Decades after the physicist scribbled the solution, researchers deciphered and tested it.
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A famous physicist’s scribbles reveal the answer to a quintessential dilemma: When dining out, is it better to stick with an old favorite or try something new?
Richard Feynman, Nobel Prize-winning physicist known for his love of problem solvingpondered this question with a lunch companion in the 1970s. Feynman turned this into a math problem and solved it on the spot – with his inscrutable writing.
Feynman, who died in 1988, never officially published his solution. It remained undeciphered until a team of researchers recognized, in Feynman’s scribble, a solution to a class of mathematical questions known as stopping problems. This allowed them to make sense of the scribbles. Feynman – living up to his reputation – found the optimal solutioncognitive scientist Brian Christian and colleagues report in the June 2 Proceedings of the National Academy of Sciences.
Feynman posed the problem of choosing dishes in a single restaurant; Christian and his colleagues rephrased it as choosing among multiple restaurants, although the underlying calculation is the same. Each restaurant is assigned a rating to indicate its quality. The objective is to maximize the cumulative score over a given number of evenings.
Feynman came up with an equation for a threshold to which you compare the best restaurant you’ve tried so far. Every night you compare your favorite. If your favorite scores higher, come back for the remaining nights; if not, try a new place. The threshold is not fixed: it starts high and decreases as your remaining nights decrease. At first, with many nights left to enjoy a great find, it’s worth waiting for something extraordinary. On your last night, you don’t have much to gain by searching, so you should settle for something better than average.
Quality also matters. Feynman assumed that a given dish (or restaurant) was as likely to be good as bad or mediocre. Christian and his colleagues found that the threshold equation changes if, for example, most restaurants in an area are lousy but a few offer quite delicious food.
To test how people actually decide, researchers surveyed more than 2,500 people online. Participants did not use the ideal strategy. But they used a simpler one that came close – resulting in similar scores without the full mental gymnastics.
People don’t always do what’s optimal, says Christian, of the University of California, Berkeley. “They use these heuristics and these shortcuts. But the heuristics they use are surprisingly, or strangely, good.”
