The crowd had simply arrived at the same conclusion—without ever speaking to one another.… On an October morning in Tokyo, meteorologist Haruka Arai noticed something strange. The official forecast on her phone said there was only a 30 percent chance of rain. Yet, as she walked from the station to her research institute, she counted umbrellas everywhere. One person carried a transparent convenience-store umbrella. Another wore a compact rain jacket. A third had tucked an umbrella into the side pocket of a backpack. At the crosswalk, she counted twenty pedestrians. Fourteen had some form of rain protection. Haruka stopped. “Thirty percent?” she muttered. Her colleague Sato, walking beside her, laughed. “You’re trusting the crowd more than the forecast?” “Not exactly.” She looked down the street. “I’m treating the crowd as another sensor.” That idea had become increasingly interesting to meteorologists and data scientists in...