Education of Structured and Unstructured Problems

Problems are all around us

Everyone is surrounded by problems. Whether it is determining the fastest way around the traffic jam, choosing the best bank for savings or developing a financial model, one faces such challenges over and over again. No doubt, there is an equally large number of ways to categorize these problems. Yet of all those, there is one that particularly stands out: Problems can be classified as either structured or unstructured.

Structured Problems

Structured problems are much easier to solve. They clearly identify what is given and what needs to be found. They exist as an isolated system with a set of characteristics that define it. Such isolated systems are included in their own abstract Universes, as they cannot exist in the real Universe, where nothing is fully isolated. They are structured because they are observed by an omnipotent observer, who finds exactly the defining characteristics and presents them in a structured manner. The observer deliberately obscures some of the parameters that he or she observed, so that there is something to solve. Those characteristics, however, can be determined given the set of laws that govern the isolated system. As neither such system nor such omnipotence really exist, the observer usually defines this system. It has the characteristics that the "observer" wishes because he or she "created" (rather than observed) it. By distancing the problem from the real world, one imposes structure onto it.

Any typical textbook gives a wealth of structured problems. At the expense of the real-world proximity, the authors of such books create their own Universes where markets are always efficient, people are always rational, distributions are always normal (the examples do not have to be purely from the financial realm). Those Universes do not really exist, but they are defined by the authors. The authors inhibit them with the characteristics they wish to see, obscuring the elements they seek to build the problem around. So, in a given example the authors may obscure the probability of a certain price movement. At the same time, in the Universe they have defined, this probability can be inferred from other characteristics. 

There is nothing wrong with these kinds of problems. Frequently, it is much easier for a person to understand a concept through them. In this respect, the educating process as a whole owes a significant proportion of its success to structured problems. They are perfect for illustration precisely due to their simplifications. Although the solution for them may not be easy, the problem-solving process itself is straightforward. Unsurprisingly, the real world carries only few (if any) of those.

Unstructured Problems

As follows, unstructured problems are just the opposite. They do not exist in abstract Universes, for which there is an omnipotent observer. Therefore, no one can give proper structure to them; no one can define the full set of their characteristics. Nevertheless, unless all characteristics are defined, the resulting Universe will again be an abstraction, an approximation of reality. The extent of the omnipotence of the observer with respect to the Universe of the problem (i.e. the real world) will determine the level of structure that can be imposed on the unstructured problem. As this omnipotence is never ultimate for an observer in real world, it is not possible to convert an unstructured problem into a structured one without a trade-off.

A good example of an unstructured problem is job search. It is simply impossible to be aware of all the characteristics that make up the Universe of this problem. There is a myriad of people with a myriad of myriads of relationships among them. Through countless series of interactions among them jobs are created. Obviously, no one can observe all of the interactions. Nonetheless, analyzing the job market would increase the omnipotence of the observer, as some interactions between people (or companies) would become apparent. One would be able to impose structure: Company A requires skill-set A for job A, while company B required skill-set B for job B. Still, this structure would not make the whole problem structured, as there are companies C,D, etc., of which the observer is not aware.

The Twist

The most interesting thing is that the process of turning an unstructured problem into a structured one is an unstructured problem of itself! The key is that this process of conversion connects the real Universe where the unstructured problem exists with the abstract Universe where the structure is present. This resulting third Universe is not observable fully (as it contains not fully observable real Universe), and hence, the resulting problem is unstructured.

In other words, the structure is created by mapping the real Universe to the abstract Universe by the means of the third, or gateway Universe. The observer can define it to some extent, but not fully, in accordance with his or her level of omnipotence.

As a result, the process of problem-solving in case of unstructured problems is complicated by the definition process. This stage was absent in the case of structured problems: for the Universe has already been defined there. The problem is that as structured problems dominate textbooks, this definition process is not well-emphasized. However, knowledge and understanding of this process allows one to convert an unobservable Universe into the one where he or she is omnipotent with the smallest trade-off in the course of transition. As minimizing this trade-off is crucial in order to allow subsequent transition back to the real Universe (i.e. making inferences based on abstraction), it should be the goal of educational institutions to inculcate the understanding of how to structure unstructured problems.

If this next step in education is successful, a scholar will have all the necessary tools to develop an app that directs him or her away from the traffic congestion; or to rank banks based on their financial health; or to build a model that tracks the stock market.