People often draw inferences about the same mechanical situation using distinct reasoning methods. When reasoning about chains of gears, for example, people may simulate the motions of successive gears, or they may use a simple odd/even rule. We consider psychological and computational evidence as to when and why people use different reasoning methods to draw inferences about mechanical situations. We describe two types of reasoning strategies and their computational implementations. One strategy uses discrete rules to describe the behavior of a system, and the other uses analog simulations to depict the behavior of a system. We develop the strengths and weaknesses of each form of reasoning as a backdrop for considering the strategic knowledge that may guide people between the two forms of reasoning. We present a rough outline of an idealized strategic hierarchy for managing reasoning methods and memory resources. People sometimes follow this idealized hierarchy, but we present new evidence revealing situations in which people do not adaptively rely on an appropriate reasoning strategy. We conclude with a discussion of why it is useful to consider the meta-knowledge that brokers the use of different forms of representation.