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Complexity

Untangling Complexity Theory

Last Updated on August 25, 2021

An excellent introductory article for anyone interested in Complexity Theory (CT) is An Introduction to Complexity Theory by Jun Park. Among other things, it provides an insight about its origins which are, I think, as diverse and complex as the theory itself (highlights are mine):

Complexity Theory and its related concepts emerged in the mid-late 20th century across multiple disciplines, including the work of Prigogine and his study on dissipative structures in non-equilibrium thermodynamics, Lorenz in his study of weather systems and non-linear causal pathways (i.e. the butterfly effect), Chaos theory and its new branch of mathematics, as well as evolutionary thinking informed by Lamarck’s perspectives on learning and adaptation (Schneider and Somers, 2006).

Prigogine’s dissipative structures can for sure explain some of the complexity of life, while Chaos theory as a branch of mathematics, can shed some light on underlying patterns of deterministic laws in recurrent (autopoietic) processes in dynamical systems undergoing apparently random states of disorder.

Not sure, though, about the usefulness of the other two “non-linear causal pathways (i.e. the butterfly effect)” and “evolutionary thinking informed by Lamarck’s perspectives on learning and adaptation“. Let’s explore those two a little bit closer:

The “Butterfly Effect”

The “father” of Chaos Theory, Lorenz was also the author of the vastly misinterpreted “butterfly effect“. His question: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” posed on December 29, 1972 in a speech given to the American Association for the Advancement of Science, was answered by a resounding “YES” in popular culture and, apparently, also by many scientists, even if Lorenz himself wasn’t so sure about it.

The problem is in that many practitioners of “Complexity Theory” interpret the “butterfly effect” as if an apparently insignificant single event somewhere on the periphery of a complex system is a sufficient condition (cause) in producing some global system level effect. The fallacy in this argument is that it disregards all of the other necessary conditions for the effect to take place. Ackoff’s (actually E. A. Singer, Jr.) “product-producer” paradigm described with the acorn and oak tree example may provide a better insight to the matter. The acorn (a butterfly?) is not sufficient for the production of an oak tree (the tornado). To get an oak tree, you will also need an environment that is providing the necessary resources (sustained move of large air masses) for the tree (tornado) to grow. The “quality”, even the very existence, of this tree depends on what is happening within its environment.

Contrary to the popular belief, “chaos” in Chaos Theory is not chaotic at all. It is highly deterministic and predictable if you happen to know the initial conditions. On the graph below is the result of a recursive calculation through ~100 “generations” on a “logistic map”, a function often used in chaos theory. The function is the same, and the “gainA=4 for both graphs. The only difference is the starting value x0 which has a difference in the fifth decimal.

As it can be clearly seen the two graphs appear as chaotic even if generated by a completely deterministic process. A beautiful overview of this, and related elements of Chaos Theory can be found in this video:

Lamarck’s “top-down” causality

A recent paper from Corning, P. A. (2020)Beyond the Modern Synthesis: A Framework for a More Inclusive Biological Synthesis“, provides an extensive account about why the repeatedly discredited Lamarck’s “theory of acquired characters” should be included in modern Complexity Theory. As Lamarck’s theory is obviously not sufficient to make its point, the paper invokes the “help” of Lynn Margulis’s theory of “symbiogenesis” about the evolution of eukaryotic, from prokaryotic organisms. The fact that “various kinds of bacteria, fungi,viruses, and protozoa perform many functions for us, from helping to digest our food to defending against pathogens and producing several vitamins” is interpreted by Corning as if they could not possibly have originated “from“random”changes in genes, genomes, and “classical” natural selection” but they must be instead the result of inherited (purposeful ?) “behavioural actions of the phenotypes, and their functional consequences” as individuals within a single generational exchange. In fact, this view that any “learned characteristics” of a phenotype during its lifetime, can be somehow transmitted to the next generation, is vastly discredited, by other, more plausible, theories about why symbiosis and cooperation between phenotypes would be naturally selected as beneficial even by a selfish gene.

