> Morse theory is basically the toy case of a very general way of thinking about Lagrangians / Energy landscapes in physics. You can think of the Morse function

> Morse theory is basically the toy case of a very general way of thinking about Lagrangians / Energy landscapes in physics. You can think of the Morse function as a kind of classical Hamiltonian, paths of steepest descent are you sure that these sentences will be useful to a non-mathematician? An easier concept to a layman may be the combinatorial properties of topographic maps. For example, the number of mountain peaks, lakes, and mountain passes on an island are not independent but must satisfy a strict numerical identity.