Home Page

One of my favorite quotes is, “If I had more time I would have written a shorter letter”.  The beauty of this statement – often attributed to Mark Twain but more likely to have been Blaise Pascal – is in its self-referential brevity and simplicity.  The point is very clear.  Brevity and simplicity are very hard to do!

Early in the 1980’s there was a lot of enthusiasm about the emerging science of Chaos Theory.  Chaos appeared to shed some light into previously unexplored areas of science.  Many thought that Chaos Theory might be the “Next Big Thing”.  If Relativity Theory and Quantum Theory were the sciences of the 20th century, then Chaos Theory and its cousin Complexity Theory were to be the sciences of the 21st century.

Some thirty years on however and this enthusiasm has waned somewhat and while Chaos may have seeped into many scientific disciplines, it most definitely has failed to live up to its initial hype!

Much of the reason for this failure can be attributed to the fact that despite all that has been written on Chaos Theory and Complexity Theory and the many obviously related areas (such as Nonlinear Dynamics, Control Theory, Systems Theory, Game Theory, Network Theory, Fractals, Self-Organization, and Emergence) there has never materialized, from all of this work, A Clear and Simple Unifying Theme that answers the questions:

  1. “What is the connection between these related fields that gives a clear and simple explanation of how they all fit together?”
  2. “What is the relevance of Chaos Theory and Complexity Theory to daily life?”
  3. “What do Chaos Theory and Complexity Theory tell us about the behavior of the universe at large?”

Writing a shorter letter is, of course, what’s difficult about science.  Good science is essentially about simplifying complexity.  It is about being able to bring apparently unrelated concepts and aspects of reality under the same umbrella.  It is about showing that each bit of seemingly unrelated complexity is in fact just a unique realization of some more general underlying simplicity.

Chaos and Complexity, for example, are not only perceived to be different yet in some way similar, but also a little too ubiquitous, too mercurial, too hard to pin down and precisely define.  The generally accepted comparison between the two is something like:

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 fail to capture the real juice of the matter.

Failing to capture the juice has meant that Chaos Theory not only has not fulfilled its full potential, but has, to a certain extent, over the years been relegated to the status of mathematical curiosity.

My goal is to reverse that relegation by simplifying the somewhat misleading current understanding of Chaos Theory and Complexity Theory and in so doing reveal that although these fields are indeed different yet similar, they are not different as in opposites, but merely different manifestations of the same unifying behavior that I refer to as

  • Coarse Damping:  spontaneous internal self-balancing process, that is unable to stabilize to a finely-tuned equilibrium, because of the system’s inability to micro-adjust.

Why is this important?  Well it is important because equilibriums are everywhere!  Equilibrium is a concept central not only to physics, but also chemistry, biology, physiology, psychology, epidemiology, ecology, climate, evolution, markets, economics, politics, and even war.  Equilibriums are ubiquitous, and the degree of coarseness in damping to equilibrium determines the degree of stability or instability in all of these systems.

Whether it be a quantum mechanical system or a solar system, the ecosystem or the economy, global politics or global climate, the spreads of ideas or the spread of infectious disease, all systems and networks can experience degrees of difficulty stabilizing to equilibrium, and in all of these cases we will find that the degree of coarse damping is always the reason.

But don’t be alarmed, the inability to fine-tune to stability, is not always a bad thing!  The inability to stabilize – to lock-in to one equilibrium – is what evolution leverages to ensure the Emergence of Diversity, and thereby ultimately to all the complex wonders of nature that we witness all around us.

Chaos Theory is the Mathematics of the Emergence of Diversity.  My aim herein is to reveal what it is about the simple inability to converge some simple mathematics into nice round numbers that explains the emergence of all things, and convince you the reader that this understanding elevates Chaos Theory from mere curiosity to the status of being a Universal Theory and its rightful position of Meta-Science: The Science of all Sciences…

Einstein once said “If you can’t explain it simply, you don’t understanding it well enough”.  Chaos and Complexity are undeniably complicated but I believe I understand them well enough.

Here is a short letter on:  What is Chaos Theory?

Here is a short letter on:  What is Complexity Theory?