What is a Model?

The term 'model' is used extensively in Computer Science, but is often left undefined by the author.  I intend to write a series of essays discussing the theory of modelling abstractly, so a natural first step is to provide a working definition.

A working definition should comprise a testable description of what constitutes a model.  The description may also suggest how a model may be used.  As we shall see, this description of a working definition also makes it a model.  The definition of a model has become recursive; Computer Scientists should feel right at home.

A dictionary is often a good place to start.  Websters' first two definitions [1] are best suited to my purposes:

1. A miniature representation of a thing, with the several parts in due proportion; sometimes, a facsimile of the same size.
2. Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.

In Wiktionary [2] Definitions 2, 3, and 5 are close to the meaning I ascribe to the word, being rendered respectively as:

•   2. A miniature representation of a physical object;
•   3. A simplified representation used to explain the workings of a real-world system or event; and
•   5. The structure design of a complex system.

These definitions are close to the mark, but they do not come up to my expectations for a working definition, since most are based on example.  The main page for "model" on Wikipedia [3] lists some 46 ramifications, which give domain-specific examples of models.  The entry for "conceptual model" [4] provides a suitably abstract starting-point:

  ... a model is anything used in any way to represent anything else.

That is the first half of my favorite definition for a model, but it lacks an indication of how a model may be used.  The other half is that the model can be used to make a prediction about the entity being represented.  This is essential, because it describes why one would want to have a model in the first place.

With that, I can put forth my definition of a model.  If you trust me, you can stop there.  My intent is to spend the rest of this blog providing examples and defending the accuracy and usefulness of the definition.

A model is one entity which represents another, the first predicting characteristics of the second.

The first thing to point out about this statement is that the two entities are not necessarily distinct.  Often the best way to make a prediction about how something will behave is to just run the experiment.  Development of a model may not so much involve seeking an abstraction among concrete objects as generalizing the characteristics of a well-known exemplar to encompass the larger concrete set.

A second observation is that the statement does not stipulate that the model is simpler than the example.  (For simplicity henceforth, I'll refer to the first entity as "the model" and the second entity as "the example".)  Neither does it require that the example is real or physical or already in existence.  If you imagine a design tool connected to 3-D printer, the model presented by the tool can be far more complex than the part that is produced, and the model certainly exists before the part does.

We also note that the statement leaves aside the notion of quality.  Models can be good or bad; they can be excellent with respect to some characteristics and awful with respect to others.  The quality of a model depends on how well it predicts the characteristics of the example.  The applicability of a model depends on whether the set of characteristics it predicts well matches up with the set of interest.

An amorphous blob of clay is a pretty poor model for a skyscraper.  They both take up space; they might be of similar color; that's about it.  The plastic model I have of an F-18 is an excellent model if my interest is in the relative dimensions of various parts of the airplane.  Aerodynamically, it's a very poor model: It flies like a rock because its scale weight is a dozen times that of the real plane.  It's a poor model structurally as well: all of the interior bracing was omitted in favor of ease-of-manufacture.  A full-scale version could not stand up under its own weight.


This blog presents my working definition of a model.  In the next entry, I'll explore why models are so important.


References:
[1] machaut.uchicago.edu?resourc=Webster's&word=model&use1913=on
[2] en.wiktionary.org/wiki/model
[3] en.wikipedia.org/wiki/Model
[4] en.wikipedia.org/wiki/Conceptual_model