Editing Mathematical model (section)

===Complexity===

In general, model complexity involves a trade-off between simplicity and accuracy of the model. [[Occam's razor]] is a principle particularly relevant to modeling, its essential idea being that among models with roughly equal predictive power, the simplest one is the most desirable. While added complexity usually improves the realism of a model, it can make the model difficult to understand and analyze, and can also pose computational problems, including [[numerical instability]]. [[Thomas Kuhn]] argues that as science progresses, explanations tend to become more complex before a [[paradigm shift]] offers radical simplification.<ref>{{Cite web|url=https://plato.stanford.edu/entries/thomas-kuhn/|title=Thomas Kuhn|date=13 August 2004|website=Stanford Encyclopedia of Philosophy|access-date=15 January 2019}}</ref>

For example, when modeling the flight of an aircraft, we could embed each mechanical part of the aircraft into our model and would thus acquire an almost white-box model of the system. However, the computational cost of adding such a huge amount of detail would effectively inhibit the usage of such a model. Additionally, the uncertainty would increase due to an overly complex system, because each separate part induces some amount of variance into the model. It is therefore usually appropriate to make some approximations to reduce the model to a sensible size. Engineers often can accept some approximations in order to get a more robust and simple model. For example, [[Isaac Newton|Newton's]] [[classical mechanics]] is an approximated model of the real world. Still, Newton's model is quite sufficient for most ordinary-life situations, that is, as long as particle speeds are well below the [[speed of light]], and we study macro-particles only. Note that better accuracy does not necessarily mean a better model. [[Statistical model]]s are prone to [[overfitting]] which means that a model is fitted to data too much and it has lost its ability to generalize to new events that were not observed before.