Richard Feynman's handwritten notes on 'optimal stopping problem' decoded

Over five decades after a famed physicist scribbled down a mathematical solution to a common decision-making problem, researchers have finally deciphered his handwritten notes.

The newly-decoded work sheds light on how people decide when to stop exploring new options and settle on the best choice available. This dilemma arises in everyday situations ranging from choosing a restaurant dish to finding a life partner.

The findings revealed that Nobel Prize–winning physicist Richard Feynman’s handwritten notes on a solution tackled what researchers refer to as the “optimal stopping problem.” It is published in the Proceedings of the National Academy of Sciences (PNAS) journal.
What is the optimal stopping problem?

The optimal stopping problem revolves around a simple question: how long should a person keep searching for something better before settling for the familiar, most loved one?

The concept applies to numerous real-world scenarios. People encounter it when deciding whether to continue searching for a new home, accept a job offer, choose a parking spot, order an unfamiliar meal at a restaurant, or even determine who to marry.

While exploring new options can provide valuable information, continuing to search indefinitely reduces the opportunities available to benefit from the final choice.

The story behind Feynman’s discovery

The origins of the solution date back to the 1970s when Richard Feynman visited a Thai restaurant in Glendale, California, with his friend Ralph Leighton.

During lunch, Leighton found himself debating whether to order his favourite dish — ginger chicken — or try something new that might turn out to be even better. What appeared to be a routine dining decision immediately caught Feynman’s attention.

Rather than viewing the dilemma as a simple personal choice, the renowned physicist transformed it into a mathematical problem. He worked out a solution and recorded it in handwritten notes, but never formally published his findings.

“Richard Feynman described a decision-making problem and its solution in handwritten notes, but the meaning of the notes has been a mystery for almost 50 years,” the author said.

Decoding the mystery

A team of researchers has now successfully interpreted Feynman’s original calculations and confirmed that it was effective. The study not only explains Feynman’s solution but also proves its optimality and extends it to a broader range of decision-making scenarios.

According to the researchers, Feynman’s approach relies on establishing a decision threshold that gradually declines over time. Initially, individuals should be willing to explore a wide range of options. However, as opportunities begin to run out, the threshold for trying something new should decrease, making it more sensible to choose the best option already discovered.

To determine whether people naturally behave in a way similar to Feynman’s predictions, researchers conducted experiments involving 2,520 participants.

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“We show that people tend to explore more than predicted by linear thresholds, and that different distributions of quality result in thresholds with the same slope but different intercepts. These results indicate that people adapt linear thresholds used in optimal stopping tasks in a way that is sensitive to the underlying distribution — a simple strategy that we show is nearly as effective as Feynman’s solution,” they added.

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