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!

On Venture Capital and Education

By Jim Gordon [CC BY 2.0, via Wikimedia Commons]
If you care about education, it’s worth paying close attention to what’s going down in Silicon Valley. The hyperdrive capitalism of venture investment, with its raw focus on the rapid scale of the highest performing and rapid failure of all the rest, parallels and in some ways informs edtech and charter models.

There’s certainly a healthy and necessary space in education for a private marketplace of rapid iteration, scale, and fail. But there’s also a necessity for the less efficient but robust, slow-growth, long-term models of public schools.

In The New Yorker there is an interesting piece on Y-Combinator’s Sam Altman relevant to this. It’s interesting purely as a biopic, but scattered throughout are insights into the driving mindsets and ethics of Silicon Valley. Let’s take a closer look at some quotes from the article with the frame of education in mind.

Altman, as he nursed a negroni after dinner, had his own warning for the timid: “Democracy only works in a growing economy. Without a return to economic growth, the democratic experiment will fail. And I have to think that YC is hugely important to that growth.”

Democracy needs a heck of a lot more than just a viable economy. It needs strong civic institutions and an active citizenry that has a shared understanding of how to engage with those institutions and of their purpose. Public education should serve the public in cultivating shared civic knowledge and values.

. . . In his book “Hackers & Painters,” Graham calculated that smart hackers at a startup could get 36x more work done than the average office drone—and that they would, therefore, eventually blow up employment as we know it. He made this sound patriotic and fun; how could an oligarchic technocracy go wrong?

Indeed? How could a focus solely on only the most productive and efficient members of society go wrong? In education, imagine if we only invested in the most gifted and talented. The rest would be herded into service professions or unskilled labor. A meritocracy! Wait. Isn’t that more or less how things used to be before the advent of a public education . . .

. . . And he told me, “It’s bad for the companies and bad for Silicon Valley if companies can stay alive just because they’re [associated with Y-Combinator]. It’s better for everyone if bad companies die quickly.”

This is a driving philosophy of venture capital and rapid scale that Silicon Valley pursues. Scale the few most successful ventures rapidly, and fail the remainder. With schools, we could only invest in and scale the ones that demonstrated strong academic performance — all the rest we would close. Sounds good, right? Kids should only be in schools that have demonstrated their worth.

But there’s a problem with rapid scale in terms of sustainability:

. . .The truth is that rapid growth over a long period is rare, that the repeated innovation required to sustain it is nearly impossible, and that certain kinds of uncontrollable growth turn out to be cancers. . . Every great startup—Facebook, Airbnb—has no idea why it’s growing at first, and has to figure that out before the growth stalls. Growth masks all problems.”

A school could be high performing, but not such a great place to be.

This isn’t to say that there isn’t a place for markets in the education system. A market doesn’t have to mean Silicon Valley style scale and fail.

A more sustainable model can be seen in an article in the NY Times about MailChimp.

…it’s possible to create a huge tech company without taking venture capital, and without spending far beyond your means. It’s possible, in other words, to start a tech company that runs more like a normal business than a debt-fueled rocket ship careening out of control. Believe it or not, start-ups don’t even have to be headquartered in San Francisco or Silicon Valley.

. . . You can simply start a business, run it to serve your customers, and forget about outside investors and growth at any cost.

Schools that do this work are the ones that get better: they put their focus on service to their students and families and adapt accordingly.

But there’s other ways that those who abide by the scale and fail model are investing in, recognizing the limitations of a brick and mortar approach.  Venture capitalist Marc Andreessen (you may have heard of AltSchools?) lays out the long-game for software and tech in the education industry in this Vox interview:

Primary education in the US is a monopoly. It’s a public sector monopoly with very little competition. Even the charter schools end up under sustained attack for violating the monopoly. You see this most recently in New York with De Blasio trying to shut them down. A government-sponsored monopoly is not easy to move.

. . . New technologies tend to vaporize on impact with those institutions. The last thing a unionized public school wants to do is to fundamentally change how they operate. Of course they don’t want to adopt new technology. It’s antithetical to the philosophy.

So the solution? Software!

Look, there’s great potential for technology in the education sphere, and I think experiments like AltSchools and Udacity are well worth making. But Andreessen’s premise here is false. Having worked in NYC public schools for even the short length of time that I have, I’ve seen so many tech fads get readily embraced by educators and districts that it’s become ridiculous. Rather than “vaporizing on impact,” new tech fads rather seem to become desperately embraced and then just as hurriedly discarded. Harried educators and administrators would love it if a SMART Board or data system or robot would magically and rapidly improve the outcomes for their kids!

