I would like to present a case study that exposes shortcomings in the practice-based accounts of models of Cartwright as well as Morrison and Morgan. The case study stems from the field of communications engineering: the additive white Gaussian noise (AWGN) communication channel model. My research question is: How can one understand the AWGN communication channel model through a practice-based account?

Mathematical models in engineering fields purport to offer a mathematical description of aspects of real-world systems. The subject matter of these fields is the design of those systems subject to constraints in terms of the available resources and desired performance within the application context. As application-oriented fields, context-dependence is therefore a key factor to understanding their inner workings in general, and how engineering models bear their fruit in scientific practice in particular.

Cartwright's practice-based account of models in mathematical physics and Morrison and Morgan's of models in the natural and social sciences examine models in context. That is, in order to address philosophical questions of scientific representation (model semantics) and explanation (model epistemology), the aforementioned accounts examine how the respective models are built and used while accounting for the model aims in particular contexts. A common feature in both accounts is the emphasis on the intertwined nature of model semantics and epistemology. 

At first sight, it would seem that the mathematical models in engineering fields bear resemblance to those in mathematical physics according to the aforementioned practice-based accounts. One may be led to believe that answers to similar questions on semantics and epistemology can readily be read off the accounts. This is true up to an extent, however – context-dependence carries the day afterall. Extending the accounts to mathematical engineering models would lend the accounts further credibility as far as their thesis concerning the central role of models throughout scientific practice is concerned. 

I will first show that Cartwright's account does not satisfactorily address the representation problem in the new context of the case study. Morrison and Morgan's account relates models' representational aspects to their construction via the new notion of rendering. While the latter account enables a better understanding of the AWGN model in terms of its construction, instrumental function, its interventional character, and its role in scientific understanding and knowledge production in an engineering application context, the new notion of model representation as rendering is – as I will show – where the Morrison and Morgan's account falters, be it in the particular case of the engineering model or perhaps more generally in special disciplines where physics and engineering intersect. I will therefore suggest a way to modify the notion for wider applicability.

Selected References

- Cartwright, N. (1983): "Fitting Facts to Equations", in: How the Laws of Physics Lie, Oxford: Clarendon Press, pp. 128–142.

- Morrison, M. and Morgan, M. S. (1999): "Models as mediating instruments", in: Models as Mediators: Perspectives on Natural and Social Science, ed. by M. S. Morgan and M. Morrison, Ideas in Context, Cambridge: Cambridge University Press, pp. 10–37.