By comparing its search dynamics to that of a simple O(n ²) heuristic, we are able to analyze the behavior of the simple genetic algorithm on second order functions, whose optimization is shown to be an NP-equivalent problem. It appears that both algorithms approach these fitness functions in the same, intuitive way: they start by deciding the obvious and most probable, and then they proceed to make more difficult decisions. Useful information about the optimization problem is, among others, provided by statistical physics: lattice gases can be modeled as second order functions.