I have not posted for a while, because it seems the scientific method itself is in discussion - see What's Wrong With the Scientific Method? The conclusion of this blog post is: science is about building or changing a model - and I add: forget a few science words namely "hypothesis", "theory" and "scientific law".
I like the provocation coming along with this statement, because it suggests science is not just a systematic approach, it has much game elements and FUN.
I needed to think a bit more ...
In my understanding a "model" is something that makes objects described in the language of "object mathematics" fit for a theorem, a set of theorems build a theory ... a constructive theorem proof can be understood as an algorithm that answers questions or solves a problem. This is a "logic-driven" view on models, I need to confess.
In a general view, a model can be a physical model, a conceptual model, a mathematical model, ... and playing is probably more important than assumed in scientific circles ... In math we like to play with pathologic cases (no, all, ..) and especially in algorithmic math we simulate a lot.
Philosophers of the speculative realism movement, like Quentin Meillassoux, say (simplified by me): if we do not know more properties of a real behavior than our mathematica models have, our models are reality - mathematics is what reaches the primary quality of things ...
This is a motivation to think of The Blank Swan of Metal Treatment with model calibration and re-calibration as it is recommended in quantitative finance but valid also cross-sectoral.
In Computational Knowledge Provide More, I have compiled how Emanuel Derman distinguishes models and theories and "shows" that modeling financial markets cannot be scientific.
Provocatively speaking, maybe we should take the notions not too "seriously" and continue writing adequate, blazingly fast and robust programs ... that improve math and use more math methods for "better" results. Maybe this is one model of models?