I was reading a publishers pre-announcement newsletter and came across a reference to Complex Adaptive Systems and Project Management.

The concept that "Agile Project Management is like a Complex Adaptive System" is popular in the literature and discussion forums. Having training in physics (undergrad and grad experiences with deep inelastic scattering in the late 70's) leads me to believe that the use of these terms slightly out of context.

Some things fit well, others are a stretch:

- Edward Lorenz was a meteorologist involved in statistical weather forecasting, who concluded that small changes in the input to his model of the earth's atmosphere and the ocean resulted in large changes in outcomes. His paper "Deterministic Nonperiodic Flow,"
*Journal of Atmospheric Sciences*, 1963 described how small differences have big consequences. We're all familiar with projects that behave in the same way. - Phase space is the domain of CAS and Chaos processes. Phase space is the representation of an object using the coordinates of "phase." If a pendulum's location were defined as X and Y (looking from the front), then the phase space representation of the pendulum's movement would be a circle . This approach allows coordinates system information (in any coordinates not just X and Y) to be described as a complete state of knowledge in a dynamical behavior coordinate system - the phase space. Steady, periodic, and quasi-periodic systems can be represented in clear and concise pictures of their phase space. Disrupting the underlying system can be visually represented in phase space. Turbulence is one of those interesting physics problems that is amenable to phase space representations.

There are other interesting topics in chaos theory, but let's move on.

__Complexity Theory__

In the 1980's chaos theory moved into real world applications. It became and experimental science. And of course was captured by the populist authors to describe things in ways that seemed to make sense, but had little mathematical connection with the underling equations of complexity theory. Oh well, if it works of the masses, it must be right, right? Maybe. Remember *The Tao of Physics*? Not much physics in the *Tao of Physics* BTW.

Complexity theory is also non-linear dynamics. Non-linear dynamics is the non-linear description of linear dynamics. Linear dynamics is best described by sets of linear differential or partial differential equations. The non-linear part comes from the non-linear differential equations that describe the behavior of the dynamical system.

Where would we find the family of non-linear partial differential equations in a complex adaptive system project? Good question. They can be found in compressible fluid flow, in turbulence equations, in a simulation of an internal combustion engine cylinder head. Stuff like that. But the CAS project discussion use these terms without the underlying math. Such is the popularization of scientific terms. Like the Heisenberg Uncertainly principles used in management discussions. I'd bet a pile of money that few, if any, of the business authors using that term could solve the matrix form solution of the two-state hydrogen atom Heisenberg used in his original paper.

The other characteristic of a CAS is its adaptability. The A in CAS. Complex systems are not passive. They respond actively to transform their behavior. Species adapt. Markets adapt. This adaptation can appear random - if I could predict the market I wouldn't be on vacation from work. I'd be on vacation period.

Complexity is concerned with how things *happen*. Chaos observes and studies unstable and aperiodic *behavior*. Chaos seeks to understand the underlying dynamics. Complexity ask larger questions.

__Skipping to the End__

The KAM Theorem, Kolomogrov, Arnold, Moser is one basis of much of the discussion of emergent behavior and it states...

For a simple linear system for which a solution exists, a small perturbation results in a qualitatively similar system.

The domain of the KAM Theorem is called non-linear Hamiltonian Dynamics. The original paper has some lecture notes as well. Note there must be a solution, it must be linear, and the perturbation must be small. Turns out the interesting thing is that there are system where a small perturbation DOES disrupt the stability of the system and move it to another stable point. These occur all the time in dynamics. But do they occur in projects or human systems? In the same way as they do in dynamic systems? With the accompanying equations?

At this point there are many branches of physics, biology, weather (I have a neighbor who owns a circulation model at NCAR), quantum mechanics and other interesting domains. The popularization of these concepts has entered the philosophical domain, then the slightly speculative domain of human behavior and finally our domain of project management.

The connections include:

- Instability
- Emergent stable behavior
- Non-linear stable behavior

Terms often found in project management. The question is

Where are the families of non-linear partial differential equations?