Cause and Effect: When exploring the cause-and-effect relationship between several experimental factors and one or more experimental outcomes, the majority of scientists have been taught to hold all other things constant and study only one factor at a time. It turns out that this is usually not a good approach.

A Bad Plan: In fact, I would like to show why this is one of the worst ways to approach the optimization of a system under study. I will do so by comparing the activity of optimization to that of walking up a hill. In either case, we wish to reach the top of the hill as the optimum of the system under study. (Minimization is akin to optimizing by walking down hill.)

Equipment: In this example, however,let us imagine that we have a serious limitation. The compass that we are using has the peculiar characteristic that only allows us to travel on either an exactly North-South line or an exactly East-West line (equivalent to one factor at a time).

Case Study 1: Thus, our optimization plan has two parts, one for each direction. The first phase is to find the highest point possible in our North-South study (maximize factor 1). In part two, we will explore in an East-West fashion until we have found the top of the hill.

Now, we will use this topographical map to chart our progress. We will begin at the X and travel in the North-South direction until we are at the highest point. This occurs at the intersection of the solid vertical and dashed horizontal line. A right turn, and we go up the hill to the top.

Well done! However, go to Didactics 2 for an alternative interpretation of ones results.