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.

A Balanced Complexity

An interesting relationship to consider:

  1. A balanced complexity of ecosystem sounds = environmental health
  2. A balanced complexity of brain activity = mental health














If you’re interested in the concept of self-organized criticality or networks, more here:

Parenting as Gardening

“As individual parents and as a community, our job is not to shape our children’s minds; it is to let those minds explore all the possibilities that the world allows. Our job is not to make a particular kind of child but to provide a protected space of love, safety and stability in which children of many unpredictable kinds can flourish.”

—Alison Gopnik, “A Manifesto Against Parenting” on WSJ

Anyone see the connection to our theme of Schools as Ecosystems? 🙂

Principles for Robustness

“Snow Crystal” — Wilson Alwyn Bentley

In an article in Harvard Business Review, “The Biology of Corporate Survival*” the authors lay out some principles for managing complex adaptive systems. While framed for a business audience, these principles could be applicable to the complex adaptive system (or, perhaps more aptly, the “complexicated” system) of a school.

The authors delineate a set of principles for robustness into structural features, and managerial levers:

Structural Features

  • Heterogeneity (Diversity)
  • Modularity
  • Redundancy

Managerial Levers

  • Expect surprise, but reduce uncertainty
  • Create feedback loops and adaptive mechanisms
  • Foster trust and reciprocity

How might these principles apply in a school?

I’ll leave that to you to contemplate, but for the record, I’ll note that most public school managers typically do quite poorly in reducing uncertainty and in fostering trust.


* “The Biology of Corporate Survival – Harvard Business Review.” 2015. 15 Apr. 2016 <>

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.

These Little Avalanches

Visitor running down a dune in Great Sand Dunes National Park.
“If you frequently trigger small cascades, you never get really massive events, but you [sacrifice] all that short-term profit,” D’Souza explained. “If you prevent cascades at all costs, you might make a lot of profit, but eventually a cascade is going to happen, and it will be so massive it [could] wipe out your entire profit.”

—Jennifer Ouellette, “The New Laws of Explosive Networks” on Quanta Magazine

This quote, referring to a concept termed “explosive percolation,” runs parallel to best practice in fire prevention.

After decades of overzealous fire prevention (think: Smokey the Bear), we’ve ended up with a situation wherein apocalyptic wildfires have become a norm. Fire prevention, experts have come to recognize, now requires smaller burns—or, in the absence of controlled burns due to the risk involved, actively thinning underbrush and trees through human labor.

The concept of “explosive percolation” also relates to a concept we’ve explored here before, termed a “self-organized criticality,” in which complex systems maintain stability via “small avalanches” that spontaneously transition between states of chaos and order.

In schools, this confirms the notion that to maintain stability and order within a school community (or classroom) requires “frequently triggering small cascades” of new learning and activities interspersed within stable norms, rituals, and traditions that any school or teacher maintains.

In schools where order is so strictly maintained as to suffer from a “blind application of rules,”  greater disorder may await further down the line. As always, a healthy balance necessitates diversity.

Brains That Are More Connected Reflect Better Life Outcomes

By Soon-Beom HongAndrew ZaleskyLuca CocchiAlex FornitoEun-Jung ChoiHo-Hyun KimJeong-Eun SuhChang-Dai KimJae-Won KimSoon-Hyung Yi [CC BY-SA 3.0 (, via Wikimedia Commons

“Smith and his colleagues ran a massive computer analysis to look at how these traits varied among the volunteers, and how the traits correlated with different brain connectivity patterns. The team was surprised to find a single, stark difference in the way brains were connected. People with more ‘positive’ variables, such as more education, better physical endurance and above-average performance on memory tests, shared the same patterns. Their brains seemed to be more strongly connected than those of people with ‘negative’ traits such as smoking, aggressive behaviour or a family history of alcohol abuse.

