Since the dawn of geopolitics, there has always been tension between the world's greatest power and the world's greatest emerging power. No great power likes to cede its No. 1 spot. One of the few times the top power ceded its position to the No. 2 power peacefully was when Great Britain allowed the United States to surge ahead in the late 19th century. The basic reason seems cultural: One Anglo-Saxon power was giving way to another.

Today, the situation is different. The No. 1 power is the United States, standard-bearer of the West. No. 2, rapidly catching up, is China. If China passes America in the next decade or two, it will be the first time in more than a century that a non-Western power has emerged as No. 1. (According to economic historian Angus Maddison's calculations, China was the world's No. 1 economy until 1890.)

The logic of history tells us that such power transitions do not happen peacefully. Indeed, we should expect to see a rising level of tension as America worries more and more about losing its primacy. Yet it has done little to act on these fears thus far. It would have been quite natural for America to carry out various moves to thwart China's rise. That's what great powers have done throughout history. That's how America faced the Soviet Union.

So why isn't this happening? Why are we seeing an unnatural degree of geopolitical calm between the world's greatest power and the world's greatest emerging power?

It would be virtually impossible to get Beijing and Washington to agree on the answers to these natural questions, as there are two distinct narratives in the two capitals.

The view in Beijing is that the calm in Sino-American relations is a result of the extraordinary patience and forbearance shown by China. Chinese leaders believe they have followed the wise advice of Deng Xiaoping, the late reformist leader, in deciding not to challenge American leadership in any way or in any area. China has felt that it also has followed Deng's advice when directly provoked, by swallowing its humiliation.

Few Americans remember any instances of provocation; Chinese leaders remember many. In May 1999, during the NATO bombing of Yugoslavia, a U.S. plane bombed the Chinese Embassy in Belgrade. America apologized, but no Chinese leader believed it was a mistake.

Similarly, a Chinese fighter jet was downed when it crashed into a U.S. spy plane near Hainan Island, China, in April 2001. Here, too, China felt humiliated.

Few Americans will recall the humiliation Premier Zhu Rongji suffered in April 1999 when he went to Washington to negotiate China's entry into the World Trade Organization (WTO); Chinese elites haven't forgotten. In their minds, China has been responsible for the low levels of tension in U.S.-China relations because China has swallowed such bitter pills time and again.

The view in Washington is almost exactly the opposite. Few Americans believe that China has been able to rise peacefully because of China's geopolitical acumen or America's geopolitical mistakes.

Instead, the prevailing view is that America has been remarkably generous to China because the United States is an inherently virtuous and generous country. There can be no denying that the United States has been generous to China in many real ways: allowing China's accession to the WTO (under stiff conditions, it must be emphasized, but stiff conditions that ironically benefited China); allowing China to enjoy massive trade surpluses; allowing China to join multilateral bodies like the Asia-Pacific Economic Cooperation forum, and, perhaps most important, allowing hundreds of thousands of Chinese students to study in American universities.

But it is also true that the United States allowed China to rise because it was so supremely self-confident that it would always remain on top. China's benign rise was a result of American neglect, not a result of any long-term strategy. China acted strategically; America did not.

After the 9/11 attacks, for instance, the United States focused on the Middle East instead of the rise of China, leading Hong Kong journalist Frank Ching to write, "The fact is, it's not going too far to say that China owes a huge debt of gratitude to Osama bin Laden."

America has been sensitive to criticisms about its lack of a long-term strategy. I can speak about this from personal experience. In February 2009, Hillary Clinton visited China on her first overseas visit as U.S. secretary of state. I wrote at the time:

There's little evidence Clinton has engaged in any serious strategic thinking about U.S.-China relations. ... China seems to have a clear, comprehensive strategy. The United States has none.

Officials in Washington reacted angrily. A senior official at the National Security Council called the Singaporean Embassy in Washington to complain about a Singaporean criticizing U.S. foreign policy — even though, in theory, America welcomes debate and a free marketplace of ideas.

I tell this story to illustrate how sensitive the establishment in Washington has become to any discussion on the nature of Sino-American relations. The real truth about this relationship is that, while there is a lot of calm on the surface, tension is brewing below.

I am convinced that there is great simmering anger in Beijing about being pushed around by Washington. The Chinese resent, for instance, allegations of Chinese cyberspying that make no mention of America's own activities in this area. The Chinese do not believe that they are the only ones playing this game.

Given the many simmering tensions, it would be unwise to assume smooth sailing ahead for the United States and China. The need to cooperate is rising each day, as is the potential for a major U.S.-China misunderstanding.

In November 2011, then-Secretary Clinton announced loudly and boldly a "pivot" to Asia, signifying a turning point in U.S. foreign policy that would reduce the focus on the Middle East. Barack Obama's administration took pains to avoid saying that this was America's response to a rising China, but nobody, including China, was fooled. Other countries saw it as a clear signal that Sino-American geopolitical competition was heating up.

We should be prepared for global turbulence if the U.S.-China relationship follows the millennium-old patterns and no longer remains on an even keel.

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Kishore Mahbubani is dean of the Lee Kuan Yew School of Public Policy at the National University of Singapore and author most recently of "The Great Convergence," from which this excerpt was adapted.