Asymptotic Reasoning: Explanation, Reduction, and Emergence

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

99-83696 -- Robert W. Batterman (Ohio State University) "Asymptotic Reasoning: Explanation, Reduction, and Emergence" A form of reasoning involving mathematical asymptotics is employed in many different contexts in scientific investigations. This project examines "asymptotic reasoning" as applied mathematicians and physicists use it. In many instances, the mathematical investigation of equations in an asymptotic regime, which involves a kind of physically motivated simplification, can yield formulas describing the salient and dominant features of the phenomenon of interest. The project aims to illuminate the nature of this asymptotic "simplification" and to understand why it is often very fruitful. The project also argues that this special type of simplification results in a deep understanding and explanation, unavailable by other means, of the salient features of the phenomenon of interest. It is argued that the extant philosophical theories of explanation and understanding overlook this widespread form of reasoning. The research will result in new insights about the nature of scientific understanding, explanation, and emergence. It builds upon past investigations into the nature and importance of asymptotic limiting relations between theories. That earlier work focused on the fact that in certain asymptotic regimes between theories (for instance, the semiclassical regime "between" quantum and classical mechanics) salient structures emerge which play crucial explanatory roles. The current project focuses on the questions of why and how this asymptotic reasoning is as fruitful as it is.