We only argue about things that are uncertain; otherwise, there’s no point in having a debate. Argumentation not only allows participants to test their reasoning and persuade others, but can also lead to new insights. This is particularly true in complex, “wicked” problems where a question can only be grasped by attempting to fashion a solution.
If a discussion involves the question “But what do you mean by X?” it’s probably on the edge of intelligibility. Social debates thrive in this zone. For example, what does “life” mean in the phrase “Life begins at conception?” The abortion debate hinges on when organic matter becomes a human being. This is a very complex question where any answer raises question about the meaning of the term “human” (at least for non-partisans).
Or: what does “information overload” mean? There’s more information today, but are we more overloaded than our forebears? How would we know? The concept is so broad that we probably can’t measure information overload today, let alone estimate it for past generations. Adam Gopnik argues in “Bumping into Mr. Ravioli”  that no-time-to-meet-your-friends busyness is a very modern affliction. Samuel Pepys, a very busy man, never complains of busyness. Gopnik contends that until the middle of the nineteenth century, the defining bourgeois affliction was boredom, not frenzy. Perhaps they had information underload... regardless, both ennui and overload live under the sign of meaninglessness, and thus at the edge of intelligibility.
We oscillate between excitement and boredom because we crave both novelty and predictability. When we have predictability, we become bored and seek novelty; as soon as we’re stimulated, we become agitated and seek refuge in predictability. This experience is probably common to all animals since it’s a good heuristic for finding food and staying safe.
Likewise, we seek both perplexity and reassurance. When it swept the world, sudoku was a two-fer: a perplexing novelty. The daily news is another two-fer: a ritual reassurance that the world hasn’t changed, even as it changes. Derek Lowe points out that there are a number of news templates that are used over and over again, like How The Mighty Have Fallen, or Just Like You Thought. As we alternate between perplexity and reassurance, we skate on the edge of intelligibility. Journalists are very good at giving readers just as much information as they can deal with, and then a little more, adding a pinch of perplexity to the comfort food of understanding.
Donald Rumsfeld provided a multi-layered lesson in intelligibility during a Department of Defense news briefing on Feb. 12, 2002. Since his pronouncement is sometimes edited for clarity , here’s what the transcript says:
“Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend [sic] to be the difficult
Rumsfeld’s model sums up the context in which decision makers operate. “Tops” like the Secretary of Defense not only inhabit a world of complexity and responsibility, as Barry Oshry would have it, but also live in the perpetual twilight between the known and unknown.
The cusp between competence and risk is another productive margin. Mihaly Csikszentmihalyi argues in Flow: The Psychology of Optimal Experience that we find most productive and rewarding states of being when a challenge tests but does not exceed our skill. For intellectual performances, the search for flow will take us to the edge of intelligibility.
The edge of intelligibility is at different places for different people. Someone who can grasp a theorem in trigonometry in a glance might struggle to make sense a situation on the football field; a good quarterback might have trouble reading the motives of people around a meeting table. Since there are so many cognitive competencies , there is always justification for anybody to feel those around them are ignoramuses, or to feel that they are out of their depth compared to the expert next to them.
The edge of intelligibility is a subjective question that involves personal expertise and communal standards. Peter Dear’s wonderful new book The Intelligibility of Nature: How Science Makes Sense of the World argues that Newton’s Principia was not considered to be valid natural philosophy by many leading scientists because it did not provide a mechanical explanation of how gravity worked. Getting the right answer wasn’t sufficient to qualify as science; it had to provide a meaningful explanation, too.
The question of intelligibility is related to my pursuit of hard intangibles, but I’m not yet sure exactly how. A problem must be recognizable as such to be tractable, and is thus intelligible to a certain extent. However, it’s hard because so much about it is difficult to grasp. Hopefully the pursuit of puzzlement will eventually lead to more clarity!
 “Bumping into Mr. Ravioli” by Adam Gopnik. First published in the New Yorker, September 30, 2003. Reprinted in The Best American Essays 2003.
 See e.g. Howard Gardner’s work on Multiple Intelligences. He argues that there are seven distinct intelligences: linguistic; logical-mathematical; spatial; musical; bodily-kinesthetic; interpersonal; and intrapersonal. Each person has a different mix of these skills
 Many poked fun at the Secretary for this formulation. It’s true that he was dodging a question about the lack of evidence of a direct link between the Iraqi government and terrorist organizations, and his reply is more than a little convoluted. But to his credit, it’s not easy to discuss epistemology using a 2x2 matrix in a couple of sentences in a live interview. He left out the entry “unknown knowns,” that is, things that you know without realizing that you do. An example from the War on Terror might be when an organization has important information tucked away in a regional office but top executives aren’t aware of it. I wouldn’t be surprised if this fourth quadrant had been discussed at the Pentagon.