The complicated and the complex

Continuing this post, in this interview Krakauer notes a distinction between complicated and complex systems. Examples of the former are simple relationships like billiard balls bouncing off each other or the orbits of planets. Such systems scale well with repeating patterns. But complex systems like human beings have highly connected components that are integrated over different time and spatial scales with no dominant factor, so models of them require the same sort of complexity to describe them. Simple, mechanical, complicated models are not sufficient.

That's my issue with power laws in general and the model of hierarchical complexity in particular. It seems to take the notion of power laws that might apply to some relatively simple, complicated mechanics and apply them to everything. Whereas complex systems require a different mathematical model that itself adapts to a system at more complex scales. But instead theorists look for short-hand, merely complicated descriptions that force-fit the phenomena into its tidy little equations.

Which also reminds me of Cilliars below discussing the distinction between complicated and complex systems.

"Chaotic behaviour—in the technical sense of ‘deterministic chaos’—results from the non-linear interaction of a relatively small number of equations. In complex systems, however, there are always a huge number of interacting components. Despite the claims made about aspects of the functioning of the olfactory system, or of the heart in fibrillation, I am unsure whether any behaviour found in nature could be described as truly chaotic in the technical sense. Where sharp transitions between different states of a system are required, I find the notion of self-organised criticality (see Chapter 6) more appropriate than metaphors drawn from chaos. This might sound too dismissive, and I certainly do not want to claim that aspects of chaos theory (or fractal mathematics) cannot be used effectively in the process of modelling nature. My claim is rather that chaos theory, and especially the notions of deterministic chaos and universality, does not really help us to understand the dynamics of complex systems. That showpiece of fractal mathematics, the Mandelbrot set—sometimes referred to as the most complex mathematical object we know—is in the final analysis complicated, not complex. Within the framework of the present study, chaos theory is still part of the modern paradigm."

At 13:13 in this Dave Snowden interview they also discuss the difference between the complicated and the complex. The complicated can be taken apart and put back together again. The complex cannot because "the properties of the whole are the result of the interactions between the parts and their linkages and constraints. In a complex system how things connect is more important that what they are."