Past and modern Japanese physicists analyzed packed trains to secure seat

The Mainichi

08-07-2025

TOKYO -- A renowned Japanese physicist and writer analyzed trains in Tokyo about a century ago to ride less crowded cars, and another physicist in modern Japan has apparently succeeded in predicting available seats by following suit.
Enduring a packed train ride is a familiar struggle for many commuters in Japan, and the desire to quickly find a vacant seat is universal. Torahiko Terada (1878-1935), known for the saying "Natural disasters occur when they are forgotten," faced the same train challenge roughly 100 years ago but did not settle for merely enduring the ordeal. Armed with a pocket watch, he observed passing trains at a station. What method did he uncover using physics?
Terada left behind a treasure trove of essays connecting everyday life with physics. In his 1922 essay whose title roughly translates to "On train congestion," the physicist and author wrote, "Clinging to the straps in a crowded train, being pushed and jostled, is almost unbearable torture."
While observing crowded trains, he noticed periodic "peaks" and "off peaks" in congestion. As trains depart from the terminus, delays accumulate. Late arrivals at stations lead to more passengers boarding, increasing further departure delays and congestion. Using mathematical formulas, Terada deduced that an average of every three to four trains become notably crowded, while the following two to three trains are less so.
He then examined the congestion and arrival intervals of streetcars at Tokyo's Jimbocho stop, confirming his theory to some extent. He concluded, "Letting the crowded train pass and boarding the next less crowded one appears to be more convenient and 'efficient' for oneself and others."
A modern physicist has also pondered how to secure a seat on crowded trains. Kyoto University professor Koji Hashimoto, who once spent four hours round trip commuting to and from work on packed trains, shared his secret: "Identify those who are getting off."
Hashimoto stood at the platform's edge, observing incoming trains from end to end. Once he identified crowded cars, he rode them from the starting station to the terminal to determine why they were jammed. By noting the stations where uniformed high school students and company workers alighted and checking connections with other lines and express trains, he could predict available seats.
Hashimoto remarked, "Physics is often seen as detached from daily life, but like Terada's essays, the appeal lies in systematically understanding human movement and applying it for personal gain."
(Japanese original by Yurika Tarumi, Lifestyle, Science & Environment News Department)