Bifurcations
The moment at which a system may go two ways, and one of the concepts underlying what in practice we sometimes call a ‘tipping moment’.
A bifurcation usually stands for a branching point: a moment in the dynamics of a system at which it could go two (or more) ways. Which way it eventually goes depends on a combination of factors, some of which we cannot always oversee well.
The distinction between a phase transition (see that entry) and a bifurcation is subtle, but useful. A phase transition usually refers to the change itself: water freezing, a depression going into remission. A bifurcation refers rather to the point at which such a change becomes possible, with more than one possible direction.
An image that may help here is that of a small stream flowing down a slope and meeting a boulder. The water has to pass it on the left or on the right. Which side it takes depends on small differences: a millimetre more or less, a twig in the way, the precise shape of the bed. In this image the boulder marks the bifurcation. Beyond it, two streams flow on, each with a course of its own.
Bifurcations in a human being
In a person's life we often recognise bifurcation points in hindsight. A choice that seemed small at the time later turns out to have been a turning point. Someone who says "if I had not chosen that degree" or "if I had not met her that evening" is describing, in everyday language, something that resembles a bifurcation: things could have turned out differently.
In a psychiatric context the idea appears, among other places, in research on transitions between states: from working to sick leave, from laborious recovery to sudden gains, from stability to relapse. In time series, precursors can sometimes be seen before such a transition becomes clinically visible: variance increases, autocorrelations shift, and the system seems to 'hesitate' between two possible states.
Bifurcations have ‘control parameters’
In the mathematics of complex systems, every bifurcation has a control parameter: a quantity whose change determines whether the system is approaching a branching point. A well-known example is the logistic equation, a simple formula that, depending on a single parameter, shows calm, periodic or chaotic behaviour.
In people, control parameters are harder to name unambiguously. The idea nevertheless remains useful: there are often a few underlying factors, such as sleep, daily rhythm, social connectedness, physical health or hormonal state, that help determine how stable someone is and how close to a branching point. Some interventions can then be understood as attempts to influence those control parameters rather than the symptom directly.
A small caution
It is tempting to call every important moment in someone's life a bifurcation, but in doing so the concept loses its meaning. In the technical sense, a bifurcation is the point at which the behaviour of a dynamic system changes qualitatively, for instance because instead of one stable state, two or more become possible. To recognise this in people, we depend on measurements as well as on stories.
For the consulting room the concept has another advantage: it is a reminder that change does not always proceed gradually. Sometimes a person balances on a narrow edge for a while, and then things tip. Often in the direction in which the system has already invested most, but certainly not always.