Forty-six hours before Rüdiger Koch officially seized the Guinness World Record for the longest time spent living in an underwater fixed habitat, New York Times Magazine reporter Mark Yarm took a 15-minute motorboat ride from Linton Bay Marina, in north-central Panama, to visit him. It was a warm afternoon in January, and Koch was approaching a full 120 days spent working, eating, sleeping, drinking and smoking cigars in a room 36 feet below the surface of the Caribbean.

His 304-square-foot habitat was inside the underwater buoyancy chamber that helps stabilize a floating home called SeaPod Alpha...