Numerical methods use numbers to simulate mathematical processes, which in turn usually simulate real-world situations. This implies that there is a purpose behind the computing. To cite the motto of the book, The Purpose of Computing Is Insight, Not Numbers. This motto is often thought to mean that the numbers from a computing machine should be read and used, but there is much more to the motto. The choice of the particular formula, or algorithm, influences not only the computing but also how we are to understand the results when they are obtained. The way the computing progresses, the number of iterations it requires, or the spacing used by a formula, often sheds light on the problem. Finally, the same computation can be viewed as coming from different models, and these different views often shed further light on the problem. Thus computing is, or at least should be, intimately bound up with both the source of the problem and the use that is going to be made of the answers—it is not a step to be taken in isolation from reality.