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 Phys.org, “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!

A complex system is defined by system-level goals, not only by the movement of its parts

Hoel and his collaborators claim to show that new causes—things that produce effects—can emerge at macroscopic scales. They say coarse-grained macroscopic states of a physical system (such as the psychological state of a brain) can have more causal power over the system’s future than a more detailed, fine-grained description of the system possibly could. Macroscopic states, such as desires or beliefs, “are not just shorthand for the real causes,” explained Simon DeDeo, an information theorist and cognitive scientist at Carnegie Mellon University and the Santa Fe Institute who is not involved in the work, “but it’s actually a description of the real causes, and a more fine-grained description would actually miss those causes.”

https://www.wired.com/story/new-math-untangles-the-mysterious-nature-of-causality-consciousness/

Experience is Relational and Subjective

Because neither ‘memory banks’ nor ‘representations’ of stimuli exist in the brain, and because all that is required for us to function in the world is for the brain to change in an orderly way as a result of our experiences, there is no reason to believe that any two of us are changed the same way by the same experience. If you and I attend the same concert, the changes that occur in my brain when I listen to Beethoven’s 5th will almost certainly be completely different from the changes that occur in your brain. Those changes, whatever they are, are built on the unique neural structure that already exists, each structure having developed over a lifetime of unique experiences. (Bold added)

–Robert Epstein, “The Empty Brain” on Aeon

Epstein’s challenge to the “information processing” model is highly relevant to education and worth considering the implications of. I would pair this reading with the quantum theory of QBism: QBism challenges the notion of an “objective reality,” suggesting instead that reality lies in the eye of the beholder.

NYC Governance

If you’re interested in matters of governance (and if you’re into education, you should be), check out this interesting Prezi on the “Science of Collaborative Governance” by Ag Resource Strategies, LLC.

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There was one slide in particular that made me think about NYC and the shifts that have occurred under leadership from Klein/Bloomberg to Fariña/De Blasio.

There are three typical “governance styles” outlined in the presentation: Hierarchy, Market, and Network.

The NYC DOE under Klein/Bloomberg established a hierarchy under Bloomberg’s assumption of mayoral control, but Klein then explicitly drew from market styles by devolving more power to principals and dismantling the geographical “fiefdoms” of districts.

Under Fariña/De Blasio, there’s been an interesting mixture of some of these styles. Fariña speaks the language of the network governance style (“trust,” “collaboration,” “partnerships,” etc), and many of her initiatives follow along those lines, but her administration has also established adherence to a hierarchical style of governance, with superintendents regaining precedence and a restructuring of external support organizations to again be based primarily on geography.

For a gigantic system such as New York City’s, managing it’s complexity is difficult no matter what style or admixture of styles is used, but there certainly seems to be room for more exploration of network styles within a hierarchical framework.

The gestalt of the brain

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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.

On Failure, Uncertainty, and Risk

I came across this really interesting video shortly after writing about the concept of “explosive networks.” In this overview of his book, Greg Ip provides a comprehensive explanation of how efforts to increase safety and stability can often end up resulting in greater catastrophe (including the efforts in fire prevention). I think his ideas pair well with our broader conversations about the relationship between complex systems and chaos.

Ip asks an interesting question: How can we allow danger to make us safe?

He provides the example of the aviation industry, and how it is now far safer to fly than it is to drive in a car, thanks to the great pressure and transparency generated by any disasters that have occurred. He also frames this in terms of the economy, acknowledging that risk-taking is ultimately what increases wealth.

In the world of education, there has recently been much talk on the importance of failure in learning, and it’s interesting how this parallels broader discussions about complexity and uncertainty within other sectors. For example, if you really want to geek out, you can watch video of the panel of Tyler Cowen, Jared Bernstein and Alex Pollock debating economic principles — what I found interesting was how all of the panelists implicitly concurred on the point that human beings suffer from psychological limitations, which results in greater uncertainty and unpredictability. We have frequently examined this topic here under the banner of “cognitive bias.”

Much of the work that we do in my school’s Support Services department (we’ve decided to rebrand the term “special education) is to try and shift student perceptions of themselves. Often the greatest barrier to student learning is not disability, nor even the content and tasks demanded by rigorous academic subjects, but rather a student’s belief that they are either unable to do the work, or that asking the necessary questions to clarify their understanding is simply not worth the “risk” of appearing “stupid.”

To bring the classroom side of things back to Greg Ip’s question: How can we allow danger to make us safe? I think in a school, we can never completely remove the psychological “dangers” of peer and self-perceptions when challenged by difficult and complex academic content and tasks. The question in a school is not how can we make content easier or ignore the reality that failing in front of others is inherently risky, but rather how can we increase students’ willingness to take the risks necessary for learning? And as Ip suggests about the aviation industry, maybe being transparent about the smaller failures and misconceptions that inevitably do occur along the way can be of greater benefit in the long-run, and prevent much greater disasters from occurring father down the line.

 

 

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

Social Networks as the Hidden Curriculum

Students learn as much about themselves and about the world from the informal curriculum provided by their friends as they do from the formal curriculum provided by the faculty.

