an orderly readout function to stably map the network state to outputs. The critical state would be maintained not by temperature, but the balance of neural excitation and inhibition. If the balance is tipped in favor of more inhibition, the brain is “frozen” and nothing happens. If there is too much excitation, it will descend into chaos. The critical point is analogous to an attractor.

This notion that a complex system hovers somewhere in the balance between chaos and order is a fascinating one, especially when you connect it to the idea of a school. It reminds me of a joyous classroom of students engaged in meaningful and challenging work. There's a warm buzz of controlled but spontaneous activity and creativity. Students can very easily go off the rails, and it's the teacher's job to hold them in that "hinterland between the inflexibilities of determinism and the vagaries of chaos," as Barrow eloquently phrased it.

Order and disorder enjoy a symbiotic relationship, and a neuron’s firing may wander chaotically until a memory or perception propels it into an attractor. Sensory input would then serve to “stabilize” chaos. Indeed, the presentation of a stimulus reduces variability in neuronal firing across a surprising number of different species and systems, as if a high-dimensional chaotic trajectory fell into an attractor. By “taming” chaos, attractors may represent a strategy for maintaining reliability in a sensitive system. Recent theoretical and experimental studies of large networks of independent oscillators have also shown that order and chaos can co-exist in surprising harmony, in so-called chimera states.

This idea of attractors is also fascinating to me. As I read this passage on the subway on the way to class this morning on my little smartphone screen, I thought back to the idea of perceptual illusions and their relation to powerlessness. I also thought about the effect of isolation on the brain. And I wondered if this concept of "sensory input" stabilizing chaos that Clancy just outlined can be taken almost literally, as in how the loving touch of a mother has been shown to be important in brain development. And how beyond touch, the tone and manner in how adults and students speak to one another, the colors displayed on the wall, and all the other contextual factors of the environment can be so fundamental to "taming" the chaos that lies both in extreme isolation (ever been alone in the wilderness? Your mind goes nuts) or in overcrowded, confined spaces (the ghetto). Schools can provide that stabilizing influence.

Again, we find echoes of this idea of harmony and symbiosis in Barrow:

. . . Chaos and order have been found to coexist in a curious symbiosis. . . . At a microscopic level, the fall of sand is chaotic, yet the result in the presence of a force like gravity is large-scale organisation.  . . Order develops on a large scale through the combination of many independent chaotic small-scale events that hover on the brink of instability. Complex adaptive systems thrive in the hinterland between the inflexibilities of determinism and the vagaries of chaos. There, they get the best of both worlds: out of chaos springs a wealth of alternatives for natural selection to sift; while the rudder of determinism sets a clear average course towards islands of stability.” (Bold added)

Now that I've geeked out on chaos, back to work . . .

In our last post, we examined an interesting analogy between quantum physics and human behavior made by George Soros. While we're on the physics tip, here's an intriguing article on a theory of the brain that incorporates understandings from physics in describing how systems balance  order and disorder, "Toward a Theory of Self-Organized Criticality in the Brain" by Jennifer Ouellette in Quanta Magazine.

Termed a "self-organized criticality" by Danish physicist Per Bak, the gist of the idea is that dynamic systems—such as the brain, a school, or traffic—maintain a semblance of stability by spontaneously transitioning between states of order and disorder. These spontananeous transitions are akin to small avalanches, and the concept is explained most concretely by an analogy to a pile of sand:

Think of sand running from the top of an hourglass to the bottom. Grain by grain, the sand accumulates. Eventually, the growing pile reaches a point where it is so unstable that the next grain to fall may cause it to collapse in an avalanche. When a collapse occurs, the base widens, and the sand starts to pile up again — until the mound once again hits the critical point and founders. It is through this series of avalanches of various sizes that the sand pile — a complex system of millions of tiny elements — maintains overall stability.

For close readers of this blog, this description will bring to mind our exploration of the concept of emergence and thresholds, and indeed, these ideas are interrelated.

How a self-organized criticality factors into the equation lies in the term "self-organized." As the article explains it:

The precise moment of transition — when the system is halfway between one phase and the other — is called the critical point, or, more colloquially, the “tipping point.” Classical phase transitions require what is known as precise tuning: in the case of water evaporating into vapor, the critical point can only be reached if the temperature and pressure are just right. But Bak proposed a means by which simple, local interactions between the elements of a system could spontaneously reach that critical point — hence the term self-organized criticality (bold added).

In other words, what appears to the observer as something incredibly complex and based on a fragile and precise set of conditions can be adequately described as an accumulation of small, local interactions. The elegance of this idea lies in the implication that there is an underlying simplicity behind seemingly unintelligible processes, and that such simple mechanisms can be determined in a mathematical sense.

"Self-organized criticality" still remains more of a tantalizing idea than an applicable theory to organizations such as brains and schools, but even still, there is an underlying understanding that we can draw from it now. Let's return to the article:

A complex system that hovers between “boring randomness and boring regularity” is surprisingly stable overall, said Olaf Sporns, a cognitive neuroscientist at Indiana University. “Boring is bad,” he said, at least for a critical system. In fact, “if you try to avoid ever sparking an avalanche, eventually when one does occur, it is likely to be really large,” said Raissa D’Souza, a complex systems scientist at the University of California, Davis, who simulated just such a generic system last year. “If you spark avalanches all the time, you’ve used up all the fuel, so to speak, and so there is no opportunity for large avalanches.”

