Normalizing relations with India could help starve Pakistani militancy of oxygen. So it is significant that the prospects for peace between the two nuclear-armed countries look better than they have in some time.

India and Pakistan share a lengthy land border, but they might as well be on separate continents, so limited is their trade with each other and the commingling of their people. Visas, traditionally hard to get, restricted to specific cities and burdened with onerous requirements to report to the local police, are becoming more flexible for business travelers and older citizens. Trade is also picking up. A pulp manufacturer in Pakistani Punjab, for example, told me he had identified a paper mill in Indian Punjab that could purchase his factory’s entire output.

These openings could be the first cracks in a dam that holds back a flood of interaction. Whenever I go to New Delhi, many I meet are eager to visit Lahore. Home to roughly a combined 25 million people, the cities are not much more than half an hour apart by plane, and yet they are linked by only two flights a week.

Cultural connections are increasing, too. Indian films dominate at Pakistani cinemas, and Indian songs play at Pakistani weddings. Now Pakistanis are making inroads in the opposite direction. Pakistani actors have appeared as Bollywood leads and on Indian reality TV. Pakistani contemporary art is being snapped up by Indian buyers. And New Delhi is the publishing center for the current crop of Pakistani English-language fiction.

A major constraint the two countries have faced in normalizing relations has been the power of security hawks on both sides, and especially in Pakistan. But even in this domain we might be seeing an improvement. The new official doctrine of the Pakistani Army for the first time identifies internal militants, rather than India, as the country’s No. 1 threat. And Pakistan has just completed an unprecedented five years under a single elected government. This year, it will be holding elections in which the largest parties all agree that peace with India is essential.

Peace with India or, rather, increasingly normal neighborly relations, offers the best chance for Pakistan to succeed in dismantling its cult of militancy. Pakistan’s extremists, of course, understand this, and so we can expect to see, as we have in the past, attempts to scupper progress through cross-border violence. They will try to goad India into retaliating and thereby giving them what serves them best: a state of frozen, impermeable hostility.

They may well succeed. For there is a disturbing rise of hyperbolic nationalism among India’s prickly emerging middle class, and the Indian media is quick to stoke the fires. The explosion of popular rage in India after a recent military exchange, in which soldiers on both sides of the border were killed, is an indicator of the danger.

So it is important now to prepare the public in both countries for an extremist outrage, which may well originate in Pakistan, and for the self-defeating calls for an extreme response, which are likely to be heard in India. Such confrontations have always derailed peace in the past. They must not be allowed to do so again. In the tricky months ahead, as India and Pakistan reconnect after decades of virtual embargo, those of us who believe in peace should regard extremist provocations not as barriers to our success but, perversely, as signs that we are succeeding.