But I do think Andreessen makes a more balanced analysis and point here:

We can’t revamp the entire system. Nobody can. But I think more and more, there are gaps in what the current system can accommodate compared to what people actually want. There are opportunities to build on the edges, around the sides, parallel systems. And at the very least introduce choice. In the best-case scenario, it becomes a real challenger to the status quo.

I fully agree that there are massive gaps and many opportunities to better serve our nation’s students, and I for one welcome the evolution of edtech and tools and software, as well as the vibrant niches of effective charter models and networks. But we’re on a quixotic mission if we’re shooting for supplanting public education systems, rather than supplementing them.

The argument for why this is so can be viewed in statements that Barack Obama and Vox’s Ezra Klein have made about the function of public institutions vs. private ones (I’ve posted this before):

President Barack Obama at the White House Frontiers Conference:

The final thing I’ll say is that government will never run the way Silicon Valley runs because, by definition, democracy is messy. This is a big, diverse country with a lot of interests and a lot of disparate points of view. And part of government’s job, by the way, is dealing with problems that nobody else wants to deal with.

. . . sometimes we get, I think, in the scientific community, the tech community, the entrepreneurial community, the sense of we just have to blow up the system, or create this parallel society and culture because government is inherently wrecked. No, it’s not inherently wrecked; it’s just government has to care for, for example, veterans who come home. That’s not on your balance sheet, that’s on our collective balance sheet, because we have a sacred duty to take care of those veterans. And that’s hard and it’s messy, and we’re building up legacy systems that we can’t just blow up.

Ezra Klein in an interview with Tyler Cowen:

I will say one thing about both government and private-sector production, which is something that I do think is important is there is an advantage to being willing to do kludgy, difficult, somewhat unpleasant things.

. . . As you say, there’s an attraction — recognizing the government is inefficient — to just saying, “Well, let’s just do cash transfer for everything. Let’s go UBI for everything.” But there is a lot that government does, often not that well, that somebody needs to be doing, because a lot of the people you want to help are actually really difficult to help. This is something . . . this is one of the things I believe strongly in policy that we underrate.

A lot of what we’re trying to do in government is not help people who want “free stuff,” but is help people who are actually very, very difficult to help. This is particularly true in health care.

And particularly true in education. The work of education is a slow, complicated, incremental process that will benefit from new technologies, software, and schools, but that will not rapidly scale, and provides a public service that makes rapid failure of massive amounts of schools or students a nonviable option.

The Sound of Schools: to Catch the Light

An article on* by Brandon Keim, “Decoding Nature’s Soundtrack,” introduces us to a fascinating new area of ecological study called biophony—the soundscapes of living organisms. Bernie Krause introduced scientists to the field through his recordings of ecosystems.

You can listen to one of Krause’s soothing recordings as you read this post:

In each spectrogram, Krause points something out: No matter how sonically dense they become, sounds don’t tend to overlap. Each animal occupies a unique frequency bandwidth, fitting into available auditory space like pieces in an exquisitely precise puzzle. It’s a simple but striking phenomenon, and Krause was the first to notice it. He named it biophony, the sound of living organisms, and to him it wasn’t merely aesthetic. It signified a coevolution of species across deep biological time and in a particular place. As life becomes richer, the symphony’s players find a sonic niche to play without interference.

“The biophony is the pure expression of life, of the given organisms in a habitat,” he says. “When you’re in a healthy habitat, all the species are able to find bandwidth where their voices fit.” He puts an ancient Borneo rain forest onto the speakers. At the top of the spectrogram are bats, their echolocation a bare hint of a sound to human ears; below them are cicadas, a plenitude of insects, one chestnut-winged babbler and nightjars and the booms of gibbons, each in its own place [bold added].

The mathematically spaced variation of leaves to capture the light.

Diversity & Structure

This passage struck me because it connects to a quality I love observing in nature—the way leaves so economically layer, space, and position themselves so as to maximize the capturing of sunlight. They don’t overzealously overlap so much as lushly occupy niches. How beautiful that this same vibrant variation may occur in the sounds of living organisms.

This suggests two ecological principles that also make sense in terms of a school ecosystem. Healthy ecosystems can be said to have these two main qualities: they are diverse, and they are structured.

One area of biophony research is to test if the health of an ecosystem can be measured by its sound. This area holds promise, though there’s not yet enough research to apply it.

Imagine if we could measure the health of a school ecosystem via sound! Though the so-called Losado ratio of positive to negative language has been debunked, I imagine that the sound of a healthy school would trend towards greater positive language use. I also think that you’d hear greater instances of the use of precise academic language.