This is a wonderful way to describe a high functioning school. In any school or classroom, regularity, rituals, and structure are key to providing a positive learning environment. But educators also know that children also require events and changes that mix it up every now and then. But if there's too many random and chaotic events, effective teaching and learning is difficult—and I can attest to this, as many other educators can, having worked in a school where schedules were upset so frequently that I walked in each day assuming chaos, and announcements were made over the loudspeaker all throughout the day, interrupting teaching and learning.

In other words, there should be a healthy balance between boring but safe regularity, and taxing randomness.

Following a link on Twitter from Bill Moyers, I found this recent New Yorker blog post critiquing the notion of "preparedness" for climate change relevant to past discussions we've had on this blog around complexity and unpredictability.

In "Is It Too Late to Prepare for Climate Change," Elizabeth Kolbert points to a knotted problem endemic to complex adaptive systems: it is difficult to make accurate predictions, and thus attempting to establish certainty in the face of chaos and randomness is a fool's enterprise. The most effective recourse we have, therefore, may be to make decisions that focus immediately on daily practices that will obliquely—and more effectively—prevent us from crossing thresholds that may nudge our world into extinction.

As Kolbert puts it:

"Promoting “preparedness” is doubtless a good idea. As the executive order notes, climate impacts—which include, but are not limited to, heat waves, heavier downpours, and an increase in the number and intensity of wildfires—are “already affecting communities, natural resources, ecosystems, economies, and public health across the Nation.” However, one of the dangers of this enterprise is that it tends to presuppose, in a Boy Scout-ish sort of way, that “preparedness” is possible.

As we merrily roll along, radically altering the planet, we are, as the leaked I.P.C.C. report makes clear, increasingly in danger of committing ourselves to outcomes that will simply overwhelm societies’ ability to adapt. Certainly they will overwhelm the abilities of frogs and trees and birds to adapt. Thus, any genuine “preparedness” strategy must include averting those eventualities for which preparation is impossible. This is not something that the President can do by executive order, but it’s something he ought to be pursuing with every other tool." [bold added]

Let me repeat the sentence above that really resonated with me: "any genuine "preparedness" strategy must include averting those eventualities for which preparation is impossible."

This points us back to Nassim Taleb's idea in Antifragile that we must seek to benefit from volatility, rather than seek to avoid it.

So let's pivot these ideas back to school ecosystems. Schools operate very much in the moment. As a teacher in a public middle school, I am immersed in the daily eye of that storm. It's hard to explain to those who are not teachers, but let me simply say that teaching is a maelstrom, with barely space to breathe, sit down, reflect.

Seeking to better the work we do in the midst of this chaos and complexity thus requires us to harness the networking power of the human and social capital in the building: our teachers, administrators, staff, and children.

I'm going to leave this thought there, though it is woefully incomplete. Maybe you can help me fill it in. I'm too tired to keep writing after a long day! Over and out.

I've discussed thresholds on this blog before in relation to ecosystems, and the reality that we don't really know when such thresholds may be crossed.

To review, thresholds—in an ecological sense—refers to when some small, seemingly insignificant nudge suddenly results in an abrupt transformation of the entire ecosystem, resulting in loss of diversity and possible extinction. Keen readers of this blog may recognize a relation to the concept of hysteresis, which Will introduced us to.

An article on Ensia explores thresholds, depicting the battle of scientists trying to determine some method for uncovering early indicators of the crossing of such thresholds.

We live in a precarious age in which ecological thresholds have been crossed in such wanton abandon that those of us who do have an inkling of what is occurring sometimes prefer to bury our awareness in the veritable sand. It's gotten so bad that there's talk about scrapping such quaint notions as "conservation" and "sustainability" as they currently exist, and rather acknowledging that whatever future plants and animals might have is wholly dependent on the space that we might delegate for them in the margins of our busy lives of mindless consumption.

The great engine of human evolution, such as it is, will not wind down anytime soon. Max Planck once said, "A scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it."

Unfortunately, in this case, the scientific truth of the ecological devastation generated by our collective actions would then be realized by a generation much too late to do much about it other than mitigate desperately against it's effects. Which is more or less what we are beginning to see taking place (catastrophic forest fires, rising sea levels, violent storms).

But I'm going off on an preachy tangent here. My point in bringing up the article was to highlight an example of possibly misguided energy. Rather than seeking predictive power to better visualize approaching thresholds, wouldn't it be much better to change our practices now with the assumption that we should prevent any devastation from occurring, as much as possible?

A scientist quoted in the article acknowledges the limitation of attempting to quantify thresholds:

“I hope there are universal early indicators. If we have to figure this out for every system, then we’re up a creek without a paddle,” says Aaron Ellison, a forest ecologist at Harvard University. “If we have to spend 30 years on a system that we want to manage in some way, they’ll all be gone before we have a chance.”

