Few issues capture observers’ attention like the rivalry between China and the United States. Analysts scrutinize political trends and profile political leaders in both countries. Economists track indicators of relative financial and commercial strength, pondering the paradox of two economic behemoths that are both incompatible and interdependent. And military experts watch the balance of forces with increasing concern as China’s conventional and nuclear capabilities grow in number and quality. As captivating as the day-to-day drama is, a look back at history can offer new ways of understanding the trajectory of U.S.-Chinese relations . The political scientist Graham Allison famously warned that the two countries could fall into what he called “the Thucydides trap,” based on the idea that war is likely when a rising state threatens to overtake the leading power.…