To the southeast, China clearly seeks to dominate the South China Sea and beyond. The main barrier to its doing so is the autonomy of Taiwan. Were Taiwan ever to be reintegrated with China, it would be difficult for other regional powers to successfully challenge a united China for control of the basin. In the future, it is entirely possible that China will come to dominate these, its own coastal waters. This would be a minor setback to an America accustomed to dominating all of the world’s seas, but it would not constitute a serious strategic threat to the United States.

Across the East China Sea, China faces Japan and South Korea—two of the most prosperous, technologically advanced and militarily best-equipped countries in the world. Historical enmities ensure that China will never expand in that direction. Worse for China, it is quite likely that any increase in China’s ability to project power beyond its borders will be matched with similar steps by a wary, remilitarizing Japan.

The countries on China’s southern border are so large, populous and poor that it is difficult to imagine China taking much interest in the region beyond simple resource exploitation. Chinese companies may seek profit opportunities in Cambodia, Myanmar and Pakistan, but there is little for China to gain from strategic domination of the region. There will be no Chinese-sponsored Asian equivalent of NATO or the Warsaw Pact.

Farther abroad, much has been made of China’s strategic engagement in Africa and Latin America. Investment-starved countries in these regions have been eager to access Chinese capital and in many cases have welcomed Chinese investment, expertise and even immigration. But it is hard to imagine them welcoming Chinese military bases, and equally hard to imagine China asking them for bases. The American presence in Africa is in large part the legacy of centuries of European colonialism. China has no such legacy to build on.

Above all, however, the prospects for future Chinese hegemony depend on the prospects for future Chinese economic growth. Measured in per capita terms, China is still poorer than Mexico. That China will catch up to Mexico seems certain. That China will continue its extraordinary growth trajectory once it has caught up to Mexico is less obvious. In 2011, when the Chinese economy was growing by more than 10 percent a year, I predicted that China was headed for much slower growth. At the time, the IMF was projecting a long-term growth rate of 9.5 percent. Today, the same IMF projections assume 7 percent growth.

Even at 7 percent annual growth, the Chinese economy would account for more than half of total global output by 2050. The United States in its post–World War II heyday never achieved that level of dominance. But exponential extrapolations are inherently tricky. If China continues to grow at 7 percent while the world economy as a whole grows by 3 percent per year, China will account for 90 percent of global economic output by 2100 and 100 percent by 2110. After that, China’s economy will be even larger than the world’s economy, which of course is impossible unless China moves a large portion of its production off-planet.

A more reasonable assumption is that China’s economic growth will eventually settle down to global average rates. The only question is when. Existing demographic trends make it almost certain that the answer is: soon. The U.S. Census Bureau has projected that China’s working-age population would reach its peak in 2014 and then go into long-term decline. In the twenty years from 2014 to 2034, China’s working-age population will fall by eighty-seven million, while its elderly population will rise by 149 million. In the language of economic punditry, China will “grow old before it grows rich.”

The U.S. population, by contrast, is young and growing. In 2034, the U.S. population is projected to be growing at a rate of 0.6 percent per year (compared to -0.2 percent in China), with substantial immigration of talented, productive people (compared to net emigration from China). The U.S. median age of 39.2 will be significantly younger than the Chinese median age of 44.8. Over the long term these trends may change, but the twenty-year scenario is almost certain, because for the most part it has already happened. Economic trends can turn on a dime, but demographic trends are mostly immutable: tomorrow’s child-bearers have already been born.

IN THE ancient Mediterranean world, Rome rose to regional hegemony a century or two after the passing of the Athenian empire. The hegemonic Roman Republic was a hybrid political entity. It consisted of Rome itself, Roman colonies, Roman protectorates, cities conquered by Rome and cities allied to Rome. For four hundred years before 91 BC, the Italian cities allied to Rome were effectively part of the Roman state despite their formal political independence. They participated in Rome’s wars under Roman command. They did not pay taxes or tribute to Rome, but they were fully incorporated into a political system centered on Rome. When Hannibal crossed the Alps in 218 BC, most of the Italian cities did not rise up against Rome as he expected. They stood with Rome because they were effectively part of Rome.

In a similar way, the effective borders of the American polity extend well beyond the Atlantic and Pacific coasts. If the Edward Snowden leaks have revealed nothing else, they have shown the depth of intelligence cooperation between the United States and its English-speaking allies Australia, Canada, New Zealand and the United Kingdom. These are the so-called Five Eyes countries. These English-speaking allies work so closely with the United States on security issues that they resemble ancient Rome’s Italian allies. Despite their formal political independence, they do not make major strategic decisions without considering America’s interests as well as their own.

Curiously, America’s English-speaking allies resemble the United States in their demographic structures as well. While East Asia’s birthrates have fallen well below replacement levels and parts of continental Europe face outright depopulation, the English-speaking countries have stable birthrates and substantial immigration. The most talented people in the world don’t always move to the United States, but more often than not they move to English-speaking countries. It doesn’t hurt that English is the global lingua franca as well as the language of the Internet.

One surprising result of these trends is that the once-unfathomable demographic gap between China and the English-speaking world is narrowing. According to U.S. Census Bureau projections, in 2050 the U.S. population will be 399 million and rising by 0.5 percent per year while the Chinese population will be 1.304 billion and falling by 0.5 percent per year. Throw in America’s four English-speaking allies, and the combined five-country population will be 546 million—nearly 42 percent of China’s population—with a growth rate of 0.4 percent per year. No longer will China have the overwhelming demographic advantage that has historically let it punch above its economic weight.

Is it reasonable to treat America’s English-speaking allies as integrated components of the U.S. power structure? Of course, they are not formally integrated into the U.S. state. But the real, effective borders of countries are much fuzzier than the legal lines drawn on maps. The United States exercises different levels of influence over its sovereign territory, extraterritorial possessions, the English-speaking allies, NATO allies, other treaty allies, nontreaty allies, client states, spheres of influence, exclusionary zones and even enemy territories. All of these categories are fluid in their memberships and meanings, but taken together they constitute more than just a network of relationships. They constitute a cooperative system of shared sovereignty, something akin to the power structure of the Roman Republic.

No other country in the world possesses, has ever possessed, or is likely to possess in this century such a world-straddling vehicle for the enforcement of its will. More to the point, the U.S.-dominated system shows no signs of falling apart. Even the revelation that America and its English-speaking allies have been spying on the leaders of their NATO peers has not led to calls for the dissolution of NATO. The American system may not last forever, but its remaining life may be measured in centuries rather than decades. Cycles of hegemony turn very slowly because systems of hegemony are very robust. The American power network is much bigger, much stronger and much more resilient than the formal American state as such.

A RECURRING meme is the idea that the whole world should be able to vote in U.S. presidential elections because the whole world has a stake in the outcome. This argument is not meant to be taken seriously. It is made to prove a point: that the United States is uniquely and pervasively important in the world. At least since the Suez crisis of 1956, it has been clear to everyone that the other countries of the world, whether alone or in concert, are unable to project power beyond their shores without American support. Mere American acquiescence is not enough. In global statecraft, the United States is the indispensable state.