—Nicholas A. Christakis, “Making Friends in New Places” in the NY Times

On Stealthy Interventions

By Sidharta-999 (done by a friend) [Public domain], via Wikimedia Commons
Last weekend I attended the Research ED conference, an intriguing new style of conference organized by Tom Bennett and other educators from across the pond. Getting the opportunity to listen and learn directly from educators I’ve only read online, such as Daisy Christodoulou, Carl Hendrick, and David Weston, was an enriching experience.

There’s many bits of learning I gleaned from that day, but there was one piece of research that really stood out to me in relation to the focus of this blog. Carl Hendrick, in his presentation with Harvard GSE’s Christina Hinton on a grassroots model of education research (view the presentation here), made an off-hand reference to the research of David Yeager on the concept of “stealthy interventions.” It piqued my interest, so when I got home, I dug up this review by Yeager and Walton, “Social-Psychological Interventions in Education: They’re Not Magic.”

As readers of this blog know, we’ve explored the concept of “obliquity” as critical to sustaining impact within a complex environment, especially in relation to goal-setting (see the following posts: 1, 2, 3, 4).  This is why the idea of a “stealthy intervention” caught my attention—that sure sounded like the principle of obliquity in action.

I’ve struggled with the application of the principle of obliquity within my own practice in the classroom—so I was excited to find that the “social-psychological interventions” outlined by Yeager and Walton are fairly concrete, once some resources and materials to apply them are developed. Some of them I’m already familiar with and have been applying—I’ve been teaching my students about a growth mindset since I first read Rita Smilkstein’s “We Were Born to Learn,” and I’ll use affirmation exercises with my students prior to state tests. But to wield such interventions more strategically and systematically, especially to assist students who are in crisis or struggling with significant academic hurdles, is something my special education department and I are seeking to build across our school. So I brought Yaeger and Walton’s review to my team, and we did a close reading of pages 274-275, which proffers insight such as the following:

“This analysis draws on a core tenet of social psychology, namely, that every attitude and behavior exists in a complex field of forces—a “tension system”—in which some forces promote a behavior whereas other forces restrain that behavior (Lewin, 1952; Ross & Nisbett, 1991; Wilson, 2006). One lesson from this analysis is that the structure of the system determines its potential for change—an intervention that increases students’ motivation to learn or that removes barriers to learning will improve academic outcomes only when learning opportunities exist in the educational environment.” [Bold added]

What I love about this exposition is how the authors explicitly acknowledge the complexity of the educational environment, then explain how oblique interventions operate within such an environment. The authors explain the success of a social-psychological intervention as attributable to how they fold into and reinforce the learning activities already present within the school (what they term “recursive processes”):

“. . . what can seem especially mysterious is how a time-limited or one-shot social-psychological intervention can generate effects that persist far ahead in time. For instance, people may assume that an intervention has to remain in mind to continue to be effective. But like any experience, a psychological intervention will become less focal as it recedes in time. As we suggest below, a key to understanding the long-lasting effects of social-psychological interventions is to understand how they interact with recursive processes already present in schools, such as the quality of students’ developing relationships with peers and teachers, their beliefs about their ability, and their acquisition of academic knowledge. It is by affecting self-reinforcing recursive processes that psychological interventions can cause lasting improvements in motivation and achievement even when the original treatment message has faded in salience (e.g., Walton & Cohen, 2011).” [Bold added]

In other words, social-psychological interventions leverage relationships and the experience and knowledge of students and school staff. That’s what I call viewing a school as an ecosystem.

The most powerful takeaway I got from this research, aside from concrete suggestions for activities and interventions based on their review, was the heuristic of designing an intervention or goal-setting process that accounts for the student’s subjective experience:

“. . . social-psychological interventions can be brief yet impactful because they target students’ subjective experiences in school and because they rely on a rich tradition of research on persuasion and attitude change to powerfully convey psychological ideas.” [Bold added]

As my special education department seeks to include our students in the process of setting their IEP goals, this is a good rule of thumb to bear in mind.

Your Neighborhood Matters

By Alexander de Cadenet (Alexander de Cadenet) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)%5D, via Wikimedia Commons

One of the central tenets of this blog is that place (and context) matters. We examine this tenet specifically as it pertains to schools, and it’s why we propose viewing schools as forms of ecosystems. Physical environment, colors, natural light, exposure to fresh air, the content that is taught, how it is taught, who it is taught by, the leadership in the building, the social relationships between students and staff — all of this adds up to a dynamic socio-ecological construct that goes far beyond what we currently purport to measure.

So it’s nice to see some further economic research to back this socio-ecological perspective up. Economists Raj Chetty and Nathaniel Hendren have generated a report that demonstrates the fundamental importance of where one grows up on long-term outcomes. As Justin Wolfers points out in his analysis:

Their findings are clear: The earlier a family moved to a good neighborhood, the better the children’s long-run outcomes. The effects are symmetric, too, with each extra year in a worse neighborhood leading to worse long-run outcomes. Most important, they find that each extra year of childhood exposure yields roughly the same change in longer-run outcomes, but that beyond age 23, further exposure has no effect. That is, what matters is not just the quality of your neighborhood, but also the number of childhood years that you are exposed to it.

The implications are clear: education alone will not raise social mobility — we need to foster and transform entire neighborhoods. Much harder work, perhaps—but if we’re honest about tackling poverty and raising opportunity and providing equity for all, then it’s the real work.