Chaos – 101

Over the last 15 or 20 years or so “Chaos Theory” has found itself pretty much relegated to the minor leagues of science, even to the point of being considered by some as nothing more than an “over-hyped mathematical curiosity”.

Chaos theory as it stands today is a bit of a mishmash of concepts and doesn’t really have an agreed upon definition, but is generally associated with so-called “Butterfly Effect” (or as the academic community like to say “sensitive dependent on initial conditions”).  This association has, in my opinion, done more harm than good for it is misguided, and its misdirection has merely served to mask the true nature of chaos.

In my opinion chaos is not primarily characterised by sensitivity to initial conditions; but by emergence of decisions points and the resultant sensitivity to choice.  Chaos is simply “adaptive instability”; it is “unresolved internal adaptation to feedback, surfacing as turbulent diversity on the system level”.  So, in the simplest possible terms, we could say that

“Chaos is Incompressible Adaptive Diversity”…


The Demise of Chaos

Back in the 1980’s many thought that the “new” science of 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 close cousin Complexity Theory were to be the sciences of the 21st century.  But by the end of the 20th century however, this enthusiasm had waned somewhat; and while Chaos may have provided some interesting insights into many different and diverse scientific disciplines, it most definitely failed to live up to its earlier high expectations.

The reason for the “Demise of Chaos” was most likely because despite the vast quantity of articles and books written on the subject (and many related subjects) there never materialized, from all this work, a clear and concise understanding of what chaos theory is actually all about.  And so over the last 15 or 20 years or so chaos theory has found itself pretty much relegated to the minor leagues of science, even to the point of being considered by some as nothing more than an “over-hyped mathematical curiosity”.

But this belief is way off the mark. For despite the fact that nobody seems to have picked up on it,  “Chaos Theory” has, for almost 50 years now, been hinting at the “universality of incompressible dynamics”…

Compressible Dynamics

Physics is the ultimate science of deterministic cause and effect.  Physicists like to build “models” of the real world.  The power of physics relies on the fact that we can compress real-world behaviour into a “mathematical” model.  Sometimes these models are unbelievably concise, and can be written as a single equation in linear-form, and when this happens we confidently call the model a deterministic “Law of Physics”.

So physics is the science we have come to rely on to explain and predict the behaviour of the universe, but as it turns out physics fails miserably when it comes to dealing with deterministic chaos and nonlinear dynamics…


Linear Dynamics

Physicists like to describe their science as the hardest of “hard science” because physics can claim to be governed by hard and fast scientific “Laws”.  This of course would seem to imply that many of the so-called “soft sciences” are in some way not quite as elevated, not quite as good.

In truth however we could say that physics is an “easy science”, and the soft sciences are “difficult” because, unlike physics, these so-called soft  sciences have to deal with our everyday messy world where most things are continually battered and buffeted by “constantly changing feedback” which can generate wild “nonlinear dynamics”.

In reality all dynamics have feedback (and resultant nonlinearity), it is just that some dynamics have much less feedback than others.  Physics is, in a sense, the science of “dynamics with negligible feedback”, the science of “linear dynamics” — or in other words it is the science of the nonlinear stuff that can be safely “compressed into neat linear mathematical cause and effect”.

[Note: In the simplest possible terms, linear dynamics are dynamics where the effect is proportional to the cause, and nonlinear dynamics are where the effect can be disproportional to the cause]

Incompressible Nonlinear Dynamics

It could be said that throughout its 400 years history physics has actively avoided dealing with non-linearizable nonlinear dynamics, because these dynamics with excessive amounts of feedback are messy, and mathematically incompressible.

Unfortunately however most of the really interesting stuff in the 21st century will likely deal with complex systems which exhibit incompressible dynamics and are therefore unpredictable.  And so while we might like to build a mathematically predictive model of economics, we cannot because of its incompressible dynamics.  And although we might want to build a mathematically predictive model of the climate, we will not be able to because of its incompressible dynamics.  And maybe we might even want to try to build a mathematically predictive model of evolution, but this will not happen because of its incompressible dynamics.

The Power of Incompressible Dynamics

In deterministic physics we are used to the idea that the present determines the future and a slightly different present determines a slightly different future.   In deterministic chaos however, while the present still determines the future, a slightly different present determines a very different future, due to the presence of incompressible dynamics.

Complex systems are unpredictability because the presence of feedback means we cannot take mathematical shortcuts into the future; to know where the system is going — even in the short to medium term — we must literally compute each individual step (in order to determine what effect feedback and adaptation is having on the system’s evolution).

But just because all complex systems are mathematically incompressible does not mean that they are completely unpredictable.  Chaos Theory alerts us to a mathematical universe previously hidden from our awareness; a universe of nonlinear attractors. This suggests that some dynamics and behaviours are more likely than others which further suggests there is a degree of universality in the emergent behaviour of complex adaptive systems — behaviour that cannot be reduced to linear cause and effect, but behaviour that is to be expected nonetheless…