Summary and Terms

Chapter 2 Summary

In this chapter you learned about models, some of which you may have been using long before you started this class. Models are tools we use to conceptualize problems in useful ways, from describing the structure of objects that are difficult to visualize, such as atoms and molecules, to computational models designed to mathematically predict the outcome of a system.

Models may leave a lot out, as in our rudimentary forest fire model, or they may include complicated relationships like the models real scientists use to study wildfires. One of the most important thing models illustrate however is emergence, whereby something we didn't explicitly design for in a model appears when we look its predictions. In our forest fire model, a critical threshold for tree density emerged which we could use to predict whether most or very little of the forest would burn based on where the observed density was in relation to this metric. In this way, even the simplest models can produce useful findings.

Models are an integral part of the research process, and thinking about models in terms of what they can offer a scientist and what they inevitably get wrong is an invaluable skill to any researcher.

Terms

Models: Tools which help to conceptualize problems. Section 2.3.1

External Representation: The actual outputs of a model, images, code, diagrams etc. Section 2.3.1, Section 2.7.1

Structural Models: Models which attempt to explain some physical aspect of an object, such as a map explaining the geography of the world or a model that describes the arrangement of atoms in a molecule. Section 2.4.2

Categorical Models: When things are grouped together in terms of a given characteristic, the category they fall into cal be seen as a model that describes them. Section 2.4.5

Equation-Based Models: Models which rely on mathematics to predict the state of a system, such as the position of a car given its velocity and the elapsed time. Section 2.4.6

Computational Models: Models which use computer-based rules (i.e. code) to predict the state of a system. Computational models are essentially many equation-based models combined into one. Section 2.4.7

Mental Model: A user's understanding of a model, that is, what the model's external representations correspond to in terms of the actual phenomenon they attempt to explain. In general, external representations are useless without a corresponding mental model to make sense of them. Section 2.4.7