In the face of such great complexity and unknown, we can't wait for research to clarify every last thing. We need to rely on our ground-level observations and local knowledge. But how do we gain clarity at that ground level?

“When you get to the field, you have to deal with particular ecological patterns. You have to deal with the technology and methodology that’s available for collecting data. You have to deal with the reality of sampling, and figure out how you’re going to use those samples and analyze them,” explains Craig Allen, a research ecologist with the U.S. Geological Survey who’s studied transitions in the American Southwest.

It's complex, as this scientist points out.

But there are observable clues that we can detect.

Given that detecting thresholds could take decades, researchers are looking for a shortcut — namely, indicators that can be applied to any arid region and require the ecological equivalent of a thermometer under the tongue.

The most promising of these is changing vegetation patterns. The beginning of a grassland’s transition to desert is marked by localized outbreaks of relatively sparse shrubs. Where soil once held by the grasses’ roots had acted like a sponge, water no longer penetrates. Wind blows faster over bare ground, piling eroding earth at the base of shrubs, which require more of the system’s water.

This reminded me of the "broken windows" theory of crime prevention--that paying attention to and addressing lower-level problems can be a means of preventing greater calamity.

It also made me consider the importance in developing simple and clear heuristics and checklists in the face of complexity. If we don't pay attention to small, incremental changes, then we will lose sight of the bigger picture, and may not notice potentially cataclysmic transformations until too late.

My advice is to avoid waiting for magical algorithms to determine where heretofore invisible thresholds may or may not be crossed. Instead, develop clear and straightforward management heuristics for paying attention to and addressing smaller issues.

In a school, this means addressing the peeling paint in the hallway immediately, rather than waiting until the summer. Immediately calling the parents of the child who has suddenly grown sullen and won't say good morning to any of his teachers. Having that awkward conversation with a challenging colleague. And so on.

In my last post, we looked at the geometric features of resiliency, which included diversity, web-network structures, distribution across a range of scales, and the capacity to self-adapt and self-organize.

We can learn more about the characteristics of web-network structures in a fascinating article in Quanta Magazine, "In Natural Networks, Strength in Loops" by Emily Singer.

The article describes how complex networks form into an architecture of a random series of interconnected, hierarchically nested loops. Such nested loops increase the resiliency and robustness of networks. This resilient architecture can be seen in leaves, insect wings, cerebral vasculature, fungi networks, and the Eiffel Tower.

"The cheapest network to operate is a simple branching tree structure, which is employed by some ancient plants. Though efficient, this structure is not very resilient. When a link is damaged, parts of the system suffer loss of fluid and die."

This is a theme that you can also hear reverberating throughout business and management literature. What seems to be most efficient on the surface—simple hierarchies with clearly delineated pathways of power and resources—is also most fragile.

"[Researchers] found that an architecture of hierarchically nested loops — meaning loops within loops within loops — is most resistant to damage. “Loops make the network redundant.""

Redundancy, as we've explored here before in optical fiber networks and social networks for disadvantaged college students, decreases fragility and increases robustness.

"The researchers also found that loop networks can better handle fluctuations in fluid flow as environmental conditions change."

The world we live in today is increasingly volatile. Communities, markets, and states are increasingly subject to external or internal turbulence. This is why modern leaders increasingly talk about agility and adaptiveness, rather than domination and control.

"In a paper published in Nature Neuroscience in July, the researchers showed that the capillaries form a continuous network. “This means that the microvessels — capillaries — are fully connected among each other,” said Kleinfeld. “There are no regions of isolated vessels, no gated communities in real estate terms.”"

Isolation increases fragility. This principle made me think of another excellent article, "The Social Life of Genes" by David Dobbs, which I will dive into further in a future post. In his discussion of researcher Steve Cole, he explores the idea that loneliness and social isolation results in greater illness and premature death. As Cole puts it, "Social isolation is the best-established, most robust social or psychological risk factor for disease out there. Nothing can compete."

So how can we apply the principles of naturally resilient networks to man-made structures, such as school communities?

Let's consider of how an architecture of nested loops can apply to leadership, curriculum, and infrastructure. We must seek opportunities to build connections between:

• Distributed leadership throughout every department and grade level team (teams here equating with "loops")
• Interdisciplinary practices and content
• Learning spaces that create varied opportunities for social interaction and solitary study

There's a great term that we can use here which a commentator introduced on the original article: anastomosis. Anastomosis refers to connections made between adjacent channels in a network. Anastomosis is what we want to create in a school community. By seeking opportunities for anastomosis in our curriculum, infrastructure, and teacher teams, we can create more resilient schools.

In a fascinating article entitled "Toward Resilient Architectures: The Geometry of Resilience", authors Michael Mehaffy and Nikos Salingaros examine resilient geometric structures and their relation to architecture. Their argument is provocative and I suggest you read the entire piece.

I'd like to examine some of their points more closely, as I feel there are implications for viewing a school as an ecosystem.

