Imagine a student who plans in advance that every Tuesday will be for algebra, every Thursday for computer science, and every Friday for a girlfriend or boyfriend – and sticks to this schedule for the entire semester. That is a rigid plan. In contrast, a student who decides each day what is worth doing – algebra, computers, or perhaps spending the whole day with a partner – is using feedback.
This lecture is a kind of mathematical theater, designed to popularize a model of catching fish in a lake, taken from V.I. Arnol'd's masterpiece Catastrophe Theory. The model demonstrates the advantages of optimization by feedback over a rigid plan. I have added detailed calculations and explanations. Alongside the fishing example, the lecture also includes the dynamics of love between two young people, B and G. Of course, fish and love can be replaced by money, politics, health, or anything else – without exception.
You don't need to be a mathematician to realize that feedback is far better than a rigid plan. But in many situations, it is hard to accept this truth. The mathematical theater may help.
Those with no mathematical background will understand a large part of the lecture. Those who know basic facts about autonomous first‑order ordinary differential equations will understand everything.