The “Wobble” Breaks Through Previous Theories (Mid-1970s)

The three preceding theories can only manage stable distributions; this chapter looks into the issue of unstable distributions. For stable distributions, risk estimates and their confidence intervals can be assumed to merge at infinity. However, for “unstable” distributions, those with infinite variances, risk estimates may “wobble.” This chapter will therefore address the key question of bridging the gap between the infinite population assumed by probability and statistics with the finite samples of experience. This chapter contains a discussion of catastrophe (“stability”) measures and their relationship to power laws. Power laws are a simplified means to show how estimating risk to systems can be cognitively dangerous if only because the systems themselves as studied can be very “fragile,” or unpredictable. So, while it may be obvious that in science various “shocks” may be very challenging to predict, it may also be true that nonlinear behavior in systems can make evaluation of risk to these systems cognitively challenging, if not dangerous.