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.

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