How Do You Use a Model?

A model is one entity which represents another, and enables some predictions about the latter.  Its ability to predict is only realized by exercising it.  A complete model contains both a representation and a process.  The process gives an indication of how the model can be used and also how it can be abused.

My plastic model F-18 is a good dimensional representation of the aircraft.  The knowledge that it is a 1/72nd scale model is an important part of the representation.  But lacking that knowledge, one measurement from the real aircraft would provide the needed calibration.  To make a prediction about the dimensions of a part of the real airplane, I can measure the model with calipers and multiply the result by 72.  The representation part of the model is the glued-together collection of plastic parts.  The procedure for producing a prediction is to measure the part of interest and multiply by the scale factor.

Since the model is dimensional, such geometrical predictions ought to be acceptably accurate.  On the other hand, the model airplane is not intended to be an aerodynamic model.  Launching the plastic model like a paper airplane would lead you to conclude that an F-18 would never get off the ground.  The representation is the same, but the procedure is not right for this particular model.

To obtain good predictions about how an F-18 will fly requires either a better representation or a different procedure.  Perhaps placing the plastic model in a wind tunnel would yield better results.  The faster airflow might more closely simulate the forces the real plane experiences in flight.  It should be clear that models may be easier to abuse than to use correctly.  Understanding how to run a model is at least as important as the model itself.

Using a simple model may be as easy as porting a few measurements from the example to the model, running the model and reading out the result.  The measurements supply calibration or initial conditions that allow the model to make an accurate prediction.  On the other hand, models may be complex enough that they can answer many different questions.  The question you intend to answer must be properly framed for the model's result to be of value.  The model's intended use must be specified before it can be determined whether the chosen model is appropriate or not.

If a model is an analog of the example, then performing an experiment on the model is analogous in the same way to performing an experiment on the example.  One can consider the framing of a question and the exploration of the model to be an application of the scientific method to the exploration of the model.

The mapping between the example and the model often involves a number of assumptions.  When examining the results of a simulation, and mapping these back onto the example, it is important to bear these assumptions in mind and check their validity.  Assumptions or approximations may reduce the accuracy of the model or its results, so calibration against the example is important.

Therefore, I conclude that the complete description of a model must include the instructions for its use.  I noted that how a model is used can be influenced by the answer one is seeking, so a model may be incomplete until one devises and performs an experiment upon it.