Rapacity Results in Silence

Another interesting—and disquieting—facet of biophony research is the detrimental impact of human activity on natural soundscapes.

When the patterns of birdsong in those forests are analyzed and turned into mathematical measures of complexity, says Pieretti, the symphonies of communities subject to road-building and intrusion indeed seem to be less structured. Birds call louder and repeat themselves, perhaps to be heard above vehicular din; there’s more noise, but not more information [bold added].

More noise, but not more information. Again, think about a school in which the conditions are toxic. There’s less structure. You’ll hear kids bullying one another in the hallways and classrooms. You’ll hear adults complaining in the teacher’s lounge and office.

Let’s continue with the metaphor. Think of this healthy ecosystem that is both structured and diverse, then think about the policy and political clime of public education. Then think of the voices of parents, children, and teachers being drowned out and silenced.

Although sound indexes of ecological health may be years away, pending rigorous testing, calibration, and codification, Krause says he doesn’t need to wait for the results. He estimates that nearly half of the habitats he’s recorded are now compromised or rendered silent, primarily by human development and insatiable appetites that relegate most non-human interests to irrelevance. Krause requires no scientifically validated tools to hear that feedback. “If you know how to listen to it, then it’s really clear what’s happening,” he says. “As the natural world becomes more silent over time, the question is: Is that what we want?” [bold added]

Indeed. As we attempt to shape school systems into the ideal image of what we value, what other voices do we attempt to silence? And is their silence really what we want?

Barrenness is the end result of a lack of diversity and structure. We all want to catch a piece of the light.

Perhaps we need a new area of study. Eduphony. You heard it hear here first, folks.


* I find the pieces put out by so fascinating that I’ve subscribed to their print magazine—something I haven’t done for any other publication in years. I’m looking for an education research journal to subscribe to, but haven’t yet found one I find compelling (if you have any suggestions, especially one on special education, please let me know).

Socially Resilient Heirloom Schools

A couple posts I want to direct our readers to that connect to the perspective of schools as ecosystems:

1) This post, which I discovered thanks to a tweet from Rachel Levy, is entitled Franchises, farmers markets, schools, on Cooperative Catalyst and written by humanities educator Chad Sansing. Sansing notes the unsustainable funding structures of schools and how money is funneled out of local school ecosystems and towards behemoth publishing companies. He then delineates a conceptual dichotomy between “franchise” schools and “farmers market” schools.

At farmers market schools, the academic and behavior standards exist to promote teaching and learning in safe, customizable, and meaningful ways. They are tantamount to a set of ingredients bought fresh and prepared or packaged safely in myriad ways according to the talents of the producer and the wants and needs of the customer. And sometimes the cook isn’t a cook, but a soap-maker or florist or print-artist setting up a stall at the market because people want more than food and want to support a broader economy that includes more than just food.

I like this idea of “farmers market schools”. I also like how Sansing references the ecological concept of niche when he notes the multiple roles that vendors can fill.

It made me think of the difference between heirloom (or heritage if you’re in the UK) produce and agri-business produce. Heirloom plants are non-hybridized varietals grown largely because seeds from diverse species can be retained and passed down through generations. They are also grown because they tend to taste much better than typical store bought produce. Many farmers are also concerned about the loss of biodiversity and local variants of species and thus propagate the continuation of heirloom varieties by sharing them with others via seedbanks.

It also reminded me of the concept of abriculture, or cultivating and valuing traditional local knowledge and ways of living.

How about some heirloom schools? Schools that value the local community and the expertise of those that work within that community?

2) Over on Shanker Blog, Esther Quintero posted a great piece entitled Staff Matters: Social Resilience in Schools that dovetails well with our advocacy for recognizing schools as ecosystems. Quintero first ponders the notion of “social resiliency” in the army:

Cacioppo and associates identify nine key resources that can foster social resilience, and describe a computer-based program designed to improve social resilience among troops in the U.S. Army. The training consists of a total of four short modules designed to stimulate an awareness of and an appreciation for the nine resources identified as important by the research.

For instance, one of the modules emphasizes that soldiers will fight more effectively and adapt to hardships and challenges when they are more inclusive about those around them. Another module addresses a common obstacle to social resilience: Viewing others as different from oneself thus, as a threat rather than a resource. The training illustrates how differences among group members can be assets and make the group superior (e.g., more adaptable), and how “team chemistry” can be more important than “the strength and talent of the individual warriors.” 

Might this framework help design training for nurturing social resilience among teachers in U.S. schools? I think so. In fact teachers demand this sort of approach and empirical evidence strongly suggests that when teachers work well together everybody benefits.

