Chapter 11: Agent-based Modeling: The Right Mathematics for the Social Sciences?
Paul L. Borrill and Leigh Tesfatsion 11.1 INTRODUCTION As in the physical sciences, theoretical modeling in the social sciences typically entails the specification and analysis of parameterized systems of differential equations. Many critical insights have been obtained by social scientists using this powerful classical mathematics approach. Nevertheless, it is extremely difficult to capture physical, institutional and behavioral aspects of social systems with empirical fidelity and still retain analytical tractability. Entities in social systems are neither infinitesimally small nor infinitely many, nor are their identities or behaviors necessarily indistinguishable from one another. Common simplifications, such as assumed homogeneous behaviors or the existence of single representative agents, are thus problematic. Moreover, the social sciences cannot separate observers from ‘the real world out there’. Rather, social scientists must consider multiple observers in a continual co-evolving interaction with each other and with their environment. This leads us to question whether other forms of traditional mathematics, or even new forms of mathematics, might better serve the purposes of social scientists. In short, what is the ‘right’ mathematics for the social sciences? Moreover, if a ‘right’ mathematics exists for the social sciences, what are the implications for the physical sciences? And what can the social and physical sciences learn from each other? As elaborated in Bridges (2009), constructive mathematics is distinguished from classical mathematics by the strict interpretation of ‘there exists’ (E) as ‘we can construct’, classical mathematicans accept the law of the excluded middle (LEM): for any proposition P, either P is true or its...
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