Qualitative Modeling And Similarity In Back Of The Envelope Reasoning

Back of the envelope reasoning involves generating quantitative answers in situations where exact data and models are unavailable and where available data is often incomplete and/or inconsistent. A rough estimate generated quickly is more valuable and useful than a detailed analysis, which might be unnecessary, impractical, or impossible because the situation does not provide enough time, information, or other resources to perform one. Such reasoning is a key component of commonsense reasoning about everyday physical situations. This paper presents a similarity-based approach to such reasoning. In a new scenario or problem, retrieving a similar example from experience, sets the stage for solving the new problem by borrowing relevant modeling assumptions and reasonable values for parameters. We believe that this tight interweaving of qualitative and analogical reasoning is characteristic of common sense reasoning more broadly. Understanding the feel for magnitudes is another crucial aspect of such reasoning, and incorporating effects of quantitative dimensions in similarity judgments and generalizations, hitherto unexplored, raises very interesting questions.