Wicked problems

In a way, the title is a paradox. Almost by definition, wicked problems cannot be modeled perfectly or completely because of the many, often-conflicting perspectives on the problem itself.

We might say that all wicked problems are complex, but not all complex problems are wicked. Natural systems, such as the physical processes manifested as the Earth’s climate, are an example. Scientists may disagree about exactly how those processes work and which are the most important, while still agreeing on their character and their boundaries.

Any problem that involves human societies brings with it the possibility, even the likelihood, of incompatible perspectives. Poverty, overpopulation, and anthropogenic climate change are obvious examples. Poverty is always relative to some point of view; people categorized as “poor” in one part of the world may have standards of living far higher than poor people in another place, while some people seen as “poor” by others may not even experience their own condition as one of lack or difficulty. The causes of poverty may be construed as un- or under-employment; as a result of class warfare, lack of education, racism, or deliberate repression; as an inevitable result of economic globalization; as a national, local, or personal issue; and so on. Thus, even characterizing “the problem” is fraught with issues of personal, collective, and institutional stakes. Disagreement on the nature of the problem leads to conflicting ideas about its solution. As a result, few if any societies have ever eliminated poverty. Similar things can be said about any wicked problem.

Mental models

Human beings do not, and cannot, perceive the world in its full complexity. Our perceptual systems are attuned to some kinds of stimuli but ignore others. We do not see ultraviolet light at all, though it can burn our skin. We usually notice nearby moving objects, but do not see things—such as the ends of our own noses—which are always present in our field of vision. Our brains simplify reality, and while we can extend our perception (with difficulty, and with assistance from instruments or from other people), we normally function with highly simplified (and skewed) versions of reality that can be called “mental models.”

In our workshop, we used the example of a simple doubling problem to show how these mental models often fail us. A piece of paper is about 0.1 mm thick. Fold the piece of paper in half, then in half again. Now it is 0.4 mm thick. Imagine that you fold the paper in half forty more times. How thick is it now? Do not use a calculator.

Solving this problem engages your mental models of paper, folding, and doubling. The formula for the solution is 0.1 mm x 242—yielding an answer of almost 440,000 km, greater than the distance from the Earth to the moon. In an experiment with ninety-five MIT students, none even approached the correct answer, and the same was true of our class. The example demonstrates the skewness of human beings’ ability to imagine even this simple interaction of paper and doubling. It shows the need to deploy external capabilities—in this case, simple mathematics—to check our understanding. This is the basic principle of modeling.