Many in the Agile community like to use words like *Self Organizing,* *Emergent*, *Complexity,** *and *Complex Adaptive Systems,* without actual being able to do the mathematics behind these concepts. They've turned the words into platitudes. This is the definition of *popularization* - a core idea from science and mathematics (physics many times) without the math.

These popularizations, spawned a small industry of using the words in ways no longer connected with the actual mathematical model of self organizations, complexity, complex adaptive systems, and emergence of the underlying simplicity into a complex outcome.

There is a pop-psychology approach to core mathematics and the physics of complex systems as well.

Self Organization requires several conditions for it to be in place and be observed

- A High Degree of Structure
- The capacity for coordinated action
- A mechanism for system-wide feedback and amplification
- Some means to transform a small event into a larger driving force for the system to
*organize*itself into a coherent system

The key is coordination across boundaries and the capacity for action. This implies - quite explicitly - a deterministic response to external stimulus. The self-organization properties require structured communication channels to be in place for the systems to posses this property.

So next time you hear *self organizing teams are the best* ask to see what structures are in place to provide the channels for coordinated actions. What mechanisms are being used for system-wide feedback within that highly structured process framework, and what are the means of transforms small - potentially very small stimuli - into the collective actions of the whole?

In the broader sense, these concepts all live in a world *governed *in a deterministic manner through...

- Feedback - the return of a portion the output of a process or system to the input. These means modeling the transform function - usually G(S), where S is the system dynamic model, and G is the transform function. Both can be represented by non-linear differential equations
- System Dynamics is the next level of modeling for the
*structured, coordinated, system-wide feedback and amplification*(both positive and negative). - This involves
*state-space*modeling or*phase space)*where an abstract space - a mathematical model of in which all possible states of a system - are represented, with each possible state of the system corresponding to one unique point in the state space. Dimensions of state space represent all relevant parameters of the system. For example state space of mechanical systems has six dimensions and consists of all possible values of position and momentum variables. - The Trajectory of the system describing the sequence of system states as they evolve.
- A fixed point in the state space where the system is in equilibrium and does not change. In complex projects and systems they represent, this is the
*steering signal*needed to compare the feedback to so corrective actions can be taken by the system to maintain equilibrium and run off the cliff. - The Attractor is a part of the state space where some trajectories end.
- The actual dynamics of the system - where the set of functions that encode the movement of the system from one point in the state space to another. This is the foundation of the mechanism for feedback and structuring of the disconnected components of the system. These dynamics are many times modeled with sets of differential equations containing the
*rules*for the interactions.

The complex part of complex systems is the subtle - and poorly understood without the mathematics - property, that a deterministic system can have *emergent *and *very different* outcomes from the sensitivities of the starting conditions.

The double pendulum is a nice example. The equations of the Double Pendulum are a classic two year physics student problem. My introduction to FORTRAN 77 was to code the solution to the Double Pendulum problem in the Dynamics course.

Or maybe that person is just fond of using words they don't actually know the meaning of - at the mathematical level. As a classic example *self organizing *is defined (first used by William Rose Ashby in 1948) as the ability of the system to autonomously (without being guided or managed by an outside source) * increase* its complexity. So when we hear self-organizing is good, the system we're applying it too is getting

*complex without any external guidance. Wonder if that's what we actually wanted.*

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