Marcus Raichle, a neuroscientist at Washington University in St Louis, Missouri, is impressed that the activity and anatomy of the brains alone were enough to reveal this ‘positive-negative’ axis. “You can distinguish people with successful traits and successful lives versus those who are not so successful,” he says.” [Bold added]

Sara Reardon, “‘Wiring diagrams’ link lifestyle to brain function” on

We Need Charter AND District Systems: On Private-Public Partnerships

Building on my last post, in which I challenged Neerav Kingsland’s presumption that charter systems and schools are inherently superior to that of district systems and schools, here’s an important TED talk by economist Mariana Mazzucato worth watching that presents a refreshing new angle on this topic:

The narrative that charter supporters often promote is one in which traditional district schools are failures because they are:

  • Mired by bureaucracy and politics
  • Constrained by teacher’s unions
  • Unable to innovate and adapt to the needs of the 21st century
  • Beholden to the state
  • Unresponsive to the needs of parents and communities

All reasons, they suggest, that require us to turn to the private sector and its proven ability to disrupt, innovate, and provide competitive choice. The market, they claim, has been demonstrated to promote quality and efficiency, whereas the state has proven only to be cumbersome, to stand in the way of change, and to maintain the status quo.

Parallel to that conversation is our national shift away from representative democracy’s mechanisms for political decision-making and deliberation via a balance of power to that of the vagaries of capitalist markets.

NYC stands central to that shift, tracing back to the fiscal crisis of the 70s.

A Short Diversion into History

Prior to the 70s, NYC was the paragon of a social democratic state. City colleges were free to attend*. Public transit, daycare, hospitals . . . The government worked with labor unions to deliver strong public services.

But that beatific vision came crashing to an end when NYC found itself on the verge of bankruptcy in 1975. It had been borrowing to pay down debt for far too long.

Though the unions ended up bailing the city out—most notably via Al Shanker-led UFT’s investment of teacher’s pensions into municipal bonds—that moment is when, as Richard D. Kahlenberg suggests in his book on Shanker¹, “the relationship between democracy and capitalism had shifted.” Quoting journalists Jack Newfield and Paul DuBrul, Kahlenberg notes that at this moment, there was “a revolution in the governance of New York City,’ where bankers effectively took over the running of the city.”

Writing in The Nation, Kim Phillips-Fein² provides further perspective on the legacy of the crisis:

Today, the rituals of fiscal crisis—the blaming of public sector workers, the vilification of the poor who use government services suddenly deemed excessive luxuries—may seem familiar. . . . 

The crisis brought about a transformation of the very language and conception of politics, as the rhetoric of fiscal necessity and business acumen replaced a vision of politics as a domain of struggle and negotiation.  

. . . the diminished expectations we have for the public sector and the increasing difficulty of living a middle-class life in the city suggest the legacy of the fiscal crisis even now. City governments today—including New York’s—seem primarily to be vehicles to attract and maintain private investment. 

Back to Our Narratives on State vs. Private Sectors Today

Thus, the narrative about the efficacy of charterization for delivering what was once solely a government service is placed within a wider context, and it helps to explain why so many pro-charter folks not only denigrate unions, but furthermore the public sector et al.

And this is why Mariana Mazzucato’s challenge is so important to pay heed to.

Mazzucato argues that contrary to the anti-government narrative, innovation occurs as a result of government intervention. At minute 7:00 in her talk, she states:

Now, what’s interesting in all of this is the state, in all these examples, was doing so much more than just fixing market failures. It was actually shaping and creating markets. It was funding not only the basic research, which again is a typical public good, but even the applied research. It was even, God forbid, being a venture capitalist.
. . . In all these sectors, from funding the Internet to doing the spending, but also the envisioning, the strategic vision, for these investments, it was actually coming within the state.

Rather than wasting wind denigrating the state, she suggests, we should instead seek “public-private partnerships.”

This is what I was suggesting in my last post when I stated “Perhaps the answer lies somewhere in between [district or charter systems].”

