In his final lecture Christopher Zeeman introduces his young audience to the fundamentals of Catastrophe theory, in which we learn how gradually changing variables can produce sudden effects.
Moving from a simple model with one variable, up to situations involving thousands, Zeeman illustrates how catastrophe theory can plot states of stable and unstable equilibria across a three dimensional surface. These multidimensional surfaces categorised as 'elementary catastrophes' visualise the point at which a system can shift suddenly from one state of equilibrium to another.
We are then introduced to how this field of mathematics can be extended into the world of physics, in particular to the study of light caustics (the bright patterns of light in rainbows, or rippling along the bottom of swimming pools) and astronomy.
Finally Zeeman turns his attention to the field of psychology, where catastrophe theory is being used to model changes in mood, attention and decision making, specifically in the ‘fight or flight’ response. It is here that he hopes mathematics will aid science in reducing the ‘arbitrariness of description’.
Sir Christopher Zeeman