The Extension of Neural Complexity

In the last chapter of his book Networks of the Brain, Olaf Sporns extends his neural processing and, thus, cognition beyond the brain and to the body and the body's environment. This is the feature of neurophysiology that finally destroys all my old ideas about cognition, thought, and knowledge, for no longer can I think of thoughts as belonging only to the brain. Thoughts and emotions – all forms of cognition – flash through the brain, through the body, into the environment, and then back through the body and into the brain. I have only to think of some of the lively and spirited conversations that I have had over the years to see how my thoughts at any given time were not my brain's alone, not even mine alone, but the reiterative, feedback process of patterns flashing through the conversational space from my brain to my colleague's brain and back to me and back to them, over and over. Sporns, of course, says it more scientifically precise:

By acting on the environment, the brain generates perturbations that lead to new inputs and transitions between network states. Environmental interactions thus further expand the available repertoire of functional brain networks. … The body forms a dynamic interface between brain and environment, enabling neural activity to generate actions that in turn lead to new sensory inputs. As a result of this interaction, patterns of functional connectivity in the brain are shaped not only by internal dynamics and processing but also by sensorimotor activity that occurs as a result of brain-body-environment interactions [which] can be conceptualized as an extension of functional connectivity beyond the boundaries of the physical nervous system. (306)

Sporns follows the argument of Andy Clark to say that

the minds of highly evolved cognitive agents extend into their environments and include tools, symbols, and other artifacts that serve as external substrates for representing, structuring, and performing mental operations. If this view of cognition as extending into body and world is correct, then cognition is not "brain bound" but depends on a web of interactions involving both neural and nonneural elements. The networks of the brain fundamentally build on this extended web that binds together perception and action and that grounds internal neural states in the external physical world. (309)

Those who are familiar with Stephen Downes' thoughts on this issue (for example, here) will quickly recognize his ideas about the extension of knowledge through a social network, so that anyone person's – say, Susan's – knowledge of the French capital Paris is a network of flashes across Susan's brain, body, and interaction within the general, historical discussion about Paris as well as with the actual city of Paris. For Susan, then, cognition of Paris is the interplay of patterns in her head, in her body, in her conversations with others (mediated by voice, text, image, networks, and other media) and with Paris itself. Indeed, the more sophisticated Susan's Paris network becomes, the richer is her repertoire of ways to think Paris. At any one time, Susan will likely never use the entire network of meaning available to her, but because she has such an extensive, rich network, then she can think significantly about Paris in almost any situation for any reason.

I have a couple of quick observations to make about this view of knowledge as a kind of cognition. First, we can only have personal knowledge. By that I mean that Susan must always view Paris from the center of her meaning network. With lots of training and hard mental work, she can perhaps learn to look at Paris from other points of view than her own, but she can never not think of Paris from her own point of view (I think that's the correct combination of negatives. Count'em). Even if she changes her mind about Paris, she is simply knowing Paris from a different center, but still her own.

Second, knowledge can never be merely personal. Yes, this contradicts my first observation, but there it is. Susan's knowledge of Paris always extends throughout her ecosystem to include shared language, shared social groups, shared experiences, and so forth. Susan must form her knowledge from the center, but she must also form it in dialog with others who are likewise working from their own centers. Any attempt by Susan to look at Paris from another's center is a sometimes useful exercise in fiction. It's a God's view that Susan can sustain for only a short time. Any attempt by Susan to look at Paris only from her own center is a fatal entrapment in fiction. Knowledge depends on what Morin terms the dialogic principle: the constant interaction of any entity from its own center with its environment and the other entities in that environment interacting from their own centers. Knowledge is that zone of tension between loss of self in its own center and loss of self in the centers of others. Susan interacts with her world – sometimes skillfully, sometimes not so skillfully – and that's what makes Susan who she is. Education is the attempt to help Susan interact more skillfully.

Complexity and Cognition

You might think that complex systems are complicated, but they often aren't.

