1. The inadequacy of measures of complexity as represented by graphs and networks.
a. These graphs or "networks" are visualized, or modeled, as interconnected links and nodes/edges and vertices/lines and dots (pick your synonym pair).
i. One measure of the complexity of such structures (c.f., Shannon entropy) results in the characterization of both a completely disconnected and completely connected network of nodes being of the same and simplest level of complexity, with the transition from one level to the other being considered the more complex.
ii. Other measures of the complexity of nodal structures (e.g., global complexity, average complexity, and topological complexity) suggest ways in which the complexity of a fully connected network is more complex than a fully disconnected network.
iii. Take away point – the analysis of the geometry of complexity lands us where Skinner landed in the definition of a response as an operant (Bx—SR/r), an event paired to its effect on the environment.
2. The primacy of emergent properties
a. As elements pair to create a dynamical system, and elemental dynamical systems pair to create networked dynamical systems, those networked systems may show emergent, adaptive properties.
i. Complex systems “may” show emergent, adaptive properties, but not always. One model for this bonded property of networked dynamical pairs (e.g., pairs of mutually entailed operants participating in sets of combinatorial mutually entailed operants) as being both adaptive and generative is the Mendalbrot set (c.f., https://www.youtube.com/watch?v=ovJcsL7vyrk&list=PLe9YrQN9NHY2T7zlEcewtn7MrDAbhILlz&index=2&t=567s ).
b. Emergent properties (e.g., the Feigenbaum constants of growth/decay maths) establish conditions for analysis of the both the structure giving rise to the emergent properties AND to the study of the natural laws that only influence the larger structure that gives rise to the emergent properties of that structure. This requires a functional analysis at the level of the emergent structure, similar to using CBA measures to assess the generative effects of lesson sets within a scope-and-sequence curriculum.
3. On the edge of chaos
a. Stuart Kauffman – “…complex systems live on the edge of chaos’
b. What is known and modeled by the Mandelbrot Set, is complexity and emergent properties live within boundaries of chaos. Fibrillation is chaotic functioning. The heart is returned to patterned functioning via defibrillation procedures (in this case electric shock).
c. The purpose of clinical intervention is to restore or establish adaptive, organized and rhythmic patterns of behavior.
d. The promise of CBT, Contructionalism, RFT and the HDML is a promise of how to establish and maintain adaptive, organized and rhythmic patterns of adaptive behavior.
e. The effect of science is to maintain organized human behavior within the bonderies of chaos.