Some American observers are billing Hu Jintao's visit to Washington as the most important state visit in three decades — and not without good reason.

His trip comes at a time when there is a widespread belief — in both Washington and Beijing — that the U.S. is in decline. According to a new poll by the Pew Research Center, 47 percent of Americans believe that China is the world's leading economic power, compared to 31 percent who believe that America is. Although America's GDP is currently over twice as large as China's, it seems likely that China's economy will become the world's largest within the next two decades, if not sooner (The Economist has even introduced an interactive graphic that allows readers "to predict when China will overtake America" by inputting different growth rates for each country going forward).

While disconcerting to Americans, the economic convergence between the U.S. and China aligns well with China's own historical view. China was the world's dominant economy for roughly 18 centuries prior to the Industrial Revolution; far from being the norm, the past two centuries are an anomaly, as far as the Chinese are concerned. China is now the world's largest exporter, manufacturer, holder of foreign-exchange reserves ($2.85 trillion at last count) and holder of U.S. debt, and it is quickly accumulating other such distinctions.

Economics is not the only factor at play. During Secretary of Defense Robert Gates's recent visit to China, the PLA tested the country's first radar-evading combat aircraft, apparently without the knowledge of President Hu. The consensus up until now — that China's military modernization is focused almost entirely on Taiwan — is slowly giving way to the belief that China aims to project power beyond its neighborhood. The U.S. remains the world's undisputed military power, and it is unlikely that China will come close to rivaling it in that realm for several decades, if not more. Again, however, trends are more important than the static picture.

One of the reasons why it is difficult to interpret these trends is that, despite the amount of commentary on U.S.-China relations, it is not exactly clear how we see China. It is certainly not an adversary in the way that the Soviet Union was, and yet it is not a strong ally like the U.K.

Furthermore, we do not know what China's intentions are. Does it simply want to be a regional power? Does it want to be on par with the U.S.? Does it want to be the world's leading power? One can speculate, but only China's leaders know the answers — and perhaps even they do not know. The swiftness of China's rise has taken China itself by surprise, and it could be the case that the leadership's ambitions for China will evolve as its global stature rises.

What we do know for sure, however, is that a U.S.-China "Cold War" would be disastrous not only for the two participants, but also for the rest of the world. Tensions between dominant powers and rising ones are inevitable, but they do not have to end in conflict: Consider the shift of power from the U.K. to the U.S. in the 20th century.

Here is how Henry Kissinger summarized the challenge for U.S. and Chinese policymakers in a recent article: "In the American-Chinese relationship, the overriding reality is that neither country will ever be able to dominate the other and that conflict between them would exhaust their societies. Can they find a conceptual framework to express this reality?"

One hopes that Hu's visit will offer some clues.

Kathy Kemper is founder and CEO of the Institute for Education, a nonprofit foundation that recognizes and promotes leadership and civility locally, nationally and in the world community.