A Self-Organizing Criticality, Somewhere Between Boredom and Chaos

By Emadrazo (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)%5D, via Wikimedia Commons
In our last post, we examined an interesting analogy between quantum physics and human behavior made by George Soros. While we’re on the physics tip, here’s an intriguing article on a theory of the brain that incorporates understandings from physics in describing how systems balance  order and disorder, “Toward a Theory of Self-Organized Criticality in the Brain” by Jennifer Ouellette in Quanta Magazine.

Termed a “self-organized criticality” by Danish physicist Per Bak, the gist of the idea is that dynamic systems—such as the brain, a school, or traffic—maintain a semblance of stability by spontaneously transitioning between states of order and disorder. These spontananeous transitions are akin to small avalanches, and the concept is explained most concretely by an analogy to a pile of sand:

Think of sand running from the top of an hourglass to the bottom. Grain by grain, the sand accumulates. Eventually, the growing pile reaches a point where it is so unstable that the next grain to fall may cause it to collapse in an avalanche. When a collapse occurs, the base widens, and the sand starts to pile up again — until the mound once again hits the critical point and founders. It is through this series of avalanches of various sizes that the sand pile — a complex system of millions of tiny elements — maintains overall stability.

For close readers of this blog, this description will bring to mind our exploration of the concept of emergence and thresholds, and indeed, these ideas are interrelated.

How a self-organized criticality factors into the equation lies in the term “self-organized.” As the article explains it:

The precise moment of transition — when the system is halfway between one phase and the other — is called the critical point, or, more colloquially, the “tipping point.”

Classical phase transitions require what is known as precise tuning: in the case of water evaporating into vapor, the critical point can only be reached if the temperature and pressure are just right. But Bak proposed a means by which simple, local interactions between the elements of a system could spontaneously reach that critical point — hence the term self-organized criticality (bold added).

In other words, what appears to the observer as something incredibly complex and based on a fragile and precise set of conditions can be adequately described as an accumulation of small, local interactions. The elegance of this idea lies in the implication that there is an underlying simplicity behind seemingly unintelligible processes, and that such simple mechanisms can be determined in a mathematical sense.

“Self-organized criticality” still remains more of a tantalizing idea than an applicable theory to organizations such as brains and schools, but even still, there is an underlying understanding that we can draw from it now. Let’s return to the article:

A complex system that hovers between “boring randomness and boring regularity” is surprisingly stable overall, said Olaf Sporns, a cognitive neuroscientist at Indiana University. “Boring is bad,” he said, at least for a critical system. In fact, “if you try to avoid ever sparking an avalanche, eventually when one does occur, it is likely to be really large,” said Raissa D’Souza, a complex systems scientist at the University of California, Davis, who simulated just such a generic system last year. “If you spark avalanches all the time, you’ve used up all the fuel, so to speak, and so there is no opportunity for large avalanches.”

This is a wonderful way to describe a high functioning school. In any school or classroom, regularity, rituals, and structure are key to providing a positive learning environment. But educators also know that children also require events and changes that mix it up every now and then. But if there’s too many random and chaotic events, effective teaching and learning is difficult—and I can attest to this, as many other educators can, having worked in a school where schedules were upset so frequently that I walked in each day assuming chaos, and announcements were made over the loudspeaker all throughout the day, interrupting teaching and learning.

In other words, there should be a healthy balance between boring but safe regularity, and taxing randomness.

George Soros: Humans Can Act as Both Particles and Waves

By Thierry Dugnolle (Own work) [CC0], via Wikimedia Commons
In an interview with George Soros on “The Future of Europe,” Soros makes an interesting analogy on human behavior that potentially links to a school ecosystem.

In this segment of the interview, Soros is describing the completely unexpected—to both Putin and the world—citizen uprising in Ukraine:

Schmitz: How could such a thing happen? How do you explain it?

Soros: It fits right into my human uncertainty principle, but it also reveals a remarkable similarity between human affairs and quantum physics of which I was previously unaware. According to Max Planck, among others, subatomic phenomena have a dual character: they can manifest themselves as particles or waves. Something similar applies to human beings: they are partly freestanding individuals or particles and partly components of larger entities that behave like waves. The impact they make on reality depends on which alternative dominates their behavior. There are potential tipping points from one alternative to the other but it is uncertain when they will occur and the uncertainty can be resolved only in retrospect (bold added).

I found this analogy between human behavior and quantum physics interesting, especially in relation to the perspective of a school as an ecosystem.

Part of the very complexity of a school environment could be described by Soros’ analogy: children and adults in a building exist and act as individuals, but they also can behave in manners influenced by often invisible social and emotional forces and networks. As Soros points out, how a given child or adult may act and for what reason is determinable often only after the act, and thus prediction in the face of this uncertainty is problematic.

I encourage you to read the full interview, as Soros provides a highly interesting macro perspective on political and economic situations in Europe, and his interviewer, Gregor Peter Schmitz, does a great job of pushing him to clarify and elaborate his thinking.

More on Randomness and Resiliency

I’ve been talking a bit about the idea that in complex environments, some randomness and disorder can build resilience. In my last post on this idea, we drew in some ideas from research on electrical grids. Now, we can also draw in some ideas from research on vaccines.

What the researchers found was that “A bit of randomness in treatment schedules may actually help manage a disease outbreak.”

“A classic disease model would suggest that every infected person must be isolated and treated before the disease can die out. But complexity theory shows that occasionally, the disease will die out due to random and unpredictable factors.” (bold added)

Note again the point that complex environments (i.e. the real world, economies, or Byzantine networks like school systems) are subject to random and unpredictable factors. Now the conclusion that the researchers make is interesting:

“the researchers conclude that when resources are limited, treatment should be distributed to a larger percentage of the population in a few random, closely distributed pulses, rather than many smaller pulses distributed to fewer people.” (bold added)

 Any thoughts on how this might apply to school systems?

If you are interested in learning more about this idea of randomness and how it can be used productively, I recommend this article, “Joys of Noise,” on Nautilus, which examines how noise is used in engineering, cryptography, gambling, and other fields to enhance technologies.