### CHAPTER 19

### COMBING THE HAIR ON A COCONUT

*Let chaos storm!Let cloud shapes swarm!I wait for form*.—Robert Frost, “Pertinax”^{1}

Many scientists use mathematics as a tool to predict behavior. A scientist may have an equation or a system of equations that describes the interactions of the quantities in their model. Then they use mathematics to draw conclusions from these equations.

Often the mathematical models are *differential equations*. These describe the rates of change of various quantities as a function of time. For example, an ecologist might use a system of differential equations to model the population dynamics of rabbits and foxes living in a wildlife refuge driven by their predator-prey relationship. When the number of rabbits is large, the ...