Properties of Complex Systems

A nice introduction to Complex System thinking can be found in the Complexity Theory Course from Systems Innovation

In one of their introductory videos, a complex system is tentatively defined as a system having the following properties:

  1. Large number of elements distributed through a hierarchy of interconnected subsystems
  2. Interdependence and non-linearity and fast phase transitions caused by positive and/or negative feedback loops
  3. Large number of possible connections between elements forming a complex network structure, and
  4. Adaptation and self-organization at the local level of relatively autonomous and diverse components of the system

Hierarchy of Complexity

The system is first defined as the usual “set of elements and the relations between them” and then,”when these parts are arranged in a specific order for them to function as an entirety we get what is called the process of emergence” of “a new level of organization” producing in such a manner a hierarchy of “subsystems“.

The complexity of the “overall system” is then identified in this category due to the large number and complexity of it’s (autonomous) subsystems on lower levels. This can be understood as a new form of reductionism, because of an attempt to explain a global change with a distant local “cause” such as the “butterfly effect“.

What is not taken in account in such a theory is the fact that all those nested subsystems (individual, organization, society) reside within “non-intersecting phenomenal domains” and according to the theory of autopoiesis, (Maturana 2011 emphasis mine):

All systems are composite entities that exist in two not intersecting operational-relational domains, the domain of the operation of their components, and the domain of their operation as totalities. Due to this the totality does not operate as an argument in what happens with its components, and the components do not operate as arguments in what happens with the totality.

In other words, elements and their interactions must be selected from just one level of that hierarchy of non intersecting phenomenal domains, and can not be “mixed and matched” with elements from other levels. The system’s behavior is identified in its domain of interaction as a totality while its functioning can be analyzed at the next (lower) level of its components. For example, if the system under examination is the global economy, elements of this system may be local (national) economies or sectors and their relationships that define the global economy, not individual businesses and/or consumers which are elements of different (sub)systems.

Fast Phase Transitions

One of the tenets of complexity theory is the notion that nonlinear systems may grow or decay at an exponential rate due to feedback loops and a, so called, “sensitivity to initial conditions“. These are called phase transitions: “Some small change in input value to the system can through feedback loops trigger a large systemic effect.” Examples of this central idea within chaos theory (the butterfly effect) can be seen in “financial crises and the collapse of ecosystems such as coral reefs“.

We discussed previously the “butterfly effect” and showed it has little to do with complexity. What current complexity theory does not discuss is the fact that in order for a fast phase transition to happen the system must be in a particular (unstable) state so that a small perturbation (the straw that broke the camel’s back) can cause an “avalanche” of sudden exponential growth or collapse.

The path for the system to get in such a state, far from equilibrium, has nothing to do with complexity, non linearity or “sensitivity to initial conditions“, but rather with gradual changes caused by some unidentified or neglected global trends in the system. The “bubble” that suddenly bursts didn’t just appear out of nowhere. It took some time for it to grow up to the bursting point. A stable system would have dealt with this anomaly long before it came to the point of no return.

Networks Connectivity and Communication

The last two properties of complex systems are somehow connected because, even if they are often cited as elements that hinder the possibility of an adequate control of complex systems, they can actually provide a solution for dealing with complex systems in a way that they become more stable and predictable (manageable).

A large number of possible connections between a large number of elements forming a complex network structure is a prerequisite for adaptation. In order to adapt to an increasing variety in the environment the system must have the capability to “rewire” itself to better cope with the new perturbation.

Connections are normally greater between elements confined to the same or nearby location. Also “end-to-end” connections tend to be stronger (regardless of location) between elements having similar function or purpose within the system (e.g. elements of the same “subsystem“).

Work in Progress …

Adaptation

Adaptation and self-organization at the local level of relatively autonomous and diverse components of the system is how the system as a whole responds to perturbations in the environment. Complex, dynamical systems have the ability to “rewire” themselves to respond to

Work in Progress from this point forward …

‘learning to dance’ with a complex system is definitely different from ‘solving’ the problems arising from it. — Roberto Poli

7 Differences between complex and complicated – Sonja Blignaut

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