2.2.3 Using Information in Mathematical Models

In this example, Professor Tapia obtained the result from the simple model. He was not satisfied with this value because he knew that D should be a whole number. Since the computed value of D was only slightly closer to 6 than to 5, he could not justify setting D to 6 without the use of additional information. Even though he did not have enough data to use the more complicated model, he was able to use the fact that T₁ < T₂ to help him decide the appropriate value of D. The lesson here is that there is value in cleverly using all of the known information about the problem.

This example illustrates the type of difficulties that can occur when one attempts to model a situation when all of the facts are not available. Often computational scientists must return to their original model and make changes after discovering omissions in their formulations or errors in their assumptions. Frequently, the scientists who pose the problems do not provide (usually inadvertently) all of the information to the computational scientists, and the problem cannot be solved as presented. As you can see, modeling a real-world scenario is not always as clear-cut as many textbooks make it seem.