The Vâhanas and Avatâras.
Some have professed to find indications of totemism in the Vâhanas and Avatâras, the “Vehicles” and the “Incarnations” of the mythology; but this is far from certain. It has been suggested that these may represent tribal deities imported into Hinduism. Brahma rides on the Hansa or goose; Vishnu on Garuda, half eagle and half man, which is the crest of the Chandravansi Râjputs; Siva on his bull Nandi; Yama on a buffalo; Kârttikeya on a peacock; Kâmadeva on the marine monster Makara, or on a parrot; Agni on a ram; Varuna on a fish. Ganesa is accompanied by his rat, whence his name Akhuratha, “rat-borne.” This an ingenious comparative mythologist makes out to represent “the pagan Sun god crushing under his feet the mouse of night.”[31] Vâyu rides on an antelope, Sani or Saturn on a vulture, and Durgâ on a tiger.
The same is the case with the Avatâras or incarnations of the deities. Vishnu appears in the form of Vârâha, the boar; Kurma, the tortoise; Matsya, the fish; Nara Sinha, the man-lion; Kalki, the white horse. Rudra and Indra are also represented in the form of the boar.