More than any other single factor, what happens between Beijing and Washington will decide whether the 21st century is tranquil or turbulent. It will determine whether the United States, China and the global economy briskly prosper and advance or dwindle in feeble repose.

It will have a major bearing on whether the world's monetary and financial systems regain solvency and are able to support continued growth in trade and investment. It will facilitate or impede the management of global climate change and environmental remediation, the stewardship of energy, food and mineral supplies.

It will also determine whether there will be an updating of international law to accommodate new realities and the emergence of more effective systems of global governance than we now possess. It will drive our respective relationships with other rising or reviving powers like India, Indonesia, Japan, Russia, and maybe even Brazil and the EU.

China's leaders clearly understand what's at stake. Across the global and regional amphitheaters, with rare lapses, they have been playing a prudent, patient, low-risk game. It is less clear that Americans, who are far less risk averse than the Chinese, grasp what the consequences of messing up our interactions with China might be.

The United States has been playing different games in different arenas. Americans are lawyerly and cautious on trade and currency issues, demanding and sometimes petulant on political questions, and increasingly adventuresome — even bellicose — on military matters.

The message this sends is mixed. It enables the Chinese to hear the worst, if that's what they want to hear. Many do. Lots of people in China imagine that the United States is determined to keep their country down and to deny it the role and influence in its region to which its history, size and achievements entitle it.

There are not a few Americans who apply the same techniques of selective listening and conspiracy theorizing to China. Their suspicions are inflamed by a small army of pundits and polemicists determined to unearth the ghost of Fu Manchu in today's China. (The fictional Dr. Fu was an evil genius, prone to dispatching the targets of his wrath with crafty criminal deceptions and astonishingly peculiar weaponry.)

In the imaginations of an increasing number of U.S. securocrats and military planners — not to mention screenwriters in Hollywood — someone like Dr. Fu now directs Chinese strategy. This interpretation of China's intentions and capabilities is at least as neurotic as China's distorted image of America, and equally harmful.

Self-fulfilling paranoia is not a sound basis for cooperative relations between nations. In our own respective national interests, China and America need to cooperate with each other. Despite the problems in our mutual perceptions, the prospects for our doing so are not bad at all.

This is because the possible causes of conflict between us are receding, the need to cooperate is increasingly compelling, and the opportunities to accomplish things together are ever more obvious.

China is adjusting its economic model, in which investment and exports drove growth, to stress consumption and domestic markets. Its global trade surplus shrank to around 2.7% of its GDP in 2011, the lowest ratio in close to a decade. This is below the 4% level that the U.S. Treasury considers a sign of an undervalued currency.

Meanwhile, China is moving quite rapidly toward the internationalization of the yuan and allowing it to trade more freely. Over the decade since China entered the World Trade Organization, it has been by far the fastest growing export market in the world for U.S. goods and services.

In recent years, U.S. exports to China have been growing at an annual average of 21%. They are projected to continue to rise at a much faster rate than imports during the rest of this decade, as China overtakes the United States as the world's largest market.

China and America are now married to each other economically. As anyone who is married can attest, interdependence — even affectionate interdependence — begets bickering.

It's an election year in the United States. In such years, we are accustomed to hearing our politicians blame foreigners for all our ills and belabor yesterday's problems as though they were tomorrow's.

It's already clear that 2012 will be no exception to this practice. We are hearing a lot about China, but much of what has or will be said has been or is being overtaken by events. Of course, as the issues shift, the political whining and posturing will just change focus.

But, barring extraordinary lapses of judgment by one or the other of us, the United States and China seem destined to become more, not less intimate. The world economy will be the better for that and so will we.

Change is coming

Despite our bilateral frictions, China and America have a common interest in achieving a smooth transition to a new financial and monetary order. The existing, dollar-dependent system is in a state of decay that threatens the well-being of developed and newly wealthy nations alike.

We can manage change or wait for it to impose itself. Either way, change is coming. Within a decade, China's economy will begin to grow larger than America's by a widening margin.

At the same time, the gap between America and still other nations will narrow. To achieve renewed financial security for the world, the international monetary system and its institutions must evolve. China and other rising economies must begin to play roles in sustaining the stability of the global economic commons commensurate with the benefits they derive from them.

In this context, it seems entirely natural to me that the countries of Asia should seek the reassurance of strong ties with the United States as they accommodate the reality of rising Chinese power. Confidence on their part is good for stability, which is a prerequisite for a peaceful international environment.

That is what China requires for its continued domestic tranquility and development and what the United States needs as a Pacific power. China recognizes the contribution of an American presence in the Asia-Pacific to the peace of the region and has not opposed it.

But if the American purpose is now to prevent rather than ease the inclusion of Chinese power in the regional balance, or the United States is seen to have that purpose, then disharmony and confrontation between the countries are certain. This would shape the course of events in this century to the disadvantage of both peoples and the world as a whole.

Americans have been in the habit of demanding greater strategic transparency of China. In our own interest, we need to think carefully about American strategy and be more transparent about it to ourselves, China and the world.