In the 1970s, physicist Richard Feynman sat down for a meal with a friend who faced an age-old traveler's dilemma: order the trusted favorite dish, or risk trying something new? Rather than settle the debate with conversation, Feynman did what Feynman did best—he turned it into a math problem, scribbling his solution directly onto pieces of paper during dinner. Decades later, researchers discovered those handwritten notes and not only deciphered the elegant solution Feynman had worked out, but also tested it against how real people actually choose restaurants in unfamiliar cities.
The question Feynman pondered—whether to explore new options or exploit the ones you've already found satisfying—is a classic dilemma that confronts anyone navigating a new place with limited time. Feynman's mathematical approach revealed something counterintuitive: people should try somewhere new every night until they discover a restaurant that exceeds a certain quality threshold. But here's the clever part: that threshold shouldn't stay fixed. Instead, it should decline as your remaining nights in the city dwindle. You can afford to be picky on night one; by night ten of a twelve-night stay, you should be more forgiving.
Scientists led by Brian Christian took Feynman's unpublished solution and expanded it further, developing equations that account for different city conditions—whether a place is filled mostly with mediocre restaurants or blessed with abundant excellent ones. They then put the theory to the test with 2,520 participants in an online experiment where each person faced a virtual version of the restaurant-selection problem.
What they discovered was both surprising and reassuring. Rather than following Feynman's nonlinear threshold—the mathematically optimal solution—participants actually used something much simpler: thresholds that declined linearly as the proportion of remaining nights decreased. In other words, humans intuitively adopted a streamlined version of the physicist's formula, one that was easier to remember and execute without requiring advanced calculus.
The remarkable finding is that this simplified human approach proved nearly as effective as Feynman's optimal solution. "People thus seem to follow a simple strategy that can be easily modified to accommodate differences in both total nights and distribution, allowing them to come close to optimal performance while minimizing cognitive effort," the researchers wrote in their paper, published in the Proceedings of the National Academy of Sciences. The brain, it turns out, has already solved the explore-exploit problem through a kind of elegant approximation—we don't need perfect mathematics to make nearly perfect choices.
What makes this discovery hopeful is what it reveals about human decision-making. We are not hapless wanderers making random selections in unfamiliar cities. Instead, we've evolved or learned an intuitive strategy that balances exploration with exploitation, one that adjusts naturally as time runs short. Feynman's napkin notes, preserved and finally unlocked by modern researchers, show us that the great physicist's insight wasn't just academically interesting—it revealed something true about how we already navigate the world. Sometimes the wisdom we need has been scribbled down all along, waiting to be rediscovered and understood.