Master Class [159]: Nonlinear Aspects of Problem Solving
People become problem solvers when they have to find a way to create a new course of action, improvise, notice difficulties way in advance, or figure out what is causing a difficulty. The concept of leverage points opens the way to think about problem solving as a constructive process. It is constructive in the sense that solutions can be built up from the leverage points and that the very nature of the goal can be clarified while the problem solver is trying to develop a solution. In rock climbing, there is no correct solution. The climber looks at the available holds and figures out what direction makes good sense.
This approach to problem solving can be traced back to the German research psychologist Karl Duncker, one of the central figures in the Gestalt psychology school in Europe. The Gestalt school emphasized perceptual approaches to thought. Rather than treating thought as calculating ways of manipulating symbols, the Gestaltists viewed thought as learning to see better, using skills such as pattern recognition.
Duncker (1935/1945) had asked people to think out loud (so he could gain insights into their thought processes) while solving well-defined and ill-defined problems. One of the tasks he used was the X-ray problem: you are a physician needing to treat a patient with a tumor. You can use X-rays to destroy the tumor, but the radiation will also damage healthy tissue. What can you do?
There are a few acceptable approaches (as befits an ill-defined problem). One of the more satisfactory solutions is to use several X-ray sources. Each could transmit low-level radiation that would not be harmful to healthy tissue yet could be aimed to converge on the tumor and destroy it. To find this solution, the subjects had to elaborate the goal of destroying the tumor. The goal included the property of not injuring healthy tissue. Eventually the problem solver identified a new goal of exposing healthy tissue to only small amounts of radiation.
Duncker found that as his subjects worked on these problems, they simultaneously changed their understanding of the goal and assessed solutions. A subject might think of a solution, try it out, realize it would not work, realize what was missing, and then add to the definition of the goal. This new definition would suggest new approaches, and when these approaches failed, they helped to clarify the goal even further.
To solve ill-defined problems, we need to add to our understanding of the goal at the same time we generate and evaluate courses of action to accomplish it. When we use mental simulation to evaluate the course of action and find it inadequate, we learn more about the goal we are pursuing.
Failures, when properly analyzed, are sources of new understanding about the goal.
The leverage point account of problem solving requires a nonlinear rather than a linear approach. We can think of problem solving as consisting of four processes: problem detection, problem representation, option generation, and evaluation (see figure below).
The account shown in the above figure does not have an output stage, because each of the components can lead to different types of outputs. Problem detection is itself an output, as in the forecast offices set up by governmental agencies whose job is to provide early detection of problems. Problem representation is another output, sometimes the necessary and sufficient output for determining how to proceed. There are medical diagnosticians whose responsibility is primarily to provide skillful problem representations. Generating forecasts is itself a professional specialty in many fields.
Constructing a course of action is the component most people think of as the output of problem solving: generating a plan for achieving a goal. Regardless of how the option is generated, it will need to be evaluated, often using mental simulation. The evaluation process can lead to adoption of the option, result in selecting between options, or identifying new barriers and opportunities, thereby triggering additional problem solving.
The problem-solving process contains different types of outputs, depending on what is needed in the situation.
The above figure shows why this is an interactive process. The goals affect the way we evaluate courses of action, and the evaluation can help us learn to set better goals.
The goals determine how we assess the situation, and the things we learn about the situation change the nature of the goals. Goals define the barriers and leverage points we search for, and the discovery of barriers and leverage points alters the goals themselves. The way we diagnose the causes leading to the situation also affects the types of goals adopted. Further, the leverage points (fragmentary action sequences) we notice grow out of our own experiences and abilities—another layer of interaction.
To review this nonlinear account, we will examine each of the components, starting with the problem detection process. Something happens, something anomalous, and we may notice it. Perhaps a rock climber notices that the route has more debris on it than usual. Or an expectation is violated or something expected did not occur.
The problem representation function covers the way a person identifies and represents the problem. Is there a gap between what we have and what we want? Is there an opportunity to achieve more than we expected? Both gaps and opportunities can trigger problem-solving efforts, either to remove the gap (and obtain what you want) or to harvest the opportunity.
Say that the rock climber gets a little higher and notices that there has been a small avalanche. The pitons she counted on using are covered up, so she may have to find another route, maybe retracing her steps. Or she can find better holds and keep going.
Leverage points are part of the problem representation. We try to detect the leverage points that can turn into solutions, as well as the choke points that can spell trouble ahead. In some cases, identifying the leverage points can count as the critical type of problem representation, emphasizing the lines of reasoning that may be most important.
Not all gaps or opportunities lead to problem solving. They must be important enough, and the problem solver must judge that the gap or opportunity will not be resolved without special effort.
Then comes a difficult judgment: the solvability of the problem. Somehow, we use our experience to make this judgment even before we start working to come up with a solution. Part of our situation awareness is whether this is a problem we should be able to solve without too much work, versus a problem that can take days or weeks and get us nowhere.
Therefore, the function of problem representation includes goal setting because the problem solver must judge whether to try to come up with a solution or turn to other needs. For ill-defined goals, we can expect to see a lot of goal modification during the problem-solving effort.
When a gap or opportunity is identified, often we will try to diagnose it. This is the mental simulation function in which we try to weave together the causes that might have led to the current situation. Because diagnosis is not always required, it is portrayed as an elaboration of problem representation in the figure above and is shaded. We may also want to project trends based on the diagnosis, to see how the situation may change. This is the forecasting process.
In many situations, the primary need is to build a reliable forecast in order to determine whether the difficulty will disappear on its own, or will get worse and require action (for instance: new variant of COVID). The problem representation and diagnosis processes are linked to forecasting, which usually requires mental simulation.
The next function is directed at generating a new course of action, in many cases, a straightforward process: we recognize what to do, and do it. At other times, we do not recognize what to do and must rely on leverage points in order to construct a new course of action. If we blindly press forward trying to reach goals and remove barriers, we may miss these leverage points.
Experience lets us detect them and provides a chance to improvise in order to take advantage of them. We also have to be careful not to pursue opportunities too enthusiastically since they might distract us from our more important goals. We have to balance between looking for ways to reach goals and looking for opportunities that will reshape the goals.
The fourth function is to evaluate plans and actions, to play out a scenario to see what will happen. If the evaluation is favorable, we carry out the action. We also can learn from the evaluation, perhaps discovering new gaps or opportunities, resulting in problem detection or in a new way to represent the problem, as when we would modify our goals.
The concept of problem solving appears incomplete without the aspect of discovering opportunities. There is an infinite set of instances in which problem solving should be initiated. We do not have all the money we want or all the vacation time. We are not driving cars that are as luxurious or sporty as we want, and so forth. So, the potential for problem solving exists on a massive level. Yet we are not defining each of these as problems and wasting time worrying about these discrepancies.
De Groot (1945) and Isenberg (1984) have suggested that what triggers active problem solving is the ability to recognize when a goal is reachable. In the standard view, this seems paradoxical, since it claims that a course of action that is generated after a goal is defined is evaluated for plausibility and used to determine whether to pursue that goal in the first place. There must be an experiential ability to judge the solvability of problems prior to working on them.
Experience lets us recognize the existence of opportunities. When the opportunity is recognized, the problem solver working out its implications is looking for a way to make good use of it, trying to shape it into a reasonable goal. At the same time, the opportunity is shaping the goal by raising the level of aspiration and identifying additional goal properties.
That’s it folks!
Happy New Year to you! I hope that this year brings you all that your heart desires!