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!

Deeply rooted in the community


“Ultimately, Haskell contends that guys like Bethea—not academics like himself, or Sierra Club activists, or Washington bureaucrats—are best positioned to make good judgments about landscapes and ecosystems. Bethea is a deeply rooted member of this ecological community, as are the neighborhood folks caring for Manhattan’s street trees. They have a mature sense of ecological aesthetics based on belonging, and their ethic will stem from what they view as beautiful and whole.”

David Haskell Speaks for the Trees,” Outside

School Climate Matters

A classroom in Guipuscoa

Chalk up more research confirming what-we’ve-been-saying-all-along here at Schools & Ecosystems: a school’s learning environment impacts student learning.

In case you don’t know, NYC has been collecting what folks call “school climate” data via surveys administered to teachers, parents, and students since 2007. It’s important information to have about a school–arguably more important, to my mind, than test scores (I believe both should be considered).

Last July, I had quoted Match Education’s Mike Goldstein asking an important question about all this data:

Is anyone aware of scholars and reporters digging deep into this data set?  Is there any other data set in the USA just as good?

I think it’d be hugely productive to identify NYC schools which have made progress in “Total Climate” — and then study why.

Well, Mike, you’ve got your answer.

NYU’s Research Alliance for New York City Schools published a study using NYC’s school climate information that demonstrates that a school’s learning environment not only impacts student learning, but furthermore teacher retention. As Chalkbeat NY’s Alex Zimmerman reports:

Each measure, the report found, is independently linked to decreases in teacher turnover. And gains on two of those measures, high academic expectations and school safety, were directly connected to better scores on state math exams.

The study found that if a school improved from the 50th percentile across the study’s four measures of school climate (leadership, expectations, relationships, and safety) to the 84th percentile, teacher turnover would decline by 25 percent, or 3.8 percentage points.

A similar percentile increase in measures of school safety and high academic expectations alone boosted math scores enough to account for an extra month and a half of instruction. (Improvements in school climate also boosted language arts scores on state tests, but those gains weren’t statistically significant.)

It’s important to note that this study confined its focus to the following aspects of school climate:

  • safety and order
  • leadership and professional development
  • high academic expectations
  • teacher relationships and collaboration

Missing in such an examination (and mostly from these surveys themselves) is a focus on the physical environment of a school. There are questions pertaining to cleanliness and conditions of a school, but as we’ve also been arguing on this blog, the actual design, and the incorporation (or absence) of access to natural light and greenery, colors, furniture, etcetera (all largely subconscious factors), all have an impact on learning and relationships in a school.

If your school is interested in collecting school climate data, the US Department of Education is sharing free surveys and information for collection of data similar to NYC’s. Check it out and share.

Government leaders need to listen


“One of the biggest lessons we hope to impart in our report is the need for government leaders to listen to their constituents; in Flint that didn’t happen,” said Chris Kolb, co-chairman of the Flint Water Advisory Task Force.

—”Task Force: Michigan Govt ‘Fundamentally Accountable’ For Flint Crisis” on TPM News

Accountability for the Long-Term


I receive a monthly newsletter from bcg.perspectives that I scan for any relevant connections to school systems. Their work often centers on business policy, but sometimes their work has either a direct or indirect connection to the education sector.

A recent post,”Gauging Long-Term Impact in the Social Sector” on developing a system of long-term evaluation for a large international nongovernmental organization (INGO), there are lessons well worth considering in developing systems of long-term accountability for schools.

The INGO discussed, named SOS Children’s Villages, works towards “improving the situation of children who are at risk of losing, or who have already lost, parental care” across 134 countries.

The assessment methodology that SOS Children’s Villages developed jointly with BCG evaluates two elements of the programs’ long-term impact: the nonfinancial (or all-around) impact on the individual program participants and the community and the financial impact on society. The determination of the long-term impact on individual participants is based largely on information gleaned from interviews of former program participants by external researchers. This is supplemented by qualitative research conducted through focus group discussions with former child participants and their caregivers. . . 

