Reasoning tasks in spatial, temporal, and physical domains often involve quantities at vastly different scales. A cross country trip of three thousand miles begins by backing up the car six feet; the 150 foot Challenger rocket exploded because of a 1/200 inch gap in the O-rings; the shining of the sun is explained in terms of the interaction of nuclear particles. Automating such reasoning raises issues of representations and inference techniques that do not arise in reasoning at a fixed scale, particularly in cases where the level of detail and the precision of information available varies widely across different components of a single system. A number of different aspects of this problem are under study, including calculi for order of magnitude reasoning; the use of dimensional and structural hierarchies; and the composition of physical theories of different granularity. The result of this research will be a body of tools and techniques for reasoning across multiple scales that can be used in automated physical reasoners over many different domains.
