The term “critical” in mathematics and physics relates to or denotes a point of transition from one state to another. These critical points before a transition are studied within the domain of nonlinear dynamics called catastrophe theory. Catastrophe theory studies dramatic changes within the system’s topology, the most famous of which being what is called the cusp curve where the topology dramatically folds back on itself, creating a cliff-like structure.
A system is said to be critical if its state changes dramatically given some small change in an input value to a control parameter. Once the system reaches its critical point, even the smallest perturbation can have major consequences and it becomes uncontrollable. As the system grows more critical, its eventual collapse becomes greater and its eventual transformation becomes more inevitable; but less predictable. Collapse is inevitable as any small event can trigger it at this stage; since it is in this critical state and so many small events can trigger the transformation, we do however not know exactly which one or when it will eventually do so.
Beyond the critical point we get some runaway effect, a tipping point has been passed and the system moves into a phase transition. As it is now irreversibly moving into a new state, at this stage the system becomes extremely nonlinear, cause and effect break down almost completely and massive direct interventions within the system can have very negligible effect. For example, a government can put billions into the market buying up toxic assets and only have a negligible effect on the price level. Because the failure is distributed out and any small event can trigger a large systemic effect, there is no real possibility for control in this situation. Instead, previously unknown interconnections and interdependencies become revealed and random events can determine significant outcomes.