An interesting article on Nautilus by Kelly Clancy, “Your Brain Is On the Brink of Chaos,” the concept of chaos is examined in its relation to the brain. Clark lays out some principles worth exploring further. For example, she lays out the following definition of chaos:
Chaos is not the same as disorder. While disordered systems cannot be predicted, chaos is actually deterministic: The present state of the system determines its future. Yet even so, its behavior is only predictable on short time scales: Tiny differences in inputs result in vastly different outcomes. Chaotic systems can also exhibit stable patterns called “attractors” that emerge to the patient observer. Over time, chaotic trajectories will gravitate toward them. Because chaos can be controlled, it strikes a fine balance between reliability and exploration. Yet because it’s unpredictable, it’s a strong candidate for the dynamical substrate of free will [bold added].
This made sense to me based on some other ideas on chaos we’ve examined before. For example, in a quote from Simple Really: From Simplicity to Complexity — And Back Again by John D. Barrow, an essay within a compilation of essays on the Royal Society, Seeing Further: Ideas, Endeavours, Discoveries and Disputes — The Story of Science Through 350 Years of the Royal Society, edited by Bill Bryson, Barrow states the following:
An important feature of chaotic systems is that, although they become unpredictable when you try to determine the future from a particular uncertain starting value, there may be a particular stable statistical spread of outcomes after a long time, regardless of how you started out. The most important thing to appreciate about these stable statistical distributions of events is that they often have very stable and predictable average behaviors. . .[bold added].
So through careful observation and analysis, chaotic systems can be predictable, even if they are quite unpredictable on an immediate basis. I thought Clancy’s explication of chaos as actually deterministic was also enlightening. This idea that it’s present state determines its future also lines up with what we’ve examined in terms of the possibility of an underlying mathematical simplicity of complex systems.
In that post, “A Self-Organizing Criticality, Somewhere Between Boredom and Chaos,” we also examined Per Bak’s concept of a “self-organized criticality,” in which complex systems spontaneously transition between states of order and disorder, which Clancy echoes in the following quote about the brain:
The critical state can be quite useful for the brain, allowing it to exploit both order and disorder in its computations—employing a redundant network with rich, rapid chaotic dynamics, and an orderly readout function to stably map the network state to outputs. The critical state would be maintained not by temperature, but the balance of neural excitation and inhibition. If the balance is tipped in favor of more inhibition, the brain is “frozen” and nothing happens. If there is too much excitation, it will descend into chaos. The critical point is analogous to an attractor.
This notion that a complex system hovers somewhere in the balance between chaos and order is a fascinating one, especially when you connect it to the idea of a school. It reminds me of a joyous classroom of students engaged in meaningful and challenging work. There’s a warm buzz of controlled but spontaneous activity and creativity. Students can very easily go off the rails, and it’s the teacher’s job to hold them in that “hinterland between the inflexibilities of determinism and the vagaries of chaos,” as Barrow eloquently phrased it.
Order and disorder enjoy a symbiotic relationship, and a neuron’s firing may wander chaotically until a memory or perception propels it into an attractor. Sensory input would then serve to “stabilize” chaos. Indeed, the presentation of a stimulus reduces variability in neuronal firing across a surprising number of different species and systems, as if a high-dimensional chaotic trajectory fell into an attractor. By “taming” chaos, attractors may represent a strategy for maintaining reliability in a sensitive system. Recent theoretical and experimental studies of large networks of independent oscillators have also shown that order and chaos can co-exist in surprising harmony, in so-called chimera states.
This idea of attractors is also fascinating to me. As I read this passage on the subway on the way to class this morning on my little smartphone screen, I thought back to the idea of perceptual illusions and their relation to powerlessness. I also thought about the effect of isolation on the brain. And I wondered if this concept of “sensory input” stabilizing chaos that Clancy just outlined can be taken almost literally, as in how the loving touch of a mother has been shown to be important in brain development. And how beyond touch, the tone and manner in how adults and students speak to one another, the colors displayed on the wall, and all the other contextual factors of the environment can be so fundamental to “taming” the chaos that lies both in extreme isolation (ever been alone in the wilderness? Your mind goes nuts) or in overcrowded, confined spaces (the ghetto). Schools can provide that stabilizing influence.
Again, we find echoes of this idea of harmony and symbiosis in Barrow:
. . . Chaos and order have been found to coexist in a curious symbiosis. . . . At a microscopic level, the fall of sand is chaotic, yet the result in the presence of a force like gravity is large-scale organisation. . . Order develops on a large scale through the combination of many independent chaotic small-scale events that hover on the brink of instability. Complex adaptive systems thrive in the hinterland between the inflexibilities of determinism and the vagaries of chaos. There, they get the best of both worlds: out of chaos springs a wealth of alternatives for natural selection to sift; while the rudder of determinism sets a clear average course towards islands of stability.” (Bold added)
Now that I’ve geeked out on chaos, back to work . . .
Schools & Ecosystems 