  This chapter first presents a rather personal view of some different aspects
of predictability, going in crescendo from simple linear systems to
high-dimensional nonlinear systems with stochastic forcing, which exhibit
emergent properties such as phase transitions and regime shifts. Then, a
detailed correspondence between the phenomenology of earthquakes, financial
crashes and epileptic seizures is offered. The presented statistical evidence
provides the substance of a general phase diagram for understanding the many
facets of the spatio-temporal organization of these systems. A key insight is
to organize the evidence and mechanisms in terms of two summarizing measures:
(i) amplitude of disorder or heterogeneity in the system and (ii) level of
coupling or interaction strength among the system's components. On the basis of
the recently identified remarkable correspondence between earthquakes and
seizures, we present detailed information on a class of stochastic point
processes that has been found to be particularly powerful in describing
earthquake phenomenology and which, we think, has a promising future in
epileptology. The so-called self-exciting Hawkes point processes capture
parsimoniously the idea that events can trigger other events, and their
cascades of interactions and mutual influence are essential to understand the
behavior of these systems.
