Chapter

Scale Matters

Christopher Pincock

in Mathematics and Scientific Representation

Published in print January 2012 | ISBN: 9780199757107
Published online May 2012 | e-ISBN: 9780199932313 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199757107.003.0005

Series: Oxford Studies in the Philosophy of Science

Scale Matters

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This chapter considers the complicated interactions between mathematics and the scale of a scientific representation. Some aspects of scale echo the contributions found in chapters 3 and 4. Others relate to the simplification of a representation using techniques drawn from perturbation theory. Two detailed examples of this are developed corresponding to the distinction between regular and singular perturbation theory. These cases allow a clarification of how some sorts of idealization allow scientists to formulate accurate representations which can be tested and eventually confirmed. One challenge which singular perturbation techniques pose is that it becomes difficult to properly interpret the resulting representations. This challenge is illustrated by some recent debates about the proper interpretation of some successful scientific representations.

Keywords: scale similarity; idealization; perturbation theory; multiple scales; boundary layer theory

Chapter.  16332 words.  Illustrated.

Subjects: Philosophy of Science

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