Good Old-Fashioned AI and Genetic Algorithms: An Exercise in Translation Scholarship

In both the GA and GOFAI traditions, invention or design tasks are viewed as instances of problem solving. To invent or design is to describe an object that performs, in a range of environments, some desired function or serves some intended purpose; the process of arriving at the description is a problem-solving process. In problem solving, the desired object is characterized in two different ways. The problem statement or goal statement characterizes it as an object that satisfies certain criteria of structure and/or performance. The problem solution describes in concrete terms an object that satisfies these criteria. The problem statement specifies what needs to be done; the problem solution describes how to do it [9]. This distinction between the desired object and the achieved object, between problem statement and problem solution, is absolutely fundamental to the idea of solving a problem, for it resolves the paradox of Plato's Meno: How do we recognize the solution of a problem unless we already knew it in advance? The simple answer to Plato is that, although the problem statement does not define a solution, it contains the criteria for recognizing a solution, if and when found. Knowing and being able to apply the recognition test is not equivalent to knowing the solution. Being able to determine, for any given electrical circuit, whether it would operate, to a sufficiently good approximation, as a low-pass filter does not imply that one knows a design for a circuit that meets this condition. In asserting that we do not know the solution in advance, we must be careful to state accurately what the problem is. In theorem proving, for example, we may know, to the last detail, the expression we are trying to prove; what we do not know is what proof (what sequence of expressions, each following inferentially from the set of its predecessors) will terminate in the specified one. Wiles knew well the mathematical expression that is Fermat's last theorem; he spent seven years or more finding its proof. In the domain of theorem proving, the proof is the problem solution and the recognition criteria are the tests that determine whether each step in the proof follows from its predecessors and whether the proof terminates in the desired theorem.