Chaos Theory
and The Butterfly Effect
An angry sea today The waves not so much cresting as erupting
When Edward Lorenz capsulized Chaos Theory, surely, surely, he must, like me today, have been contemplating a large angry water.
Wiki word has it that Chaos Theory is that branch of mathematics that studies chaos (actually: apparent chaos) — i.e., states of dynamic systems whose apparently-random states of disorder and irregularities are often (as in always) governed by deterministic laws that (while extremely hard if not impossible to detect in their entirety) are (just like life) highly sensitive to each and every minute initial condition.
More specifically, Chaos Theory states that, within the apparent randomness of chaotic complex systems (like a raging sea), there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, self-organization and so on.
The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, meaning that each state is always sensitive to and dependent on initial conditions.
A metaphor for this behavior is that a butterfly flapping its wings in China can cause a hurricane in Texas.
Hence, small differences in actual versus estimated initial conditions, such as those due to minute errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior pretty much impossible. This can happen even though these systems are deterministic, meaning that their future behavior does follow a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems rarely if ever makes them predictable.
This behavior is known as deterministic chaos, or simply chaos.
Or as Lorenz puts it: “When the present determines the future, but the approximate present does not approximately determine the future, we’re looking at Chaos.”
He elaborated: “Two states differing by imperceptible amounts may eventually evolve into two considerably different states. If, then, there is any error whatever in observing the present state — and in any real system such errors seem inevitable — an acceptable prediction of an instantaneous state in the distant future may well be impossible.
“Accordingly, in view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent.”
In other words, the actual and precise present state of things does indeed determine their future, but not in ways that we can easily (if at all) observe or predict.
Well, let’s put it another way: our powers of observation and attention span, when it comes to a trillion, trillion, trillion microscopic details, are not up to tracking the near infinite number of infinitesimal details that interact and cause-and-effect each other to the larger future outcome.
The Pacific Ocean during a storm is as good an example as any.
Another case in point is the Buddhist concept (and posited law) of Dependent Origination, along with the concept and workings of Karma.
Both Dependent Origination and Karma deal with Cause and Effect; with Causes and Effects; with many, many — trillions, trillions, and yet more trillions of trillions of minute, in every microscopic moment, Causes and Effects. No human can spot and track and predict them all and those who try usually resort to the usual suspect: the scapegoat infinity. But the causes and their effects are not infinite. They are near enough to infinity to confound even the widest and most unusually accurate and detail-oriented mind, but it’s as far from that far horizon to infinity as from zero, or right here, to infinity.
Chaos is, of course, just our word for insufficient attention to detail.
Yet another case in point is the Physical Universe as a whole. Lots of confounding causes and effects at play, constantly, simultaneously, ever and ever.
Let me just add that if all causes and their effects were easy to trace and track, we’d have untangled this universal mess (Samsara) long ago: it’s the intricacies and our inability to trace it all back to the beginning that keeps it running, us — all apparently helpless — in it.
Had we the attention span and eye for detail of, say, God, there would be no Chaos Theory, there would be just Theory. No Chaos, just…
Oh, well.
© Wolfstuff