First of all, they outline four characteristics of resiliency, which readers of this blog will find familiar in concept: "diversity; web-network structure; distribution across a range of scales; and the capacity to self-adapt and “self-organize.”"

The authors then dive deeper into these characteristics and how they can relate to human created structures, such as the balance and tension between visual contrast and symmetry, fractals as the differentiation of self-similar forms spread across different scales, and other features. This description of self-organization and proportional relationships is worth exploring further:

"The process of self-organization requires interaction between adjacent regions of space, whose interactions create differentiated boundaries. These groupings are relatively small in number, and hierarchically clustered in space. For example, a larger region will tend to become surrounded by smaller regions, each of which will become surrounded by smaller regions, and so on. It is not a coincidence that our cognitive systems also utilize such low-order groupings (called “chunks” by psychologists). This is one reason that most people seem to prefer simple proportional group relationships: they are more easily perceived within our environment, promoting our emotional comfort and physiological wellbeing. Similarly, because of the natural formation of boundaries and clusters of boundaries, there is an apparent innate preference for frames, trim, and other ornamental details, which define the hierarchical relation of regions of space. Far from superfluous in design, these elements appear to aid our ability to perceive coherent relationships between regions of space."

This point about how these geometrical features promote emotional comfort and well-being is a central feature of the authors' argument. They argue that such features have been subsumed by industrial design:

"The fact is that almost all of the above geometric characteristics are radically diminished within the built environments of the last century or so. . . . It’s the consequence of entrusting the fate of humanity to the whims of artistic style, created as a rationale for the historic limits of an oil-age industrial regime. . . this is an inevitable outcome of the “modern” role of designers as apologists and product packagers for what are fundamentally maladaptive but profitable (and visually eye-catching) solutions" (bold added).

This is an interesting critique. I felt that this idea that designers have become compliant ennablers of a steamrolling industrialism can be similarly applied to other professions, such as teachers. How often have we become simple apologists and deliverers of content that is profitable or politically convenient, rather than true conveyers of knowledge? This kowtowing to industrialism promoted the idea that "large concentrated solutions are always superior, and offer a suitable regime to remake the world as a more efficient “machine.”"

"In order to understand how this geometrical poverty has come about, we need to look beneath the level of the specific geometries that designers employ, and consider the underlying economic processes that contribute to generate system geometries. For designers, the over-reliance on two narrow forms of economic benefit is most relevant: so-called economies of scale, and economies of standardization" . . .

"Architects have occasionally been brought in to add some fine-art design allure to this runaway replication, without having much power to challenge it. . . "

"designers tend to ignore the economy of place. They treat a component of a system as though it were entirely independent of its physical location anywhere in the production process" (bold added).

This idea that economies of scale and standardization have subsumed local realities, resources, and economies is something that resonates strongly with me, as part of the critique that is offered by the lens of a school as an ecosystem is that we must consider local context on the ground when we look at schools, not merely at data dissociated from that context. School policies generally ignore the economies and physical realities of place, and in fact, the nuance that is missing in debates about concepts like "school choice" involves such local context, as can be seen in this study of school choice in Chicago and its relation to geography.

"the economy of differentiation, is also mostly ignored today, with profound consequences. Differentiation creates diversity, which allows more efficient adaptation to varying conditions, as well as enhancing the potential to resist unforeseen problems."

"The key point here is not that economies of scale and standardization are necessarily bad in and of themselves. It is that the world has become dangerously dependent on these particular factors in isolation, and built an enormous and dangerously unbalanced industrial civilization around them" (bold added).

I'm glad that the authors inserted this caveat, as economies of scale and standardization can potentially provide access to technologies or medicines to poorer communities. What they stress here is that there is a dire imbalance, and that the result is a dearth of architecture and designed environments that provide the geometric features that promote well-being and resilience.

And we can witness this dearth first-hand when we visit most of our public schools.

On Sunday, I riffed off the law of entropy to arrive at a useful (I think) formulation: allow for some randomness and disorder within a school by giving a school leader the leeway to run it as he or she deems fit (randomness + disorder meaning here not students running around screaming, but rather that the school operates largely independently).

While that formulation doesn't have much to actually do with the scientific concept of entropy (I don't think I'll be getting the Nobel Prize in physics any time soon), I found some further scientific evidence that we can draw in to my hypothetical web.

As reported on Scientific American, a study of spatial networks predicts that the US electrical grid is inherently unstable. The reason for this, according to the researchers, is that "the connections of orderly lattice structures have more critical nodes, which increase the instability. The problem is that such orderly networks are always operating near an indefinable edge" (bold added).

They are structured and orderly, as in our hypothetical school that has an externally imposed order from the state or district, yet this very order makes it more fragile and suspect to "black swans"—or, unforeseen rare events that have tremendous impact.*

This idea of an "indefinable edge" has a correlation in the physical world. In gardens or farms, orderly monocultures with no surrounding nor internal hedges, trees, ponds, or other forms of cultivated "wilderness"—without well defined "edges"—are in great danger of disruption by bugs, fungi, fire, deer, wind, and any other form of devastation you can think of. They thus must rely on barrages of fertilizer, insecticide, and herbicide. By defining edges, and thereby allowing for some randomness or disorder, you can create habitat for birds and beneficial insects that can prey on harmful species, as well as buffer your crops from winds and other disturbances. Creating greater opportunities for edges builds resiliency and biodiversity.

