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Reconstructing RealityModels, Mathematics, and Simulations$
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Margaret Morrison

Print publication date: 2015

Print ISBN-13: 9780199380275

Published to Oxford Scholarship Online: January 2015

DOI: 10.1093/acprof:oso/9780199380275.001.0001

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Abstraction and Idealisation

Abstraction and Idealisation

Understanding via Models

(p.15) 1 Abstraction and Idealisation
Reconstructing Reality

Margaret Morrison

Oxford University Press

It is commonly thought that the greater the degree of abstraction used in describing phenomena, the less understanding we have with respect to their concrete features. As a result, it is often puzzling how mathematical models that embody highly abstract descriptions can assist us in knowing and explaining facts about physical, biological, and economic systems. While mathematical models may be indispensable for prediction, their contribution to physical understanding is often thought to be extremely limited. This chapter challenges that myth by showing how mathematical abstraction used in modeling can aid our understanding in ways that more empirically based investigations sometimes cannot. Although much of the discussion focuses on the role of mathematics in biology, specifically population genetics, some examples from physics are also examined in order to highlight the ways in which understanding via mathematical abstraction in these two fields can be strikingly similar.

Keywords:   population genetics, Hardy-Weinberg law, thermodynamic limit, understanding, explanation, laws

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