“If I had more time I would have written a shorter letter!” The beauty of this famous quote 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 be answering questions no one had ever previously 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 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 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!
Writing a shorter letter is, of course, what’s difficult about science! 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.
Writing a shorter letter has proved 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 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 interrelated in some way; 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, but Chaos in particular!
Failing to capture this vital essence of Chaos, has meant that not only has Chaos Theory not fulfilled its full potential, but on the contrary, it has been over the years virtually relegated to the status of mere mathematical curiosity.
My goal is to reverse the misfortunes of this misunderstood gem of mathematics. My aim is to bring to light the vital essence of both Chaos Theory and Complexity Theory; and in so doing, I hope to reveal that although these fields are different, they are yet indeed similar; for they are not different as in opposites, but merely different manifestations of the same unifying underlying behavior : a behavior that could be best described as “Coarse Damping” to equilibrium!
- Coarse Damping: A tendency to resist the gravitational pull of a finely-tuned, highly symmetric, but fundamentally bland and featureless equilibrium.
So why is this important? It is important because equilibriums are everywhere; and Chaos Theory shows us that there is more to equilibrium than meets the eye!
Equilibrium is a concept central to physics, chemistry, biology, physiology, psychology, epidemiology, ecology, climate, evolution, markets, economics, politics, and even war. Equilibriums are a central concept to systems of all sorts; and practically everything in the universe is both a system in itself, and part of a larger system in some form or other!
So, 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 experience degrees of difficulty settling down to a stable equilibrium, and in all of these cases we will find that it is the degree of coarseness in the damping to equilibrium that that determines the system’s degree of equilibrium stability!
The inability to fine-tune to equilibrium, however, is not always a bad thing! Complexity Theory shows us that coarsely damped structures are central to the emergence of all things!
So as it turns out, the ability to resist absolute uniformity – to resist the pull of bland featureless equilibrium – is what Mother Nature leverages, to ensure the Emergence of Diversity, and the nature’s Progressive Evolution to ever greater Complexity!
Chaos Theory is the mathematics of emergent diversity; it is the coarse mathematics of progressive evolution!
My aim herein is to reveal what it is about some very simple mathematical ideas, that explains the emergence of all things; and in so doing will hopefully convince you the reader that this understanding elevates Chaos Theory from mere curiosity to its rightful position more akin to A Universal Theory; A 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 both well enough to write:
A short letter on: What is Chaos Theory?
A short letter on: What is Complexity Theory?