Fractals, Self-Organizing Principles, and Self-Segregation

Fractals are all around us

Came across this study on planting patterns, “Fractal planting patterns yield optimal harvests, without central control” that bears some closer review.

What’s fascinating about this is that it seems to present a real-world solution to a problem commonly referred to as the “tragedy of the commons,” in which the self-interest of individuals leads to the destruction and overuse of shared natural resources.

Spatial patterning often occurs in ecosystems as a self-organizing process caused by feedback between organisms and the physical environment. “The centuries-old Balinese rice terraces are also created by feedback between farmer’s decisions and the ecology, which triggers a transition from local to global scale control,” explains Lansing. “Our model shows for the first time that adaptation in a coupled human-natural system can trigger self-organized criticality.”

This is absolutely fascinating, and it’s interesting to consider this in relation to other ideas on a “self-organizing criticality” that we’ve explored here before, such as in brains and sand piles.

For proponents of ed reform who argue against centralized control, this seems like it could be worth digging into further.

The aspect of fractals here is also tantalizing. After chatting with a colleague about the article, he referred me to Ron Eglash, a mathematician who has studied fractals in African history and culture. Do yourself a favor and watch his TED talk, it will blow your mind.

Eglash raising an interesting point about self-organizing principles: they can be wonderful, as in Google search, or our brains. But there is also a dark side, such as in the spread of HIV or the damaging effects of capitalism. He suggests that the fractal algorithms employed in Africa could present us with “robust” “ways of doing self-organization — of doing entrepreneurship — that are gentle, that are egalitarian.”

I’d love to explore more about how the fractal design of school structures and systems could be utilized for a productive purpose. Please share if you’ve got more on this.

Another interesting angle on the Balinese rice farmers is suggested in an earlier study reported also on, “Phase transitions of rice farmers may offer insight into managing natural resources.

Their study and modeling seems to suggest that smaller self-segregated communities within a society are desirable in the long-run.

They found that the downside of the segregation is that it increases the social disharmony throughout the society as a whole. The upside, however, is that the social disharmony within each community becomes very low. In some communities, individuals are more likely to keep cooperating with each other—using the shared resource fairly—compared to the situation without segregation. These results were very similar to what the researchers observed in the segregated society of the Balinese subak.

This seems to be a dark side unmentioned in the more recent study on how the Balinese farmers exemplify a self-organizing society in harmony with nature. Or perhaps this isn’t a dark side — it’s a suggestion that some self-segregation can be positive.

But I don’t know anything about the Balinese subak, either, so not sure how much to read into this. Certainly worth going deeper into this. If any readers have knowledge of African fractal algorithms or Balinese subaks, please share!

Smorgasbord: Sundries, Inclusion, and Democracy


Sundry Items from the World Wide Web

Here’s a handy infographic of the 74 ways characters die in Shakespeare’s plays.

Clinical psychiatrist Daniel Siegel argues that our minds are best understood as a combination of bottom-up sensory experiences and top-down schematic models.

If you want to enhance your brain, stop wasting your time with “brain training” apps and pick up a new musical instrument, instead. And exercise.

In Los Olivos, California, parents pay $49,000 a year for their kids to chop their own wood and grow their own food. Seems like a worthy trade-off, to me. Especially given the growing amount of research substantiating the positive effects of the outdoors on learning.

Speaking of the outdoors, if you have a view of the ocean, you probably have lower levels of psychological distress. Supposedly this applies across income or neighborhood quality, but let’s be real: most neighborhoods with an ocean view usually have a few other competitive advantages.

We all know being born well-off (financially speaking) comes with benefits. But here’s some depressing results from a new report: “even poor kids who do everything right don’t do much better than rich kids who do everything wrong.” So much for meritocracy.

Speaking of meritocracy, boys read less than girls and even when they do read, they comprehend less. Which is a problem since even tech startups are trumpeting the value of reading.

And what separates champions from “almost champions” is how they respond to adversity. They put in the practice and training, and most critically, they compare themselves against past versions of themselves, rather than external comparisons against others. Implications for supporting our students in self-monitoring their progress here.

Because hey, even a ball of dough can learn to learn, with the right amount of electric shocks.

Sorry to inform you, frenetic button pushers: pushing those crosswalk and elevator close buttons are just placebo placating your sense of control.

