1.1 MODELS AND MODELING
Modeling is the process of creating a simplified representation of reality and working with this representation in order to understand or control some aspect of the world. While this book is devoted to mathematical models, modeling itself is a ubiquitous human activity. In fact, it seems to be one of just a few fundamental ways in which we humans understand our environment.
As an example, a map is one of the most common models we encounter. Maps are models because they simplify reality by leaving out most geographic details in order to highlight the important features we need. A state road map, for example, shows major roads but not minor ones, gives rough locations of cities but not individual addresses, and so on. The map we choose must be appropriate for the need we have: a long trip across several states requires a regional map, while a trip across town requires a detailed street map. In the same way, a good model must be appropriate for the specific uses intended for it. A complex model of the economy is probably not appropriate for pricing an individual product. Similarly, a back-of-the-envelope calculation is likely to be inappropriate for acquiring a multibillion-dollar company.
Models take many different forms: mental, visual, physical, mathematical, and spreadsheet, to name a few. We use mental models constantly to understand the world and to predict the outcomes of our actions. Mental models are informal, but they do allow us to ...