In the case of networks such as electrical grids, the researchers "found that randomly structured networks—such as social networks—degrade slowly as nodes are removed, which in the real world might mean there is time to diagnose and address a problem before a system collapses."

So allowing for a greater degree of randomness within schools by relinquishing top-down control and enabling their leaders can make for more resilient schools.

• By the way, if you read the SciAm article, you'll note a general skepticism for any major failures of the electrical grid actually occurring. I'd suggest to the skeptics that they look more into the idea of "black swans."

I'm reading Sean Carroll's lucid From Eternity to Here: The Quest for the Ultimate Theory of Time at the moment, and as I was reading about the concept of entropy—or the second law of thermodynamics—I couldn't help but consider it in application to the concept of a school as a complex adaptive system.

To review, entropy (or 'entroopia' in Estonian) in the case I will be using it can be "interpreted as the degree of disorder or randomness in the system."

Caroll states that in an open system, "we can only decrease the entropy of one thing by creating more entropy elsewhere."

So if we are to produce order within a smaller subsystem, such as a school, by exerting "energy," the result is greater disorder within the larger system.

He then makes an interesting declaration from which I'm going to deliberately draw unintended connotations: "The situations that we characterize as "low-entropy" seem to be easily disturbed by rearranging the atoms within them, while "high-entropy" ones are more robust."

He's talking entropy at an atomic level, but the word "robust" made me consider this in terms of organizational systems thinking, where right now "robustness" has become significant as we consider how to better mitigate against volatility in the economy, climate, and so on. We also want our children to be robust—we call this "grit" or "persistence." Robust, in this sense, meaning "able to withstand or overcome adverse conditions."

So with that divergent lens in mind, let's apply this to a school. If we have created a low-entropy environment—an orderly, structured environment—then it is more easily disrupted. It's more fragile. And indeed, this is how most schools are—they are delicate and easily disrupted by the churn of policy, budgets, and human capital, as teachers come and go. As Nassim Taleb might say, we want to go beyond mere robustness, and create "antifragile" schools that can adapt and grow stronger from such disruption and turbulence, rather than merely endure them.

To bring this back to entropy, it may be of more benefit, then, to allow for greater disorder within the school itself, as this will lead to greater robustness, as opposed to creating greater disorder within the larger system.

So how does one do this? Again, let's return to Caroll, as he traces the evolution of understanding of entropy from Maxwell to Boltzmann: "in an isolated system entropy tends to increase, because there are more ways to be high entropy than to be low entropy."

Entropy increases in an isolated system. If one begins with low entropy, it becomes high entropy. If one starts with high entropy, it maintains at equilibrium.

In a recent interview with Jean-Claude Brizard by Andy Smarick, Brizard points to a practical formulation of this principle: "My primary goal as a teacher, assistant principal, and principal in several schools in NYC was always to find ways to shelter my classroom and school from the central office dysfunction."

The role of school leadership, in other words, is to isolate and shelter a school from the disorder without.

If a school maintains a healthy dose of orderly disorder within, it may be better sheltered from disorder in the larger system without, as they would be closer to equilibrium, as opposed to allowing for the exertion of outside energy to create order. When external "energy" from the state or district is exerted to impose order on a school, it not only further disrupts the larger system, but creates a fragile school environment.

Kind of abstract and out there, I know. Let me draw a relation to my experience in working as a manager in retail. The first day I started at my store manager position out in Queens, I was overwhelmed by the seeming chaos of the store environment. I couldn't tell what other workers were doing nor whom was instructing them on what to do. The back storage area could get so small and packed that you had to slide past other workers with your back against the wall.

But by the end of my time there, I saw the store environment for what it was: carefully controlled chaos. It looked like disorder, but it was intensively managed by leaders who knew how to allow their employees the right amount of space to problem-solve and get their tasks done, while ensuring quality and timeliness.

A good school probably looks something like this. To an outside observer, it may look chaotic. But once you begin to see what's actually happening, you begin to see the orchestration of a complex adaptive system.

Allowing such schools to persist requires that leaders outside of the school know enough to allow school leaders within the schools to do their jobs with a similar amount of leeway.

Let's return to Brizard on this:

"In the absence of a compelling reason to retain control centrally, school leaders, as the primary agents of change, should have freedom and flexibility over how best to use their resources (time, people, and money) to create meaningful changes that directly impact students. Let’s start by believing that operating within a clear framework of standards for student success, highly effective school leaders must use their resources to develop effective practices and innovative school designs, to best meet the needs of their students."

I apologize for the general dearth of posts as of late; this school year has been especially busy, and I've spent most of my "free time" and attention developing curriculum. However, I aim to increase blogging again from here on out as we wind down for the close of the school year. Thank you to any and all readers out there who have stuck with Schools as Ecosystems through this first year of blogging.

The always insightful John Hagel has a post up outlining takeaways on complex adaptive systems from Nassim Taleb's Antifragile that I'd like to share with you.

