Theresa O’Connor

Triangles Rock! (and Category Theory rocks too!)

I’m taking a business and engineering ethics class this term. The case that we talked about today is what prompted the train of thought recorded here, so here’s the relevant background info:

  1. This company manufactures containers. Its engineers supervise the installation of the containers at client sites. Evidently, the installation process is sufficiently complicated such that really bad things can happen if it doesn’t go right.
  2. When a new engineer is hired, he or she undergoes a 30 day training program. He or she performs the above installations under supervison of a veteran company engineer over the course of those 30 days, and upon completion is considered to be a full engineer with the company.
  3. Charles and Tom are engineers at this company. Specifically, Tom is a trainee and Charles is his supervisor. Charles has been thoroughly impressed with Tom’s performance during the training. In fact, Charles has never had a better trainee.
  4. Over the course of the last week of Tom’s training, Charles falls ill. He’s already used his sick days for the year, and the installation that he and Tom are working on is already late.
  5. Charles asks Tom to perform the procedure alone. He’ll sign off on it; he trusts Tom’s ability.

The discussion in class about this case was mainly directed as to what Tom should do in this situation. But, as so often happens in this class, I found the following to be the case:

To elaborate on the second point in light of the class, I was much more interested in what this situation had to say to someone designing a training program. How do you structure a program that is more resiliant to these kind of problems?

Much of the discussion revolved around the nature of the 30-day rule. How rigid is that rule? If we let Tom be an autonomous engineer at 29 days, then why not 28? 27? (And so on and so forth.)

This got me to thinking of this supervisor-trainee, bilateral relationship. I thought about the weaknesses of this relationship that manifest themselves in the above situation.

I brought up an analagous situation: that of legal adulthood. Upon reaching the age of 18 (read: completing the 30-day training period), you (legally) cease being a child and become an adult (trainee → engineer). Now this legal process differs from the above training program in at least one crucial way: There exists an established procedure for handling exceptions to the rule. In one sense, the choice of the age 18 is arbitrary. Why not pick 19 or 17? On the other hand, by the age of 18 virtually everybody is physically and mentally capable of at least holding their own in the world. Some people are mature enough to be considered adults well before this time, and some people never deserve to be considered adults. In the first case, we have an established legal procedure by which the child can become a legal adult before 18.

So there is this triangular relationship between parents, their children, and the law which clearly delineates (or at least should clearly delineate) ways to handle this sort of thing in a robust fashion. This sort of structure is resiliant and strong.

In regard to the ethics case above, here is a structure that would handle such situations better: instead of having the bilateral relationship between supervisor and trainee, include a third person into the mix. Let’s call this person the training program supervisor for now. The supervisor should train the trainee, and the training program supervisor should regularly check with both others on individual and group basses. In order for training to be completed and for the trainee to move on, the approval of the training program supervisor should be required. In this way, if the trainee is ready early, and this fact can be adequately demonstrated to the training program supervisor, the trainee can move on before the end of the 30 days. This also allows for the possibility that the 30 days has not been sufficient to train the individual.

Now, I’m a student at an engineering school. One of the fun facts of reality that people tend to be aware of here is that the triangle is just about the most sound structure that we can make. I’d like to make the case that this holds true in interpersonal relationships too.

The classic example in political philosophy is the division of power in government between distinct branches, such that each branch checks the ability of the other two to abuse their authority. The geometry works out that way. If you tried to have four or more branches sharing power, the combinatorics of interbranch relations gets out of hand really fast, just as any discrete mathematician will tell you.

I think this could also be a decent case for two-parent families. I really think that, on the average, such families work out better than one-parent ones. Certainly, specific families are exceptions to this rule, but I think that such situations are due to the unusually awesome people in them rather than the structure of the situation. Such situations work out in spite of, not due to, the structure.

Consider the following quote from Ron Merrill in light of the above:

Every society must have rules of various sorts—not just laws, but management procedures, and above all customs and manners. But no set of rules, however complex, can handle all the situations that can come up in human society. So rules must always have exceptions.

The effectiveness of a society is determined by how it handles exceptions. If it is too hard to make exceptions, the society becomes rigid, stifling, and ultimately ossified. If, on the other hand, rules are allowed to break down, society dissolves.

The good society grants exceptions generously—but insists that they be acknowledged to be exceptions.

Triangles rock. Triangular relationships are typically more stable than their two-dimensional counterparts, and handle exceptional situations with robustness. Think about the strutures of your life and how you could improve them.

I should mention that, although triangular relationships are wicked cool and really neat, this is not a model that fits all human relationships and all that. There are a lot of situations (romantic love, just to name one) in which other models are most probably better. (Props to Curtis for having me point this out.)

Did you think this was interesting? Am I just completely full of it? Whatever the case, feel free to pass along any comments you may have.