That may be a bit too cutesy, but it does make a nice distinction between complexity and complication in network systems. Modern jet fighter planes and computer circuit boards are complicated structures – they are composed of millions of parts arranged in intricate ways for a myriad of purposes – but they are not complex. Why? Because they don't change, and if they do change, then that change usually breaks them. They are rather rigid structures, with regular, predictable, and reliable interactions among their parts. After all, you don't want a jet fighter that suddenly decides to start behaving differently in a dog fight.

On the other hand, complex structures such as the human body change constantly, acquiring new cells, functions, and capabilities and discarding old ones. They are dynamic, and not just in the sense of moving parts. They are dynamic in the ways the parts within the structure interact with each other and in the ways all those structural parts interact with the ecosystem that encloses them. And the trigger for this dynamism is sometimes quite simple. In Networks of the Brain, Sporns paraphrases Herbert Simon to say:

First … most complex systems can be decomposed into components and interactions possibly on several hierarchical levels. Second, complexity is a mixture of order and disorder, or regularity and randomness, which together account for the nontrivial, nonrepeating nature of complex structures and their diverse dynamics. (279)

Brains, then, owe their neural complexity to "the union or coexistence of segregation and integration expressed in the multiscale dynamics of brain networks" (278), to the mix and tension of "some degree of randomness and disorganized behavior with some degree of order and regularity" (281,282), and to "rich and dynamic contextual influences" (286). This dynamic complexity in the brain is what gives rise to the emergent property of consciousness, or as Sporns says it, "Consciousness emerges from complex brain networks as the outcome of a special kind of neural dynamics" (298).

I see, then, two elements that generate neural complexity and, thus, consciousness:

1. nodes and clusters of nodes – from single neurons to social networks and natural ecosystems – that are able to form meaningful patterns within any given scale and across all scales (segregation and integration of functions)
2. a fluid tension between regularity and randomness, order and chaos, as patterns form, fade, and reform across the web of nodes as nodes form their own patterns and then harmonize those patterns with the other patterns forming, fading, and reforming elsewhere in the neural network

I need a better picture, so I'll call again on the image of the brain as two musical groups: a left hemisphere orchestra and a right hemisphere jam band. Imagine the New York Philharmonic meets The Allman Brothers Band on the same circular, floating stage: the Philharmonic stage left, the Brothers stage right. The musicians can hear both each other and the speakers that circle the stage, filtering and focusing the sound from two omnidirectional microphones pointed out toward the world. (The musicians can also see, feel, smell, and taste, but let's not overcomplicate this metaphor. Sound will suffice, I think). Finally, they have microphones on stage through which they can play, or not, their sounds to the outside world.

Both bands are mature. They know their chops, their instruments, and each other. They know how to make music on their instruments and how to blend their individual music into the music being made by the other instruments on the stage AND to the music coming in over the speakers from the outside world. When they are all rested and focused, then they can make wonderful sounds that harmonize internally with the other sounds on the stage and externally with the sounds coming over the speakers from outside. When they are not rested or they've had too much to drink, then they make silly, discordant sounds, sometimes truly awful sounds.

Because they are mature musicians, they are dedicated to learning more about their instruments, each other, and their music, so much of the time they are focused on their internal, on-stage noodling, trying this new combination of instruments, this new musical motif or riff, or practicing and honing old motifs and riffs to have ready at hand when they need them. They have a huge repertoire of different sounds that they can call upon at an instance, and they know which among them can make which sounds. None of them can make all sounds, and some of them can make only a few sounds, but they all know how to group and regroup themselves as needed. Sometimes they group as strings, which will pull together the violins and guitars, sometimes as low register instruments, which pulls together the tubas and bass guitars.  The point is that they have a rich repertoire of established sounds, and they are constantly working to add to that repertoire.

But they are also keenly aware of the sounds coming from outside, and they will respond to sounds they hear. They can faithfully reproduce and harmonize with sounds that they know and other bands with which they've played before, creating a pleasing musical interlude, melodies and movements arcing back and forth between the different bands both on a single stage and across the different stages. 