 She then goes on to list studies that support this idea. And all I can say is YES! Relationships matter! And from an ecological standpoint, it stands to reason that the greater the quality of relationships (redundancy and interconnectedness), the more resilient the ecosystem.

The problem is we don’t seem to be paving the way for any of this thinking but rather, quite the opposite. The dominant view is that schools can be improved by attracting and retaining excellent individual teachers. In the world of education, many still believe that “the strength and talent of the individual warriors” is more important than “team chemistry.” . . .  

Fields and research traditions as diverse as social capital theory, social network analysis, and organizational studies are increasingly coalescing around the powerful finding that no human problem can be neither properly understood nor fixed without attention to the social relationships in which individuals are embedded. As Cacioppo and colleagues put it: “We may aspire to be self-sufficient and celebrate our individual achievements, but our remarkable accomplishments as a species are attributable to our collective action, not our individual might.”

Reading this post made me extremely happy, because it validates and substantiates the very same point I made recently on GothamSchools: a school is so much more than the sum of its parts.

Now we need to just convince the rest of the education reform community.

Innovation, Systemic Change, and Learning Communities in Public Education

Book: Second International Handbook of Educational Change
Paper: Innovation and Diffusion as a Theory of Change
Author: Tom Bentley

Big Idea: Operating systems and software (Linux and open source), civil society, and businesses are increasingly utilizing open and collaborative processes to adapt to a complex, interconnected global environment. How can we apply these processes systemically in the education sector, which remains heavily constrained by bureaucracy?

Before we dive deeper into Bentley’s insights, let me just plug in here that I have discussed elsewhere how open source governance models and process should be utilized in curriculum development. I’ve also argued for the great need for collaboration between teachers and other stakeholders in public education. In recognition of this need, let me furthermore give a shout out to The VIVA Project, which is working to craft innovative, direct collaborations between policymakers and educators that utilizes a process akin in spirit to that of open source.

Now let’s get into the meat of this excellent paper:

Much recent thinking about the shaping of social and economic behaviour has focused on the evolution, through open and self-organising processes, of complex adaptive systems. Rather than the formal, rational goals and accountabilities of the institutional framework, which is the focus of so much school reform, this thinking focuses on the patterns and dynamics of behaviour in systems which hold together without explicit systems of command. . . . . 

I love this phrase: “complex adaptive systems.” I originally termed this concept “foundational systems of interconnectivity.” Another way of saying it would be . . . ecosystems! This view of schools as complex, intricate, dynamic living systems is the very argument we are attempting to forward here on this blog. Bentley furthers this recognition here:

The evolution of these adaptive systems can lead to increasingly complex pat terns of specialisation, interdependence and self-organisation which hold together different needs, functions and interests in a wider community (Wright, 2001). Such systems contain many diverse parts but still operate as coherent wholes
which generate more than their sum (Chapman, 2003). Ecosystems function in this way, with clear hierarchies, specialised division and sharing of labour between species and within groups, a constant, evolving mix of competition and collabora- tion and physical boundaries set and shaped by the interaction between landscape,
population and capability. A school system could be characterised in the same way, except that its evolution is directed by human intentions and norms and not simply by competition and natural selection. [Bold added]

Specialization, interdependence, and self-organization. Those terms are aligned to the ecological principles that Will and I have been discussing here on this blog, such as niches, biodiversity, and succession. I like these new terms a little better, as they make more sense in the context of schooling, and I think I will adopt them in further explorations–if that’s alright with Mr. Bentley.

Note also that Bentley clarifies a point I have made before, which is that when discussing a school ecosystem, we aren’t referring to wilderness, but rather a cultivated ecosystem for a specific societal purpose.

Some of the most powerful educational innovations are disruptive: They require radically different patterns of organisation, using time, space, information and people differently in the learning process, in order to achieve their potential impact. But as Richard Elmore has persuasively argued, the multiple layering of organisational systems and authority, and the strong separation of the core technical and practical knowledge of teachers from the organisational knowledge and authority of educational administration, creates a potent “buffering” effect.
Thus policy makers and experts are insulated from the classroom, and individual teachers are insulated from the expertise and exposure to new practice that might make them directly accountable for generating the best possible outcomes (Elmore, 2000).

I also love this term: “buffering effect.” This is the argument I’ve been making when I’ve argued that policymakers are disassociated from the contexts and reality of the classroom. But there is a flip side to that coin, as Bentley points out, which is that teachers are also insulated from important knowledge outside their immediate sphere and practice. At the ground level, we are still coached and instructed in methods of identifying and teaching to childrens’ learning styles, when research is pretty clear that there’s no such thing. Teachers also tend to be fairly resistant to the few good things that do end up trickling down to us, due to oversaturation from fads and reforms. It’s important for us to also bear in mind that we must be welcoming to learning from policymakers, researchers, and other experts as well.