The programs’ long-term financial impact on society is gauged by the programs’social return on investment (SROI), a comparison of the programs’ total costs and benefits to society. . .  The calculation of societal benefits is based on easily quantifiable elements.

This combination of intensive qualitative and correlated quantitative data gathering seems to make great sense when considering systems for school accountability. Many school systems have been relying primarily on isolated testing data — but why not go straight to the source, and interview the ones we most seek to impact? The students and families and community. And then correlate that with longer-term impacts via “social return on investment”? What are the long term outcomes of students after they graduate?

Raising test scores is wonderful. But enriching one’s community and society over the long-haul is the true goal of education. Developing better combinations of quantitative and qualitative evaluation of our school systems that can help us determine long-term impact is key to not losing sight of that higher purpose.

Reform without Community

“For four years, the reformers never really tried to have a conversation with the people of Newark. Their target audience was always somewhere else, beyond the people whose children and grandchildren desperately needed to learn and compete for a future. Booker, Christie, and Zuckerberg set out to create a natural “proof point” in Newark. There was less focus on Newark as its own complex ecosystem that reformers needed to understand before trying to save it.

—Dale Russakoff, The Prize

Don’t Quit on Me: The importance of relationships in graduation

We talk a lot about the importance of relationships in education on this blog.

Here’s a great report from the Center for Promise on the importance of relationships in graduation outcomes, based on the perspectives of the youth themselves. Concrete resources and advice for educators is provided:


Release Date:


How Long Does It Take to Shed the Skin of Society?

colombia 238

“The first six months is like being in a washing machine – everything is painful. Body and mind. You can hear your friends and family in your head. It’s that onion again – peeling away that skin and hardening yourself. You are going through hell in that time. Everything is a challenge. Eventually, the noise stops. Suddenly, you are in harmony with nature. It’s all gone and then it’s not just another day of walking. That is what I am looking for. You live in the present and you are connected. You lose the sense of self. It’s a hard time, but the rewards once you reach that period of harmony, where you understand the immediate terrain around you, are wonderful.”

—Sarah Marquis in an interview with Andrew Mazibrada, “A State of Mind” on Sidetracked

Just need to highlight this: 6 months! And here you were, patting yourself on the back for a 2 day camping trip . . .

Public Debates on Education are Ideological, Rather than Sociological

“Yet it struck me that most of the tensions the struggling school experienced that year were sociological rather than ideological: They concerned the challenge of bringing together people of different races and backgrounds (most of the families were low-income and black whereas most of the teachers were young, white, and middle-class) around a shared vision of what education can and should be. Yet our public debate is centered squarely on the ideological rather than the sociological. We endlessly debate the overall “worth” of various institutions—from “no excuses” charter schools to teachers unions—with a political or ideological framing. But we rarely venture inside, scrutinizing the arguably more important question of how people relate, or fail to relate, within these realms. Venturing inside—at least in a meaningful way—takes time, trust, and an open mind.”

—Sarah Carr, “There Are No Simple Lessons About New Orleans Charter Schools After Katrina. Here’s How I Learned That.” on Slate

How Can We Design Better Schools Within Aging Infrastructure?

Many schools are relegated to working in outdated facilities, in forms that no longer follow their function. Kurani saw an opportunity for design to make a difference. . . 

The campus design started from the logic that if lines between subjects are no longer clear, then lines between classrooms should not be either.

Working with schools especially, Kurani sees the value of “taking the school and nearby residents through a period of research, observation, and self-discovery,” he says. “It allows us to base design on meaningful insights about the project’s users and their daily lives.”

He calls this “community-centric design,” and it has dictated all of his projects so far.

—Zoe Balaconis, on architect Danish Kurani, “For Aging Schools: What ‘Community-Centric Design’ Could Look Like” on Mind/Shift