This is where it gets fun. If you are lead guitarist Duane Allman (an individual neuron in the right hemisphere of the brain), then you are listening to your bandmates Dicky Betts, Gregg Allman, Butch Trucks, Jai Johnny Johnson, and Berry Oakley AND to the New York Philharmonic just across the stage with tonight's guest cellist Yo Yo Ma AND to the sounds coming from the other orchestra/jam band made up of the Boston Pops and the Grateful Dead. You are listening for a place for you to fit in. You at last hear a space for you and you make your sound. It's a particularly pleasing, clever riff, so Yo Yo Ma echoes it. You echo back. It's picked up by Phil Lesh of the Dead, reworked slightly, and comes back to you again. You restate it, then rework it again, expanding it by a few bars. The woodwinds in both orchestras join in, and the musical pattern soars. Everybody's happy. Everybody understands the same thing. The band has created a pattern of sound that you, Duane Allman, could not have produced alone but that could not have been produced without you.

Or perhaps you make an awkward sound, something that just doesn't work in the current flow. The musical pattern becomes chaotic for a moment until the other musicians ignore you. The music rights itself, and the bands move on as Brother Gregg leans over and whispers to you, "We're playing in G, dude."

Why did Gregg do this for you? Because – and this is the most important point – there is no conductor, no central processing unit, no boss. The musicians (the individual neurons) are all on their own, seeking a way to integrate their individually produced contributions into the whole. They are each guided by their own, unique abilities to produce unique sounds and by a shared interest in harmonizing, synchronizing, and otherwise fitting their sounds into all the other sounds to create a pleasing, workable whole.

In resourceful, well-tuned bands (brains), each musician finds a way to fit into the whole, most of the time playing a supporting, complementary role, sometimes taking the lead, but always looking to add her own unique sound to the group and its music. In damaged or deranged bands, the musicians are stuck playing the same tune over and over, or they cannot integrate with each other so that no coherent music emerges from their individual sounds.

If I understand Sporns, this is how cognition takes place: emerging, dynamic patterns of firings of individual nodes that group, fall apart, regroup in clusters across the left and right hemispheres of an individual brain AND across different brains, mediated by our actions and symbol systems.

So what does this view of cognition mean? Well, for me as an English teacher, it means that if I want to understand fully the meaning of Shelley's poem Ozymandias then I must be mindful of the complex interactions within Shelley's mind, the complex interactions of the symbol system he used to compose the poem (English language, poetry, sonnet, etc.), the complex interactions of Shelley with his ecosystem (natural, social, intellectual, etc.), the complex interactions of the poem with its ecosystem (production printing, distribution, consumption, etc.), the complex interactions of Shelley's readers with the poem and with each other, the complex interactions of all those interactions with me, and the complex interactions within my own mind.

This effectively describes an approximately infinite number of dynamic interactions that I must master in order to understand completely one fourteen-line poem, and it's why we can write about one poem for two hundred years and still not exhaust it. Basically, what it shows is that we can form a richer understanding of Ozymandias, but we cannot form a complete understanding. This is a crisis for students confronted with a regime of objective tests. In the face of this crisis, students do the only sensible thing: they either demand to know the correct answer, or they walk away. We force them to choose either to play the one correct tune over and over or to degenerate into chaos. Let us hope they are able to choose wisely.

The Hierarchy of Neural Complexity

Sporns says that "brain connectivity is organized on a hierarchy of scales from local circuits of neurons to modules of functional brain systems" (258). His use of the word hierarchy presents me with some problems as I have for the last few years contrasted hierarchical structures with network structures. In general, I have assumed that hierarchies were rigid, closed, traced, arboreal structures (to use terms from Deleuze and Guattari) while networks were flexible, scaleable, open, mapped, rhizomatic structures. Hierarchies admit only sanctioned, homogenous nodes within its structure and then fix them into a well-defined place with well-defined relationships to all other nodes; whereas,  networks admit heterogenous nodes within its open structure and allow nodes to develop relationships with any or all other nodes for any reason. For me, then, hierarchies and networks are not the same, and I cringe just a bit each time Sporns uses the term hierarchy to describe an aspect of neural networking.

