In this chapter, I use the term theory to represent "general propositions used as principles" and not "conjectures or proposals."
A number of major disciplines (and their associated design methodologies) have some type of theoretical basis. Structural engineers design an unlimited variety of structures using the theories of physics. Composers create beautiful symphonies and orchestral pieces using the concepts found in music theory. The automobile industry uses aerodynamics theories to design more fuel-efficient automobiles. The airplane industry uses the same theories to design airplane wings that reduce wind drag.
These examples demonstrate that theory is relevant and very important. The chief advantage of theory is that it helps you predict outcomes; it allows you to predict what will happen if you perform a certain action or series of actions. You know if you drop a stone, it will fall to the ground. If you are agile, you can get your toes out of the way of Newton's theory of gravity. The point is that it works every time. If you chisel a stone flat and place it on another flat stone, you can predict that it will stay where you put it. This theory allows you to design pyramids and cathedrals and brick outhouses. Now consider a database example. Let's assume you have a pair of tables that are related to each other. You know that you can draw data from both tables simultaneously simply because of the way relational database theory works. The data you draw from both tables is based on matching values of a shared field between the tables themselves. Again, your actions have a predictable result.
The relational database is based on two branches of mathematics known as set theory and first-order predicate logic. This very fact is what allows the relational database to guarantee accurate information. These branches of mathematics also provide the basis for formulating good design methodologies and the building blocks necessary to create good relational database structures.
You might harbor an understandable reluctance to study complicated mathematical concepts simply to carry out what seems to be a rather limited task. You're sure to hear claims that the mathematical theories on which the relational database and its associated design methodologies are based don't have any relevance to the real world, or that they are somehow impractical. This is not true: Math is central to the relational model and is what guarantees the model's viability. But cheer upit isn't really necessary for you to know anything about set theory or first-order predicate logic in order to use a relational database! You certainly don't have to know all the details of aerodynamics just to drive an automobile. Aerodynamic theories may help you understand and appreciate how an automobile can get better gas mileage, but they won't help you learn how to parallel park.
Mathematical theory provides the foundation for the relational database model, and thus makes the model predictable, reliable, and sound. Theory describes the basic building blocks used to create a relational database and provides guidelines for how it should be arranged. Arranging building blocks to achieve a desired result is defined as "design."