All this might sound so intuitive as to seem silly. None of us needs the advice of the United States Navy to start searching for a lost item in the place we think we’re most likely to find it, and all of us automatically move on to more improbable locations from there. (In a desperate moment, who among us has not checked to see if we somehow put our keys in the refrigerator?) Yet search theory formalizes something important about the process of seeking: looking for anything requires resources, which, because they are finite, need to be allocated with care. Calculating the best way to do so might not matter very much when you are looking for your daughter’s backpack, but it matters very much indeed when you are looking for your daughter.
Searches like that are too urgent to leave up to intuition—and, much of the time, they are also too complex. Theory of Optimal Search begins by looking at the simplest type of search problem: “finding a stationary target when no false targets are present.” But those tidy conditions rarely apply. Maybe instead of a stationary target, you are looking for a raft adrift on the ocean or a lost hiker who, rather than hunkering down and waiting for help, is moving in unknown directions—possibly including back into a sector you’ve already searched. Or maybe false targets are present. Since all of the sensors we use to look for things are imperfect (eyes, ears, radar, sonar, cameras), any of them may mislead us. You think you’ve finally found your car in the airport parking garage, but it turns out to be someone else’s gray Honda Accord; you think you’ve discovered a sixteenth-century shipwreck, but it turns out to be just an old schooner, scuttled in the 1970s and breaking apart on the ocean floor.
Worse still, it is not just a wrong target that can draw our attention. Sometimes we home in on entirely the wrong search area. Your lost wallet might be lodged beneath the passenger seat of a friend’s car, not in your apartment; your lost hiker might have quit an hour into his trip and headed back to town or left the trail and gone for a swim. It is a dispiriting truth about looking for something that we can only know with certainty where it went missing after we find it.
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All this makes looking for something sound dry, somewhere between a low-level hassle and a high-level statistics course. But in fact it is often thrilling, at least if the collective creative output of humanity is to be believed: stories about searching for something are among the oldest, most enduring, and most popular tales we tell. The typical object of these quest narratives is something of immense value stashed somewhere unknown or far away. As with the real things we look for, that object may be concrete or abstract, something the hero has lost or something he or she has never seen before: Jason and the Argonauts searched for a golden fleece, Psyche searched for her lover, Harry Potter searched for Horcruxes, and everyone from Galahad to Indiana Jones searched for the Holy Grail.
Like the inventors of children’s games, the creators of quest narratives understand the intrinsic pleasure of discovery, and they know that they can convince an audience to stick with them simply by deferring it. Suspense, after all, is not a product of being unaware that something is out there; it’s a product of knowing that it is out there but not knowing when, where, or how you will find it. As that suggests, a search also has the great virtue of being, all by itself, nine-tenths of a plot. It gives you a goal (trying to find X) and a climax (finding X) and in between it gives you an excuse to explore interesting new terrain. “When you search for a needle in a haystack,” one version of the saying goes, “you come to know the haystack.”
That is an elegant way of restating a different cliché: it’s not about the destination, it’s about the journey. In keeping with that philosophical outlook, many quest narratives are chiefly if covertly about the protagonist’s emotional or spiritual development. Never mind the ostensible object of the quest, these stories suggest; the real thing we need to find is ourselves. Before he turned his attention to the Valley of Lost Things, Frank Baum made this point explicit by sending the characters in The Wonderful Wizard of Oz out to find their heart, their brain, their courage, and—like a long lineage of questing heroes stretching from Dorothy all the way back to Odysseus—their home.
Other quest narratives make this same case by way of a negative example: a protagonist who fails to mature and instead grows dangerously fixated on finding what he seeks. According to Theory of Optimal Search, the challenge of looking for something is twofold: “how to search and when to stop.” In stories like these, the protagonist fails to stop, even long after the value of the missing object has been eclipsed by the toll the search has taken in time, money, sanity, and lives. Perhaps the finest example of the quest narrative as cautionary tale is Moby-Dick, but there are many others as well. In Treasure Island, for instance, the titular treasure barely figures at all; the book is really about greed, obsession, na?veté, hubris, and violence. In the end, when the heroes finally find the treasure, they are, as one hears about lottery winners, no different, better, or happier for having done so.
Taken collectively, the moral of these stories is a sound one: be careful what you spend your time looking for. Pick the right thing and you will be rewarded, sometimes beyond your wildest dreams; pick the wrong thing and you may lose more than you find. The good news is that you don’t need to make that choice on your own, since figuring out what to seek in life has been a central concern of philosophy for thousands of years. The resulting wisdom is close to unanimous in cautioning us that our happiness does not lie in the pursuit of material things, à la Treasure Island, or the pursuit of revenge, à la Moby-Dick. Frank Baum came closer when he sent his characters off in search of hearts and brains and courage and homes, not to mention what they found along the way: friends. Such things truly do make our lives different, better, and happier. The difficulty is that they present search problems of their own.
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Of all the things that can make finding something difficult—false positives, false negatives, moving targets, incorrect search areas, lack of resources, the vagaries of chance, the general immensity of the world—one of the thorniest is this: sometimes, we don’t really know what we’re looking for. Maybe you are trying to find the perfect wedding gift for that notorious Friend Who Has Everything. Maybe you are trying to find someone to date in order to someday have a wedding of your own. Maybe you are trying to find a drug that will impede the development of plaque in the brain. In all of these cases, you are looking for something that is wholly new to you and, in some instances, wholly new to the world. How, then, are you supposed to find it?
That’s the question the Thessalian statesman Meno posed to Socrates almost twenty-five hundred years ago. The two men are discussing virtue, and when Socrates confesses that he doesn’t know what it is, Meno is troubled. “How will you look for it,” he asks Socrates, “when you do not know at all what it is?” And “if you should meet with it, how will you know that this is the thing which you did not know?” Taken together, those two questions became known as Meno’s paradox: if you don’t know what you’re looking for, you can’t find it, and if you do know what you’re looking for, you don’t need to search for it. As a result, you should never bother looking for anything, because your search will be either unnecessary or impossible.