In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a (...) discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

The literature in agent-based social simulation suggests that a model is validated when it is shown to ‘successfully’, ‘adequately’ or ‘satisfactorily’ represent the target phenomenon. The notion of ‘successful’, ‘adequate’ or ‘satisfactory’ representation, however, is both underspecified and difficult to generalise, in part, because practitioners use a multiplicity of criteria to judge representation, some of which are not entirely dependent on the testing of a computational model during validation processes. This article argues that practitioners should address social epistemology to achieve (...) a deeper understanding of how warrants for belief in the adequacy of representation are produced. Two fundamental social processes for validation: interpretation and commensuration, are discussed to justify this claim. The analysis is advanced with a twofold aim. First, it shows that the conceptualisation of validation could greatly benefit from incorporating elements of social epistemology, for the criteria used to judge adequacy of representation are influenced by the social, cognitive and physical organisation of social simulation. Second, it evidences that standardisation tools such as protocols and frameworks fall short in accounting for key elements of social epistemology that affect different instances of validation processes. (shrink)