India, Aug. 13 -- Every time Karnataka and Tamil Nadu argue over how much water flows south, they are fighting over more than irrigation schedules. The Cauvery has shaped cultures, empires and harvests for over a thousand years, and that history is what makes the modern dispute so combustible.

The river is mentioned across religious texts, including the Puranas, which offer an origin myth: Lord Shiva filled sage Agastya's pot with water from the Kaveri, and Ganesha - in the form of a crow - tipped it over, sending the river across a drought-stricken land. The spot where this is said to have happened, Talakaveri in Karnataka's Kodagu (Coorg) district, takes its name from that story: "the head, or source, of Kaveri". Hindus regard the rive...