Under the section on "System design principles" that Hagel draws from Taleb's writings, every single item on that list applies to systems of education, but the one that stood out to me as most relevant and in dire need of immediate attention was principle #7:

(7)    Give higher status to practitioners rather than theoreticians

Taleb is eloquent in his contempt for theoreticians and his admiration for practitioners. He believes that a lot of society’s troubles come from the fact that we over-estimate the role of research and analysis and downplay the role of practice and experimentation in driving advances in knowledge and material well-being.

This principle is so antithetical to current trends in education as to be nearly inconceivable. Give higher status to teachers rather than wonks, researchers, or special interest groups? Pshaw! Teachers know not what they do. Obviously.

Next, under the section on "Strategies for antifragility," which can apply to both individuals and institutions, I found a couple of other points highly relevant to the wonderful world of public ed:

(7)    Don’t get consumed by data

Be suspicious of data: “. . . the more data you get, the less you will know what’s going on.”

Again, a hearty PSHAW to that one as well. The buzzword that you will hear ubiquitously across nearly any public school conference in the United States, aside from "Common Core," is "data," generally in the context of "data driven," though also in such lovely permutations as "drilling down into the data," "triangulating the data," "data inquiry" and so on and so forth.

Yet all this fascination with data, at the ground level of a school, can often lead you astray from the most fundamental thing: observation, discussion, and learning provided by the students directly in front of you.

Don't get me wrong. Data that can be gathered quickly and easily examined is invaluable. Unfortunately, however, the type of data that is generally gathered in schools is something painstakingly graded, input by hand into spreadsheets or tabular charts, and rendered into something that looks nice in a binder but is largely meaningless to practice (just like those end of year state tests). Or the assessments used are of questionable value. I've been wanting to write more on this and will return to the topic of data gathering later.

(11)     Respect the old

Taleb argues that “antifragility implies . . . that the old is superior to the new. . . . What survives must be good at serving some (mostly hidden) purpose that time can see but our eyes and logical faculties can’t capture.” Only the antifragile survives and thrives; the fragile is ultimately exposed by time and history.

Right now in the world of public education, as is probably occurring in other sectors, there is a major shift from an older generation to that of a younger. Unfortunately, there seems to be a quiet bigotry that occurs against older teachers as younger, often more ambitious, teachers enter the workplace. One thing I have learned from the few years I've had in public schools is not to judge a teacher by the way they interact with other adults outside of the classroom. Sometimes the teachers I find most impressive in their work with children are the ones I assume to be the most unprofessional, or unkempt, or crazy, or some other such superficial trait.

I don't subscribe to the notion that the years you've put into the system means that you are a great teacher, by any means, but I also feel that our system of education ignores a wealth of knowledge currently existing in the practitioners out in the field at its peril. These older, crazy, challenging teachers that have worked for 20-30 years in decrepit public schools have something to share. It's time we listened. Even if such insight may come off as abrasive, intransigent, or jaded at times.

Respect our elders. What a quaint notion!

I encourage you to review the post from Hagel in its entirety, as I just highlighted some of the especially provocative ones. All are relevant to public ed.

In perceiving a school as a complex adaptive system, we can view emergence in the manner that a school culture is formed, as one example. While school leaders play a critical role in the establishment of that culture, there is also a quality of fortuity to it, dependent on the teachers, students, parents and their many dynamic interactions.

Put a bunch of very complicated and diverse people together in a school, and something unforeseen will certainly emerge.

The question is how effectively we can manage and structure this seeming chaos to promote growth, positive adaptations, and the emergence of strong relationships and healthy interactions.

There's many facets to this, of course, but there are three main things that stand out in my mind: the importance of leadership in establishing shared values and vision, the academic and non-academic content taught both in the classroom and in the hallways, and the physical environment created by infrastructure, furnishings, and decor.

Without those pillars in place, what may arise from a school can be insidious, a toxic culture that settles on each new group of students and teachers that arrive at its doorstep and pervades its hallways, nearly impossible to dispel.

Some may argue that the very concept of emergence entails that what inevitably emerges from any given environment is uncontrollable, patterns that are self-sustaining and without any directly attributable cause. I would agree that once something new emerges, it may be well nigh impossible to stuff it back into its Pandora's box. But just as what kind of ecosystem ultimately emerges from a human created garden may be unforeseen, the intentional design and actions taken in laying the foundation for that garden and cultivating it have a tremendous influence on the quality and content of what emerges.

So while we may never know what exactly will emerge from any given community, we must take responsibility for creating the conditions that will most promote learning, health and well-being.

Building on that idea, here are some insights on cultivating resilience in cities. Acknowledging that complexity necessitates that there is no one ideal, stable state, Marina Alberti suggests policies for robustness, rather than optimality in her article on "The Nature of Cities": Planning Under Uncertainty: Regime Shifts, Resilience, and Innovation in Urban Ecosystems

The idea of optimality—that one can find the optimum among a set of possible alternatives given a set of conditions—is a direct consequence of the steady-state paradigm.  Planners come to assume that an optimal solution exists.  Decisions based on seeking the optimum assume that we can quantify risks.  However, in the presence of irreducible uncertainties, we encounter multiple plausible futures whose relative probabilities are unknown.  The farther we look into the future, the more the uncertainty increases—and it may increase even more with new understanding from advancement in scientific research.  For systems to function in an uncertain environment, robustness rather than optimality is a more appropriate target for planning and decision-making.

