Together, we looked out at the ocean. The tide was on its way back in; enormous green rollers were dashing themselves ecstatically against the shore. Huge overlapping circles of foam came rushing up toward us, bubbled briefly around our feet, and retreated. Beyond them, the Pacific turned deep blue, then a flat sunlit slate that extended as far as we could see. We laughed; so much for the sunglasses. Then, because we had to return to camp that night and our long break on the rocks meant we were dangerously close to missing the tide window, we turned and started back the way we came.
By the time we reached that first beach again, it was unrecognizable. The stones we had sprawled on lay a hundred feet out in the ocean and who knows how far beneath it; the tide was so high that the swells were breaking against the dense understory of the jungle. Our own spirits, by contrast, were ebbing. Hungry and sun-saturated and tired, we were ready to be done with a lovely but very long hike whose final miles now promised to be difficult. We grabbed tree branches to keep our balance as we walked, getting soaked to the waist and smacked by driftwood and coconuts with each incoming wave. I could barely hear over the surf when my friend, who was behind me, said my name, her voice urgent and strange. A head taller than I am, she had seen what I had missed, trapped in a tangle of branches and seaweed. When I turned around, she was wearing her sunglasses, still strung with a strand of kelp from their unlikely journey home.
It doesn’t matter, in moments like that, whether you believe that God has blessed you, that fate has smiled on you, or simply that, in a stochastic world, very unlikely odds have broken in your favor. What matters is that you will feel the presence of some force outside yourself—one that, whether or not it is intrinsically benevolent, occasionally and indisputably produces benevolent ends. A pocket of the universe turns inside out and something that has gone missing shakes loose. Poseidon returns a pair of Ray-Bans. That day in Costa Rica, our hunger and exhaustion and general desire to be done vanished as swiftly as the sunglasses appeared, replaced by an entirely different set of emotions. Amazement, gratitude, wonder, awe: the feelings inspired in us by serendipitous finds are the same ones inspired in us by the cosmos as a whole, and for the same reason—because life gave us something splendid that we did not expect, did not ask for, and did not in any particular way deserve.
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Finding something by deliberately searching for it is a different story. Unlike our lucky finds, which involve essentially no effort at all, intentional finds require patience, planning, resources, time, and work. At their triumphant conclusion, they can resemble their serendipitous kin, since no matter how long you look for something, you will generally find it in an instant—and may feel, upon doing so, equally pleased with yourself and with the universe. But right up until then, searching for something is less about the thrill of discovery than about the practical questions of where and how to look.
Answers to those questions abound; good answers, however, are scarce. Plenty of parents, self-help gurus, and psychics will offer to help you find lost stuff, but most of their suggestions are either obvious (retrace your steps; calm down; clean up), suspect (the “eighteen-inch rule,” whereby the majority of missing items are supposedly lurking less than two feet from where you first thought they would be), or New Agey (“picture a silvery cord reaching from your chest all the way out to your lost object”). Catholics might suggest that you pray to Saint Anthony, patron saint of lost things, while technophiles urge you to solve your problem through gadgets. In certain narrow cases, this last method will actually work, as you know if you’ve ever had your girlfriend call your missing cellphone, acquired one of those little Bluetooth-enabled tracking devices that attach to everyday objects, or used the button on your key fob to make your Toyota Camry honk at you.
But these tricks, while helpful, have their limitations. Your phone needs to be on and non-dead; your car needs to be within range; you need to have the foresight to stick a tracking device onto the thing you’re going to lose before you’ve lost it. If those conditions don’t apply, or if you are looking for something that was not previously in your possession, such technologies are no more useful than the eighteen-inch rule. If you are really serious about finding something—or, more gravely, if you have lost something really serious—you do not need gadgets or visualization exercises. You need expertise.
This was the realization the U.S. military arrived at during the Second World War, when navy higher-ups, concerned about enemy submarines, began wondering if there was some way to determine where they lurked. To address the problem, they organized the Anti-Submarine Warfare Operations Research Group, perhaps the first entity in history to regard finding missing objects as a math problem. Although the research group was tasked specifically with finding U-boats, it was essentially trying to figure out the best way to locate any entity at all of unknown location. To do so, its members gradually settled on—to borrow the title of the cornerstone work in the field they pioneered—a theory of optimal search.
These days, optimal search is most closely associated with operations research and computer science, and is best known for helping to lay the foundations for recent advances in artificial intelligence. But the original version applied to the physical realm, and although the math at the heart of it has improved over time, it still forms the basis for sophisticated real-world searches, whether for missing persons or Malaysia Airlines Flight 370. The mathematical details are complex, but the gist is simple. At the beginning of any search, you generate as many plausible hypotheses as you can about where your missing object might be. Those hypotheses define your search area, which may be known and contained (“my apartment”) or huge and indeterminate (“somewhere in the Indian Ocean”). Then you divide that search area into sectors and assign two different values to each one. The first reflects the likelihood that your lost object is there. The second reflects the likelihood that, if it is there, you will find it. Thus, the odds that your missing wallet wound up in the medicine cabinet might be low, but if it did, you have a one hundred percent chance of finding it there. Conversely, satellite data and fuel capacity might indicate that MH370 almost certainly went down in a particular sector of the ocean, but you are nonetheless unlikely to find it if the water there is twenty-six thousand feet deep. Once you have these two numbers, you combine them to determine the odds of finding your missing object in each sector, then use the combined figures to construct a probability map of the entire search area. Only then do you start looking, beginning with the place you are most likely to succeed and moving on to less likely locations.