More amazing than size, though, is what we see when we look more closely. These two sperm whales are stripped of the oils and monumental blubber that made them such valuable plunder for fuel seekers, revealing their inner structure. Yet while skeletons generally seem like the frames of living shapes, that is not the case here. The cubic bulk of the whale’s head is gone. The top of the skull is actually a concave scoop of curiously thin plates that thrust forward and split apart, looking like a forked bird’s beak. And while the bottom of the jaw is lined with thick, close-set teeth, it is as peculiarly narrow as it is long, like a protuberance designed for probing.

And the skeleton’s overall shape? Appendages looking like little hands protrude from its sides, like forgotten limbs. The spine sleekly curves, shrinking toward the tail. The animal seems like something that slithers with the currents rather than plows the deep; it even has some resemblances to a bird or a lizard. But we know otherwise. It is a mammal. It breathes air. And it lives like a fish.

So this is the largest toothed predator of the animal kingdom? It is as if having distilled the whale into its structural essence, we end up with something even more mysterious, testing the boundaries of all familiar categories. And I haven’t even described the most startling sights here, offered almost too soon to be absorbed, right after entering the exhibition.

This show is unusual for this museum since it originated elsewhere, at the Museum of New Zealand Te Papa Tongarewa, which has one of the largest whale collections in the world. But in its original form, the exhibition seems to have devoted almost as much attention to the use of these creatures by New Zealand’s indigenous Maori as to the world’s cetaceans — an order of more than 80 species of living whales, dolphins and porpoises — and their ancestors.