Early on the morning of Sept. 26, 1983, Stanislav Petrov helped prevent the outbreak of nuclear war. A 44-year-old lieutenant colonel in the Soviet Air Defense Forces, he was a few hours into his shift as the duty officer at Serpukhov-15, the secret command center outside Moscow where the Soviet military monitored its early-warning satellites over the United States, when alarms went off. Computers warned that five Minuteman intercontinental ballistic missiles had been launched from an American base. “For 15 seconds, we were in a state of shock,” he later recalled. “We needed to understand, ‘What’s next?’ ” The alarm...