LAUSR

I guess you can call me a box collector. I save almost all of the boxes that I get from Amazon, and whenever I send presents to grandchildren or other relatives, I pick out an appropriately sized box to contain the gifts. I do not buy presents based on the size of the boxes in the basement; however, I have not had to buy boxes because I maintain an adequate inventory. Linear programing optimizes a linear model having linear constraints. The linear constraints are inequalities that form boundaries or the sides of the solution box. A corner point occurs at the vertex of the box (a polygon). If an optimum exists, it occurs at one or more of the corner points or along a line segment between two corner points. In other words, the best solution pushes the boundary of the box. The problems we solve in electromagnetics have boundary conditions in the spatial domain and initial conditions in the time domain. The conditions define the box for our problem. Without them, Maxwell’s equations are nice mathematical constructs, but they have no practical use. If we want to design an antenna, we have to define the constraints, or the box, that contains the antenna. The term “thinking outside the box” originated with a nine-dot puzzle where three-by-three equally spaced dots are connected by drawing four straight lines without lifting the pencil (Figure 1). Most assume that the lines cannot go outside the imaginary box containing the dots, so they cannot solve the problem. False assumptions limit the potential of simple yet innovative solutions. Some of the problems we face in life have clearly defined boxes while others are merely dots permitting innovative thinking and new approaches. Identifying dots and boxes is the first step to finding an optimum solution. Many situations have clearly defined constraints that do not actually exist. For example, Einstein broke out of the Newtonian box and Tesla broke out of the dc power transmission box. To deal with the problem at hand, it is important to ask two questions: 1) what is the end goal? and 2) why have we been approaching it in this manner? In too many scenarios, the answer to the second question is “because that is how we have always done it.” By revisiting these types of problems and using creative problemsolving skills, we are led to superior solutions that lie outside of the presumed constraints. Ethics defines our problem-solving boundaries. It is much easier to face ethical dilemmas when morals and core values are well defined; ethics act as constraints, similar to linear programing problems. Optimum solutions exist at the vertexes where morals and core values meet. The answer to the second question in these scenarios is “because this is what is morally and ethically right.” When my daughter was taking a speech class in college, she asked me to listen to her presentation and provide her with feedback. She was very sensitive to criticism at the time, so I knew she would not take any negative comments well. However, I wanted to help her succeed and improve her publicspeaking skills. The normal approach would be to listen to her, then give the criticism, but she may not take it well, Ethical Boxes