The sonorous pre-dawn call to prayer mingled with the roar of warplanes last week in Srinagar, the summer capital of Indian-controlled Kashmir. Less than 100 miles from the Himalayan city, two nuclear-equipped armies were fighting duels in the sky.

It was a week of milestones in the abysmal relationship between the subcontinent’s two biggest powers: the first time India bombed Pakistani territory in five decades; the first publicly acknowledged dogfight between their jets in as many years; and the closest the pair have come to war so far this century.