The following article treats the 'applicational turn' of modern fluid dynamics as it set in at the beginning of the 20th century with Ludwig Prandtl's concept of the boundary layer. It seeks to show that there is much more to applying a theory in a highly mathematical field like fluid dynamics than deriving a special case from a general explanatory theory under particular antecedent conditions. In Prandtl's case, the decisive move was to introduce a model that provided a physical/causal conception (...) of viscous flow at high Reynolds numbers. It facilitated an approximate solution to the Navier-Stokes equations, which in turn gave rise to many special applications. After a detailed account of Prandtl's achievement, the article discusses the role of the physical model and its experimental and mathematical significance. It is shown that the mathematical simplification provided by the physical model greatly expanded the explanatory capacity of the theory which the Navier-Stokes equations alone could not provide. (shrink)

It is often supposed that mathematical argument provides a model of precision for the sciences. In contrast to this view, the present article proposes to distinguish between mathematical exactness as a ideal regulating the inner standards of mathematical argumentation and precision as a norm governing the relation between products of mathematical reasoning in scientific contexts and empirical or practical data. By discussing a major achievement in the mathematization of flight, Ludwig Prandtl's lifting line theory of wings, it is shown that (...) exact reasoning does not necessarily lead to scientific precision, and that the achievement of precision may even require to loosen existing standards of exactness. It is argued that the main contribution of mathematical argument to generating precision in science lies in its capacity to provide sophisticated tools for the production of data, rather than in its adherence to an ideal of exactness. (shrink)

Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...) the application, comparison, construction, and communication of theories. Modularity conveys some global unity to physics through the sharing of modules by diverse theories. This alternative to rigid hierarchies and holistic totalities permits a dynamical, plastic, and symbiotic approach to physical theory. (shrink)