When we create numerical models of a real-world system, we usually go through a few phases (from Abramowitz 2010):
- a perceptual model, where we consider the relevant components of the system
- a conceptual model, where we consider the relationships between those components
- a mathematical model, where we come up with equations and formulae to express the conceptual model
- a numerical model, that allows the computer to estimate the results of the mathematical model on a given spatiotemporal scale
Divide by zero errors are a pretty common cause of premature model death. Sometimes that's just due to poor programming. But if we exclude that possibility (assume a perfect programmer), is a divide by zero error an indication that the conceptual model is wrong? That is, is it reasonable to assume that the equivalent of a divide-by-zero error never happens in the real world? I guess that this question presupposes that mathematics is in some way "real", comments on the relevance of that would also be appreciated.
- Abramowitz, Gab 2010, Model Independence in Multi-Model Ensemble Prediction. Australian Meteorological and Oceanographic Journal 59: 3–6. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.222.5811&rep=rep1&type=pdf.