A model refers to a simplified version of a physical system (that would probably be unfeasible to fully describe otherwise).
Models are built in our hypothesis during the induction phase of the scientific method, and they are the result of observation plus experience.
Our hypothesis involve modeling when:
- We neglect certain influences on the system that are considered minor effects. This means that the variables describing those influences do not appear in our model. Yet, these influences will appear in our experiments! mostly in the form of stochastic noise or biases. The simpler the model is, the better, but we must be careful when selecting what to neglect or not.
- For instance, when we mentioned that the force exerted by a human on the Earth is negligible, we are modeling a bidirectional interaction by a unidirectional one.
- In the pendulum experiment, there are several minor effects neglected, like the rod mass, friction, or the Coriolis force from the Earth’s rotation.
- The relationships between the surviving variables are idealized in a simple fashion, including mathematical approximations (neglecting variables could actually be regarded as an extreme form of simplification).
- These models usually have a range of validity in which the model is applicable. The most common is the linear approximation, since any smooth enough function can be approximated by a linear function in small intervals. Example: linear polarization/magnetization of electric/magnetic materials.
A useful model is one that simplifies a problem so that is is manageable, while capturing its essence. The answer to the question ‘is this a good model?’ also depends on the question ‘how good do you want your predictions to be?’. There is normally a trade-off between accuracy and model complexity. The best models explain more using less.
How does modeling affect the validity? Obviously, the validity of the predictions we make using a model is limited by the validity of the model.
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Measurements and Units