But I think I have a resolution to my concern. I don't think Sporns is using hierarchy as I do; rather, he is describing various physical and functional layers of the brain and how they interact. As he says: "A recurrent theme in studies of collective behavior in complex networks, from epidemic to brain models, is its dependence on the network's multiscale architecture, its nested levels of clustered communities" (261). He is not so much describing a pyramidal structure as an onion structure. He's talking about layers enclosing layers enclosing layers and so on. This might be a mere quibble over visual metaphors but for his concepts of heterogenous coupling and multiscale dynamics, and some others like them. These principles prevent Sporns' neural hierarchies from calcifying into rigid hierarchies, as I have used the term. Indeed, heterogenous coupling in neurophysiology reminds me much of Deleuze and Guattari's first principle of the rhizome given in the first chapter of their book A Thousand Plateaus (1988): "any point of a rhizome can be connected to anything other, and must be. This is very different from the tree or root, which plots a point, fixes an order" (7). I think Deleuze and Guattari would be most comfortable with Sporns' concept of heterogenous coupling as very rhizomatic.

Sporns also talks about the brain's metastability, or tendency toward chaotic itinerancy:

the itinerant or roaming motion of the trajectory of a high-dimensional system among varieties of ordered states. Chaotic itineracy is found in a number of physical systems that are globally coupled, that are far from equilibrium, or that engage in turbulent flow. … It has also been observed in brain recordings … and neural network models … Over time, systems exhibiting chaotic itineracy alternate between ordered low-dimensional motion within a dynamically unstable "attractor ruin" and high-dimensional chaotic transitions. System variables are coherently coupled, their dynamics slow down during ordered motion, and they transiently lose coherence as the system trajectory rapidly moves between attractor ruins. (263, 264)

This chaotic itinerancy of neural networks with their roaming motions and trajectories and their constant transitions between coherent couplings and incoherent chaos is strongly reminiscent of another characteristic of rhizomes: the principle of asignifying rupture. Deleuze and Guattari say of asignifying ruptures:

Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees. There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome.

Rhizomatic structures, then, deterritorialize and reterritorialize only to deterritorialize again. If I understand what Sporns is saying, then it seems that neural networks have a chaotic itinerancy that is at least a Rorschach of asignifying ruptures. Perhaps, Deleuze and Guattari's asignifying ruptures have deterritorialized and reterritorialized as chaotic itinerancy.

Seems possible. Anyway, chaotic itinerancy seems to fit nicely with D&G's whole idea about nomadology and motion in reality. Anyone know for sure?

Dynamic Hierarchies

So the brain is a dynamic system, if Sporns is correct. How does this dynamism arise?

I've just reread the chapter, and I confess that I am not yet ready to talk confidently about the physiology of the brain, but I think I have gleaned enough to make some general statements that might be useful. The brain's dynamics rest on heterogenous coupling and multiscale dynamics, both of which Sporns says are "ubiquitous features of the brain" (258).

Heterogenous coupling suggests that any given neuron, cluster of neurons, or brain region will connect to (couple with) most any other neuron, cluster, or region, and multiscale dynamics suggests that the neural activity at any neural level – neuron, cluster, or region – affects the activity of the enclosed and enclosing levels. Sporns says:

Brain connectivity is organized on a hierarchy of scales from local circuits of neurons to modules of functional brain systems. Distinct dynamic processes on local and global scales generate multiple levels of segregation and integration and give rise to spatially differentiated patterns of coherence …. Neural dynamics at each scale is determined not only by processes at the same sale but also by the dynamics at smaller and larger scales. (258)

Just as neural dynamics unfold across different spatial scales, they also unfold across different time scales "from fast synaptic processes in the millisecond range to dynamic states that can persist for several seconds to long-lasting changes in neural interactions due to plasticity" (262). As a neural pattern is created or expressed (or blooms, ripples, or flashes) across the spatial and temporal structures of the brain, it is invariably modified by endogenous brain activity and by external inputs. All neural "brain dynamics is inherently variable and 'labile,' consisting of sequences of transient spatiotemporal patterns that mediate perception and cognition" (262). Sporns calls these brain dynamics "that are neither entirely stable  nor completely unstable" metastable.

