Complex systems do not act like simple or even complicate systems.
"They can appear stationary for a long while, then without anything changing, they exhibit jumps in variability—so-called “heteroscedasticity.” For example, if one looks at the range of economic variables over the past decade (daily market movements, GDP changes, etc.), one might guess that variability and the universe of possibilities are very modest. This was the modus operandi of normal risk management. As a consequence, the likelihood of some of the large moves we saw in 2008, which happened over so many consecutive days, should have been less than once in the age of the universe.
Our problem is that the scientific desire to simplify has taken over, something that Einstein warned against when he paraphrased Occam: “Everything should be made as simple as possible, but not simpler.” Thinking of natural and economic systems as essentially stable and decomposable into parts is a good initial hypothesis, current observations and measurements do not support that hypothesis—hence our continual surprise. Just as we like the idea of constancy, we are stubborn to change. The 19th century American humorist Josh Billings, perhaps, put it best: “It ain’t what we don’t know that gives us trouble, it’s what we know that just ain’t so.”
So how do we proceed? There are a number of ways to approach this tactically, including new data-intensive techniques that model each system uniquely but look for common characteristics. However, a more strategic approach is to study these systems at their most generic level, to identify universal principles that are independent of the specific details that distinguish each system. This is the domain of complexity theory.
Among these principles is the idea that there might be universal early warning signs for critical transitions, diagnostic signals that appear near unstable tipping points of rapid change. The recent argument for early warning signs is based on the following: 1) that both simple and more realistic, complex nonlinear models show these behaviors, and 2) that there is a growing weight of empirical evidence for these common precursors in varied systems.
A key phenomenon known for decades is so-called “critical slowing” as a threshold approaches. That is, a system’s dynamic response to external perturbations becomes more sluggish near tipping points. Mathematically, this property gives rise to increased inertia in the ups and downs of things like temperature or population numbers—we call this inertia “autocorrelation”—which in turn can result in larger swings, or more volatility. In some cases, it can even produce “flickering,” or rapid alternation from one stable state to another (picture a lake ricocheting back and forth between being clear and oxygenated versus algae-ridden and oxygen-starved). Another related early signaling behavior is an increase in “spatial resonance”: Pulses occurring in neighboring parts of the web become synchronized. Nearby brain cells fire in unison minutes to hours prior to an epileptic seizure, for example, and global financial markets pulse together. The autocorrelation that comes from critical slowing has been shown to be a particularly good indicator of certain geologic climate-change events, such as the greenhouse-icehouse transition that occurred 34 million years ago; the inertial effect of climate-system slowing built up gradually over millions of years, suddenly ending in a rapid shift that turned a fully lush, green planet into one with polar regions blanketed in ice."
I'm not sure about our ability to find early warning signs in complex systems. Right now to me these attempts remind me of people trying to find ways around the second law of thermodynamics. People were always inventing perpetual motion machines only to have scientists eventually point out the flaw in the machine. Many people refused to believe that nature was so perverse as to not be completely reversible. (See note at end.)
I'm not sure that it's reached the state of a law of complex systems but it sure looks like one: that the future state of a complex system cannot be be predicted. That destroys everything that we thought we knew about logical determinism.
Note: The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and explains the phenomenon of irreversibility in nature. The second law declares the impossibility of machines that generate usable energy from the abundant internal energy of nature by processes called perpetual motion of the second kind.