There’s Nothing Like Real Experience: I

As the saying goes, the point on a pencil is the inspiration and the other end with the eraser is the experience. A pencil without an eraser is next to useless, as I have found out. Yes, I know that, instead of using pencils, we all type on computers these days, but the principle still holds: Experience tempers our creative endeavors with realistic expectations. Whether we are considering engineering solutions to outstanding problems or are considering more broadly how to live our lives, real-life experiences guide our every move.
I have certainly had my share of experiences to remember. There was the time when, as a new graduate student at Cornell University, I was in an electrical engineering laboratory with two other electrical engineering students in our small group. We were to perform some sort of experiment using several pieces of equipment, but the oscilloscope would not work, and we had to have that scope in order to proceed. We pushed the on/off button a few times without any success. At that point, the other two students began to try to figure out what was wrong. They went through many theoretical hypotheses about the cause of our trouble. I listened for a while, admiring the amount of theoretical knowledge that they obviously had retained from their previous courses, until my attention turned to the mass of plugs that was associated with the many instruments and power supplies at our bench station. It was then that I noticed that one plug was not plugged in. When I reached over and inserted it into the outlet, the scope immediately came to life. And, I must admit I felt a little smugness coming over me.
There was another incident in which the roles were reversed. As a research assistant being supported by departmental funds, I was asked to help for a few days with a field trial of a kidney bean harvester that was being tested by another, more senior, grad student several years ahead of me in the same department. The trial was being conducted 30–40 miles north of the university where kidney beans were being grown as a cash crop, and I needed to drive there early in the morning.
The harvester was to be powered with hydraulics, but, to our chagrin, the hydraulics worked for only a short time after being activated. When the engine was started the first time, everything worked fine for a few seconds, and then nothing would happen after that. If the engine was turned off, and restarted after five minutes or so, the same thing would happen. If the engine was restarted immediately, then the hydraulics would not work. We were stumped. The other grad student tried to figure out what was wrong. Although I was not the person responsible for the trial, and as a green young grad student, I tried to help by recalling everything I could think of in my previous engineering education that would even remotely bear on the problem. The other student tolerated my suggestions, but I could see that he was not impressed with my opinions. We ended that day without any progress.
The next day, after again making the long drive to the trial site, I learned that the other student had found the cause of the intermittent hydraulic system. He had drained the hydraulic tank overnight, and found that someone had thrown a crumpled-up used brown paper lunch bag into the tank. The hydraulic system would work only as long as the bag was not obstructing the tank outlet. When the system was shut off, the bag floated to a spot away from the outlet, and there was enough hydraulic fluid for the pump to circulate through the hoses. As soon as the bag was drawn to the outlet, it plugged the outlet and starved the pump of fluid. So, there was no theoretical reason for the hydraulic system to act the way it did; there was a very real and practical explanation for the problem.
From these two incidents, which I have carried in my memory for these many years, I have learned to look for the simplest explanation first, before any more involved reason. Sometimes, a little time spent looking at the problem from a distance pays off with a much simpler solution than would be the case if I had gone headlong into attempting to solve the problem.
That works for mathematical solutions as well as physical ones. I have learned to try a simplified mathematical problem before the one I really need to solve in order to gain some understanding about how to find the solution to the problem. That way, I have a better idea about how to judge the correctness of the more involved solution because I have already understood the simpler solution.
Students, I have found, do not generally like mathematics. They do not have facility with visualizing what an equation tells them. This is probably the fault of the way in which calculus and other mathematics courses are taught. If more complex problems and solution techniques were not attempted before the students had gained a familiarity with simple examples, especially ones with some connection to their past experiences, then mathematics instruction would probably be improved.
The point is that experience is a great teacher, and one not easily forgotten.