If I understand this correctly, then, all thoughts and emotions are metastable, always expressed somewhere on a scale between completely stable and completely unstable. To use my two bands model of the brain (left: orchestra, right: jazz band), each time I sound the thought Connectivism, I sound a recognizable but variable musical motif. Like Jimi Hendrix, I never quite play the song riff the same way, even if, like a classical guitarist, I'm trying to. And  even if I managed to play it exactly the same twice, it would still sound different if I were playing at the Fillmore East, at Woodstock, or in the studio.

It just won't ever be exactly the same. Thoughts, concepts, and emotions are dynamic, metastable expressions. So what's the point for education? Our effort to impart the same knowledge to 30 different students in a single class is pointless and impossible, so let's give it up. Let's shift gears and devise a different goal. Thirty students cannot learn the same thing, so let's quit teaching as if they can.

Okay, you rightfully ask, if we don't teach them all the same thing in the same way, then what do we teach them and how? I thought you might ask that. Fortunately, I've run out of time for writing today. Later.

Dynamics and 21st Century Education

In Chapters 12 and 13 of Networks of the Brain, Olaf Sporns tackles the issues of dynamics and complexity in neural networks. I have the feeling that I will be reading both chapters again to digest them, but what I understand so far is highly exciting. It's also beginning to feel somewhat natural to me. Nice that.

Sporns describes a very dynamic brain structure and function, radically different from the traditional views that "place much greater emphasis on serial processing, noise-free signal transmission, and reliable encoding and retrieval of information" (274). To me, this traditional view of neural activity sounds a lot like traditional education with its serial processing in a lock-step curriculum, noise-free signal transmission in a quiet classroom focused totally on the teacher, and reliable encoding and retrieval of information in rote memorization of a collection of facts and regurgitation on objective exams. Of course, as Sporns notes, the traditional approach to brains has "been remarkably successful in well-defined problem domains and in the absence of conflicting or competing demands" (274). The same with education, I think. So long as you are teaching a well-defined, fairly focused knowledge domain within a totally controlled environment with no conflicting demands, then traditional education, or training, works pretty darn well, but what happens when you encounter a rapidly shifting knowledge domain in a space with lots of conflicting demands—you know, like real life? Then the traditional models don't seem to work so well. What are the alternatives? Sporns suggests that the brain takes a dynamic path.

Why a dynamic path? First, Sporns suggests, for self-preservation, or self-expression. Apparently, diverse dynamics are important for self-organization and robustness within complex systems. Sporns notes W. Ross Ashby's law of requisite variety, which says that any system "must have a matching variety of responses at its disposal with which to counter [environmental perturbations] in order to maintain internal stability" (256). Thus, complex, dynamic environments demand complex, dynamic entities. Or, if historian David Christian is correct in his recent TED talk, then the universe is on a path of increasing complexity, and dynamic, complex environments and their composite entities are emerging together. In a marvelous dialogic, more dynamic and complex environments bring out more dynamic, complex entities which bring out more dynamic, complex environments. On and on, endlessly complexifying.

This has a strong lesson for education: the world our students live in today is much more dynamic and complex than the world of 19th Century industrialism that gave rise to modern education (see Sir Ken Robinson's RSA talk on this issue). It's time we moved on from that model to develop "a variety of responses" with which to counter the dynamic and complex environmental perturbations that bombard our students daily. Industrial thinking, while still valuable, has no response to iPhones, iPads, and Facebook-augmented revolutions. We must move education beyond its industrial mind-set, which does not have "a matching variety of responses at its disposal with which to counter [the 21st Century] in order to maintain internal stability." Just as an increasingly dynamic and complex Universe elicits an equally dynamic and complex consciousness, so too does an increasingly dynamic and complex society elicit an equally dynamic and complex educational system.