A random walk on water (Henry Darcy Medal Lecture)

According to the traditional notion of randomness and uncertainty, natural phenomena are separated into two mutually exclusive components, random or stochastic, and deterministic. Within this dichotomous logic, the deterministic part supposedly represents cause-effect relationships and, thus, is physics and science (the “good”), and randomness has little relationship with science and no relationship with understanding (the “evil”). We can argue that that such views should be reconsidered by admitting that uncertainty is an intrinsic property of nature; that causality implies dependence of natural processes in time, thus suggesting predictability; and that even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon. With these premises it is possible to shape a consistent stochastic representation of natural processes. In such a representation, predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components. Deciding which of the two dominates is simply a matter of specifying the time horizon of the prediction.