Chapter 9, titled "Landing on the level," explores how the specific wording of a problem statement dictates the "semantic level" at which a person attempts to solve it, often determining whether a solution is found quickly or not at all. Through a series of experiments involving a simple line drawing of a circle, the authors demonstrate that altering descriptors—such as changing "very familiar" to "very unfamiliar"—radically shifts the respondent's perception and creativity. The chapter posits that problem solvers naturally gravitate toward a semantic level that offers them the most psychological comfort or safety, illustrated by how students interpret exam questions to match a professor's expectations rather than offering genuine opinions. Ultimately, the authors warn that while context is critical, one must guard against over-complication, advising readers to occasionally "check back home" to ensure they haven't bypassed the most obvious and correct definition in favor of a complex one.
The chapter begins by presenting a visual puzzle to illustrate how humans process visual data based on linguistic cues. The authors present a simple figure—a line drawn in a continuous loop—and ask, "Problem 1: The figure above shows a very familiar object. What is it?". The authors note that the vast majority of people respond to this question immediately and without hesitation, identifying the figure as a circle.
This raises a fundamental question about problem solving: why are some problems, like this one, solved largely instantaneously, while others require lifetimes of effort?. The authors suggest that the speed and nature of the solution are heavily dependent on the phrasing of the problem statement itself. In this specific instance, the inclusion of the word "familiar" serves as a significant aid to the solver, narrowing the scope of interpretation to the most obvious geometric shape.
To test this hypothesis, the authors propose a scientific experiment or a "party game" involving slight alterations to the text accompanying the image. They introduce three variations of the original problem statement to see how respondents change their answers:
The authors analyze the responses to these variations to understand the process by which people establish "What am I solving?".
When the prompt includes the word "familiar" (Problem 1), there is an overwhelming consensus that the object is a circle. However, as the descriptors change, so do the certainty and uniformity of the answers. When the word "very" is omitted, the percentage of people identifying it as a circle drops. It drops even further when the word "familiar" is removed entirely.
The most dramatic shift occurs in Problem 4, where the object is described as "very unfamiliar." In this scenario, the standard answer ("a circle") plummets to zero. Forced to abandon the obvious geometric interpretation, respondents shift their semantic level to find answers that fit the new description. The authors list a variety of creative, and occasionally bizarre, responses that emerge from this constraint:
While Problem 4 generates creativity in some, it produces paralysis in others. The authors note that a significant number of people refuse to answer Problem 4 at all, despite being willing to answer the first three versions. When interviewed about their silence, these participants explain that they felt the likelihood of "solving" the problem correctly was so low that it was not worth the risk of making an error.
The paralysis caused by Problem 4 highlights the psychological aspect of problem definition: the fear of being "wrong." To counter this, the authors suggest a fifth variation:
By explicitly asking for the "most far-out thing," the problem statement shifts from a request for a factual "right" answer to a request for an opinion. Under these conditions, the threat of error is removed. The authors observe that almost everyone has an opinion and considers themselves an expert on their own opinion, so the reluctance to answer vanishes.
This leads to the concept of the "semantic level." When a person recognizes a problem, they instinctively "give it the 'once over'" to place it on a level of meaning (semantics) where they feel most comfortable. The authors illustrate this with an academic example regarding a final exam question about Henry the Eighth:
A student analyzing this problem makes a judgment call about the semantic level of the phrase "express your views." The student likely concludes that the professor is not actually asking for a personal opinion, but rather for the "right" answer derived from the course material. The student understands that the "real" reasons for the killings are historical facts (or the professor's interpretation of them), not matters of student speculation.
The authors argue that we interpret problems to land on the semantic level that lends the most comfort. This comfort is derived from knowing how to solve the problem at that specific level. In the case of the Henry VIII exam:
Comfort in problem solving comes from knowing the context, the source, and the nature of the problem—a feeling of "rightness" that guides the definition.
The chapter concludes by analyzing how the context of the book itself influences the reader's problem-solving process. In the first problem (the circle), the word "familiar" pushed most people toward the semantic level of "simple geometry". However, if the exact same problem were presented in a children's puzzle book—"Dick and Jane's Golden Book of Puzzles"—readers would likely shift to the semantic level of "toys," identifying the circle as a hula hoop or a Tinkertoy part.
Conversely, the authors point out a specific danger for the readers of Are Your Lights On?. Because the book is a "sophisticated problem definition book" that has explicitly warned readers about "traps for the unwary," the readers are primed to over-analyze. Faced with the simple circle in Problem 1, few readers of this specific book would accept "simple geometry" as the correct level. They would assume "a circle" is too obvious and must therefore be a trap.
This creates an irony where the sophisticated context forces the solver to overlook the obvious solution in favor of an "unbelievably intricate context". The authors suggest that sometimes a problem really is just what it appears to be.
The chapter ends with a postscript emphasizing the importance of grounding one's analysis. The authors advise that if a reader is convinced the figure is subject to "countless interpretations," they should compare it to a "true" circle to see if that alters their conclusion. This leads to the final principle of the chapter:
"As you wander along the weary path of problem definition, check back home once in a while to see if you haven't lost your way".
The accompanying illustration of a "non-conformist bee" highlights the danger of straying too far from the standard interpretation; sometimes, in the search for a deep or clever definition, the problem solver may miss the simple reality standing right in front of them.