Our focus here is on nonlinearity. Many complex systems, including markets, have critical points where small incremental condition changes lead to large-scale effects. Researchers in both the physical and social sciences have known about these critical points for a long time; so much so that terms like phase transition and tipping point have slipped into our day-to-day language. Still, critical points throw a monkey wrench into our mostly linear cause-and-effect thinking.
Critical points help explain our perpetual surprise at fat-tail events: We don’t see them coming because the state change is much greater than the perturbation suggests. Water does not undergo a dramatic change as it drops from 35 to 33 degrees Fahrenheit, but two degrees of additional cooling changes its state from liquid to solid. Likewise, large changes can occur in markets without visible manifestation in asset price change, while small additional changes can flip the price switch.
Critical points are also important for proper counterfactual thinking. For every critical point we do see, how many were lurking but never triggered? Like water temperature dropping to 33 degrees and again rising, there are likely many near misses in the markets that elude our detection.