On July 20, 1969, moments after mission control in Houston had given the Apollo 11 lunar module, Eagle, the O.K. to begin its descent to the moon, a yellow warning light flashed on the cockpit instrument panel.

“Program alarm,” the commander, Neil Armstrong, radioed. “It’s a 1202.”

The alarm appeared to indicate a computer systems overload, raising the specter of a breakdown. With only a few minutes left before touchdown on the moon, Steve Bales, the guidance officer in mission control, had to make a decision: Let the module continue to descend, or abort the mission and send the module rocketing back to the command ship, Columbia.

By intercom, Mr. Bales quickly consulted Jack Garman, a 24-year-old engineer who was overseeing the software support group from a back-room console.

Mr. Garman had painstakingly prepared himself for just this contingency — the possibility of a false alarm.