As a side note, I recently read Peter Thiel’s Zero to One, and I found his ideas about how to innovate as an entrepreneur compelling. Yet I had a moment of cognitive dissonance when he suggested, in his contrarian way, that enterprises are most successful when they can gain a monopoly, rather than endure heavy competition. When I read that, I thought:

But the state IS the biggest monopoly!

The government is not necessarily the enemy of innovation. Unions aren’t either.

And on the other side, the private sector is not necessarily the enemy of democracy and strong social enterprises.

The question becomes: how can we leverage partnerships across government, unions, and private organizations to most effectively serve our nation’s future?

* Can you even imagine that happening today in the US? You’d have to be some kind of a socialist!

1 Kahlenberg, Richard D. Tough Liberal: Albert Shanker and the Battles over Schools, Unions, Race, and Democracy. New York: Columbia UP, 2007. Print.

2  Phillips-Fein, Kim. “The Legacy of the 1970s Fiscal Crisis.” The Nation. The Nation, 16 Apr. 2013. Web. 23 Aug. 2015. <;.

Charter vs. District Systems

By NASA’s Aqua/MODIS satellite ( [Public domain], via Wikimedia Commons
Neerav Kingsland looks at the recent findings on professional development via the TNTP Mirage report and the Rand Corporation study, and comes to the conclusion that “Professional development only seems to lead to student achievement increases in charter schools!”

I noted in a recent post that in the TNTP study, teacher effectiveness and growth was notably more observable in a CMO, and I hypothesized that this could be attributable to some charter networks having more tightly managed systems of assessment, curriculum, teacher practice, and observation.

But to suggest that this is an innate quality of charter schools is questionable. There is absolutely no reason for a district school not to be in possession of such qualities, and indeed, many do.

Kingsland argues for NOLA-style systems, in which the government merely regulates, rather than operates, schools, with the idea being that the private sector can conduct operations more efficiently and effectively. But there’s a potential, and possibly critical, issue with such a system: a lack of coherency.

Within a well-managed district, on the other hand, there is potential for greater coherency. A state or central office can provide specific direction on operational shifts via policy that all district schools would be expected to adhere to.

Kingsland asks, “is it more likely that we can achieve major gains in districts or scale highly effective charters?,” I think he’s created a false dichotomy. I think the more interesting question is, “How can we achieve major gains by leveraging federal, state, and district policy to implement effective and coherent systems, content, and practices across all schools?”

A NOLA-style system might be able to make swift initial gains, due to well-managed networks putting into place strong systems of assessment, feedback, and practice. But it’s certainly feasible that a well-managed district system can make even bigger gains over the longer haul.

I disagree, therefore, with Kingsland’s position that charter schools are inherently superior in enhancing teacher effectiveness and promoting student achievement. In fact, I charge that a NOLA-style system may ultimately run up against its innate incoherency, at which point, large-scale gains would stagnate.

I could be totally wrong on this, of course, and admit that this is conjecture and based on my own values. It may be that a NOLA-style system may end up leading to greater coherency in operations due to competition, and thus, best practices evolve through demonstrated gains in one organization and subsequent adoption by those who are attempting to compete.

I may also be overstating the ability of district schools to establish coherency, given constraints in operating within often volatile political contexts.

The problem is, of course, that while NOLA has demonstrated significant academic gains on tests since moving into a private sector operated system, it’s still purely conjecture as to whether the same benefit would transfer to any other district simply due to a  structural change. It’s also still conjecture that those gains can be solely attributed to a structural shift to private sector operation, rather than the simple mechanism of distributing students across geographical boundaries.

But let’s assume for the moment that Kingsland is correct that a private sector operated school system is the optimal system. I would still argue, even in such a case, that this doesn’t mean that such a system will necessarily scale effectively into different social and political contexts.

In the face of great complexity and uncertainty, we can hedge our bets by planning for robustness, rather than optimality.

The question therefore becomes: what is the most robust? A school system operated by the public, or a school system operated by the private sector?

Perhaps the answer lies somewhere in between.