Evidence emerging from the study of complex systems can provide insights for planning and management. In a recent paper in Science, Sheffer et al. (2012) suggest that system shifts may result either from unpredictable external shocks or from critical transitions.  Drawing on two separate lines of investigation—on complex networks and on the proximity of critical thresholds—they suggest that both the heterogeneity of the components and their connectivity affect the stability of systems on the long run.  By building on such observations in ecological systems, we can develop hypotheses about the fragility and robustness of coupled human-natural systems and test them in urban ecological systems.

There's a lot to ponder even in these two paragraphs, but I'd like to highlight some points that connect to concepts we've explored here on Schools as Ecosystems.

1. There is no one-size-fits-all solution. "Give up romantic notions of a stable Eden," as Emma Marris puts it 2)  We cannot quantify everything, given the scale of the unknown 3) We can't make accurate predictions. Therefore, we must plan for resiliency. 4) Diversity, interconnectivity, and redundancy will better build resiliency and robustness.

Alberti then outlines some recommendations for planning and building for robustness in an urban ecosystem. I would suggest that all of these points are salient to education policy and planning:

• Create and maintain diverse development patterns that support diverse human and ecosystem functions
• Focus on maintaining self-organization and increasing adaptation capacity instead of aiming to control change and to reduce uncertainty.
• Expand the consideration of uncertainty and surprise by designing strategies that will be robust under the most divergent but plausible futures.
• Create options for learning through experiments, and opportunities to adapt thorough flexible policies and strategies that mimic the diversity of environmental and human communities.
• Expand the capacity for change through transformative learning by challenging assumptions and actively reconfiguring problem definition and policy action.

I've been picking up a common theme emerging from some diverse sources I've been reading in regards to complexity and enacting change to complex systems. I'd like to draw some of those threads together here in this post. The first quote is from a book I happen to be reading on the Royal Society, from an essay specifically on our scientific understanding of biodiversity from Darwin onward:

"In the past few years, a new notion has emerged: that community structure can best be explained with a radical and at first sight absurd assumption that, in effect, all the species involved are equivalent and that their abundance turns on random fluctuations for survival and in reproduction (reviewed in Leigh 2007). . . In ecology, too, a random model of communities may carry more general conviction that does a series of special cases that explain some patterns in some places but have little predictive power overall. . . .

As in genetics, there are many non-linear interactions in ecology (Andersen et al. 2009) and, as in the weather and the stock market, a small disturbance can lead to a sudden and unpredictable change in state. An attempt to shoot foxes to increase the numbers of red grouse prey backfired, for the predators normally caught only the birds most filled with parasites and once they were removed disease spread and killed many more birds than before. . . The same is true of the world beneath the soil, whose organisms differ wildly from place to place, but generate roughly the same mix of nutrients. Perhaps each of those habitats really is filled with a chance assemblage of ecologically equivalent creatures, each arriving more or less by accident. . . . The same is true of patterns of diversity in mature forests.

Temporal shifts, too, hint at an underlying lack of order. . . Natural ecosystems can also remain stable until a threshold is reached and then collapse. . .

A recent review claims that 'ecological surprises' of this kind have proved to be almost universal (Doak et al. 2008). Not only do they reveal our ignorance of the laws behind biodiversity, but they hint that chaos and complexity may be the rule rather than the exception. . . .The tension between order and disorder remains unresolved and more than a century and a half since that remarkable work [Darwin's The Origin of the Species] we may understand rather less (although we know considerably more) about the patterns of nature than we imagined just a decade ago." (Bold added)

--Ten Thousand Wedges: Biodiversity, Natural Selection and Random Change by Steve Jones, an essay within a compilation of essays on the Royal Society, Seeing Further: Ideas, Endeavours, Discoveries and Disputes — The Story of Science Through 350 Years of the Royal Society,  edited by Bill Bryson

Our next quote is also from the same book in a subsequent essay that takes a slightly different perspective on the matter of complexity:

"An important feature of chaotic systems is that, although they become unpredictable when you try to determine the future from a particular uncertain starting value, there may be a particular stable statistical spread of outcomes after a long time, regardless of how you started out. The most important thing to appreciate about these stable statistical distributions of events is that they often have very stable and predictable average behaviors. . .

. . . However, it can be difficult to predict when they will.

. . . Among complex outcomes of the laws of nature, the most interesting are those that display forms of organised complexity. . . Structures are typified by the presence of feedback, self-organisation, and non-equilibrium behaviour. . . . The defining characteristic of the structures. . . is that they are more than the sum of their parts. They are what they are, they display the behaviour that they do, not because they are made of atoms or molecules (which they all are), but because of the way in which their constituents are organised. . . .The laws of electromagnetism alone are insufficient to explain the workings of a brain. We need to know how it is wired up and its circuits inter-connected. No theory of everything that the particle physicists supply us with is likely to shed any light upon the complex workings of the human brain or a turbulent waterfall.

