One should be skeptical about such dire projections. Americans go through cycles of declinism every decade or so, but that tells us more about America's psychology than its power resources. Not only is the United States likely to remain the most powerful country in the first half of this century, but China still has a long way to go to catch up in military, economic, and soft power.

In contrast, Germany had already surpassed Britain in industrial power by 1900, and the kaiser was pursuing an adventurous, globally oriented foreign and military policy that was bound to bring about a clash. But China today has focused its policies primarily on its region and its own economic development. China's "market-Leninist" economic model is attractive in authoritarian countries, but this so-called Beijing Consensus has the opposite effect in most democracies.

And even if China's GDP passes U.S. GDP around 2027 (as Goldman Sachs now projects), the two economies would be equivalent in size, not equal in composition. China would still face massive rural poverty and enormous inequality, and it will begin to encounter demographic problems from the delayed effects of its one-child policy. Moreover, as countries develop, there is a natural tendency for growth rates to slow. By my calculations, if China's annual growth goes down to 6 percent and the U.S. economy grows at 2 percent per year after 2030, China will not equal the United States in per capita income until decades later. So China is a long way from posing the kind of challenge to America that the kaiser's Germany posed to Britain in 1900.

None of this means the dangers of conflict can be completely ruled out in Asia, as China's recent disputes over various contested island chains remind us. But given shared global challenges like financial stability, cybercrime, nuclear proliferation, and climate change, China and the United States also have much to gain from working together. Unfortunately, faulty projections that create hubris among some Chinese and unnecessary fear of decline among some Americans could make it difficult to ensure this future.

Not every power's rise leads to war -- witness America's peaceful overtaking of Britain at the end of the 19th century. So remembering Thucydides's advice, it is important to prevent exaggerated fears from leading to a self-fulfilling prophecy. Or, to paraphrase Franklin D. Roosevelt, we can make ourselves safer by being wary of fear itself.

Joseph S. Nye Jr. is University Distinguished Service Professor at Harvard University and author of The Future of Power.