Nonlinear systems, however, are not so well behaved. 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.”