Indeed, inside the foam and fiberglass model is an iron frame, which connects to a large cylindrical steel pipe 16 inches in diameter that extends up into the roof. To see how it is all held together requires a journey that begins in a freight elevator, leads out a locked door that is opened by remote control in a separate location, and onto what Steven Warsavage, the museum’s associate director of construction, said is actually the roof of Building 9, which houses the Hall of Biodiversity. Yes, he said, the museum feels like one entity but it is actually 26 different buildings linked together.

The Hall of Ocean Life is Building 10, built in the 1920s, with steep stairs leading to an interior with a catwalk around those false skylights. After ducking under some protruding beams and climbing over others, you reach the entrance to the room above the whale. There, Mr. Warsavage and Karen Quigley, senior director of construction and facilities, showed that the steel pipe does not do all the work alone. “Those other steel bars coming off that one connect to trusses in the room,” Ms. Quigley said. “That allows the load, the weight of the whale, to be transferred to all that other steel.”

According to Stephen Christopher Quinn’s book, “Windows on Nature” about the museum’s dioramas, Lyle Barton, the museum manager in charge of installing the whale in 1968, was so anxious that something would go wrong that he got a rod the exact distance from the whale’s chin to the floor. While the rest of the hall was being completed, he would make certain every day that the whale was holding its own.

The crew building the exhibit so resented Mr. Barton’s lack of confidence, Mr. Quinn writes, that they dribbled an imperceptible bit of glue on the rod each morning until enough layers had accumulated so that when Mr. Barton checked one day, the rod no longer fit underneath the whale’s chin. He had a moment of panic, thinking the whale was finally sinking.