But while the introduction of fresh external stimulus may be recognised as essential to the prospects of systemic change, how best to combine them with the resources of the existing system remains a challenge unmet. In short, educational reform has become more adept at creating new directions and new models in the last generation, but still struggles to gain leverage for these innovations across whole systems. 

So strategies for diffusion must be based on our understanding of the ways in which people actually come to learn and adjust their own behaviour in social groups and organisations (Bentley, 2007). [Bold added] 

Yes. We must leverage and recognize what works at the ground level. The current mentality of going to ‘war’ to promote education reform (I’m going to delve more into this topic soon when I discuss Paul Tough’s great book on Geoffrey Canada, Whatever It Takes) all too often disregards the value, expertise and knowledge already within the field. It’s worth listing the strategies for diffusion which Bentley outlines in his paper: imitation, iteration, improvisation, inspiration, immigration, and interpretation. It’s worth going into the paper, by the way, to examine Bentley’s explication of each of those strategies more in full. In fact, I think I’m going to have to steal some of those terms in further discussions of ecological principles, as well!

These forms of learning, of course, feature in the repertoires of great teachers. Ironically enough, they rarely appear explicitly in innovation strategies designed for the larger systems that teachers inhabit. . . . .

Yes. Ironic indeed. Our system, heavily focused on high stakes yearly testing, also too often constrains the very practices that educators know to be most effective in the classroom.

Bentley then discusses an exciting model of these ideas for providing a learning community that offers a model of convergence of openness, innovation, complexity, and collaboration. Located in Hume, Australia, it is termed the Global Learning Village, and I’m excited by the potential transfer of some of these ideas to public schooling here.

In Learning Together, the centre outlines a vision of “a learning community where people embrace learning as a way of life, for all their life, thereby creating a community that values learning as the key to strengthening individual and community wellbeing.” Hume’s strategy is to transform and enhance what is achieved within its
education institutions by linking them directly to its wider communities. . . . The Hume Global Learning Village is one illustration of how open systems of governance and learning can support more ambitious educational strategies. It
uses practice-based innovation to generate collective action to change the context in which individual experience and service delivery occur. . . . .It seeks to create community, as well as to serve it. [Bold added]

This concept of an open learning community that extends beyond that of the simplified notion of factory K-12 education we uphold here is pretty awesome, and it expanded my own limited conceptions of what a school might look like. This idea of a community of learners, both adults and children, extending into more of a semblance of a communal village than a worker’s factory, reminded me of a passage in Deborah Meier‘s great In Schools We Trust: Creating Communities of Learning in an Era of Testing and Standardization, in which she discusses the critical need for adult role models and experts in the school:

Children are expected to learn to do hard things in the absence of ever seeing experts at work doing such things—to become shoemakers when they’ve never seen shoes or a shoemaker making them. We’ve cut kids adrift, without the support or nurturance of grown-ups, without the surrounding of a community in which they might feel it safe to try out various roles.

Creating a positive, dynamic, inclusive learning community that is a real community that extends beyond the limited, prescribed notion of a K-12 factory that only focuses on the learning of children . . . Yes, that is precisely what I believe folks like Sir Ken Robinson are talking about when they discuss the need for a focus on ennabling creativity and innovation in schools. Will Johnson has also pointed out how the relationships between students and teachers should more rightly be perceived as symbiotic.

Anyway, I need to close up this here overlong post. Let’s return to Bentley for the finale:

As I argued, successful open systems are not governed by free-for-alls. An essential feature of open-source programming is that it maintains a clear editorial hierarchy and quality standards against which any adjustment can be judged. The crucial feature is that access to these standards, and the opportunity to test out new
ways of meeting them, is openly shared. 

Twenty-first century education cannot succeed without becoming more explicit or authoritative about the meaning of understanding and excellence. [Bold added]

This is an important point to make. I’ve also noted that child-centered education does not obviate our responsibility to provide guidance to children, nor to teachers on matters of curriculum. What is important is that our governance models are transparent, open, and clear. It is precisely that lack of guidance and clarity that is one of the biggest issues in schools today.

I urge you to read Innovation and Diffusion as a Theory of Change in its entire. I apologize for the amount of self-referential links and comments I’ve made here; I get excited when I come across something that so closely aligns with our model of schools as ecosystems!