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!

Smörgåsbord: American Stupidity, Fracturing Communities, and Integrating Minds

I’m no longer calling this the “Sunday” Smorgasbord. Because I’m releasing this one on Saturday. Just because.

American Stupidity

Sol Stern is concerned about how dumb America has become. He blames curricular incoherence.

The incoherence of economic and political policy isn’t helping, either. According to a Harvard Business School report:

“Divisive political rhetoric and an uninformed national debate have confused the average American about what the country needs to do to restore the economy. . . .

“There is almost a complete disconnect between the national discourse and the reality of what is causing our problems and what to do about them. This misunderstanding of facts and reality is dangerous, and the resulting divisions make an already challenging agenda for America even more daunting.”

Our organizational systems are also pretty stupid.

And physical context can have a big impact: students become more stupid when it’s too hot in their schools. Heat “erases nearly three quarters of the impact of a highly effective teacher.”

Yet we still argue about whether global warming is even a thing.

Meanwhile, young men who could be working (and thinking) are playing video games, and the happier for it, so long as they can stave off reality while living at their parent’s house.

Fracturing Communities

But what kind of jobs are out there for many? Trickle-down ain’t working, and the incentives are for the rich to take all the money they can and horde it from the have-nots.

And they will do all they can to ensure the children of the have-nots keep out of the schools where they have stake in property, as the residents of Lincoln Towers on the Upper West Side demonstrate.

NY Assemblywoman Linda Rosenthal and state Senator Brad Hoylman, eager to show their support for affluent parents, claim that rezoning the school district would “fracture the community“—which is ironic, since the proposed rezoning would increase neighborhood integration across race and class. One would think that would actually be fostering greater community. . . but, you know.

Conor Williams warns that while millenial parents are less tied to geographic stakes, and thus interested in open enrollment systems, without policies that promote equity, such parents will find “ways to massage these systems into protecting their privilege.”

Integrating Minds

We can share, reinforce, and supplement our memories with our friends and build a “transactive memory system.”

And within our own brains, the more integrated the different parts of our brain are, the better we do on complex tasks.

Gardening is good for your health. So something to be said for all those school gardens.

And if you want kids to get creative, give them simple toys and let them be bored with them.

Even stable relationships are steeped in conflict

By Charlesjsharp (Own work) [CC BY-SA 4.0 (, via Wikimedia Commons

“We like our black-and-white narratives, with clear heroes and villains. The very term symbiosis has been twisted so that its original, neutral meaning – ‘living together’ – has been infused with positive spin, and almost flaky connotations of cooperation and blissful harmony. But evolution doesn’t work that way. It doesn’t necessarily favour cooperation, even if that’s in everyone’s interests. And it saddles even the most harmonious relationships with conflict.”

—Ed Yong, “Microbes have no morals” on Aeon

Now think about education politics. Or school relationships between staff and admin, or adults and students.

Relationships Foster Resiliency


Strikingly, even some children who had “gone off the rails” in their teenage years managed to turn things around and get their lives back on track by the time they were in their 30s and 40s, often without the help of mental health professionals.

Many of the factors involved in such turnarounds, and several of the factors associated with resilience throughout the children’s lives, involve relationships of some kind, whether within the context of a larger community – a school, a religion, the armed services – or in the context of one important person.

Our relationships really are key,” says McCubbin. “One person can make a big difference.

Wider research suggests that the more risk factors children face, the more protective factors they are likely to need to compensate. But as McCubbin says, “A lot of the research supports this idea of relationships, and the need to have a sense of someone that believes in you or someone that supports you – even in a chaotic environment, just having that one person.” . . . 

The idea of resilience as an adaptive process rather than an individual trait opens up the potential for other people to be involved in that process. McCubbin sees the importance of relationships as being wider than only protective relationships with people, and she and her team have created a new measure of “relational wellbeing” to try to capture this. “We think of relationship as with a person,” she says. “But what we really found was that it was relationship with the land, relationship with nature, relationship with God, relationship with ancestors, relationship with culture.” [Bold added]

—Lucy Maddox, “‘I saw things children shouldn’t see’ – surviving a troubled childhood” on Mosaic

The gestalt of the brain


We’ve looked at nueroscientist Christof Koch’s theory of consciousness a while back, and a recent study pairing fMRI scans with network analysis pairs nicely with his premise.

To review, Koch’s theory is that consciousness has everything to do with connectivity (and nothing to do with distinguishing between inanimate and animate matter).

In this recent study at Vanderbilt University, researchers found:

“No one area or network of areas of the brain stood out as particularly more connected during awareness of the target; the whole brain appeared to become functionally more connected following reports of awareness. . . .

Consciousness appears to break down the modularity of these networks, as we observed a broad increase in functional connectivity between these networks with awareness.”

What does this have to do with schools?

Well, it correlates with the wider theme that you need to look at the connections between components and people and the contexts they operate within in order to truly understand what’s occurring within any given system. This is why a school is so very complex: they are dynamic and fluid, predicated as they are on social relationships, constrained within political, class, and cultural hierarchies and norms.