Complexity, Chaos, and Emergence

George Siemens

October 19, 2009

Complexity and chaos are somewhat vague and misunderstood concepts. Terms like “emergence”, “adaptive systems”, “self-organizing systems”, and others are often tossed about with such casualness and authority as to suggest the speaker(s) fully understand what they mean.

In reality, these concepts lie at the heart of a fairly new science. For example, chaos theory has long existed in small glimpses throughout history. Henri Poincare discovered the concept when he was working on a math problem for a state (king) funded competition. He won, but then realized he had erred in his own calculations that resulted in the discovery of chaos. And then nothing happened. For 70 years, his insight was largely ignored. In different sciences, glimpses of chaos – such as found in gases – where occasionally encountered. However, lacking an eye to see what existed, these were often ignored. It wasn’t until the work of Edward Lorenz on weather patterns in the 1960’s that chaos theory started to gain broad interest. Complexity theory follows a similar path. As both readings and the video this week indicate, understanding these theories is not an easy task.

Assumptions

How then, can we talk about these difficult subjects in CCK09? We are making two assumptions:

1. The underlying concepts of both chaos and complexity can be broadly understood. Advanced mathematical basis underlying each theory, however, is well beyond the scope of this course. However, concepts like emergence can be understood based on common everyday occurrences.
2. The general principles of chaos, complexity, and emergence can be partly translated into social sciences.

Getting personal

A short personal story. When I was about eight or nine years old, I spent one particularly lazy afternoon reading and reflecting. I’d read a paragraph in a book. Pause, Reflect. And generally let my mind aimless wander. For some reason, I eventually settled on the concept of eternity. I don’t know what prompted this resting place for my thoughts, but the topic seemed like perfect fodder for a restless mind. Once engaged, however, I quickly discovered the topic to be overwhelming. Eternity has a way of not having an end point. It just keeps going. While trying to grasp what this means, I used the framework of my daily life – a Groundhog's Day experience of perpetual repetition. I don’t know how much time passed, but I recall ending up in a state of panic. The concept of eternity was so elusive, so large, that I was unable to explore the many tertiary thoughts produced. The cause-effect world of aging, change, and progression didn’t exist. I was unable to comprehend eternity because I was standing in a non-eternal frame of mind. Everything in my life was rooted in the opposite of what I had turned my attention to.

Complexity and chaos are like this. They are too large to be grasped with a frame of reference that is founded on non-complex views of life.

Consider learning.

Why are complexity and chaos theory important in CCK09?

Throughout CCK09 we have focused on the importance of recognizing that no one individual is able to master a discipline. We all have gaps in our knowledge.

To address this reality, we first need a shift in our mindsets. Or perhaps a more accurate concept – we need to let go of the notion that we can know a field in its entirety. All knowledge is in the connections – how we’ve connected concepts and how we are connected to other people and sources of information. To know is to be connected.

Which leads directly into the second requirement: our best opportunity to function in complex and chaotic environments is found in structures that adapt and respond to feedback. Change requires structures that also change. To this end, we turn to networks and ecologies as a model for:

• Learning
• Knowledge/epistemology (as both process and product)
• Managing complexity
• Explaining emergence in its multiple forms in education: learner understanding, group formation, advancement of a discipline, etc.
• Designing educational systems that embody the society that learners will be expected to engage as members (ontology - learners becoming)

Definitions

To extract lessons for learning and knowledge, it’s useful to provide working definitions of key concepts.

Chaos

Steven Strogatz defines a fundamental scientific shift from Newton’s clockwork universe of pure cause-effect to a universe defined by chaos. What is chaos? Strogatz defines it as unpredictability that occurs in systems that obey predictable laws, or, more succinctly, “deterministic unpredictability”. Randomness appears to be dominant. Yet under closer consideration, a type of order – unlike what is traditionally conceived – is discovered. Consider Lorenz’ discovery of sensitivity of initial conditions in his weather model: he did not discover a universe that lacked order or structure. On the contrary, as James Gleick states in Chaos, Lorenz discovered a world of “fine geometrical structure often masquerading as randomness” (p. 22).