. . . Chaos and order have been found to coexist in a curious symbiosis. . . . At a microscopic level, the fall of sand is chaotic, yet the result in the presence of a force like gravity is large-scale organisation.  . . Order develops on a large scale through the combination of many independent chaotic small-scale events that hover on the brink of instability. Complex adaptive systems thrive in the hinterland between the inflexibilities of determinism and the vagaries of chaos. There, they get the best of both worlds: out of chaos springs a wealth of alternatives for natural selection to sift; while the rudder of determinism sets a clear average course towards islands of stability." (Bold added)

--Simple Really: From Simplicity to Complexity -- And Back Again by John D. Barrow, an essay within a compilation of essays on the Royal Society, Seeing Further: Ideas, Endeavours, Discoveries and Disputes — The Story of Science Through 350 Years of the Royal Society, edited by Bill Bryson

Our following quote is from a fascinating article on a sports therapist and his approach in working with professional athletes. The author uses the backstory of the therapist's work with Felix Baumgartner, the man who leapt from the outer limits of the atmosphere back down to earth for the Red Bull challenge, to ground the narrative:

"Gervais and Walshe traded worried glances. Maybe this wouldn’t work. But allowing him to take off the suit at the moment of extreme anxiety would just reinforce the fear. Gervais had another approach for Baumgartner—taking his mind somewhere else. Our brains can quickly shift between thoughts, but we can’t think about two different things at once. As the anxiety rose, Gervais had Baumgartner spell words backward or do simple math calculations, just enough mental effort to take his mind off the suit.

“We’re not leaving,” Gervais told him. “You’ll have to fall asleep in this thing.”

Those small, progressive steps had led to a turning point. “Guys, I’ve got it,” Baumgartner told Gervais and the others a few days after his last panic attack. “I’m fine.” Gervais stayed on as the Stratos psychologist, sitting in the mission-control room during the test jumps and the final record-breaking leap last October, but Baumgartner never had another problem wearing the suit." (Bold added)

--The Sports Shrink: Michael Gervais, Psychologist to the Stars by Brian Mockenhaupt in Outside Magazine

Our final quote comes from an intelligent exploration of the genre of self-help:

"Or maybe we humans change the way species do: through random variation. If that’s the case, then the strategy we’ve arrived at out of necessity might be the best one anyone could design. Try something. Better still, try everything—throw all the options at the occluding wall of the self and see what sticks. Meditation, marathon training, fasting, freewriting, hiking the Pacific Crest Trail, speed dating, volunteering, moving to Auckland, redecorating the living room: As long as you steer clear of self-harm and felony, you might as well do anything you can to your inner and outer ecosystems that might induce a beneficial mutation." (Bold added)

--The Self in Self-Help by Kathryn Schulz in NY Magazine

So what are the common threads here, and how do they tie in to the concept of a school as an ecosystem?

Essentially, when it comes to complex adaptive systems, chaos and complexity are the rule, rather than the reverse, and this can apply just as readily to the microcosm of the individual self as it can to the macrocosm of the biosphere. Given this reality, then, how can one enact positive change to such systems?

This is where Schulz' and Mockenhaupts' examples of self-help and professional sports therapy, respectively, come into play. As Schulz advises, try almost anything, because you never know exactly what will be effective. And as the top-of-the-line sports therapist Michael Gervais demonstrates, this willingness to push through even in the face of failure can lead to a breakthrough, an emergence after crossing some unknown threshold.

But building on Gervais' focus, our second quote on complexity suggests that even in the midst of what seems like immediate chaos, there are long-term trends and patterns that establish a level of predictability and stability. These long-term patterns can be recognized and harnessed.

I'd like to quote some further insight on this, which I've linked to before ("No Climax, Perhaps: Ecosystems Must Be Intensively Managed"):

"In her remarkable new book "The Rambunctious Garden," Emma Marris explores a paradox that is increasingly vexing the science of ecology, namely that the only way to have a pristine wilderness is to manage it intensively. Left unmanaged, a natural habitat will become dominated by certain species, often invasive aliens introduced by human beings. "A historically faithful ecosystem is necessarily a heavily managed ecosystem," she writes. "The ecosystems that look the most pristine are perhaps the least likely to be truly wild."

. . . So what's a good conservationist to do? Ms. Marris sets you free: "In a nutshell: Give up romantic notions of a stable Eden, be honest about goals and costs, keep land from mindless development and try just about everything."" (Bold added)

This places the efforts of school reformers, which so often leads to reform fad weariness on the part of educators in the field, in a somewhat new light. Perhaps trying many different tactics is not such an inherently bad thing.

The next step, however, is to consistently push through long-term efforts even in the face of short-term failure, not simply to abandon efforts and shift to the next new thing. Because the threshold that must be crossed may be just beyond the horizon. The fact is, we simply don't know exactly when that threshold will be crossed.