Early in the 1980’s there was a lot of enthusiasm about the emerging science of * Chaos Theory*. Chaos appeared to be answering questions no one had previously ever thought to ask.

Many thought that Chaos Theory might be *“The Next Big Thing”*; if Relativity Theory and Quantum Theory were the sciences of the 20^{th} century, then Chaos Theory and its cousin ** Complexity Theory** were to be the sciences of the 21

^{st}century.

Some thirty years on however, and this enthusiasm has waned somewhat; and while Chaos may have provided some interesting insights into many different and diverse scientific disciplines, it most definitely has failed to live up to, or even come close to, its initial high expectations.

Good science is essentially about simplifying complexity. It is about showing that each bit of seemingly unrelated complexity is in fact just a unique realization of some more general underlying simplicity.

Good reductive science however has proved somewhat difficult for both Chaos Theory and Complexity Theory. Much of the reason for this difficulty can be attributed to the fact that despite all that has been written on these subjects (and the many related areas) there has never materialized, from all of this work, a clear and simple unifying theme…

Chaos and Complexity are certainly perceived to be related — different yet in some way similar — but the lack of a unifying theme is likely due to the fact that both subjects have proved a little too hard to pin down and precisely define. The generally accepted comparison between the two is usually something along the lines of:

*“Chaos is a form of Complex Behavior that can arise in Simple Systems”**“Complexity is a form of Simple Order that can emerge in Complex Systems”*

Theses definitions are acceptable (if somewhat vague) but unfortunately they fail to capture the vital essence of both, and Chaos in particular.

Failing to capture the essence of Chaos, has meant that not only has it not fulfilled its full scientific potential, but on the contrary, it has been over the years virtually relegated to the status of mere mathematical curiosity.

I hope herein to reverse the misfortunes of this underestimated gem of mathematics. My goal is to try and shed some light on the vital essence of both Chaos and Complexity; and in so doing, I hope to reveal that although these fields are different, they are nonetheless very similar; for they are not different as in opposites, but merely* different manifestations of the same unifying underlying behavior* : a behavior that could be described as *“coarse relaxation”* or *“coarse stabilization”,* but probably best described as

*“Coarse Damping”.*

*“Damping”* is a term used in engineering to describe the elimination of unwanted vibrations and fluctuations in a system. Damping usually involves the external dissipation of excessive energy.

Chaos and Complexity however are not about the *external dissipation of energy;* on the contrary they are about the *internal distribution of energy.*

Chaos is about the coarse internal synchronization of competing forces which pull a system spontaneously to various forms of ** “complex behavioral equilibrium”**; and Complexity is about the internal dissymmetry/imbalance of parts, within a system, which pulls the system as a whole spontaneously to a

**.**

*“complex structural equilibrium”**So Chaos and Complexity are indeed related…*

**Chaos is a form of coarse damping in “time”:**it is short-term asynchronicity within long-term synchronicity.**Complexity is a form of coarse damping in “structure”:**it is local imbalance with global balance.

**Chaos is “Coarse Synchronicity”.**

**Complexity is “Coarse Entropy”.**

**Coarse Synchronicity:**A tendency to resist the gravitational pull of a finely-tuned, highly synchronized but fundamentally bland and stable equilibrium.**Coarse Entropy:**A tendency to resist the gravitational pull of a finely-tuned, highly symmetric, but fundamentally bland and featureless equilibrium.

**So why is any of this important?**It is important because equilibriums are everywhere. In nature, everything is some sort of system; and all natural systems spontaneously tend towards some form of equilibrium.

Mathematical Chaos shows us that there is however more to equilibrium than meets the eye. Equilibrium, it turns out, is not always so easy to fine-tune to, and so can come in **many “coarse” forms…**