How can we model the dynamics of a human community, or a business ecosystem as a complex adaptive system ? I believe the basic understanding and tools needed for deal with these tasks have been already developed in other disciplines (such as Physics and Mathematics). Most probably what is required is a just a critical cross-fertilization and re-interpretation of achievements in order to make them applicable to another context (apparently far away). Let me make an example.
Symmetries in the Alhambra Palace, Granada
Think about symmetry, which is playing a key role in our understanding of Nature. Mathematically speaking, symmetry is characterized by the invariance of some mathematical object under some transformation. For example, a parabola y=x² is symmetrical with respect to the y-axis, since it is invariant under the transformation that takes the variable x and transforms it into –x.
In physics, mathematical symmetries imply conservation laws: for instance, translation invariance implies momentum conservation, while rotational invariance implies angular momentum conservation.
Symmetry breaking is an amazing phenomenon in Nature.
There are two types of symmetry breaking: explicitly and spontaneously. To understand the difference in simple terms, let us imagine that we are watching a group of people in a square downtown in Turin. People will be walking in random directions, with local aggregation patters. Now suppose that someone on the first floor of a building in the square starts to do something spectacular, then people will all look in the same direction, eventually moving in the direction of that building. This is an example of explicit symmetry-breaking: an action external to the behavior of people in the square makes all of them to behave in the same way. Coherency emerges as a result of the symmetry breaking. It’s the same principle of the laser!
Spontaneous symmetry-breaking is more subtle. Imagine that a single person, for example in the center of the square, walking randomly among the people, suddenly stops and starts simply to look up the sky in a very curious manner. When someone else notices this, stops and looks up. This induces others. Symmetry-breaking it emerges out of the interactions of the people in the square. It’s easy to detect similar dynamics in social communities, like Facebook for example. A trend-setter – someone who popularizes a new fashion – is creating a symmetry breaking.
In Physics, spontaneous symmetry breaking is an even more general principle at the basis of a vast number of physical phenomena, ranging for example from ferromagnetism to superconductivity. Also, in the context of the physics of elementary particles, spontaneous symmetry-breaking provides a mechanism by which the masses of particles are generated.
So, it is amazing recognizing these universal characteristics of symmetry breaking: from classical to quantum physics, from biology to social dynamics analysis, to future Internet architectures (e.g. in IoT and IwT): whenever there is a sheers number of interacting entities, from particles to objects to people. At the end of the day, a new fashion, or a new business could be seen as symmetry breaking events in markets fluctuating around steady states. Importance of understanding these principles is great.
Let’s go further with this analogy. Think about the Goldstone theorem. The theorem is arguing that massless particles (Goldstone bosons), generated at the spontaneous breakdown of symmetry, which are crossing the quantum system: capturing the nature of these emergent bosons, how many of them are generated in the symmetry breaking, and their dynamic propagation would allow us to understand the behavior of the system during the symmetry breakdown. One may ask “is there an equivalent of the Goldstone boson concept in an ecosystem , in a social community, or in a market” ? I suspect so: symmetry breakings are based on universal principles, so the mathematical laws behind their instances are very much the same!