What is a Model?

Many hobby stores sell kits for car, plane, and rocket models.

Once they are assembled from their component parts, these models can be quite intricate. A completed model may share many of the essential characteristics of the object it models. It may look similar, and it may move in similar ways. The most detailed models allow us to imagine how the modeled object itself might behave.

Every model has its limitations, however. The model is never exactly the same as the real thing. To make a model, certain compromises with reality have to be made.

The situation is very similar when we use mathematics to "model" the natural world.

We build mathematical models of the elegant spirals of galaxies, the chemical reactions found in industry, and the daily swings of the stock market.

When making mathematical models, we can choose from among many different mathematical pieces. We can assemble the pieces in a variety of different ways. Just like the models from the hobby store, however, mathematical models are never quite the same as the real thing. Mathematics can never fully reproduce all of nature's complexities.