Deciding where and what to eat can be challenging even in your own city. But when dining out while travelling, the dilemma intensifies: should you stick with a safe favourite or try something new? Scientists have now deciphered a decision-making solution handwritten in the notes of late physicist Richard Feynman after 50 years, offering a mathematical approach to this common conundrum.
The Origin of the Problem
The Nobel Prize-winning physicist turned a lunch debate into a mathematical problem in the 1970s to optimise how to select the best dishes over multiple meals. At a California Thai restaurant with his friend Ralph Leighton, a discussion about whether to order his favourite ginger chicken or try something new prompted Feynman to apply a mathematical equation that addresses the dilemma with an optimal policy for switching from exploring new dishes to exploiting the best. This research was recently published in the Proceedings of the National Academy of Sciences (PNAS).
Deciphering Feynman's Notes
Feynman never published his analysis of the “optimal stopping task”—a dilemma of deciding exactly when to take an action to maximise reward—leaving only hard-to-interpret notes. Researchers from Oxford, Princeton, and the City University of New York noted: “The notes remained inscrutable for decades, until we managed to decipher them and reconstruct Feynman’s original problem and solution.” The team applied Feynman’s solution to a reframed conundrum: choosing which restaurant to dine at when visiting a city for a certain number of nights.
Experimental Validation
Researchers conducted experiments on 2,520 participants using a series of online decision-making tasks that mirrored the restaurant dilemma. Participants were introduced to the problem of selecting a restaurant each night, with the explanation that “restaurants differed in quality, but the quality could only be observed by visiting the restaurant.” According to the paper, results showed that “people tend to explore more than predicted by linear thresholds,” leaning towards exploration early in the task when there is time to benefit from discovering a better dish.
The Optimal Strategy
By applying Feynman’s approach, individuals should try a different restaurant each night until they find one that exceeds their desired quality threshold. If your favourite scores above that night’s restaurant, you should return to it for the rest of the trip; if not, try somewhere new. The longer your trip, the more time you should spend exploring new places before exploiting your favourites. Professor Tom Griffiths of Princeton University, a co-author of the study, explained: “The trick is having a threshold and then decreasing that threshold as you get closer to the end [of a trip]. And as long as you are doing something like that, that’ll actually work pretty well.”
This research not only provides a practical guide for holiday dining but also offers insights into human decision-making in uncertain environments.
