Chaos
A deterministic system that, through its sensitivity to initial conditions, becomes unpredictable in the long run.
In everyday speech, chaos usually stands for disorder. In mathematics and physics it means something else, and it is worth guarding that distinction, because otherwise the term easily seems to apply to almost anything.
A chaotic system in the technical sense is usually described as a system that is deterministic (the laws are fixed) and at the same time may, in practice, be unpredictable. This is not because we do not know the laws, but because the system is so sensitive to its initial conditions that a very small deviation at the start leads to widely diverging outcomes further on in time.
The meteorologist Edward Lorenz discovered this by accident in 1961. He was running a weather simulation on his computer and wanted to repeat part of it. To save time, he entered his initial values to three decimal places instead of the original six. He expected a comparable result. He obtained a course of weather that, after a few simulated days, was entirely different: the small rounding had grown into different weather. Lorenz later spoke of the butterfly effect, with the familiar image of a butterfly in Brazil whose wingbeat could, in principle, set off a tornado in Texas.
What chaos is not
Chaos in this sense is not disorder. A chaotic system has structure: it moves on an attractor, a region in the dynamics within which the system remains. The Lorenz attractor has the shape of two connected loops, reminiscent of the wings of a butterfly. Exactly where the system is at a given moment cannot be predicted precisely, but the shape of the attractor itself is fixed.
Chaos could therefore be called a form of structured unpredictability. We know roughly within which bounds the system moves, but not when it will be where.
And in the psyche?
Whether human functioning is truly chaotic in this technical sense remains, for now, an open question. Some studies find indications in EEG data, heart rhythm and mood time series. It is, however, difficult to distinguish chaos in the strict sense from noise, particularly in short and imprecise measurements. When the word chaos is used, it therefore sometimes really means that we do not yet understand something well.
What does seem useful to us is the realisation that even simple psychological systems can behave in such a way that precise prediction is hardly possible. This need not be due only to a lack of knowledge; it can also follow from the nature of the system. That may have a few practical consequences.
Three practical consequences
First: if a patient's system has chaotic properties, we cannot, in all honesty, give an exact answer to the question of what will happen tomorrow. We can, however, indicate within which bounds it is likely to move.
Second: small interventions may, in the longer term, have unexpectedly large consequences, or none at all. This may make timing as important as dosage.
Third: an erratic time series does not in itself say something about the patient; sometimes erratic behaviour is a property of the system. That calls for a different way of looking at patterns rather than for filtering out as much noise as possible.
Chaos in the mathematical sense is a useful concept, but for what we see in the consulting room it is a reason for caution rather than an explanation: what is deterministic need not be linearly predictable.