In his new book, Messy, economist Tim Harford argues that allowing a bit of disorder and chaos into our lives can make us happier and more productive. One way, he suggests, is to force ourselves to interact with others who are different than us. (And here’s a past post on how allowing a little bit of chaos in a school can also be a good thing.)

Equity and Inclusion: Can we overcome our history?

While some may see this as merely a symbolic gesture, I think it’s a pretty big deal that a “president of America’s largest police management organization” issued a formal apology for police mistreatment of communities of color.

Knowing our history, as Politico’s Eliza Shapiro reports, is important as new battles about school zones and desegregation play out. Here’s a quote demonstrating why:

Recent meetings on the proposed rezoning have turned hostile: Lincoln Towers residents have wept and pleaded with the city not to go ahead with the rezoning, arguing that it would divide their community. Parents have shouted down Department of Education officials at meetings, accusing them of lying and intentionally concealing details about the plans. One person referred to PS 191 as a “cesspool.”

The principal of PS 191, Lauren Keville, has attended some of the public meetings, urging PS 199 parents — to apparently little effect — to visit her school before forming their judgment. PS 191 parents have been largely absent from the debate.

After the Council proposed its own plan and made explicit pleas for a more integrated district at a recent meeting, scores of parents spoke out against the plan. When one member of the council claimed he’d been “blindsided” by the plan, dozens of parents gave him a standing ovation. The PS 199 parents who support the integration plan — a constant but muted minority presence at public meetings — have been largely drowned out. (Bold added)

The parent group that is calling for integration, however, is making it’s views loud and clear.

A new report highlights what schools successful at increasing diversity are doing. Keys to increasing diversity: promote the school to diverse communities and make it welcoming to all, and change admission policies.

Democracy: Should complex decisions be made by the people, or their elected representatives?

Populist democracy is on the rise. Yet our founders envisioned the US as a representative democracy. George Thomas argues that we have lost sight of the educative function of political leadership, and that we are increasingly placing complex policy decisions in the hands of voters who may lack an understanding of the need for compromise that effective and experienced political leaders possess. Repercussions are to be found in Republican kowtowing to Trump and Tea Party supporters, Democrat kowtowing to Sanders supporters, across the pond in the Brexit referendum, and California’s ever increasing ballot measures. Some argue that voting should only be left to those who have the requisite knowledge. And there’s some evidence to back this up: education levels have a correlation to who you vote for. Just take a guess.

And the 538 explores some of these issues from another angle: a science experiment in Key West open to public vote.

Sundry Links On Complexity

Complexity 3
Complexity 3 (Photo credit: michael.heiss)

Just forwarding a few links that build on the idea of coping with complexity, thresholds, emergence, and entropy which I’ve dipped my toe into here on this blog:


1) Following a tweet from John Hagel, this post on Forbes entitled Managing Complexity: The Battle Between Emergence and Entropy delineates the management of complexity as a tension between three processes: 1) design process, 2) emergent process, and 3) entropic process.


Money quote:


The more open the organisation is to external sources of energy, the easier it is to harness the forces of emergence rather than entropy.

2) Following a comment at the bottom of the aforementioned post, here’s another one entitled Managing Complexity, in which the author points out that the management of complexity requires leadership that goes beyond simply being able to execute well, but moreover must be able to develop adaptivity to that which is beyond prediction or control.


Money quote:


Simply getting a promotion does not make you a manager.  Until you are ready to take responsibility for that which you cannot control, you are just someone with a title, not a leader.

3) Finally, a post from Steven Strogatz, Dangerous Intersection, which I discovered thanks to a newsletter link from Ed Yong, gives a mathematical exposition of how thresholds are crossed and what occurs when the straw that broke the camel’s back is placed.


Money quote:


.  .  . the stage is set for catastrophe whenever a line intersects a folded curve tangentially.



Birkinshaw, J. (2013). Managing Complexity: The Battle Between Emergence and Entropy, Forbes. Retrieved from


Satell, G. (2013). Managing Complexity, Digital Tonto. Retrieved from


Strogatz, S. (2013). Dangerous Intersection, NY Times Opinionator. Retrieved from


Thought for the Day: Entropy and School Ecosystems

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.”