Assuming string theorists will not soon provide a compelling case for the primary theory underlying particle physics, the field will proceed as it has historically: with data stimulating and testing ideas. Ideally the soft supersymmetry breaking Lagrangian will be measured and its patterns will point to the underlying theory. But there are two new problems. First a matter of principle: the theory may be simplest at distance scales and in numbers of dimensions where direct experiments are not possible. Second a practical problem: in the foreseeable future (with mainly hadron collider data) too few observables can be measured to lead to direct connections between experiment and theory. In this paper we discuss and study these issues and consider ways to circumvent the problems, studying models to test methods. We propose a semi-quantitative method for focusing and sharpening thinking when trying to relate incomplete data to incomplete theory, as will probably be necessary.