Chapter Review: Complex Adaptive Systems, Chaos and Prediction

Chaos

Reductionism: According to the Internet Encyclopedia of Philosophy, “reductionists are those who take one theory or phenomenon to be reducible to some other theory or phenomenon. For example, a reductionist regarding mathematics might take any given mathematical theory to be reducible to logic or set theory. Or, a reductionist about biological entities like cells [or a human brain] might take such entities to be reducible to collections of physico-chemical entities like atoms and molecules. The type of reductionism that is currently of most interest in metaphysics and philosophy of mind involves the claim that all sciences are reducible to physics. This is usually taken to entail that all phenomena (including mental phenomena like consciousness) are identical to physical phenomena.”

This is a review of chapters 1 (What is Complexity?) and 2 (Dynamics, Chaos, and Prediction) of Melanie Mitchell's 2009 book, Complexity: A guided Tour. The book is easy to read and is written for a general audience. It limits discussion of mathematics to what is necessary to understand general concepts. The complex, difficult to define concepts that Mitchell discusses in chapters 1 and 2 are critical to understanding the implications of complexity research for proper understanding of humans as individuals and as they operate in societies. One implication is that knowledge from complexity science apparently contradicts some aspects of a very common and persistent belief, reductionism, about how the world works.

Complex adaptive systems -- complex collective behavior:In chapter 1, Mitchell describes complex systems. Complex systems ranging from the behavior of army ants, a person's immune system or a human brain to a whole society, economies and the internet all constitute complex adaptive systems (CAS). Although there is not yet a single definition of complexity or CAS, they share traits that help describe them. A key trait is that all CAS exhibit complex collective behavior where each individual component follows simple rules of behavior with no central leader or controlling source. The individual components include nerve cells in a brain, individuals using the the internet and how people behave in economies.

Another common trait of CAS is their capacity to process signals and information that arise from both internal and external sources. Behavior is thus influenced arising from both internal and external environments. Another CAS trait is complex behaviors that adapt to changing real world conditions in unpredictable ways despite a lack of central system control. Based on those three common traits, Mitchell proposes two definitions for a CAS:

1. A system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaption via learning or evolution.

2. A system that exhibits nontrivial emergent and self-organizing behaviors.

In this definition, emergence refers to the idea that although the rules that guide behaviors are simple, that generates complex behaviors in unpredictable ways. In this sense, observable behavior is emergent from the CAS as a whole.

Dynamic systems and chaotic (non-linear) systems: Systems such as the solar system, a beating heart, a human or animal brain, the stock market and global climate are dynamic systems because they change over time. The study of dynamic systems led to the finding of chaotic systems, which are systems where a even a miniscule uncertainty about a full understanding of a system in its initial state can lead to massive errors in predictions about behaviors or subsequent states of the system. The upshot is that any small error about a chaotic system’s initial state will lead over time to huge errors in predictions of future states and behaviors. In essence, prediction becomes impossible over time.

An aspect of chaotic systems is that the whole is different from the sum of their parts and inputs are not proportional to outputs. That is called being non-linear. One linear system, or nearly linear, is a cup of sugar mixed with a cup of flour. The two components are unchanged and thus linear. A cup of baking soda and a cup of vinegar is non-linear because the components change and give off carbon dioxide fizz. Most systems in nature are non-linear. Mathematician Stanislaw Ulam put it like this: “Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals.” Apparently not much in nature is linear.

This aspect of chaos is what contradicts reductionism, which holds that future behaviors and states of various systems can be predicted if enough can be known about a system in advance. That is simply not true. That can never happen due to unavoidable, inherent uncertainty in trying to fully understand any chaotic system at any point in time. Tiny initial errors will lead to massive errors over time. The figure below shows how a tiny difference in an initial parameter, x0 = 0.2 vs x0 = 0.2000000001 eventually leads to different outcomes that are unpredictable.

The political upshot: Politics is a chaotic or non-linear system in any given country. Predictions about what will happen and how policies will play out over time cannot be predicted very far in advance. Existing evidence is that the best humans can predict events up to about 5 years in advance. After that, predictions fade into the chaos of random events and become mere blind guesses. Ideologues who assert their ideology is best for the long run cannot know that to be true. That kind of belief is faith, not a matter of truth.

B&B orig: 2/27/19