The Middle East is similarly set to confound American expectations. Participatory politics may be arriving in the region, but most of the Muslim world recognizes no distinction between the realms of the sacred and the secular; mosque and state are inseparable, ensuring that political Islam is returning as coercive regimes fall. A poll last year revealed that nearly two-thirds of Egyptians want civil law to adhere strictly to the Koran, one of the main reasons Islamists recently prevailed in the country’s parliamentary elections.

And Egypt is the rule, not the exception. If nothing else, the Arab Spring has shown that democratization does not equal Westernization, and that it is past time for Washington to rethink its longstanding alignment with the region’s secular parties.

True, rising powers like India and Brazil are stable, secular democracies that appear to be hewing closely to the Western model. But these countries have democratized while their populations consist mainly of the urban and rural poor, not the middle class. As a result, both nations have embraced a left-wing populism wary of free markets and of representative institutions that seem to deliver benefits only to a privileged elite.

Rising democracies are also following their own paths on foreign policy, foiling America’s effort to turn India into a strategic partner. New Delhi is at odds with Washington on issues ranging from Afghanistan to climate change, and it is deepening commercial ties with Iran just as America is tightening sanctions. Standing up to America still holds cachet in India and Brazil, one reason New Delhi and Brasília line up with Washington less than 25 percent of the time at the United Nations.

Washington has long presumed that the world’s democracies will as a matter of course ally themselves with the United States; common values supposedly mean common interests. But if India and Brazil are any indication, even rising powers that are stable democracies will chart their own courses, expediting the arrival of a world that no longer plays by Western rules.

The 21st century will not be the first time the world’s major powers embraced quite different models of governance and commerce: during the 17th century, the Holy Roman Empire, Ottoman Empire, Mughal Empire, Qing Dynasty and Tokugawa Shogunate each ran its affairs according to its own distinct rules and culture.

But these powers were largely self-contained; they interacted little and thus had no need to agree on a set of common rules to guide their relations.