The world's largest nose belongs to the sperm whale, yet its functional significance remains equivocal. In order to help shed light on its function, the head of a postmortem neonate sperm whale was subjected to CT scanning. Geometric comparisons between homologous cephalic structures in sperm whales and dolphins (normalized for body size) show extreme hypertrophy and size sexual dimorphism in the sperm whale's lipid spermaceti organ. Anatomic geometry, energetics, and behavior suggest that this immense nasal apparatus is a bioacoustical machine. Sexual selection via an acoustic display is suggested as an explanation for the size and continuous (physiologically isolated) energy investment in the construction and maintenance of the male's spermaceti organ.