Chaos requires great care or scrutiny when applied to social sciences. Chaos’ origins are far removed from the social sciences. Pure mathematics, advanced physics, and related sciences are its birthplace. It appears rather unlikely that we can apply chaos theory specifically to learning. We can, however, broadly apply at least two critical elements: 1) the concept of sensitivity of initial conditions, and 2) recognizing that learning similarly consists of unpredictability that occurs within certain structures of form (deterministic unpredictability).

Complexity

Complexity theory has an intuitive appeal to many educators. The process of learning seems, by its very nature, to be complex.

An example I often use to distinguish complicated from complex: a puzzle and the weather. A jigsaw puzzle has a particular outcome. If we are successful in completing the puzzle, it will look like the image on the box. Many steps can be involved and the process can take a great deal of time (ever tried completing a 10,000 piece puzzle of an ocean scene??). Regardless of steps involved, a certain outcome must be achieved to be successful. In contrast, a weather system is an example of complexity. Numerous interacting elements produce varying outcomes. We can watch the weather forecast on TV tonight and be assured that tomorrow will be a beautiful sunny day, perfect for hiking. Instead, tomorrow bring a downpour. How can weather forecasters be so wrong? Weather is a system reflects how individual components interact. Perhaps different pressure systems collide, altering what was expected to happen. Or perhaps one weather system moves faster than expected. The final outcome – tomorrow’s weather – is determined by the numerous ways in which the components of the system interact.

John Miller and Scott Page provide a great definition of complexity in their text Complex Adaptive Systems: “a set of diverse actors who dynamically interact with one another awash in a sea of feedbacks” (p. 7). Whereas complicated worlds are reducible, complex systems are not. Within complexity theory, the outcome is greater than the sum of its parts.

Complexity is of course more complex than detailed here. Do complex systems translate well from physical to social spaces? According to Miller & Page, they do, but with an important consideration: “What differentiates physical systems from social ones is that agents in social systems often alter their behaviour in response to anticipated outcomes” (p. 115). The autonomy of agents – acting not as an unconscious weather system, but as volitional entities pursuing a goals or objective – adds an additional level of complexity. For our purposes, the irreducibility of learning to its individual parts, the recognition of dynamic interactions, the criticality of feedback in influencing adaptation, and openness are sufficient for our application to learning. For those wishing a greater understanding, the Sante Fe Institute (http://www.santafe.edu/ ) is a great place to start exploring the world of complexity. Research, reports, and publications are all available on the site.

How does emergence fit in? Emergence is an attribute exhibited by complex systems. The interactions of multiple agents at a local level can create or contribute to significant system-level change. The internet provides numerous examples of emergence as the activities of thousands of individuals provides an outcome or product well beyond what could have been predicted. When applied to learning, we can appeal to emergence as the outcome (understanding?) that arises from different agents interacting and producing unanticipated outcomes. On a personal level, we could argue that our learning is the emergent phenomena of our own interactions with others and how we have engaged with and connected different concepts.

How do these concepts impact learning?

Complexity and chaos, when applied to social sciences, deliver the same unmistakable message as when applied to physical sciences: the clear-cause effect world gives way to unpredictability. Consider learning outcomes created at the start of a course. Can we really ensure they are achieved? Can the complexity of learning be reduced to six or eight broad statements? Many educators feel that outcomes can be achieved. What is overlooked, however, is that much more than planned outcomes are experienced by learners. Consider CCK09. For some participants, this course has been only partly about connectivism. They’ve likely found paths that Stephen and I did not even consider in our planning. Learning is simply too complex, too multifaceted, too replete with multiple off-ramps, to be confined or reduced to a mechanistic model.

The value of complexity and chaos is found in the forced reconsideration of assumptions about learning that were at best only partly true. The same errors of Newton’s clockwork universe – and the accompanying desire to inhabit a world that can be controlled and definitively known – appear prevalent in education. As with chaos, we can appeal to deterministic unpredictability. While the experience of an individual learner can’t be reduced to an equation, the larger system in which the learner exists can be understood with reasonable accuracy. Ecologies and networks are reflective of chaos and complexity theories main tenets and provide a suitable replacement for the current classroom and hierarchical model of education.