{"id":387,"date":"2021-02-23T09:06:50","date_gmt":"2021-02-23T17:06:50","guid":{"rendered":"https:\/\/kihbernetics.org\/?p=387"},"modified":"2021-10-09T12:38:48","modified_gmt":"2021-10-09T19:38:48","slug":"untangling-complexity-theory","status":"publish","type":"post","link":"https:\/\/kihbernetics.org\/?p=387","title":{"rendered":"Untangling Complexity Theory"},"content":{"rendered":"\n

An excellent introductory article for anyone interested in Complexity Theory (CT)<\/span><\/strong> is An Introduction to Complexity Theory<\/a> by Jun Park<\/a>. Among other things, it provides an insight about its origins which are, I think, as diverse and complex as the theory itself (highlights <\/strong><\/span>are mine):<\/p>Complexity Theory and its related concepts emerged in the mid-late 20th century across multiple disciplines, including the work of Prigogine <\/strong><\/span>and his study on dissipative structures<\/strong><\/span> in non-equilibrium thermodynamics, Lorenz <\/strong><\/span>in his study of weather systems and non-linear causal pathways (i.e. the butterfly effect<\/strong><\/span>), Chaos theory<\/strong><\/span> and its new branch of mathematics, as well as evolutionary <\/strong><\/span>thinking informed by Lamarck<\/strong><\/span>\u2019s perspectives on learning and adaptation<\/strong> (Schneider and Somers, 2006).<\/cite><\/blockquote>\n\n\n\n

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.<\/p>\n\n\n\n

Not sure, though, about the usefulness of the other two “non-linear causal pathways (i.e. the butterfly effect)<\/em>” and “evolutionary thinking informed by Lamarck\u2019s perspectives on learning and adaptation<\/em>“. Let’s explore those two a little bit closer: <\/p>\n\n\n

The “Butterfly Effect”<\/h2>\n\n\n

The “father” of Chaos Theory, Lorenz was also the author of the vastly misinterpreted “butterfly effect<\/a>“. His question: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?<\/em>” 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<\/a> about it. <\/p>\n\n\n\n

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

Contrary to the popular belief, “chaos” in Chaos Theory is not chaotic <\/em>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 “gain<\/em>” A=4<\/span><\/strong> for both graphs. The only difference is the starting value x0<\/sub><\/span><\/strong> which has a difference in the fifth decimal. <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

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